School:Mathematics

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      <text bytes="17437" sha1="icy0guaktgbpv7jjjrujw14cuj9n03s" xml:space="preserve">&lt;div style=&quot;text-align: center;&quot;&gt;&lt;big&gt;'''Welcome to the School of Mathematics!'''&lt;/big&gt;&lt;/div&gt;
&lt;div style=&quot;margin-top:-3px; margin-bottom:0.3em; text-align: center; font-size: 98%;&quot;&gt;
&lt;div style=&quot;text-align: center;&quot;&gt;'''[[Portal:Science|FACULTY OF SCIENCES]]'''&lt;/div&gt;
&lt;div style=&quot;text-align: center;&quot;&gt;'''[[Portal:Physical Sciences|F&lt;small&gt;ACULTY OF&lt;/small&gt; P&lt;small&gt;HYSICAL&lt;/SMALL&gt; S&lt;small&gt;CIENCES&lt;/small&gt;]]  · [[Portal:Life Sciences|F&lt;small&gt;ACULTY OF&lt;/small&gt; L&lt;small&gt;IFE&lt;/SMALL&gt; S&lt;small&gt;CIENCES&lt;/small&gt;]] · [[Portal:Engineering and Technology|F&lt;small&gt;ACULTY OF&lt;/small&gt; E&lt;small&gt;NGINEERING AND &lt;/SMALL&gt; T&lt;small&gt;ECHNOLOGY&lt;/small&gt;]] ·  [[Portal:Mathematics|F&lt;small&gt;ACULTY OF&lt;/small&gt; M&lt;small&gt;ATHEMATICS&lt;/SMALL&gt;]]'''&lt;/div&gt;
[[School:Biology|Biology]] · [[School:Chemistry|Chemistry]] · [[School:Computer Science|Computer Science]] ·[[School:Economics|Economics]] · [[School:Mathematics|Mathematics]]· [[School:Physics and Astronomy|Physics and Astronomy]] · &lt;/div&gt;
&lt;!---------------------------end of header----------------&gt;
[[Image:Lorenz_attractor.svg|right|300px|thumb|The Lorenz attractor is a chaotic map, noted for its butterfly shape. The map shows how the state of a dynamical system evolves over time in a complex, non-repeating pattern. The attractor itself, and the equations from which it is derived, were introduced by Edward Lorenz in 1963, who derived it from the simplified equations of convection rolls arising in the equations of the atmosphere.]]
Since you're here, you either are someone wishing to share your knowledge of Mathematics, or you are someone who wishes to gain knowledge about Mathematics. If you are the first kind of person, have a look around, and see how you can contribute. If you are of the second kind, read on!

Mathematics has many facets; though it has a wealth of applications, Mathematics is also a science, and an art, in its own right. Like other sciences, Mathematics is useful, but, just like other forms of art, Mathematics is beautiful, in its own unique way. You might not see this beauty at first, but the main goal of the Wikiversity School of Mathematics is to let you see this beauty, through inquiry and learning. To achieve this goal, we want to inspire you, since inspiration is essential to learning, discovery, and ultimately, seeing the beauty of Mathematics. A little bit of inspiration can put the beauty of Mathematics, and all its facets, before your eyes.

The School of Mathematics is a work in progress. We are trying to organize our material into a logical order, create new material, and revise existing material. Although we try to keep clarity in mind, if any of the material is confusing, you don't know where to start, or you have other questions, ''do not hesitate to pose your question at [[School of Mathematics Help Desk|our help desk]]''. There is no such thing as a &quot;dumb question&quot;; learning is driven by questions!

The School of Mathematics wishes you a very warm welcome. We hope that you will benefit from what we have to offer, and we hope that we will benefit from what you have to offer, either now or in the future.

==Divisions and departments==
Divisions and Departments of the School exist on pages in &quot;portal&quot; name space. Start the name of departments with the &quot;Portal:&quot; prefix; departments reside in the [[Wikiversity:Namespaces|Portal: namespace]]. Departments and divisions link to learning materials and learning projects. Divisions can link subdivisions or to departments. For more information on schools, divisions and departments look at the [[Wikiversity:Naming_conventions|Naming Conventions]].

To add additional Divisions or Departments within the School of Mathematics, edit the list of &quot;Portal:&quot; namespaces on the [[Template:MathDeps|MathDeps Template]].

{{MathDeps}}

==Mathematics curriculum==
This Wikiversity School of Mathematics project aims to create a structured set of links to learning material and test questions for the mathematics curriculum. To start, the recently released Australian national senior secondary school curriculum is being used as a guide. It is possible to create a similar structure based on the curriculum of alternative educational systems, but copy some of the same links and material identified below. If you'd like to do this, please create another heading in this section. Alternatively, please feel free to contribute to the project based on the Australian structure. This structure is fairly generic.

===Australian national senior secondary school mathematics curriculum===
These headings will provide links to pages detailing the senior secondary school mathematics curriculum. It will be used to identify material on Wikiversity and other Wikimedia sites that might be useful to students and their supporters. It will also help show the links between different areas of the curriculum and where studying mathematics might take them in the future; in other words, some possible answers to the eternal question, &quot;why should I learn this?&quot; and help show students the doors that will open to them by learning to see the world mathematically. The recently released [http://www.australiancurriculum.edu.au/SeniorSecondary/Mathematics/Specialist-Mathematics/Senior-secondary-Mathematics-subjects Australian national senior secondary school mathematics curriculum] will be used as a guide for this Wikiversity School of Mathematics project. (This material is based on the curriculum developed by the Australian Curriculum, Assessment and Reporting Authority (ACARA), which states its curriculum material can be downloaded, copied, printed and communicated for personal or non-commercial purposes, including educational or organisational use under a Creative Commons licence: [http://www.australiancurriculum.edu.au/Copyright copyright information])

*[[Essential mathematics | Essential mathematics]]
*[[General mathematics | General mathematics]]
*[[Mathematical methods | Mathematical methods]]
*[[Specialist mathematics| Specialist mathematics]]

==School news and current events==
* '''31 December 2018''' - [[Convergence acceleration by the Ford-Sidi W(m) algorithm]] - announced on Main Page News!
* '''30 December 2018''' - [[Speak Math Now!/Week 1: Introduction To Algebra]] - announced on Main Page News!
* '''19 December 2018''' - [[Vectors and coordinates]] - announced on Main Page News!
* '''30 September 2018''' - [[Divergence (Gauss-Ostrogradsky) theorem]] - announced on Main Page News!
* '''2 June 2018''' - [[WikiJournal of Science/Spaces in mathematics]] - announced on Main Page News!
* '''20 January 2018''' - [[Mathematical Properties]] - announced on Main Page News!
* '''11 January 2018''' - [[Boolean domain]] - announced on Main Page News!
* '''6 November 2017''' - [[Legendre differential equation]] - announced on Main Page News!
* '''31 August 2017''' - [[Minimal negation operator]] - announced on Main Page News!
* '''15 July 2017''' - [[Line (Geometry)]] - announced on Main Page News!
* '''1 July 2017''' - [[Unknown coordinate systems]] - announced on Main Page News!
* '''16 June 2017''' - [[Multiple linear regression]] - announced on Main Page News!
* '''31 May 2017''' - [[Full octahedral group]] - announced on Main Page News!
* '''26 January 2017''' - [[Quadratic Equation]] - announced on Main Page News!
* '''21 January 2017''' - [[Inversion (discrete mathematics)]] - announced on Main Page News!
* '''19 January 2017''' - [[Permutation notation]] - announced on Main Page News!
* '''January 2014''' - [[Mathematical astronomy]] - announced on Main Page News!
* '''March 2008''' - [http://www.eurekalert.org/pub_releases/2008-03/icl-1yo030308.php 140-year-old math problem solved by researcher]
* '''April 2007''' - [http://www.physlink.com/News/070327AnotherDimensionE8.cfm E8 mapped...]
* '''20 August 2006''' - School founded!

==Undergraduate-level study==
===Study guides===
Not sure where to start? Consult the following guides to help you make a study plan and determine which prerequisites you might be missing.
*[[School:Mathematics/Course guide|Course guide]]
*[[School:Mathematics/Facultative courses|Facultative courses]]

===Course categories===
*[[School:Mathematics/Undergraduate/Applied Mathematics|Applied Mathematics]] &lt;small&gt;(mathematical methods, mathematical physics)&lt;/small&gt;
*[[School:Mathematics/Undergraduate/Pure Mathematics|Pure Mathematics]] &lt;small&gt;(foundations, algebra, analysis, calculus, discrete math)&lt;/small&gt;
*[[Probability and statistics|Probability and Statistics]]
*[[Math contest preparation|Math contest preparation]]
*[[School:Mathematics/Course Catalog|All Courses (Course Catalog)]]
*[[Ethics/Nonkilling/Mathematics|Nonkilling Mathematics]]--would fit better under Ethics and Philosophy

== Resources ==

===Lectures===

* [[MacLaurin series]]
* [[Draft:Mathematics|Mathematics]]

{{MultiCol}}

=== Video courses ===
* [http://apcalculusstillwater.wordpress.com  Stillwater AP Calculus Tutorial Videos ]
* [http://ocw.mit.edu/courses/mathematics/ Open Course Ware] by MIT contains lectures for most of the topics in '''College level mathematics'''
* [[wikipedia:NPTEL|NPTEL's]] [http://nptel.iitm.ac.in/courses.php?disciplineId=122 Basic courses] and [http://nptel.iitm.ac.in/courses.php?disciplineId=111 Mathematics] includes many lectures on subjects in mathematics. Recommended for '''Engineering mathematics'''
* [http://www.extension.harvard.edu/courses/subject/mathematics Harvard University Extension School] offers lectures in many subjects. Recommended for '''Abstract Algebra'''[http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra].
* [http://www.khanacademy.org/ Khan Academy] which has a [http://www.youtube.com/user/khanacademy?blend=1&amp;ob=4 youtube channel] with many easy to understand math videos from arithmetics to calculus and linear algebra. Recommended for '''School level mathematics'''
* [http://www.chycho.com/?q=math_Table_Contents Chycho], has videos on Youtube organized by [http://www.kpss2011.net kpss]subject. Author uses big chalk and street walls for presentation of material.
* [http://www.youtube.com/user/MathTV MathTV's Youtube channel]
* [http://www.mathtv.com/ MathTV's] website with the material organized by subject. They say they may start charging, but the videos will still be accessible on Youtube.
* [http://www.isallaboutmath.com/ Is all about Math] video podcast with animations explaining math.
* [http://www.patrickjmt.com/ Patrick Just Math Tutorials] patrickjmt.com is a math only website with extensive free math content; he also has a youtube channel, 'patrickjmt.'
* [http://www.youtube.com/user/Technion/videos?sort=dd&amp;view=1&amp;shelf_id=5] the Technion YouTube playlist channel contains lectures for many university level subjects, mostly in Hebrew.

=== Wikibooks ===
* {{bi|Mathematics|Browse Textbooks}}
* {{bi|Mathematics bookshelf}}
* {{bi|Beginning Mathematics}}
* {{bi|High School Mathematics Extensions}}
* {{bi|Geometry}}
* {{bi|Algebra}}
* {{bi|Introductory Linear Algebra}}
* {{bi|Linear Algebra}}
* {{bi|Trigonometry}}
* {{bi|Calculus}}
* {{bi|Applied Math Basics}}
* {{bi|Ordinary Differential Equations}}
* {{bi|Partial Differential Equations}}
* {{bi|Linear Algebra with Differential Equations}}
* {{bi|Applied Mathematics}}
* {{bi|Numerical Methods}}
* {{bi|Cryptography}}
* {{bi|Discrete mathematics}}
* {{bi|Complex Analysis}}
* {{bi|A-level Mathematics}}
{{ColBreak}}

===Wikipedia===
* {{wi|Mathematics}}
* {{wi|Areas of mathematics}}
* {{wi|List of topics in mathematics|List of Mathematics Topics}}
* {{wi|List of mathematical symbols|List of Mathematical Symbols}}
* {{wi|List of online encyclopedias#Mathematics|List of Mathematics Encyclopedias}}

===Free Software===
* [http://www.gnu.org/software/octave/ GNU Octave] - A computational program similar to (and mostly compatible with) MATLAB
* [http://www.scipy.org/ SciPy] - A [[w:Python|Python]] library for mathematical and scientific computing
* [http://maxima.sourceforge.net/ Maxima] - A computer algebra system
* [http://www.singular.uni-kl.de/ SINGULAR] - A computer algebra system
* [http://www.gap-system.org/ GAP] - A tool for computational group theory
* [http://www.r-project.org/ R] - A programming language designed for statistical computing
* [http://freemat.sourceforge.net/ FreeMat] - An open source Matlab clone
* [http://www.sagemath.org SAGE] - A packaging of many of the above software tools and more
* [http://pari.math.u-bordeaux.fr/ Pari/GP] - &quot;a computer algebra system with the main aim of facilitating number theory computations&quot; (from Wikipedia)
* [http://www.mathics.org/ Mathics] Mathics is a free, general-purpose online computer algebra system featuring Mathematica-compatible syntax and functions. 
* See a full list along with some commercial tools at our [[Mathematics software|mathematics software]] page.

===Other===
*[[Other Free Learning Resources/Mathematics]]
{{EndMultiCol}}

==External links==
* [http://aimath.org/textbooks/ Open Textbook Initiative] - mix of free-licensed and low-cost, non-free-licensed mathematics class-tested textbooks supported by the [[w:American Institute of Mathematics|American Institute of Mathematics]]
* [https://openstax.org/subjects/math OpenStax] - free textbooks from algebra, trigonometry to calculus and statistics 
* [https://mathvault.ca/hub/higher-math/math-symbols/ Comprehensive list of mathematical symbols]
* [https://tutorial.math.lamar.edu/ Paul's Online Notes] - standalone resources on algebra, calculus I, calculus II, calculus III and differential equations
* [http://www.mathabc.com/ Free online math practice with instructional videos for K-6.]
* [http://mathematicslibrary.blogspot.com/ Mathematics notes and books for undergraduates and graduate students.]
* [http://mum.edu/math_dept/courses.html An interesting perspective on mathematics.]
* [http://www.sciencenews.org/view/generic/id/31392/title/Still_debating_with_Plato 'are new mathematical truths discovered or invented?']
* [http://www.aplusclick.com/ Collection of Math Problems &amp; Answers adapted to the student ability]
* [https://mc2.bid4papers.com/blog/math-resources/ MC2 Math Links] - a collection of 486 free online Math tools: calculators, plotters and interactive visualizations.

==Active participants==
The histories of Wikiversity pages indicate who are the active participants (listed below). If you are an active participant in this school, you can list your name here (this can help small schools grow and the participants communicate better; for large schools it is not needed).

* [[User:IanVG]]--[[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 19:47, 9 June 2026 (UTC)

===Inactive participants===
{{MultiCol}}
*[[User:Marshallsumter|Marshallsumter]] Was active beginning 7 January 2012 with Mathematical astronomy
*[[User:Parthkohli99|Parth Kohli]] (Set Theory, Calculus, Algebra, Trigonometry, Logic, Applied Mathematics)
*[[User:TortoiseDream|TortoiseDream]] (Logic, Set Theory, Mathematical Physics)
*[[User:Tastymangojuice|Tastymangojuice]] (Computer Science)
*[[User:ehremo|ehremo]]
*[[User:Deltinu|Deltinu]]
*[[User:EulerGamma|EulerGamma]]
*[[User:Ravi12346|Ravi12346]]
*[[User:lgallindo|Lucas Gallindo]]
*[[User:Pgbridge2000|Pgbridge2000]] (Cryptography)
*[[User:Tachyon01|Tachyon01]] (Pure Mathematics)
*[[User:fidocancan|fidocancan]] (pre-uni teacher)
*[[User:Mo Anabre|Mo Anabre]]
*[[User:master.signal|sutton]]
*[[User:Drini|Drini]]
*[[User:Ananth nag|Ananth nag m]]
*[[User:TeapotScar|TeapotScar]] (Calculus, Number Theory, Topology)
*[[User:pbran7|pbran7]]
*[[User:Juan Marquez|Juan]] (Topology, Algebra, Geometry and Analysis)
*[[User: Ivanne|Ivanne]] (I just want to learn man)
{{ColBreak}}
*[[User:King Bee|King Bee]] (graduate student in pure mathematics)
*[[User:Verin Sedai|Verin Sedai]] (Algebra, Combinatorics, basic number theory)
*[[User:haresh kumar|haresh kumar]](analytic geometry,calculus)
*[[User:A.K.Karthikeyan|A.K.Karthikeyan]](True knowledge lies in knowing you know nothing)
*[[User:Tlep|Tlep]] (Algebra)
*[[User:Bigyan Shrestha|Bigyan Shrestha]] (Mathematical Statistics)
*[[User:Rogerh|Rogerh]]
*[[user:sarinmadhur|Madhur Sarin]] (Number system,Geometry,Calculus )
*[[User:AFriedman|AFriedman]] (Computer Science, Biology)
*[[User:fibonacci101]] (Geometry, number theory, set theory)
*[[User:mathclubowner]]
*[[User:Helloworld00|Helloworld00]]
*[[User:graie.project|graie]]
*[[user:mynameinc|mynameinc]] (Algebra, Trigonometry, Differential Calculus)
*[[user:Comrade1986|Comrade1986]] (Mathematics)
*[[user:WendyB]] (Mathematics student)
*[[user:Alchemy heels I]] (Mathematics student)
*[[John Michael Pinson I ]] (Numerology, Mathematics student)
* [[User:Tarun-Science|Tarun-Science]] (I;m a 15-year-old intersted in Physics, Mathematics and Chemistry..good in geometry and algebra)

{{EndMultiCol}} Yousaf Masih (Theologiaministry89)

== International relations ==
*[[:it:Wikiversità]] - [[:it:Wikiversità:Facoltà di Matematica|Facoltà di Matematica]]
*[[b:pt:Wikiversidade:_Ci%C3%AAncias_Exatas_e_Ci%C3%AAncias_da_Terra#Curso_de_Matem.C3.A1tica||Wikiversidade - Ciências Exatas e da Terra]]

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{{Mathematics resources}}

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    <title>Laboratory on Mathematics and Mathematics Education/Fermi Questions/Scaffolds</title>
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      <comment>/* Fermi questions: How teachers can help */ Mathematical models, structures, objects, equations reveal the manifold dimensions of the universe</comment>
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      <text bytes="5209" sha1="7c0yk909qoqoxueomnpu192xohhvmbp" xml:space="preserve">== Fermi questions: How teachers can help ==

When students are not used to Fermi questions, they have problems to solve them. It's the teachers responsibility to help them. How can students be supported when they answer Fermi questions for the first time? Collect your results! Fermi lab experiments for mathematical models, mathematical equations, mathematical expressions and the complex systems of the universe enclosed in the physical sciences of the mathematical structures and functions of the universe by scientific and Mathematical objects.

== Group 1 ==

* Os estudantes podem ficam asustados quando apresentados as perguntas de fermi, como tambem podem achar que é mera brincadeira e nao levarem a serio a questao apresentada.
* Perante as perguntas de fermi pode-se notar nos estudantes um sembrante de desespero de espanto ou de brincadeira como que diz que as perguntas nao precisam de respostas.

or
The fermi questions create in students cembrant of admiretion, create in mind of students questions for play or for relax.

* hi group 1. coment of group 7
*'''Português'''
* o grupo 7 agradece a contribuicao do grupo 1 nesta questao, porem acreditamos que nao apresenta solucoes concretas, apenas o cenario que pode suceder durante a aula, o leva concluir que estao totalmente contra o uso das questoes de Fermi no processo ensino aprendizagem
* no entanto, sugerimos que o grupo 1 entcontre a solucao do despero dos alunos tomando em conta improtancia destes na construcao do conhecimento ns sala de aula 
* melhores cumprimentos

* '''Inglês'''
* Group 7 thanks to a contribution of the group this question, but believe it does not present concrete solutions, just the scenario that may happen during class, leads to conclude who are totally against the use of Fermi questions in the learning process
* However, suggest that group 1 entcontre the solution to the despair of students taking these into account improtancia in the construction of classroom knowledge ns
OuvirLer foneticamente

* best regard

== Group 2 ==

* A Primeira reaccao dos Alunos , provavelmente, Seria de considerar e Espanto uma Pergunta Absurda , Pelo facto de O PARECER impossivel encontrar UMA Resposta exacta . UMa Vez nao descubrindo uma Resposta , desmotivados FICAM , Pelo Que o professor desen Ajuda - los um trocadilho um pesrpectiva da Questão


* A seguir, eles apresentam muita exitacao em responder esse tipo de perguntas porque julgam vagas as suas possiveis respostas.

*We are not agree because: the questions are not absurd or impossible for the student, but he is faced with a difficult question to answer, and structuring and raises a number of assumptions in an attempt to find the answer, ultimately concluding that it is not conclusive issues.

== Group 3 ==


 When the student is facing Fermi type has the following printing: 

* Are complex,
* Are non-terminating 
* Do not have a logical reasoning 
* Are difficult to design 
* Are difficult validation


 To solve these problems caused by Fermi questions  we can: 

* Raise student, showing the relevance of the questions, 
* Demonstrate with the essence of these truthful cases issues, giving an example and solving the problems.
* Demonstrate that this type of question allows the student to have different ways of solving problems and also allows you to make a good interaction between theory and practice.


 Comments about analysis of Group 4:


We agree with reality terrace by Group 4, about Fermi questions, but we have to add that permit the development of student thinking, opens the horizon analysis of the phenomena and the pursuit of various solutions.

== Group 4 ==

*Are difficult questions to answer and structuring

*Do not have a conclusive answer, are open.

*Stimulate various research

Comment
We agree your position, but we think that the playing caracter of this type stimulates to trian mind.
 thanks for your comments

== Group 5 ==

* exigem muito esforço...
* ...

== Group 6 ==

* ...
* ...

== Group 7 ==
* '''Português'''
* As questoes de Fermi devem estar ligado o dia a dia do aluno, de modo a ter uma imagem da solucao
* Definir claramente o objectivo das questoes
* Orientar o aluno com questoes mais simples que podem conduzir ao resultado problema em causa

* '''Inglish'''
* The Fermi questions must be connected on the day of the student to take a picture of the solution
* Clearly define the purpose of the questions
* To guide students with simple questions that can lead to the outcome problem in question

Ok. Talves questionar da seguinte maneira para melhor entender o vosso raciocinio: 
-Quando é que o aluno pode ter uma imagem duma soluçao com uma questao que deseja saber o numero de cabelo que ele leva na cabeça, ou seja, que tipo de soluçao ele pode trazer na mente?
-Sera que o aluno vai difinir o objectivo da questao de que modo? Por exemplo um professor questiona quantos fios de cabelo tens na cabeça, que objetivo pode surgir.
-Que questoes mais cimples, as mesmas de Fermi ou outras seria bom que detalhassem.
VALEU!

== Group 8 ==

* ...
* ...

== Group 9 ==

* ...
* ...

== Group 10 ==

* ...
* ...

[[Category:Laboratory on Mathematics and Mathematics Education]]</text>
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    <title>Template:Motivation and emotion/Book chapter structure</title>
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{{:Motivation and emotion/Assessment/Topic/Quickstarttip}}
&lt;hr&gt;
&lt;/noinclude&gt;{{title|Title goes here:&lt;br&gt;Subtitle goes here?}}
&lt;div align=center&gt;Edit the wording (and [[w:Stylistic or specialised usage|casing]]) above so that it matches the [[Motivation and emotion/Book/Current|topic list]].&lt;br&gt;[[Motivation and emotion/About/Staff|Seek approval]] for any changes.&lt;br&gt;Do not add your name; authorship is shown in the [[Special:History/{{PAGENAME}}|page history]].&lt;/div&gt;
__TOC__

==Overview==
{{RoundBoxTop|theme=3}}
[[File:A picture is worth a thousand words.jpg|right|thumb|200px|'''Figure 1'''. Use a captioned image to illustrate the scenario]]

; Introduce the topic with a scenario

Begin with an engaging scenario, example, or case study that illustrates the topic and gives readers a reason to care about it.

The scenario should:
* Start with a lead in bold, such as '''Scenario, Case study, Imagine this ...''', or another another phrase that suits the scenario.
* Describe a '''realistic problem, situation, or question''' related to the topic.
* Be engaging and accessible to a reader who is new to the topic.
* Provide a context that can be revisited when explaining the psychological concepts and research later in the chapter.
* Avoid explaining theory or research in detail— the purpose is to illustrate the problem, not solve it.
* Be presented in a [[#Feature box|feature box]].
* Include a relevant image, with a figure caption, to help illustrate the scenario. Cite the figure (e.g., see Figure 1) within the scenario.

For the [[Motivation and emotion/Assessment/Topic|topic development]], the scenario can be planned using bullet-points.

;Feature box colour
To change the feature-box colour:
# Select Edit source
# Find theme=3
# Change 3 to another theme number

{{RoundBoxBottom}}

The Overview section should consist of three parts:
# '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above)
# '''Explanation of the problem, issue, or topic''': Brief explanation of the problem, why it is important, and an outline of how psychological science can help
# '''Focus questions''': Unpack the sub-title into focus questions in a feature box

Recommended length: 180 to 330 words.

This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some template material for the topic development, but it should all be removed from the book chapter.

The topic development submission should communicate your current thinking and plans for the project. It is not expected to be a fully developed or final product.

Key resources:
* [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] explains how to edit
* [[Motivation and emotion/Assessment/Topic|Topic development guidelines]]
* [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]]

{{RoundBoxTop|theme=3}}
'''Focus questions'''

Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions.
* What is the first focus question?
* What is the second focus question? 
* What is the third focus question?

Ask [[w:Open-ended question|open-ended]] questions. For example:

{{cross}} Is there a relationship between weather and criminal behaviour? (closed-ended)&lt;br&gt;
{{tick}} What is the relationship between weather and criminal behaviour? (open-ended)
{{RoundBoxBottom}}

==Headings==
Each chapter should use this standard heading structure:
* [[#Overview|Overview]]
* 3 to 6 major headings tailored to the topic; can have sub-headings:
** avoid sections with only one sub-heading (use 0 or 2+ sub-headings)
** provide an introductory paragraph before breaking into sub-sections
* [[#Conclusion|Conclusion]]
* [[#See also|See also]]
* [[#References|References]]
* [[#External links|External links]]

==Key points==
* For the topic development, provide at least three bullet-points for each heading and sub-heading, including the Overview and Conclusion 
* Include key citations

==Figures==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]]

* For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure; this can be the figure in the scenario
* For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples
* Images must be embedded from [[commons:|Wikimedia Commons]] which hosts free-to-use media such as photos, diagrams, graphs, video, and audio
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text)
* Cite each figure at least once in the main text (e.g., see Figure 2)

==Learning features==
Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options:

{{anchor|Scenarios}}
;Scenarios
* Scenarios, case studies, or examples that illustrate concepts in action
* Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages)
* Can be real or fictional; if real, provide citation(s)

{{anchor|Feature box}}
;Feature boxes
* Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect
* Consider using feature boxes for:
** [[#Scenarios|Scenarios]], case studies, or examples
** Focus questions
** Tips
** Quiz questions
** Take-home messages

;Embedded links
* When key words are introduced, use [[Help:Links|interwiki links]] to:
** Wikipedia articles (e.g., &quot;An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]&quot;) or
** Related book chapters (e.g., &quot;If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]&quot;)

{{anchor|Tables}}
;Tables
* Use tables to organise and summarise information
* Cite each table at least once in the main text (e.g., see Table 1)
* Tables should be captioned
* [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted

'''Table 1''' 

A Descriptive Caption Explains The Table Contents and its Relevance to the Text e.g., 

The 2 x 2 Johari Window Model Showing the Relationship Between Known/Unknown and Self/Other

{| class=&quot;wikitable&quot; style=&quot;margin: auto;
|-
! !! Known to self !! Not known to self
|-
| '''Known to others''' || Open area || Blind spot
|-
| '''Not known to others''' || Hidden area || Unknown
|}

;Quizzes
* One or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=simple&gt;
{The purpose of quizzes is to provide an interactive learning feature:
|type=&quot;()&quot;}
+ True
- False

{Long and complex quiz questions are recommended:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

==Conclusion==
* Arguably the most important section
* Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking
* For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
List [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity)
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)
* [[w:Self determination theory|Self determination theory]] (Wikipedia)
* [[Motivation and emotion/Assessment/Topic/Checklist|Topic development - Checklist]] (Wikiversity)

{{tip|Suggestions for this section:
* Link to the most relevant internal resources about the topic
* Include the source in parentheses
}}

==References==
Provide the references for all citations in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. Alternatively, you can use wiki style (as used on Wikipedia), as long as the information is complete and the formatting is consistent.

APA style example:
{{Hanging indent|1=

Rosenberg, B. D., &amp; Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091

Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper &amp; Row.

}}

{{tip|Suggestions for this section:
* Important aspects of APA referencing style
** Author surname, followed by a comma, then the author initials separated by full stops and spaces
** Year of publication in parentheses
** Title of work in lower case (except first letter and proper names), ending in a full-stop
** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop
** doi as a URL which is a working hyperlink (i.e., clickable)
** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]:
*** Use &quot;Edit source&quot;
*** &lt;nowiki&gt;{{Hanging indent|1= the full list of references}}&lt;/nowiki&gt;
* The most common mistakes include:
** Incorrect capitalisation
** Incorrect italicisation
** dois which aren't clickable as working hyperlinks
** Citing sources that haven't been consulted
}}

==External links==
[[Help:Contents/Links#External_links|External links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)

{{tip|Suggestions for this section:
* Link to the most relevant external resources about the topic
* Include the source in parentheses after the link
}}&lt;includeonly&gt;

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]&lt;/includeonly&gt;&lt;noinclude&gt;
[[Category:Motivation and emotion/Assessment/Chapter]]
[[Category:Motivation and emotion/Book]]
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      <comment>/* Associate editor application of Neil Vedwan */ Reply</comment>
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{{WikiJournal editorial application top
|archive box = {{Archive box|[[/Archive 2016]]&lt;br&gt;[[/Archive 2017]]&lt;br&gt;[[/Archive 2018]]&lt;br&gt;[[/Archive 2019]]&lt;br&gt;[[/Archive 2020]]&lt;br&gt;[[/Archive 2022]]&lt;br&gt;[[/Archive 2023]]
}}
}}
&lt;/noinclude&gt;

==Associate editor application of OGUNJIMI OLUWOLE TEMIDAYO==

{{WikiJournal editor application submitted
 | position                =Associate editor
 | name                    =OGUNJIMI OLUWOLE TEMIDAYO
 | qualifications          =M.Sc. Geography and Planning
 | link                    =Linkedin.com/in/oluwole-ogunjimi
 | areas_of_expertise      =Enivironmental Management and Data Analysis
 | professional_experience =An administrator with over five years of working experience in both healthcare and education sectors. I have a Master’s degree from the University of Lagos and a Bachelor's degree from the University of Ibadan, I have developed significant research skills, especially in analyzing the impacts of human activities on water quality and understanding the socio-economic effects of environmental changes. With hands-on experience in geospatial mapping, data analytics, and programming (Python), he combines his passion for environmental conservation with a commitment to translating research findings into actionable insights.
 | publishing_experience   =Environmental and Socio-Economic Impact of Artisanal Mining in Oke Ogun Region, 2016. https://drive.google.com/file/d/1l9WTh-ZhUpKbRN_TP28oP-mvlaiWGf0S/view?usp=drive_link
Impact of Human Activities on Water Quality of Kudeti River, Ibadan, Oyo State, Nigeria, 2016.
https://drive.google.com/file/d/1N00Eo1RitC5dKoX38G1H8r7MJsKdD3Aw/view?usp=drive_link
Impact of Rural Transportation on The Distribution of Agricultural Produce in Obafemi Owode Local Government Area, Ogun State, Nigeria, 2023.
https://drive.google.com/file/d/1YMYpcdC1JqnxQO-fq5eM3eitbHpQH-HB/view?usp=drive_link
 | open_experience         =I am an active Wikipedia editor with over 300 edits.  Significant editing history on English Wikipedia under username &quot;Kamoranesi90&quot;.
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Science. [[User:Kamoranesi90|Kamoranesi90]] ([[User talk:Kamoranesi90|discuss]] • [[Special:Contributions/Kamoranesi90|contribs]]) 12:35, 18 October 2024 (UTC)
}}
* {{re|Kamoranesi90}} Please adjust your security settings for the 3 Google Drive links. I am unable to view them. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 13:32, 25 October 2024 (UTC)
*:Thank you @[[User:OhanaUnited|OhanaUnited]]. I have adjusted the security settings.  [[User:Kamoranesi90|Kamoranesi90]] ([[User talk:Kamoranesi90|discuss]] • [[Special:Contributions/Kamoranesi90|contribs]]) 14:49, 25 October 2024 (UTC)
*::Thank you. Do you have any publication examples which are peer-reviewed? For example, these could be journal articles or book chapters. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 20:12, 25 October 2024 (UTC)
*:::No, I don't but I am working on publishing my research works. Thank you [[User:Kamoranesi90|Kamoranesi90]] ([[User talk:Kamoranesi90|discuss]] • [[Special:Contributions/Kamoranesi90|contribs]]) 09:19, 26 October 2024 (UTC)
*::::I am open to '''support''' your associate editor application with mentorship from board members to support your growth in gaining experience around the publishing area. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 18:52, 14 November 2024 (UTC)
*:::::Wow. That's great. I am open to learning from your wealth of knowledge and experience. I appreciate your kind gesture. 
*:::::Thank you. [[User:Kamoranesi90|Kamoranesi90]] ([[User talk:Kamoranesi90|discuss]] • [[Special:Contributions/Kamoranesi90|contribs]]) 18:59, 14 November 2024 (UTC)
*::::::Please wait for other editorial board members to review and comment on your application. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 21:44, 18 November 2024 (UTC)
*:::::::Thank you. [[User:Kamoranesi90|Kamoranesi90]] ([[User talk:Kamoranesi90|discuss]] • [[Special:Contributions/Kamoranesi90|contribs]]) 02:59, 22 November 2024 (UTC)
*If [[User:OhanaUnited]] is happy to mentor, I think you would be a valuable addition to the team, so I would be willing to support. Associate editor positions don't need to be as experienced as board members, just willing to learn and able to work well with others, especially if someone is able to take the lead if calleging scenarios arise (e.g. confilcting peer reviews). [[User:Evolution and evolvability|T.Shafee(Evo&amp;#65120;Evo)]]&lt;sup&gt;[[User talk:Evolution and evolvability|talk]]&lt;/sup&gt; 02:48, 9 January 2025 (UTC)
*'''Support application''' Though I lack experience in such matters, I have recently learned enough to recognize this to be an easy decision. Regarding mentoring, I think I could use some mentoring myself.  Whenever appropriate, please CC me on mentor-mentee communications.  In particular, I am having trouble dealing with the large number of referee invites required to recruit volunteers. [[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 18:50, 11 January 2025 (UTC)

{{re|Kamoranesi90}} My apologies for the delay in getting back to you. 

'''Result: Accepted into the editorial board as associate editor.''' 

: [[WikiJournal User Group/Editorial guidelines#Adding editorial board members|Next steps]] (add &lt;code&gt;DONE&lt;/code&gt; or &lt;code&gt;&lt;nowiki&gt;{{Done}}&lt;/nowiki&gt;&lt;/code&gt; after someone has performed the task):

# [[{{ROOTPAGENAMEE}}/Editorial_guidelines/Message_templates#Onboarding_a_new_board_member|Send a welcome message and confirm their preferred email address]] (usually in their provided website link, else via [[Special:EmailUser]]) 
{{clickable button 2|Onboarding email template|url=https://en.wikiversity.org/wiki/{{ROOTPAGENAMEE}}/Editorial_guidelines/Message_templates#Onboarding_a_new_board_member}}
# Copy their information over to [[{{ROOTPAGENAME}}/Editorial board|editorial board page]] using the {{tlx|WikiJournal editor summary}} template
# Add their name and start data to the [d:{{WJQboard|default=Q75674277}} relevant editorial board] on wikidata
# Direct-add them to the {{WJX}}board mailing list ([https://groups.google.com/forum/?utm_medium=email&amp;utm_source=footer#!managemembers/{{WJX}}board/add via this link]) which will grant them access to the private page only visible to board members
# Welcome them at the {{#if:|wjm|WJM}}board mailing list so that they are informed
# Finally, move the application to [[Talk:{{ROOTPAGENAME}}/Editors/Archive_{{CURRENTYEAR}}|this year's archive page]]
[[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 20:12, 2 April 2025 (UTC)

{{ping|Kamoranesi90}}, can you confirm if you're still interested in joining? I have emailed you through the wiki's email function a while back but did not receive a response from you. I also noticed that [https://guc.toolforge.org/?by=date&amp;user=Kamoranesi90 you haven't edited in any WMF projects since November 2024] so I don't know if you still monitor your account for notifications. If I don't hear from you by the end of this month, I will archive this application without prejudice (i.e. you are more than welcome to continue the process to join as an associate editor when you replied back to this message). [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 03:43, 2 January 2026 (UTC)

==Editorial board application of Max Loomes==

{{WikiJournal editor application submitted
 | position                =Editorial board
 | name                    =Max Loomes
 | qualifications          =Bachelor of psychology (Hons I)(USYD), Master of Clinical Psychology (UTS), PhD Candidate (UTS)
 | link                    =https://profiles.uts.edu.au/student_Max.W.Loomes
 | areas_of_expertise      =Mental health, psychiatry, public health
 | professional_experience =Research (9 years, ~4 institutions, various areas both qualitative and quantitative, field work [ecology/education psychology], preclinical trials, project managing, clinical practice (trauma, schizophrenia), teaching (~1 year at 2 institutions for psychology undergraduate and post-graduate, some masters).
 | publishing_experience   =Published ~12 articles/chapters, reviewed for three different journals
 | open_experience         =Have updated various wikipedia pages and big believer in open access and dismantling the highly capitalistic structures that govern journal publishing
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Science. [[User:Maxwloomes|Maxwloomes]] ([[User talk:Maxwloomes|discuss]] • [[Special:Contributions/Maxwloomes|contribs]]) 06:34, 13 May 2025 (UTC)
}}

:&lt;nowiki&gt;Great to see this application! I support it; have known Max for several years and he is passionate about many of the values behind WikiJournal  ~~~&lt;/nowiki&gt; [[User:Aoholcombe|Aoholcombe]] ([[User talk:Aoholcombe|discuss]] • [[Special:Contributions/Aoholcombe|contribs]]) 20:46, 4 February 2026 (UTC)


--[[User:Maxwloomes|Maxwloomes]] ([[User talk:Maxwloomes|discuss]] • [[Special:Contributions/Maxwloomes|contribs]]) 06:34, 13 May 2025 (UTC)

:* '''Support'''. Applicant has experience in research, publishing and open access (both Wikipedia and journal). [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 00:23, 27 May 2025 (UTC)

==Editorial board application of Alex O. Holcombe==

{{WikiJournal editor application submitted
 | position                =Editorial board
 | name                    =Alex O. Holcombe
 | qualifications          =PhD in psychology
 | link                    =https://profiles.sydney.edu.au/alex.holcombe
 | areas_of_expertise      =Psychology, neuroscience
 | professional_experience =Full-time academic position for 20 years
 | publishing_experience   =Advisory board or editorial board member of journals and initiatives including PLOS ONE, Collabra:Psychology, Replication Research, Meta-ROR, Meta-psychology...
 | open_experience         =Have been an Associate Editor of WikiJournalOfScience for the last couple years, handled three articles to publication, and have attended most, I think, of the monthly meetings in the last two years
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Science. [[User:Aoholcombe|Aoholcombe]] ([[User talk:Aoholcombe|discuss]] • [[Special:Contributions/Aoholcombe|contribs]]) 20:56, 4 February 2026 (UTC)
}}
: I '''strongly support''' promoting Alex to be a full editorial board member. He has the handling editor for a number of submissions, e.g. [[WikiJournal of Science/Hypericum sechmenii|1]], [[WikiJournal of Science/The Himalayan fossil hoax|2]] and [[WikiJournal of Science/Popular Pet Reptile, the Leopard Gecko (Eublepharis macularius), Spontaneously Uses Running Wheel– Is It Locomotion Play?|3]]). He also gave insightful comments towards the operations of the WikiJournal of Science editorial board and the broader WikiJournal publishing umbrella. We need the expertise like Alex to further strengthen the board's expertise. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 18:03, 5 February 2026 (UTC)

==Associate editor application of Neil Vedwan==

{{WikiJournal editor application submitted
 | position                =Associate editor
 | name                    =Neil Vedwan
 | qualifications          =
 | link                    =
 | areas_of_expertise      =Type theory, Formal Methods, Computational Complexity, Computability, Theoretical Computer Science, Category Theory, Set Theory
 | professional_experience = Independent Researcher (in collaboration with faculty @ Montclair State University)
 | publishing_experience   =Reviewer at zbMath Open (mathematical reviewing database), In the process of getting 2 papers published
 | open_experience         =Contributor to CSLib (a library of Lean 4), OEIS Contributor (mathematical database/encyclopedia)
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Science. --[[User:Nv0011|Nv0011]] ([[User talk:Nv0011|discuss]] • [[Special:Contributions/Nv0011|contribs]]) 13:19, 29 September 2026 (UTC) [[Special:Contributions/~2026-52029-76|~2026-52029-76]] ([[User talk:~2026-52029-76|talk]]) 03:53, 28 September 2026 (UTC)
}}

:It looks like you're not logged in. Please log in and attach your signature to this application. Furthermore, I am unable to find a research by this name in Montclair State University's website with your area of expertise. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 06:52, 28 September 2026 (UTC)
::Apologies for the confusion, I accidentally submitted while logged out. 
::To clarify my affiliation: I'm an independent researcher collaborating on research with faculty at Montclair State, which is why I'm not listed in the staff directory. My active work includes reviewing papers for zbMATH Open &amp; contributing to CSLib. If you need to verify anything else, please let me know. --[[User:Nv0011|Nv0011]] ([[User talk:Nv0011|discuss]] • [[Special:Contributions/Nv0011|contribs]]) 13:34, 29 September 2026 (UTC)
:::Thank you. Would you be comfortable linking to any publications you published and the link to your CSLib/OEIS account? If you wish, you can display this information privately to me via [[Special:EmailUser/OhanaUnited]]. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 02:20, 16 October 2026 (UTC)
::::Thank you for reaching out. I just emailed the information to you, feel free to ask any questions. [[User:Nv0011|Nv0011]] ([[User talk:Nv0011|discuss]] • [[Special:Contributions/Nv0011|contribs]]) 21:48, 18 October 2026 (UTC)</text>
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  <page>
    <title>Animal Phyla</title>
    <ns>0</ns>
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    <revision>
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        <username>The Citer</username>
        <id>3110681</id>
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      <minor />
      <comment>/* Placozoa */</comment>
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      <text bytes="12854" sha1="8gr14g6cjqojkj79kx37cxlwr05te04" xml:space="preserve">[[Image:Animalia diversity.jpg|thumb|300px|right|Some examples of animal diversity.]]
A Phylum (pl. Phyla) is the largest formal major grouping within animal taxonomy.
This list is presented in alphabetical order, and not in any systematic/evolutionary arrangement.
This list is also available in [[/Table/|table form]]. Science is by no means static. There are arguments of all sizes and shapes about the taxonomy of the Animal Phyla. Other sources may combine or split these listed Phyla. However, at this time, the list presented here should stand in good stead for an introduction to the topic of animal diversity.

There are approximately 1.9 million animal species that have been described by science.

This list tries to give the following information on each Phylum:
*Phyllum Name
*A link to a sub-page discussing that Phylum in more detail (if it yet exists)
*Name Meaning (in English)
*An English Common Name, where one is in regular use
*Distinguishing characteristics of animals within the Phylum
*An approximate number of species described within that Phylum. Since zoology fortunately refuses to stand still, this number can change.

Oh! And there's a quiz at the end.
See also [[/Lesson Plan for Animal Phyla/]]. Or head to [[Introduction to Taxonomy]] for more on that topic. You can also visit [[Plant Divisions (Phyla)]], the equivalent page for plants.

==Acanthocephala==
[[Image:Macracanthorhynchus_hirudinaceus_adult_BAM1.jpg|thumb|100px|left|An Acanthocephalan, ''Macracanthorhynchus hirudinaceus'', adult.]]
[[/Acanthocephala/]]

Name Meaning: horny head 

English Common Name: Horny-headed worms

Major distinguishing characteristics: Reversible spiny proboscis

Approximate number of species described: 1,151

==Acoelomorpha==
[[File:Acoelomorpha.jpg|thumb|100px|left|Acoelomorpha]]
[[/Acoelomorpha/]]

Name Meaning: Without gut

English Common Name: Acoels

Major distinguishing characteristics: No mouth or alimentary canal

Approximate number of species described: 50,000

== Annelida ==
&lt;div id=&quot;Annelida&quot;&gt;&lt;/div&gt;
[[Image:Reef0200.jpg|thumb|100px|left|An feather duster worm of the family Sabellidae in parchment tube.]]
[[/Annelida/]]

Name Meaning: Little ring

English Common Name: Segmented worms, annelids

Major distinguishing characteristics: Multiple circular segments

Approximate number of species described: 22,000 modern

==Arthropoda==
[[Image:Chelicerae_%26_pedipalps_%288689230685%29.jpg|thumb|100px|left|A scorpion, an example of an Arthropod]]
[[/Arthropoda/]]

Name Meaning: Jointed foot

English Common Name: Arthropods

Major distinguishing characteristics: Chitin exoskeleton

Approximate number of species described: 1,134,000+
==Brachiopoda==
[[Image:Isocrania_costata_Sowerby_1823.jpg|thumb|100px|left|Brachiopod ''Isocrania costata''.]]
[[/Brachiopoda/]]

Name Meaning: Arm foot

English Common Name: Lamp shells, brachiopod

Major distinguishing characteristics: Lophophore and pedicle

Approximate number of species described: between 300 and 500 extant
==Bryozoa==
[[Image:Freshwater_Bryozoan234.JPG|thumb|100px|left|A freshwater Bryozoan, species unknown.]]
[[/Bryozoa/]]

Name Meaning: Moss animals

English Common Name: Moss animals, sea mats, bryozoans

Major distinguishing characteristics: Lophophore, no pedicle, ciliated tentacles

Approximate number of species described: about 5,000 living species
==Chaetognatha==
[[Image:Chaetognatha.PNG|thumb|100px|left|Chaetognathans.]]
[[/Chaetognatha/]]

Name Meaning: Longhair jaw

English Common Name: Arrow worms

Major distinguishing characteristics: Chitinous spines either side of head, fins

Approximate number of species described: about 100 modern species
==Chordata==
[[Image:Clavelina lepadiformis (Müller, 1776) - Banyuls-sur-Mer - 04.83.jpg|thumb|100px|left|''Clavelina lepadiformis'', a non-vertebrate chordates.]]
[[/Chordata/]]

Name Meaning: Cord

English Common Name: Chordates

Major distinguishing characteristics: Hollow dorsal nervous chord

Approximate number of species described: about 100,000+
==Cnidaria==
[[Image:Cynarina_lacrymalis.jpeg|thumb|100px|left|''Cynarina lacrymalis'' an anthozoan member of the Phylum Cnidaria.]]
[[/Cnidaria/]]

Name Meaning: Stinging nettle

English Common Name: Coelenterates, cnidarians, sea anemones, jellies, hydra

Major distinguishing characteristics: Cnidocytes (stinging cells)

Approximate number of species described: about 11,000

==Ctenophora==
[[Image:LightRefractsOf comb-rows of ctenophore Mertensia ovum.jpg|thumb|100px|left|''Mertensia'', a Ctenophore.]]
[[/Ctenophora/]]

Name Meaning: Comb bearer

English Common Name: Comb jellies, Ctenophores

Major distinguishing characteristics: Eight &quot;comb rows&quot; of fused cilia

Approximate number of species described: about 200 modern species

==Cycliophora==
[[Image:Cycliophora - Symbion pandora.png|thumb|100px|left|''Symbion pandora'', a Cycliphoran.]]
[[/Cycliophora/]]

Name Meaning: Wheel carrying

English Common Name: Symbion

Major distinguishing characteristics: Circular mouth surrounded by small cilia

Approximate number of species described: at least 3
==Echinodermata==
[[Image:Crinoideos.jpg|thumb|100px|left|''Crinoideos'', an example of Ecinoderms.]]
[[/Echinodermata/]]

Name Meaning: Spiny skin(Body)

English Common Name: Echinoderms

Major distinguishing characteristics: Five-fold radial symmetry, mesodermal layer, calcified spines

Approximate number of species described: about 7,000 living species and 13,000 extinct ones
==Entoprocta==
[[Image:Barentsa discreta suzukokemusi01.JPG|thumb|100px|left|''Barentsa discreta suzukokemusi'', a species of goblet worm.]]
[[/Entoprocta/]]

Name Meaning: Inside anus

English Common Name: Goblet worm

Major distinguishing characteristics: Anus inside ring of cilia

Approximate number of species described: about 150
==Gastrotricha==
[[Image:Chaetonotus (Chaetonotus) polyspinosus.jpg|thumb|100px|left|''Chaetonotus polyspinosus'' a species of meiofauna.]]
[[/Gastrotricha/]]

Name Meaning: Hair stomach

English Common Name: Hairybellies, hairybacks

Major Distinguishing Characteristics: Two terminal adhesive tubes

Approximate number of species described: about 690

==Gnathostomulida==
[[Image:Gnathostomula paradoxa Sylt.tif|thumb|100px|left|''Gnathostomula paradoxa'', a jaw worm.]]
[[/Gnathostomulida/]]

Name Meaning: Jaw orifice

English Common Name: Jaw worms

Major distinguishing characteristics: 

Approximate number of species described: about 100
==Hemichordata==
[[Image:Glossograptus whitfieldii 01.jpg|thumb|100px|left|Glossograptus whitfieldii, a fossil hemichordate.]]
[[/Hemichordata/]]

Name Meaning: Half cord

English Common Name: Acorn worms

Major distinguishing characteristics: Stomochord in collar

Approximate number of species described: about 100 living species
==Kinorhyncha==
[[Image:Paracentrophyes quadridentatus.jpg|thumb|100px|left|''Paracentrophyes quadridentatus'', a mud dragon.]]
[[/Kinorhyncha/]]

Name Meaning: Motion snout

English Common Name: Mud dragons

Major distinguishing characteristics: Eleven segments, each with a dorsal plate

Approximate number of species described: about 150
==Loricifera==
[[Image:Pliciloricus enigmatus.jpg|thumb|100px|left|A member of the Phylum Loricifera, ''Pliciloricus enigmatus''.]]
[[/Loricifera/]]

Name Meaning: Corset bearer

English Common Name: Loriciferans

Major distinguishing characteristics: Umbrella-like scales at each end

Approximate number of species described: about 122

==Micrognathozoa==
[[Image:Limnonathia, drawing.tif|thumb|100px|left|''Limnonathia'', drawing, a Micrognathozoan.]]
[[/Micrognathozoa/]] (sometimes called Phylum Gnathifera)

Name Meaning: Tiny jaw animals

English Common Name: Micrognathozoans

Major distinguishing characteristics: Accordion like extensible thorax

Approximate number of species described: 1

==Mollusca==
[[Image:Shells01.jpg|thumb|100px|left|A group of Gastropod shells, Phylum Mollusca.]]
[[/Mollusca/]]

Name Meaning: Thin shell

English Common Name: Mollusks or molluscs

Major distinguishing characteristics: Muscular foot and Mantle, round shell

Approximate number of species described: 85,000


==Nematoda==
[[Image:Mermis nigrescens beentree.jpg|thumb|100px|left|''Mermis nigrescens beentree'', a nematode worm.]]
[[/Nematoda/]]

Name Meaning: Thread like

English Common Name: Round worms, Nematodes

Major distinguishing characteristics: Round cross section, keratin, cuticle

Approximate number of species described: 80 000 - 1 million
==Nematomorpha==
[[Image:Gordiidae A MRKVICKA.JPG|thumb|100px|left|A Gordian worm, Phylum Nematomorpha.]]
[[/Nematomorpha/]]

Name Meaning: Thread form

English Common Name: Horsehair worms

Major distinguishing characteristics:

Approximate number of species described: about 320
==Nemertea==
[[Image:Micrura alaskensis.png|thumb|100px|left|Micrura alaskensis, a ribbon worm.]]
[[/Nemertea/]]

Name Meaning: A sea nymph

English Common Name: Ribbon worms

Major distinguishing characteristics:

Approximate number of species described: about 1200
==Onychophora==
[[Image:Euperipatoides kanangrensis crop.jpg|thumb|100px|left|''Euperipatoides kanangrensis'', a velvet worm.]]
[[/Onychophora/]]

Name Meaning: Claw bearer

English Common Name: Velvet worms

Major distinguishing characteristics: Legs tipped by chitinous claws

Approximate number of species described: about 200 modern
==Orthonectida==
&lt;div id=&quot;Orthonectida&quot;&gt;&lt;/div&gt;
[[Image:Orthonetida dict flat and cylinder.png|thumb|100px|left|Orthonetida, an Orthonectidan.]]
[[/Orthonectida/]]

Name Meaning: Straight swim

English Common Name: Orthonectida

Major distinguishing characteristics:

Approximate number of species described: about 20

==Phoronida==
[[Image:Phoronis Maria Grazia Montanucci2.jpg|thumb|100px|left|'' Phoronis hippocrepis'', a species of horseshoe worm.]]
[[/Phoronida/]]

Name Meaning: Zeus' mistress

English Common Name: Horseshoe worms

Major distinguishing characteristics: U-shaped gut

Approximate number of species described: 20
==Placozoa==
[[Image:Trichoplax adhaerens photograph.png|thumb|100px|left|''Trichoplax adhaerens'', the only Placozoan.]]
[[/Placozoa/]]

Name Meaning: Plate animals

English Common Name: Placozoans

Major distinguishing characteristics:

Approximate number of species described: 4

==Platyhelminthes==
[[Image:Gigantolina.elongata.in.vivo.png|thumb|100px|left|''Gigantolina elongata'', a flat worm.]]
[[/Platyhelminthes/]]

Name Meaning: Flat worms

English Common Name: Flat worms

Major distinguishing characteristics:

Approximate number of species described: about 25,000
==Porifera==
[[Image:Eponge à déterminer (1).jpg|thumb|100px|left|An unidentified sponge.]]
[[/Porifera/]]

Name Meaning: Pore bearer

English Common Name: Sponges

Major distinguishing characteristics: Perforated interior wall

Approximate number of species described: over 5,000 modern
==Priapulida==
[[Image:Adult priapulid.jpg|thumb|100px|left|''Priapulus caudatus'', a Priapulid worm.]]
[[/Priapulida/]]

Name Meaning: Penis

English Common Name: Priapulid worms

Major distinguishing characteristics: Retractable proboscis surrounded by papillae

Approximate number of species described: 22

==Rhombozoa==
&lt;div id=&quot;Rhombozoa&quot;&gt;&lt;/div&gt;
[[Image:Dicyema japonicum.png |thumb|100px|left|''Dicyema japonicum'', a rhombozoan.]]
[[/Rhombozoa/]]

Name Meaning: Rhombus animal

English Common Name: Rhombozoans

Major distinguishing characteristics: Single axial cell surrounded by ciliated cells

Approximate number of species described: 75

==Rotifera==
[[Image:20090730 020239 Rotifer.jpg|thumb|100px|left|An unidentified rotifer.]]
[[/Rotifera/]]

Name Meaning: Wheel bearer

English Common Name: Rotifers

Major distinguishing characteristics: Anterior crown of cilia

Approximate number of species described: about 2000
==Tardigrada==
[[Image:SEM image of Milnesium tardigradum in active state - journal.pone.0045682.g001-2.png|thumb|100px|left|Tardigrade ''Milnesium tardigradum'' in active state.]]
[[/Tardigrada/]]

Name Meaning: Slow step

English Common Name: Water bears

Major distinguishing characteristics: Four segmented body and head

Approximate number of species described: 1,000+
==Xenacoelomorpha==
[[Image:Xenoturbella bockii longitudinal section.svg|thumb|100px|left|''Xenoturbella bockii'' longitudinal section.]]
[[/Xenacoelomorpha/]]

Name Meaning: Strange hollow form

English Common Name: none

Major distinguishing characteristics: Ciliated deuterostome

Approximate number of species described: 435

==Quizzes==
* [[/Quiz/|Animal Phyla Quiz]]

==References==
{{reflist}}
*Brusca, Richard C., Wendy Moore, Stephen M. Shuster. Invertebrate Zoology 3rd ed. 2016. Sinauer. 1104 pp.
*[https://en.wikipedia.org/wiki/Phylum Phylum] on Wikipedia
[[Category:Lists]]
[[Category:Taxonomy]]
[[Category:Zoology]]
[[Category:Animals]]
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    <title>Animal Phyla/Orthonectida</title>
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        <id>3110681</id>
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      <comment>Added phylogeny!</comment>
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      <text bytes="1679" sha1="9sfhlyn0njaw096f302o4vw5vkrdwjy" xml:space="preserve">[[Image:Orthonetida dict flat and cylinder.png|thumb|300px|right|Orthonetida, an Orthonectidan.]]
*Orthonectida
*Name Meaning: Straight swim
*English Common Name: Orthonectidans
*Major distinguishing characteristics:
*Approximate number of species described: about 20

==Natural History==

==Taxonomy==
Orthonectida has two families:
*Rhopaluridae
*Pelmatosphaeridae
==Phylogeny==
{{Clade
|label1=Orthonectida
|1={{Clade
 |1=''Pelmatosphaera polycirri''
 |label2=Rhopaluridae
 |2={{Clade
  |1={{Clade
  |1=''Neosabellaria cementarium''
  |label2=''Ciliocincta''
  |2={{Clade
   |1=''Ciliocincta akkeshiensis''
   |2=''Ciliocincta julini''}}}}
|3={{Clade
|1=''Rhopalura major''
   |label2=''Intoshia''
   |2={{Clade
|1=''Intoshia leptoplanae''
|2=''Intoshia linei''
|3=''Intoshia metchnikovi''
|4=''Intoshia paraphanostomae''
|5=''Intoshia variabili''
}}
|label3=''Rhopalura''
|3={{Clade
|1=''Rhopalura elongata''
|2=''Rhopalura gigas''
|3=''Rhopalura granosa''
|4=''Rhopalura intoshi''
|5=''Rhopalura murmanica''
|6=''Rhopalura ophiocomae''
|7=''Rhopalura pelseneeri''
|8=''Rhopalura philinae''
|9=''Rhopalura pterocirri''
|10=''Rhopalura vermiculicola''}}
}}
|label2=''Stoecharthrum''
|2={{Clade
|1=''Stoecharthrum burresoni''
|2=''Stoecharthrum fosterae''
|3=''Stoecharthrum giardi''
|4=''Stoecharthrum monnati''}}
}}
}}
}}
==Anatomy==

==The Fossil Record==

==Quiz==

* [[/Orthonectida Quiz/]]
==References and Further Reading==
*[https://en.wikipedia.org/wiki/Orthonectida Orthonectida] at Wikipedia
*[http://eol.org/pages/8769/overview Orthonectida] at Encyclopedia of Life

{{Animalia}}

[[Category:Animals]]
[[Category:Biology]]
[[Category:Taxonomy]]
[[Category:Zoology]]</text>
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    <title>Animal Phyla/Phoronida</title>
    <ns>0</ns>
    <id>235223</id>
    <revision>
      <id>2841399</id>
      <parentid>2010657</parentid>
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        <username>The Citer</username>
        <id>3110681</id>
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      <comment>Added phylogeny!</comment>
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      <text bytes="1563" sha1="kv0dept7ha6wdhoo8z49ik1arzfe8c2" xml:space="preserve">[[Image:Phoronis Maria Grazia Montanucci2.jpg|thumb|300px|Right|'' Phoronis hippocrepis'', a species of horseshoe worm.]]
*Phoronida
*Name Meaning: Zeus' mistress
*English Common Name: Horseshoe worms
*Major distinguishing characteristics: U-shaped gut
*Approximate number of species described: 20

==Natural History==

==Taxonomy==
There are two genera, each characterized by development:
*''Phoronis'' (Adults)
*''Actinotrochaca'' (Larvae)
==Phylogeny==
{{Clade
|label1=Phoronida
|1={{Clade
|label1=''Actinotrocha''
|sublabel1=(Larvae)
|1={{Clade
|1=''Actinotrocha hippocrepia''
|2=''Actinotrocha vancouverensis''
|3=''Actinotrocha branchiata''
|4=''Actinotrocha sabatieri''
|5=''Actinotrocha pallida''
|6=''Actinotrocha harmeri''}}
|label2=Phoronini
|sublabel2=(Adults)
|2={{Clade
|label1=''Phoronopsis''
|1={{Clade
|1=''Phoronopsis albomaculata''
|2=''Phoronopsis harmeri''
|3=''Phoronopsis californica''}}
|label2=''Phoronis''
|2={{clade
|1=''Phoronis ovalis''
|2=''Phoronis hippocrepia''
|7={{clade
|1=''Phoronis ijimai''
|2=''Phoronis vancouverensis''}}
|4=''Phoronis australis''
|5=''Phoronis muelleri''
|6=''Phoronis psammophila''
|3=''Phoronis pallida''}}
}}
}}
}}
==Anatomy==

==The Fossil Record==

==Quiz==

* [[/Phoronida Quiz/]]
==References and Further Reading==
*[https://en.wikipedia.org/wiki/Phoronid Phoronida] at Wikipedia
*[http://tolweb.org/Phoronida/2493 Phoronida] at Tree of Life
*[http://eol.org/pages/8867/overview Phoronida] at Encyclopedia of Life

[[Category:Animals]]
[[Category:Biology]]
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[[Category:Zoology]]</text>
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    <title>Animal Phyla/Placozoa</title>
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        <username>The Citer</username>
        <id>3110681</id>
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      <comment>Added phylogeny, but there are too few species. 😔</comment>
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      <text bytes="1620" sha1="5a443hf4lbzj5htjf8c92eqzz6x0smg" xml:space="preserve">[[Image:Trichoplax adhaerens photograph.png|thumb|300px|right|''Trichoplax adhaerens'', a species within the Phylum Placozoa.]]
*Placozoa
*Name Meaning: Plate animals
*English Common Name: none
*Major distinguishing characteristics:
*Approximate number of species described: 4

==Natural History==

==Taxonomy==
This phylum is one of the fewest biodiverse phyla.
==Phylogeny==
Behold a phylum with an underwhelming number of species:
{{clade| style=
|label1=Placozoa
|1={{clade
   |label1=Polyplacotomia|1={{clade
   |label1=Polyplacotomea|1={{clade
   |label1=Polyplacotomidae
   |1=''Polyplacotoma mediterranea'' H0}}}}
   |label2=Uniplacotomia
   |2={{clade
      |label1=Trichoplacea|1={{clade
      |label1=Trichoplacidae
      |1={{clade
            |1=''Trichoplax adhaerens'' H1
         }}}}
      |2={{clade
         |label1=Cladhexea
         |1=H11
         |label2=Hoilungea
         |2={{clade
            |label1=Cladtertiidae
            |1={{clade
               |1=''Cladtertia collaboinventa'' H23
               }}
            |label2=Hoilungidae
            |2={{clade                        |1=''Hoilungia hongkongensis'' H13
                     }}
                  }}
               }}
            }}
         }}
      }}

==Anatomy==

==The Fossil Record==

==Quiz==

* [[/Placozoa Quiz/]]
==References==
*[https://en.wikipedia.org/wiki/Placozoa Placozoa] at Wikipedia
*[http://tolweb.org/Placozoa Placozoa] at Tree of Life
*[http://eol.org/pages/8773/overview Placozoa] at Encyclopedia of Life

{{Animalia}}

[[Category:Animals]]
[[Category:Biology]]
[[Category:Taxonomy]]
[[Category:Zoology]]</text>
      <sha1>5a443hf4lbzj5htjf8c92eqzz6x0smg</sha1>
    </revision>
  </page>
  <page>
    <title>Animal Phyla/Platyhelminthes</title>
    <ns>0</ns>
    <id>235225</id>
    <revision>
      <id>2841417</id>
      <parentid>2010663</parentid>
      <timestamp>2026-10-19T01:25:56Z</timestamp>
      <contributor>
        <username>The Citer</username>
        <id>3110681</id>
      </contributor>
      <comment>Added phylogeny! (completion later)</comment>
      <origin>2841417</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2140" sha1="nje7ebutxuxqtm424jlkzvbdqpnim68" xml:space="preserve">[[Image:Gigantolina.elongata.in.vivo.png|thumb|300px|Right|''Gigantolina elongata'', a flat worm in the gut of a long-necked turtle.]]
*Platyhelminthes
*Name Meaning: Flat worms
*English Common Name: Flat worms
*Major distinguishing characteristics:
*Approximate number of species described: about 25,000

==Natural History==

==Taxonomy==
==Phylogeny==
{{clade
|style=font-size:80%;line-height:80%;
|label1='''Platyhelminthes'''
|1={{clade
  |1=[[Catenulida]]
  |label2=[[Rhabditophora]]
  |2={{clade
    |1=[[Macrostomorpha]]
    |label2=[[Trepaxonemata]]
    |2={{clade
      |label1=[[Amplimatricata]]
      |1={{clade
        |1=[[Prorhynchidae|Prorhynchida]]
        |2=[[Polycladida]]
         }}
      |2={{clade
        |1=[[Gnosonesimidae|Gnosonesimida]]
        |label2=[[Euneoophora]]
        |2={{clade
          |label1=[[Rhabdocoela]]
          |1={{clade
            |1=[[Kalyptorhynchia]]
            |2=[[Dalytyphloplanida]]
             }}
          |2={{clade
            |1=[[Proseriata]]
            |label2=Acentrosomata
            |2={{clade
              |label1=[[Adiaphanida]]
              |1={{clade
                |1=[[Prolecithophora]]
                |2={{clade
                  |1=[[Fecampiida]]
                  |2=[[Tricladida]] (planarians)
                   }}
                 }}
              |label2=[[Bothrioneodermata]]
              |2={{clade
                |label1=Bothrioplanata
                |1=Bothrioplanida (freshwater)
                |sublabel2=''parasitic''
                |2=Neodermata 
[[File:Fasciola_hepatica_(Linnaeus,_1758)_2013_000-2.jpg|60px]]
                 }}
               }}
             }}
           }}
         }}
       }}
     }}
   }}
}}

==Anatomy==

==The Fossil Record==

==Quiz==

* [[/Platyhelminthes Quiz/]]
==References and Further Reading==
*[https://en.wikipedia.org/wiki/Flatworm Platyhelminthes] at Wikipedia
*[http://tolweb.org/Platyhelminthes/2477 Platyhelminthes] at Tree of Life
*[http://eol.org/pages/2884/overview Platyhelminthes] at Encyclopedia of Life

[[Category:Animals]]
[[Category:Biology]]
[[Category:Taxonomy]]
[[Category:Zoology]]</text>
      <sha1>nje7ebutxuxqtm424jlkzvbdqpnim68</sha1>
    </revision>
  </page>
  <page>
    <title>File naming</title>
    <ns>0</ns>
    <id>271189</id>
    <revision>
      <id>2841483</id>
      <parentid>2812644</parentid>
      <timestamp>2026-10-19T09:29:58Z</timestamp>
      <contributor>
        <username>Trangngo1801</username>
        <id>3112921</id>
      </contributor>
      <minor />
      <comment>Undid revision [[Special:Diff/2422889|2422889]] by [[Special:Contributions/Elominius|Elominius]] ([[User talk:Elominius|talk]])</comment>
      <origin>2841483</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="12529" sha1="tcev5g0fip2zgum2tyvyyhd5djh6jq2" xml:space="preserve">{{unknown subject}}
{{uncategorized}}
There are various ways for software to name files automatically.

This lesson describes the file naming strategies in detail, among respective benefits and shortcomings. 

Multiple strategies may be applied to the same file names, as described in {{section link||Combination}}.

== Time stamps ==
File names are automatically generated from the current date and time, usually with descending order until second (→[[:w:ISO_8601|ISO 8601]]).

;Examples:
* &lt;code&gt;{{#time: YmdHis}}&lt;/code&gt; (no separators)
* &lt;code&gt;{{#time: Ymd_His}}&lt;/code&gt; (underscore separator)
* &lt;code&gt;{{#time: Ymd-His}}&lt;/code&gt; (dash separator)
* &lt;code&gt;{{#time: Y-m-d H:i:s}}&lt;/code&gt; (note: colons in file names are unsupported by many file systems, →{{section link||Characters}})
* &lt;code&gt;{{#time: Y-m-d_H-i-s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d-H-i-s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d-H_i-s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Ymd_H\hi\ms\s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Ymd-H\hi\ms\s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d_H\hi\ms\s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d-H\hi\ms\s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d_H\h-i\m-s\s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d-H\h-i\m-s\s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Ymd\THis}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d-\THis}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d-\TH-i-s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d-\TH-i-s-T}}&lt;/code&gt;

File names may include prefixes such as &lt;code&gt;IMG_{{#time: Ymd_His}}.jpg&lt;/code&gt; and &lt;code&gt;Screenshot_{{#time:Ymd-His}}.png&lt;/code&gt;. 

If more than one file is created within one second, such as in burst [[photography]], a suffix number may be added before the file extension, such as &lt;code&gt;IMG_{{#time: Ymd_His}}_1.jpg&lt;/code&gt; or &lt;code&gt;IMG_{{#time: Ymd_His}}(1).jpg&lt;/code&gt;, or milleseconds, such as &lt;code&gt;IMG_{{#time: Ymd_His}}_228.jpg&lt;/code&gt; or &lt;code&gt;IMG_{{#time:Ymd_His}}-437.jpg&lt;/code&gt;.

Mobile phone camera software commonly uses this method.

;Benefits
This method safely prevents duplicate file names which may cause confusion and clobbering (overwriting) if handled improperly, such as when using the &lt;code&gt;mv&lt;/code&gt; command without the &lt;code&gt;-n&lt;/code&gt; flag. Naming conflicts when merging files from multiple devices into one place are also avoided.

In addition, during [[:w:file transfer|file transfer]]s between systems, the file attributes containing the date and time information may be dismissed and reset. If the file's internal meta data does not contain date and time information, the file name is the only location where the otherwise lost date and time information is stored. To avoid losing such information, a list of files with dates and times should recommendedly be created before initiating a file transfer.

Searches for files by time are facilitated, because all file searching software is able to search for files by name, while not all software is able to search by file time attributes or internal metadata time stamp usually found in photo and video files.

Time-based selection of files is facilitated using [[:w:Wildcard character|wildcards]], as usually supported by [[Command Prompt|command prompt and terminal]] software, for time-based file operations such as copying all photos and videos from a specific day or month. As an example, the asterisk wildcard &lt;code&gt;DCIM/Camera/{{#time:Ym}}*.mp4&lt;/code&gt; would match all videos captured in {{CURRENTMONTHNAME}} of {{CURRENTYEAR}}, if the camera software uses a &lt;code&gt;{{#time: Ymd_His}}.mp4&lt;/code&gt; file name format.

There is no realistic limit of possible file names at a fixed name length, while on numbered files with a too short fixed length (e.g. four digits) not split between directories, the possible number of file names might foreseeably be exhausted, where a variable digit length (e.g. &lt;code&gt;9999&lt;/code&gt; followed by &lt;code&gt;10000&lt;/code&gt;) might be presented in an incorrect order in alphanumerical file sorting, if number detection is not implemented into the file management software.

=== Pasting ===
Time stamps can be set to be pasted with a keyboard shortcut, implemented through ''AutoHotKey'' for Windows and ''xdotool'' for Linux.

;AutoHotKey (Windows)
For example, this AutoHotKey script pastes the time stamp when pressing &lt;kbd&gt;Alt&lt;/kbd&gt;+&lt;kbd&gt;2&lt;/kbd&gt;.
&lt;pre&gt;
Alt &amp; 2::
Send, %A_Now%
Return
&lt;/pre&gt;
&lt;code&gt;%A_Now&lt;/code&gt; does the same as &lt;code&gt; Send,%A_YYYY%%A_MM%%A_DD%%A_HH24%%A_MI%%A_SS%&lt;/code&gt;, which is pasting a &lt;code&gt;YYYYMMDDHHMMSS&lt;/code&gt; time stamp, such as &lt;code&gt;{{#time:YmdHis}}&lt;/code&gt;.

;xdotool (Linux)
On Linux, a keyboard shortcut can be assigned to call this example script, which can be modified to suit one's needs. It requires &lt;code&gt;xdotool&lt;/code&gt; to be installed.
&lt;syntaxhighlight lang=sh&gt;
sleep .2
xdotool type &quot;$(date +%Y%m%d%H%M%S)&quot; # Format can be changed
&lt;/syntaxhighlight&gt;

&lt;code&gt;sleep .2&lt;/code&gt; (synonymous with &lt;code&gt;sleep 0.2&lt;/code&gt;) adds a fifth-second delay before pasting the time stamp to prevent pasting prior to the key being released, possibly causing a part of the output to be omitted.

== Numbering ==
This method is commonly used among digital cameras and camcorders due to lack of internet connectivity or GPS reception which would be necessary for the clock to set automatically, and some users not bothering with setting the date and time before starting to operate the device.

When storing on a new (or cleared) memory card, some digital cameras and other software starts over counting (based on the last used file number), while others keep a memory of the last used number, stored in a local variable, the latter of which prevents duplicate file names when moving to a common place.

;Examples
* &lt;code&gt;DSCI0001.JPG&lt;/code&gt;
* &lt;code&gt;IMG_0002.JPG&lt;/code&gt;
* &lt;code&gt;00003.MTS&lt;/code&gt;
* &lt;code&gt;Screenshot (4).png&lt;/code&gt;

Digital cameras may split the files between directories per day or per 999 or 1000 files:

* &lt;code&gt;DCIM/100_PANA/P1000999.JPG&lt;/code&gt;
* &lt;code&gt;DCIM/101_PANA/P1010001.JPG&lt;/code&gt;

This naming scheme is used by at least several Panasonic ''Lumix'' digital cameras.

;Benefits
Numbered file names facilitate counting files and noticing files that possibly went missing during a transfer.

If the device's clock setting is incorrect as described above, the file names will not carry wrong date and time information. Some devices such as standalone flat bed (paper) scanners which allow direct saving to flash drives and/or memory cards may lack a clock setting entirely, which may make the date and time information appear as ''1970-01-01'', the ''Unix epoch''.

Numbered file names are usually shorter than timestamped ones. With modern file systems however which are not limited to eight-point-three file names, this benefit is only marginial.

== Combination ==
A combination of both naming strategies may be used, combining the benefits. In practice, this has not been commonly implemented so far.

;Examples
*&lt;code&gt;Screenshot_000001_{{#time:YmdHis}}.png&lt;/code&gt;
*&lt;code&gt;IMG00002_{{#time:YmdHis}}.jpg&lt;/code&gt;
*&lt;code&gt;VID_0003_{{#time:YmdHis}}.mp4&lt;/code&gt;
*&lt;code&gt;{{#time:Y-m-d-H_i_s}}.4.ogg&lt;/code&gt; (The leading zeroes for file numbers are not necessary here for correct sorting, due to the time stamp preceeding it, but they may be necessary for a constant file name length, to prevent irritatingly protruding file names in a list.)
*&lt;code&gt;{{#time:Y-m-d-H_i_s}}.00005.ogg&lt;/code&gt; (With leading zeroes.)

== Contextual ==
Contextual file names, often used in addition to a time stamp, may contain information such as location&lt;ref&gt;[https://www.gsmarena.com/samsung_galaxy_s4_active-review-935p6.php ''Samsung Galaxy S4 Active preview: First look'' (page 6)] &amp;ndash; GSMArena (05 June 2013)&lt;/ref&gt; or opened software&lt;ref name=Samsung-Oreo&gt;[https://pocketnow.com/on-android-oreo-samsung-names-screenshot-files-based-on-app ''On Android Oreo, Samsung names screenshot files based on app''] &amp;ndash; PocketNow.com (December 19, 2017)&lt;/ref&gt;.

The contextual information may be applied prior to or after the file name:

* &lt;code&gt;{{#time:Ymd_His}}_Avenue_Kléber.jpg&lt;/code&gt; &amp;ndash; Location name option in the camera software of some Samsung mobile phones since 2013.
* &lt;code&gt;Screenshot_YouTube_{{#time:Ymd-His}}.png&lt;/code&gt; &amp;ndash; Application title name, before time stamp, as used by Samsung Mobile since Android 8.0 Oreo.&lt;ref name=Samsung-Oreo /&gt;
* &lt;code&gt;Screnshot_{{#time:Y-m-d-H-i-s}}_com.mi.android.globalFileexplorer.png&lt;/code&gt; &amp;ndash; Application package name, after time stamp, as used by Xiaomi Mobile.

== Manual ==
Consider adding short notes to names of multimedia files such as screen shots, photos, videos, voice notes, etc., as they are not searchable like text.

Screenshots' text may be searchable using character recognition software, but scanning each picture for text would be far slower (presumably over 100 times) than directly machine-readable text, and as of 2021, no open-source software for this purpose appears to exist.

File names for downloaded media like videos should include a title and may include the source ID and date stamp  and author name to facilitate finding. A format example is &quot;&lt;code&gt;Will YouTube Ever Run Out Of Video IDs - Tom Scott (2016-03-21).gocwRvLhDf8.mp4&lt;/code&gt;&quot;.

Disk images' file names may include the data storage type (e. g. SSD, HDD, BD-R), the vendor name, vendor-specified size, and the approximate date of purchase. If the image is intended for long-term archival rather than a short-term backup, the current date stamp (e. g. &quot;&lt;code&gt;{{#time:Y-m-d}}&lt;/code&gt;&quot;) should be written as well. An example is &lt;code&gt;SD-SanDisk-64GB-2016.{{#time:Y-m-d}}.img&lt;/code&gt;&quot;).

Characters like a colon (&lt;code&gt;:&lt;/code&gt;) and a question mark (&lt;code&gt;?&lt;/code&gt;), as well as duplicate file and directory names with only letter case differences (e. g. &quot;&lt;code&gt;New folder&lt;/code&gt;&quot; and &quot;&lt;code&gt;New Folder&lt;/code&gt;&quot;), should be avoided from to ensure support across file systems and operating systems.

Since file managers typically allow jumping to files by typing in the file name from the beginning, choose the start of the file name by which information you would like to type in a directory listing. For example, if you wish to jump to a file in the directory listing by typing in a date, start the file name with that. If you wish to jump to a file by a name or location, put that at the beginning of the file name. As of 2022, file managers are not known to have a search feature that only searches the current directory listing without sub directories, but this can be done in the terminal with wild cards.

== Characters ==
Use of the following characters should be avoided wherever possible, due to limited support or automatic substitution among file systems and resource locator types:

* &lt;code&gt; &lt;/code&gt; (space character) — Inconvenient in Unix/Linux terminal auto completion (needs backslash escaping if not within quotation marks); substituted with &lt;code&gt;%20&lt;/code&gt; in URL and &lt;code&gt;_&lt;/code&gt; (underscore) in [[MediaWiki]].
* &lt;code&gt;:&lt;/code&gt; (colon) — Possible compatibility issues; reserved for drive letters in Microsoft Windows (e.g. &lt;code&gt;C:\&lt;/code&gt;).
* &lt;code&gt;=&lt;/code&gt; (equal sign) — Might be parsed as variable modifier in [[Bash]] and MediaWiki.

== Mistakes ==
The following mistakes should be avoided:
;[[:w:Clobbering|Clobbering]] (overwriting) existing files: This is more likely to happen on applications which use static file names (e.g. for data exports), where an existing file ''always'' causes a naming collision, but might happen on deficient implementations where numbered files are written from a local number variable without verifying that the file name is not reserved.

== Temporary names ==
Software may give files a temporary name while it is being processed. For example, the Firefox web browser appends &quot;&lt;code&gt;.part&lt;/code&gt;&quot; to the file name, and Chrome &quot;&lt;code&gt;.crdownload&lt;/code&gt;&quot;. The benefits are that it distinguishes the file, and signifies to the user that the file is incomplete if the download was interrupted. However, a disadvantage is that it interferes with streaming a multimedia file in a locally installed media player software during download.

When saving a file, a [[:wikipedia:Bak_file|&lt;code&gt;.bak&lt;/code&gt; file]] may be created to prevent corruption in case of a failed write. This may be caused by a power outage, operating system crash, or disk space exhaustion.

== Additional tips ==
* Manual file naming does not have always to be completely consistent where the benefit of sparing efforts needed for maintaining such outweighs, for example for names of text files containing drafted text snippets, where content can be &lt;code&gt;grep&lt;/code&gt;ped through rapidly when necessary.

== References ==
{{reflist}}</text>
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    </revision>
    <revision>
      <id>2841488</id>
      <parentid>2841483</parentid>
      <timestamp>2026-10-19T09:57:01Z</timestamp>
      <contributor>
        <username>NDG</username>
        <id>3006541</id>
      </contributor>
      <minor />
      <comment>Reverted edit by [[Special:Contributions/Trangngo1801|Trangngo1801]] ([[User_talk:Trangngo1801|talk]]) to last version by [[User:Atcovi|Atcovi]] using [[Wikiversity:Rollback|rollback]]</comment>
      <origin>2812644</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="12585" sha1="0hotua8ql8sgqqy3pqchm8cy7mk1wme" xml:space="preserve">{{unknown subject}}
{{uncategorized}}
There are various ways for software to name files automatically.

This lesson describes the file naming strategies in detail, among respective benefits and shortcomings. 

Multiple strategies may be applied to the same file names, as described in {{section link||Combination}}.

== Time stamps ==
File names are automatically generated from the current date and time, usually with descending order until second (→[[:w:ISO_8601|ISO 8601]]).

;Examples:
* &lt;code&gt;{{#time: YmdHis}}&lt;/code&gt; (no separators)
* &lt;code&gt;{{#time: Ymd_His}}&lt;/code&gt; (underscore separator)
* &lt;code&gt;{{#time: Ymd-His}}&lt;/code&gt; (dash separator)
* &lt;code&gt;{{#time: Y-m-d H:i:s}}&lt;/code&gt; (note: colons in file names are unsupported by many file systems, →{{section link||Characters}})
* &lt;code&gt;{{#time: Y-m-d_H-i-s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d-H-i-s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d-H_i-s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Ymd_H\hi\ms\s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Ymd-H\hi\ms\s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d_H\hi\ms\s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d-H\hi\ms\s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d_H\h-i\m-s\s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d-H\h-i\m-s\s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Ymd\THis}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d-\THis}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d-\TH-i-s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d-\TH-i-s-T}}&lt;/code&gt;

File names may include prefixes such as &lt;code&gt;IMG_{{#time: Ymd_His}}.jpg&lt;/code&gt; and &lt;code&gt;Screenshot_{{#time:Ymd-His}}.png&lt;/code&gt;. 

If more than one file is created within one second, such as in burst [[photography]], a suffix number may be added before the file extension, such as &lt;code&gt;IMG_{{#time: Ymd_His}}_1.jpg&lt;/code&gt; or &lt;code&gt;IMG_{{#time: Ymd_His}}(1).jpg&lt;/code&gt;, or milleseconds, such as &lt;code&gt;IMG_{{#time: Ymd_His}}_228.jpg&lt;/code&gt; or &lt;code&gt;IMG_{{#time:Ymd_His}}-437.jpg&lt;/code&gt;.

Mobile phone camera software commonly uses this method.

;Benefits
This method safely prevents duplicate file names which may cause confusion and clobbering (overwriting) if handled improperly, such as when using the &lt;code&gt;mv&lt;/code&gt; command without the &lt;code&gt;-n&lt;/code&gt; flag. Naming conflicts when merging files from multiple devices into one place are also avoided.

In addition, during [[:w:file transfer|file transfer]]s between systems, the file attributes containing the date and time information may be dismissed and reset. If the file's internal meta data does not contain date and time information, the file name is the only location where the otherwise lost date and time information is stored. To avoid losing such information, a list of files with dates and times should recommendedly be created before initiating a file transfer.

Searches for files by time are facilitated, because all file searching software is able to search for files by name, while not all software is able to search by file time attributes or internal metadata time stamp usually found in photo and video files.

Time-based selection of files is facilitated using [[:w:Wildcard character|wildcards]], as usually supported by [[Command Prompt|command prompt and terminal]] software, for time-based file operations such as copying all photos and videos from a specific day or month. As an example, the asterisk wildcard &lt;code&gt;DCIM/Camera/{{#time:Ym}}*.mp4&lt;/code&gt; would match all videos captured in {{CURRENTMONTHNAME}} of {{CURRENTYEAR}}, if the camera software uses a &lt;code&gt;{{#time: Ymd_His}}.mp4&lt;/code&gt; file name format.

There is no realistic limit of possible file names at a fixed name length, while on numbered files with a too short fixed length (e.g. four digits) not split between directories, the possible number of file names might foreseeably be exhausted, where a variable digit length (e.g. &lt;code&gt;9999&lt;/code&gt; followed by &lt;code&gt;10000&lt;/code&gt;) might be presented in an incorrect order in alphanumerical file sorting, if number detection is not implemented into the file management software.

=== Pasting ===
Time stamps can be set to be pasted with a keyboard shortcut, implemented through ''AutoHotKey'' for Windows and ''xdotool'' for Linux.

;AutoHotKey (Windows)
For example, this AutoHotKey script pastes the time stamp when pressing &lt;kbd&gt;Alt&lt;/kbd&gt;+&lt;kbd&gt;2&lt;/kbd&gt;.
&lt;pre&gt;
Alt &amp; 2::
Send, %A_Now%
Return
&lt;/pre&gt;
&lt;code&gt;%A_Now&lt;/code&gt; does the same as &lt;code&gt; Send,%A_YYYY%%A_MM%%A_DD%%A_HH24%%A_MI%%A_SS%&lt;/code&gt;, which is pasting a &lt;code&gt;YYYYMMDDHHMMSS&lt;/code&gt; time stamp, such as &lt;code&gt;{{#time:YmdHis}}&lt;/code&gt;.

;xdotool (Linux)
On Linux, a keyboard shortcut can be assigned to call this example script, which can be modified to suit one's needs. It requires &lt;code&gt;xdotool&lt;/code&gt; to be installed.
&lt;syntaxhighlight lang=sh&gt;
sleep .2
xdotool type &quot;$(date +%Y%m%d%H%M%S)&quot; # Format can be changed
&lt;/syntaxhighlight&gt;

&lt;code&gt;sleep .2&lt;/code&gt; (synonymous with &lt;code&gt;sleep 0.2&lt;/code&gt;) adds a fifth-second delay before pasting the time stamp to prevent pasting prior to the key being released, possibly causing a part of the output to be omitted.

== Numbering ==
This method is commonly used among digital cameras and camcorders due to lack of internet connectivity or GPS reception which would be necessary for the clock to set automatically, and some users not bothering with setting the date and time before starting to operate the device.

When storing on a new (or cleared) memory card, some digital cameras and other software starts over counting (based on the last used file number), while others keep a memory of the last used number, stored in a local variable, the latter of which prevents duplicate file names when moving to a common place.

;Examples
* &lt;code&gt;DSCI0001.JPG&lt;/code&gt;
* &lt;code&gt;IMG_0002.JPG&lt;/code&gt;
* &lt;code&gt;00003.MTS&lt;/code&gt;
* &lt;code&gt;Screenshot (4).png&lt;/code&gt;

Digital cameras may split the files between directories per day or per 999 or 1000 files:

* &lt;code&gt;DCIM/100_PANA/P1000999.JPG&lt;/code&gt;
* &lt;code&gt;DCIM/101_PANA/P1010001.JPG&lt;/code&gt;

This naming scheme is used by at least several Panasonic ''Lumix'' digital cameras.

;Benefits
Numbered file names facilitate counting files and noticing files that possibly went missing during a transfer.

If the device's clock setting is incorrect as described above, the file names will not carry wrong date and time information. Some devices such as standalone flat bed (paper) scanners which allow direct saving to flash drives and/or memory cards may lack a clock setting entirely, which may make the date and time information appear as ''1970-01-01'', the ''Unix epoch''.

Numbered file names are usually shorter than timestamped ones. With modern file systems however which are not limited to eight-point-three file names, this benefit is only marginial.

== Combination ==
A combination of both naming strategies may be used, combining the benefits. In practice, this has not been commonly implemented so far.

;Examples
*&lt;code&gt;Screenshot_000001_{{#time:YmdHis}}.png&lt;/code&gt;
*&lt;code&gt;IMG00002_{{#time:YmdHis}}.jpg&lt;/code&gt;
*&lt;code&gt;VID_0003_{{#time:YmdHis}}.mp4&lt;/code&gt;
*&lt;code&gt;{{#time:Y-m-d-H_i_s}}.4.ogg&lt;/code&gt; (The leading zeroes for file numbers are not necessary here for correct sorting, due to the time stamp preceeding it, but they may be necessary for a constant file name length, to prevent irritatingly protruding file names in a list.)
*&lt;code&gt;{{#time:Y-m-d-H_i_s}}.00005.ogg&lt;/code&gt; (With leading zeroes.)

== Contextual ==
Contextual file names, often used in addition to a time stamp, may contain information such as location&lt;ref&gt;[https://www.gsmarena.com/samsung_galaxy_s4_active-review-935p6.php ''Samsung Galaxy S4 Active preview: First look'' (page 6)] &amp;ndash; GSMArena (05 June 2013)&lt;/ref&gt; or opened software&lt;ref name=Samsung-Oreo&gt;[https://pocketnow.com/on-android-oreo-samsung-names-screenshot-files-based-on-app ''On Android Oreo, Samsung names screenshot files based on app''] &amp;ndash; PocketNow.com (December 19, 2017)&lt;/ref&gt;.

The contextual information may be applied prior to or after the file name:

* &lt;code&gt;{{#time:Ymd_His}}_Avenue_Kléber.jpg&lt;/code&gt; &amp;ndash; Location name option in the camera software of some Samsung mobile phones since 2013.
* &lt;code&gt;Screenshot_YouTube_{{#time:Ymd-His}}.png&lt;/code&gt; &amp;ndash; Application title name, before time stamp, as used by Samsung Mobile since Android 8.0 Oreo.&lt;ref name=Samsung-Oreo /&gt;
* &lt;code&gt;Screnshot_{{#time:Y-m-d-H-i-s}}_com.mi.android.globalFileexplorer.png&lt;/code&gt; &amp;ndash; Application package name, after time stamp, as used by Xiaomi Mobile.

== Manual ==
Consider adding short notes to names of multimedia files such as screen shots, photos, videos, voice notes, etc., as they are not searchable like text.

Screenshots' text may be searchable using character recognition software, but scanning each picture for text would be far slower (presumably over 100 times) than directly machine-readable text, and as of 2021, no open-source software for this purpose appears to exist.

File names for downloaded media like videos should include a title and may include the source ID and date stamp  and author name to facilitate finding. A format example is &quot;&lt;code&gt;Will YouTube Ever Run Out Of Video IDs - Tom Scott (2016-03-21).gocwRvLhDf8.mp4&lt;/code&gt;&quot;.

Disk images' file names may include the data storage type (e. g. SSD, HDD, BD-R), the vendor name, vendor-specified size, and the approximate date of purchase. If the image is intended for long-term archival rather than a short-term backup, the current date stamp (e. g. &quot;&lt;code&gt;{{#time:Y-m-d}}&lt;/code&gt;&quot;) should be written as well. An example is &lt;code&gt;SD-SanDisk-64GB-2016.{{#time:Y-m-d}}.img&lt;/code&gt;&quot;).

Characters like a colon (&lt;code&gt;:&lt;/code&gt;) and a question mark (&lt;code&gt;?&lt;/code&gt;), as well as duplicate file and directory names with only letter case differences (e. g. &quot;&lt;code&gt;New folder&lt;/code&gt;&quot; and &quot;&lt;code&gt;New Folder&lt;/code&gt;&quot;), should be avoided from to ensure support across file systems and operating systems.

Since file managers typically allow jumping to files in a directory listing by typing in the file name from the beginning, choose the start of the file name by which information you would like to type in. For example, if you wish to jump to a file in the directory listing by typing in a date, start the file name with that. If you wish to jump to a file by a name or location, put that at the beginning of the file name. As of 2022, file managers are not known to have a search feature that only searches the current directory listing without sub directories, but this can be done in the terminal (command prompt) using [[:w:Wildcard_character|wildcard character]]s.

== Characters ==
Use of the following characters should be avoided wherever possible, due to limited support or automatic substitution among file systems and resource locator types:

* &lt;code&gt; &lt;/code&gt; (space character) — Inconvenient in Unix/Linux terminal auto completion (needs backslash escaping if not within quotation marks); substituted with &lt;code&gt;%20&lt;/code&gt; in URL and &lt;code&gt;_&lt;/code&gt; (underscore) in [[MediaWiki]].
* &lt;code&gt;:&lt;/code&gt; (colon) — Possible compatibility issues; reserved for drive letters in Microsoft Windows (e.g. &lt;code&gt;C:\&lt;/code&gt;).
* &lt;code&gt;=&lt;/code&gt; (equal sign) — Might be parsed as variable modifier in [[Bash]] and MediaWiki.

== Mistakes ==
The following mistakes should be avoided:
;[[:w:Clobbering|Clobbering]] (overwriting) existing files: This is more likely to happen on applications which use static file names (e.g. for data exports), where an existing file ''always'' causes a naming collision, but might happen on deficient implementations where numbered files are written from a local number variable without verifying that the file name is not reserved.

== Temporary names ==
Software may give files a temporary name while it is being processed. For example, the Firefox web browser appends &quot;&lt;code&gt;.part&lt;/code&gt;&quot; to the file name, and Chrome &quot;&lt;code&gt;.crdownload&lt;/code&gt;&quot;. The benefits are that it distinguishes the file, and signifies to the user that the file is incomplete if the download was interrupted. However, a disadvantage is that it interferes with streaming a multimedia file in a locally installed media player software during download.

When saving a file, a [[:wikipedia:Bak_file|&lt;code&gt;.bak&lt;/code&gt; file]] may be created to prevent corruption in case of a failed write. This may be caused by a power outage, operating system crash, or disk space exhaustion.

== Additional tips ==
* Manual file naming does not have always to be completely consistent where the benefit of sparing efforts needed for maintaining such outweighs, for example for names of text files containing drafted text snippets, where content can be &lt;code&gt;grep&lt;/code&gt;ped through rapidly when necessary.

== References ==
{{reflist}}</text>
      <sha1>0hotua8ql8sgqqy3pqchm8cy7mk1wme</sha1>
    </revision>
    <revision>
      <id>2841494</id>
      <parentid>2841488</parentid>
      <timestamp>2026-10-19T10:45:45Z</timestamp>
      <contributor>
        <username>Trangngo1801</username>
        <id>3112921</id>
      </contributor>
      <origin>2841494</origin>
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      <text bytes="12513" sha1="o0tumvfzsentzhberf2l8jh2rg8t0c4" xml:space="preserve">{{unknown subject}}
{{uncategorized}}
There are various ways for software to name files automatically.

This lesson describes the file naming strategies in detail, among respective benefits and shortcomings. 

Multiple strategies may be applied to the same file names, as described in {{section link||Combination}}.

== Time stamps ==
File names are automatically generated from the current date and time, usually with descending order until second (→[[:w:ISO_8601|ISO 8601]]).

;Examples:
* &lt;code&gt;{{#time: YmdHis}}&lt;/code&gt; (no separators)
* &lt;code&gt;{{#time: Ymd_His}}&lt;/code&gt; (underscore separator)
* &lt;code&gt;{{#time: Ymd-His}}&lt;/code&gt; (dash separator)
* &lt;code&gt;{{#time: Y-m-d H:i:s}}&lt;/code&gt; (note: colons in file names are unsupported by many file systems, →{{section link||Characters}})
* &lt;code&gt;{{#time: Y-m-d_H-i-s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d-H-i-s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d-H_i-s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Ymd_H\hi\ms\s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Ymd-H\hi\ms\s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d_H\hi\ms\s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d-H\hi\ms\s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d_H\h-i\m-s\s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d-H\h-i\m-s\s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Ymd\THis}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d-\THis}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d-\TH-i-s}}&lt;/code&gt;
* &lt;code&gt;{{#time: Y-m-d-\TH-i-s-T}}&lt;/code&gt;

File names may include prefixes such as &lt;code&gt;IMG_{{#time: Ymd_His}}.jpg&lt;/code&gt; and &lt;code&gt;Screenshot_{{#time:Ymd-His}}.png&lt;/code&gt;. 

If more than one file is created within one second, such as in burst [[photography]], a suffix number may be added before the file extension, such as &lt;code&gt;IMG_{{#time: Ymd_His}}_1.jpg&lt;/code&gt; or &lt;code&gt;IMG_{{#time: Ymd_His}}(1).jpg&lt;/code&gt;, or milleseconds, such as &lt;code&gt;IMG_{{#time: Ymd_His}}_228.jpg&lt;/code&gt; or &lt;code&gt;IMG_{{#time:Ymd_His}}-437.jpg&lt;/code&gt;.

Mobile phone camera software commonly uses this method.

;Benefits
This method safely prevents duplicate file names which may cause confusion and clobbering (overwriting) if handled improperly, such as when using the &lt;code&gt;mv&lt;/code&gt; command without the &lt;code&gt;-n&lt;/code&gt; flag. Naming conflicts when merging files from multiple devices into one place are also avoided.

In addition, during [[:w:file transfer|file transfer]]s between systems, the file attributes containing the date and time information may be dismissed and reset. If the file's internal meta data does not contain date and time information, the file name is the only location where the otherwise lost date and time information is stored. To avoid losing such information, a list of files with dates and times should recommendedly be created before initiating a file transfer.

Searches for files by time are facilitated, because all file searching software is able to search for files by name, while not all software is able to search by file time attributes or internal metadata time stamp usually found in photo and video files.

Time-based selection of files is facilitated using [[:w:Wildcard character|wildcards]], as usually supported by [[Command Prompt|command prompt and terminal]] software, for time-based file operations such as copying all photos and videos from a specific day or month. As an example, the asterisk wildcard &lt;code&gt;DCIM/Camera/{{#time:Ym}}*.mp4&lt;/code&gt; would match all videos captured in {{CURRENTMONTHNAME}} of {{CURRENTYEAR}}, if the camera software uses a &lt;code&gt;{{#time: Ymd_His}}.mp4&lt;/code&gt; file name format.

There is no realistic limit of possible file names at a fixed name length, while on numbered files with a too short fixed length (e.g. four digits) not split between directories, the possible number of file names might foreseeably be exhausted, where a variable digit length (e.g. &lt;code&gt;9999&lt;/code&gt; followed by &lt;code&gt;10000&lt;/code&gt;) might be presented in an incorrect order in alphanumerical file sorting, if number detection is not implemented into the file management software.

=== Pasting ===
Time stamps can be set to be pasted with a keyboard shortcut, implemented through ''AutoHotKey'' for Windows and ''xdotool'' for Linux.

;AutoHotKey (Windows)
For example, this AutoHotKey script pastes the time stamp when pressing &lt;kbd&gt;Alt&lt;/kbd&gt;+&lt;kbd&gt;2&lt;/kbd&gt;.
&lt;pre&gt;
Alt &amp; 2::
Send, %A_Now%
Return
&lt;/pre&gt;
&lt;code&gt;%A_Now&lt;/code&gt; does the same as &lt;code&gt; Send,%A_YYYY%%A_MM%%A_DD%%A_HH24%%A_MI%%A_SS%&lt;/code&gt;, which is pasting a &lt;code&gt;YYYYMMDDHHMMSS&lt;/code&gt; time stamp, such as &lt;code&gt;{{#time:YmdHis}}&lt;/code&gt;.

;xdotool (Linux)
On Linux, a keyboard shortcut can be assigned to call this example script, which can be modified to suit one's needs. It requires &lt;code&gt;xdotool&lt;/code&gt; to be installed.
&lt;syntaxhighlight lang=sh&gt;
sleep .2
xdotool type &quot;$(date +%Y%m%d%H%M%S)&quot; # Format can be changed
&lt;/syntaxhighlight&gt;

&lt;code&gt;sleep .2&lt;/code&gt; (synonymous with &lt;code&gt;sleep 0.2&lt;/code&gt;) adds a fifth-second delay before pasting the time stamp to prevent pasting prior to the key being released, possibly causing a part of the output to be omitted.

== Numbering ==
This method is commonly used among digital cameras and camcorders due to lack of internet connectivity or GPS reception which would be necessary for the clock to set automatically, and some users not bothering with setting the date and time before starting to operate the device.

When storing on a new (or cleared) memory card, some digital cameras and other software starts over counting (based on the last used file number), while others keep a memory of the last used number, stored in a local variable, the latter of which prevents duplicate file names when moving to a common place.

;Examples
* &lt;code&gt;DSCI0001.JPG&lt;/code&gt;
* &lt;code&gt;IMG_0002.JPG&lt;/code&gt;
* &lt;code&gt;00003.MTS&lt;/code&gt;
* &lt;code&gt;Screenshot (4).png&lt;/code&gt;

Digital cameras may split the files between directories per day or per 999 or 1000 files:

* &lt;code&gt;DCIM/100_PANA/P1000999.JPG&lt;/code&gt;
* &lt;code&gt;DCIM/101_PANA/P1010001.JPG&lt;/code&gt;

This naming scheme is used by at least several Panasonic ''Lumix'' digital cameras.

;Benefits
Numbered file names facilitate counting files and noticing files that possibly went missing during a transfer.

If the device's clock setting is incorrect as described above, the file names will not carry wrong date and time information. Some devices such as standalone flat bed (paper) scanners which allow direct saving to flash drives and/or memory cards may lack a clock setting entirely, which may make the date and time information appear as ''1970-01-01'', the ''Unix epoch''.

Numbered file names are usually shorter than timestamped ones. With modern file systems however which are not limited to eight-point-three file names, this benefit is only marginial.

== Combination ==
A combination of both naming strategies may be used, combining the benefits. In practice, this has not been commonly implemented so far.

;Examples
*&lt;code&gt;Screenshot_000001_.png&lt;/code&gt;
*&lt;code&gt;IMG00002_{{#time:YmdHis}}.jpg&lt;/code&gt;
*&lt;code&gt;VID_0003_{{#time:YmdHis}}.mp4&lt;/code&gt;
*&lt;code&gt;{{#time:Y-m-d-H_i_s}}.4.ogg&lt;/code&gt; (The leading zeroes for file numbers are not necessary here for correct sorting, due to the time stamp preceeding it, but they may be necessary for a constant file name length, to prevent irritatingly protruding file names in a list.)
*&lt;code&gt;{{#time:Y-m-d-H_i_s}}.00005.ogg&lt;/code&gt; (With leading zeroes.)

== Contextual ==
Contextual file names, often used in addition to a time stamp, may contain information such as location&lt;ref&gt;[https://www.gsmarena.com/samsung_galaxy_s4_active-review-935p6.php ''Samsung Galaxy S4 Active preview: First look'' (page 6)] &amp;ndash; GSMArena (05 June 2013)&lt;/ref&gt; or opened software&lt;ref name=Samsung-Oreo&gt;[https://pocketnow.com/on-android-oreo-samsung-names-screenshot-files-based-on-app ''On Android Oreo, Samsung names screenshot files based on app''] &amp;ndash; PocketNow.com (December 19, 2017)&lt;/ref&gt;.

The contextual information may be applied prior to or after the file name:

* &lt;code&gt;{{#time:Ymd_His}}_Avenue_Kléber.jpg&lt;/code&gt; &amp;ndash; Location name option in the camera software of some Samsung mobile phones since 2013.
* &lt;code&gt;Screenshot_YouTube_{{#time:Ymd-His}}.png&lt;/code&gt; &amp;ndash; Application title name, before time stamp, as used by Samsung Mobile since Android 8.0 Oreo.&lt;ref name=Samsung-Oreo /&gt;
* &lt;code&gt;Screnshot_{{#time:Y-m-d-H-i-s}}_com.mi.android.globalFileexplorer.png&lt;/code&gt; &amp;ndash; Application package name, after time stamp, as used by Xiaomi Mobile.

== Manual ==
Consider adding short notes to names of multimedia files such as screen shots, photos, videos, voice notes, etc., as they are not searchable like text.

Screenshots' text may be searchable using character recognition software, but scanning each picture for text would be far slower (presumably over 100 times) than directly machine-readable text, and as of 2021, no open-source software for this purpose appears to exist.

File names for downloaded media like videos should include a title and may include the source ID and date stamp  and author name to facilitate finding. A format example is &quot;&lt;code&gt;Will YouTube Ever Run Out Of Video IDs - Tom Scott (2016-03-21).gocwRvLhDf8.mp4&lt;/code&gt;&quot;.

Disk images' file names may include the data storage type (e. g. SSD, HDD, BD-R), the vendor name, vendor-specified size, and the approximate date of purchase. If the image is intended for long-term archival rather than a short-term backup, the current date stamp (e. g. &quot;&lt;code&gt;{{#time:Y-m-d}}&lt;/code&gt;&quot;) should be written as well. An example is &lt;code&gt;SD-SanDisk-64GB-2016.{{#time:Y-m-d}}.img&lt;/code&gt;&quot;).

Characters like a colon (&lt;code&gt;:&lt;/code&gt;) and a question mark (&lt;code&gt;?&lt;/code&gt;), as well as duplicate file and directory names with only letter case differences (e. g. &quot;&lt;code&gt;New folder&lt;/code&gt;&quot; and &quot;&lt;code&gt;New Folder&lt;/code&gt;&quot;), should be avoided from to ensure support across file systems and operating systems.

Since file managers typically allow jumping to files by typing in the file name from the beginning, choose the start of the file name by which information you would like to type in a directory listing. For example, if you wish to jump to a file in the directory listing by typing in a date, start the file name with that. If you wish to jump to a file by a name or location, put that at the beginning of the file name. As of 2022, file managers are not known to have a search feature that only searches the current directory listing without sub directories, but this can be done in the terminal with wild cards.

== Characters ==
Use of the following characters should be avoided wherever possible, due to limited support or automatic substitution among file systems and resource locator types:

* &lt;code&gt; &lt;/code&gt; (space character) — Inconvenient in Unix/Linux terminal auto completion (needs backslash escaping if not within quotation marks); substituted with &lt;code&gt;%20&lt;/code&gt; in URL and &lt;code&gt;_&lt;/code&gt; (underscore) in [[MediaWiki]].
* &lt;code&gt;:&lt;/code&gt; (colon) — Possible compatibility issues; reserved for drive letters in Microsoft Windows (e.g. &lt;code&gt;C:\&lt;/code&gt;).
* &lt;code&gt;=&lt;/code&gt; (equal sign) — Might be parsed as variable modifier in [[Bash]] and MediaWiki.

== Mistakes ==
The following mistakes should be avoided:
;[[:w:Clobbering|Clobbering]] (overwriting) existing files: This is more likely to happen on applications which use static file names (e.g. for data exports), where an existing file ''always'' causes a naming collision, but might happen on deficient implementations where numbered files are written from a local number variable without verifying that the file name is not reserved.

== Temporary names ==
Software may give files a temporary name while it is being processed. For example, the Firefox web browser appends &quot;&lt;code&gt;.part&lt;/code&gt;&quot; to the file name, and Chrome &quot;&lt;code&gt;.crdownload&lt;/code&gt;&quot;. The benefits are that it distinguishes the file, and signifies to the user that the file is incomplete if the download was interrupted. However, a disadvantage is that it interferes with streaming a multimedia file in a locally installed media player software during download.

When saving a file, a [[:wikipedia:Bak_file|&lt;code&gt;.bak&lt;/code&gt; file]] may be created to prevent corruption in case of a failed write. This may be caused by a power outage, operating system crash, or disk space exhaustion.

== Additional tips ==
* Manual file naming does not have always to be completely consistent where the benefit of sparing efforts needed for maintaining such outweighs, for example for names of text files containing drafted text snippets, where content can be &lt;code&gt;grep&lt;/code&gt;ped through rapidly when necessary.

== References ==
{{reflist}}</text>
      <sha1>o0tumvfzsentzhberf2l8jh2rg8t0c4</sha1>
    </revision>
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  <page>
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      <timestamp>2026-10-18T13:23:19Z</timestamp>
      <contributor>
        <username>Alexis Jazz</username>
        <id>791434</id>
      </contributor>
      <comment>Updating gadget usage statistics from [[Special:GadgetUsage]] ([[phab:T121049]])</comment>
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      <text bytes="1276" sha1="58rbi5c8goci8cnolsxsyibap82sgy8" xml:space="preserve">{{#ifexist:Project:GUS2Wiki/top|{{/top}}|This page provides a historical record of [[Special:GadgetUsage]] through its page history. To get the data in CSV format, see wikitext. To customize this message or add categories, create [[/top]].}}
The following data is cached, and was last updated 2026-10-16T06:16:44Z. A maximum of {{PLURAL:5000|one result is|5000 results are}} available in the cache.
{| class=&quot;sortable wikitable&quot;
! Gadget !! data-sort-type=&quot;number&quot; | Number of users !! data-sort-type=&quot;number&quot; | Active users
|-
|CleanDeletions || 75 || 0
|-
|EnhancedTalk || 1404 || 6
|-
|HideFundraisingNotice || 841 || 7
|-
|HotCat || 923 || 7
|-
|LintHint || 120 || 2
|-
|Round Corners || 1192 || 3
|-
|contribsrange || 389 || 3
|-
|dark-mode || 137 || 1
|-
|dark-mode-toggle || 193 || 3
|-
|edittop || 522 || 7
|-
|popups || 886 || 4
|-
|purge || 739 || 9
|-
|sidebartranslate || 563 || 1
|-
|usurper-count || 120 || 0
|}
* [[Special:GadgetUsage]]
* [[m:Meta:GUS2Wiki/Script|GUS2Wiki]]
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  <page>
    <title>User:Dc.samizdat/Real Euclidean four-dimensional space</title>
    <ns>2</ns>
    <id>289273</id>
    <revision>
      <id>2841300</id>
      <parentid>2840993</parentid>
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      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
      </contributor>
      <comment>/* General relativity is special relativity in a Euclidean space of four orthogonal dimensions */</comment>
      <origin>2841300</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="109479" sha1="n4iip2isp0qxvuqc288mr17o2jjtsgk" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic; it applies to all motions of objects with mass, rotations as well as translations. A translation is relativistically equivalent to a distinct rotation in which the characteristic angle of the rotational displacement is zero. Inertia is the tendency of objects with mass to conserve a characteristic angle of rotational displacement. Because the rate of atomic scale displacements is the constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration) is proportional to the distinct rotation's characteristic displacement angle.
...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessable by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated.

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;(n+1)&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, and there exists no privileged monocentric viewpoint. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

It should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: &quot;The universe is a sphere whose center is wherever there is intelligence.&quot;{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in the Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space which is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the direct model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
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      <comment>/* General relativity is special relativity in a Euclidean space of four orthogonal dimensions */</comment>
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      <text bytes="109753" sha1="px9ok13y273lbc260p3cmt4988mzzd4" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic; it applies to all motions of objects with mass, rotations as well as translations. A translation is a simple rotation in which the characteristic angle of each rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. The rotation of the object is a change to its direction, not to its constant velocity. Because the rate of atomic scale displacements is the constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration) is proportional to the distinct rotation's characteristic angles of displacement.
...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessable by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated.

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;(n+1)&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, and there exists no privileged monocentric viewpoint. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

It should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: &quot;The universe is a sphere whose center is wherever there is intelligence.&quot;{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in the Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space which is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the direct model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
      <sha1>px9ok13y273lbc260p3cmt4988mzzd4</sha1>
    </revision>
    <revision>
      <id>2841318</id>
      <parentid>2841311</parentid>
      <timestamp>2026-10-18T17:23:55Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
      </contributor>
      <comment>/* General relativity is special relativity in a Euclidean space of four orthogonal dimensions */</comment>
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      <text bytes="110127" sha1="jkm42yw1xg0smuvgx11f70i84jes6ph" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation is a simple rotation in which the characteristic angle of each rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the rotation of the object is a change to its direction, not to its constant velocity. Because the rate of atomic scale displacements is the constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration of the object) is proportional to the distinct rotation's characteristic angles of displacement.

A human being standing on the surface of the earth is performing a distinct double rotation with two completely orthogonal angles of rotational displacement. The human's acceleration of 32'/second/second is proportional to their distinct rotation's characteristic angles of displacement.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessable by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated.

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;(n+1)&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, and there exists no privileged monocentric viewpoint. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

It should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: &quot;The universe is a sphere whose center is wherever there is intelligence.&quot;{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in the Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space which is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the direct model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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    <revision>
      <id>2841319</id>
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      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
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      <comment>/* General relativity is special relativity in a Euclidean space of four orthogonal dimensions */</comment>
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      <text bytes="110197" sha1="4hrhglt0fe56hsrgv08735k36vjhwkd" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation is a simple rotation in which the characteristic angle of each rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration of the object) is proportional to the distinct rotation's characteristic angles of displacement.

A human being standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The human's acceleration of 32'/second/second is proportional to their distinct rotation's characteristic angles of displacement.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessable by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated.

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;(n+1)&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, and there exists no privileged monocentric viewpoint. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

It should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: &quot;The universe is a sphere whose center is wherever there is intelligence.&quot;{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in the Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space which is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the direct model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
      <sha1>4hrhglt0fe56hsrgv08735k36vjhwkd</sha1>
    </revision>
    <revision>
      <id>2841320</id>
      <parentid>2841319</parentid>
      <timestamp>2026-10-18T17:34:23Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
      </contributor>
      <comment>/* General relativity is special relativity in a Euclidean space of four orthogonal dimensions */</comment>
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      <model>wikitext</model>
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      <text bytes="110196" sha1="i6zdmjq42uknwtllaqcq641ft7ez1qb" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation is a simple rotation in which the characteristic angle of each rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration of the object) is proportional to the distinct rotation's characteristic angles of displacement.

A human being standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The human's acceleration of 32'/second/second is proportional to that distinct rotation's characteristic angles of displacement.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessable by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated.

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;(n+1)&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, and there exists no privileged monocentric viewpoint. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

It should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: &quot;The universe is a sphere whose center is wherever there is intelligence.&quot;{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in the Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space which is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the direct model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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      <contributor>
        <username>Dc.samizdat</username>
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      <text bytes="110288" sha1="81c5jlx998lhv2p4uje6m9m7lvb6g0o" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation is a simple rotation in which the characteristic angle of each rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration of the object) is proportional to the distinct rotation's characteristic angles of displacement.

A human being standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The human's acceleration of 32'/second/second is proportional to that distinct rotation's characteristic angles of displacement.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, as well as by algebraic methods from Grassmann and [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;(n+1)&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, and there exists no privileged monocentric viewpoint. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

It should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: &quot;The universe is a sphere whose center is wherever there is intelligence.&quot;{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in the Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space which is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the direct model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
      <sha1>81c5jlx998lhv2p4uje6m9m7lvb6g0o</sha1>
    </revision>
    <revision>
      <id>2841326</id>
      <parentid>2841325</parentid>
      <timestamp>2026-10-18T17:47:30Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
      </contributor>
      <comment>/* Dimensional relativity */</comment>
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      <text bytes="110275" sha1="629thmu9nxhhspdooei1ba4c8yc01kl" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation is a simple rotation in which the characteristic angle of each rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration of the object) is proportional to the distinct rotation's characteristic angles of displacement.

A human being standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The human's acceleration of 32'/second/second is proportional to that distinct rotation's characteristic angles of displacement.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, as well as by algebraic methods after [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;(n+1)&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, and there exists no privileged monocentric viewpoint. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

It should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: &quot;The universe is a sphere whose center is wherever there is intelligence.&quot;{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in the Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space which is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the direct model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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      <text bytes="110268" sha1="isk48xnmybge9grju7erak1txyrepmp" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation is a simple rotation in which the characteristic angle of each rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration of the object) is proportional to the distinct rotation's characteristic angles of displacement.

A human being standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The human's acceleration of 32'/second/second is proportional to that distinct rotation's characteristic angles of displacement.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;(n+1)&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, and there exists no privileged monocentric viewpoint. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

It should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: &quot;The universe is a sphere whose center is wherever there is intelligence.&quot;{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in the Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space which is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the direct model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
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        <username>Dc.samizdat</username>
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      <comment>/* Polycentric spherical relativity */</comment>
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      <text bytes="110264" sha1="i9fml6qk7sqmmiufr7e5ci5xlhc7ur6" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation is a simple rotation in which the characteristic angle of each rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration of the object) is proportional to the distinct rotation's characteristic angles of displacement.

A human being standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The human's acceleration of 32'/second/second is proportional to that distinct rotation's characteristic angles of displacement.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;n&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, and there exists no privileged monocentric viewpoint. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

It should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: &quot;The universe is a sphere whose center is wherever there is intelligence.&quot;{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in the Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space which is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the direct model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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        <username>Dc.samizdat</username>
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      <text bytes="110267" sha1="q0a9hcjttpksgoucnvzi4bi5yv6t4vx" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation is a simple rotation in which the characteristic angle of each rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration of the object) is proportional to the distinct rotation's characteristic angles of displacement.

A human being standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The human's acceleration of 32'/second/second is proportional to that distinct rotation's characteristic angles of displacement.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;n&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: &quot;The universe is a sphere whose center is wherever there is intelligence.&quot;{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in the Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space which is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the direct model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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        <username>Dc.samizdat</username>
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      <comment>/* Polycentric spherical relativity */</comment>
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      <text bytes="110277" sha1="bpafqlcpkpu0pcqtpz5p6yknkqecqox" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation is a simple rotation in which the characteristic angle of each rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration of the object) is proportional to the distinct rotation's characteristic angles of displacement.

A human being standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The human's acceleration of 32'/second/second is proportional to that distinct rotation's characteristic angles of displacement.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;n&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: &quot;The universe is a sphere whose center is wherever there is intelligence.&quot;{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in the Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space which is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the direct model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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      <id>2841332</id>
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      <contributor>
        <username>Dc.samizdat</username>
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      <text bytes="110352" sha1="nwnkxpd3fzffh0pfr88y2yxrck8k7qa" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation is a simple rotation in which the characteristic angle of each rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration of the object) is proportional to the distinct rotation's characteristic angles of displacement.

A human being standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The human's acceleration of 32'/second/second is proportional to that distinct rotation's characteristic angles of displacement.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;n&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous and independent of Schlafli's work:
&lt;blockquote&gt;The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}&lt;/blockquote&gt;

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in the Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space which is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the direct model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
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      <comment>/* Polycentric spherical relativity */</comment>
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      <text bytes="110357" sha1="paa1duh0oe6jbe4a3l1jc2fkvpik4ng" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation is a simple rotation in which the characteristic angle of each rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration of the object) is proportional to the distinct rotation's characteristic angles of displacement.

A human being standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The human's acceleration of 32'/second/second is proportional to that distinct rotation's characteristic angles of displacement.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;n&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work:
&lt;blockquote&gt;The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}&lt;/blockquote&gt;

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in the Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space which is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the direct model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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      <id>2841336</id>
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        <username>Dc.samizdat</username>
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      <text bytes="110354" sha1="le6gaxkuu2r6a44i2q8umzdfjdyjeod" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation is a simple rotation in which the characteristic angle of each rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration of the object) is proportional to the distinct rotation's characteristic angles of displacement.

A human being standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The human's acceleration of 32'/second/second is proportional to that distinct rotation's characteristic angles of displacement.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;n&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work:
&lt;blockquote&gt;The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}&lt;/blockquote&gt;

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything in our local solar system.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in the Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space which is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the direct model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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      <text bytes="110274" sha1="8lvs0do3wzgxwsgglq3ukp2ct4yh210" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation is a simple rotation in which the characteristic angle of each rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration of the object) is proportional to the distinct rotation's characteristic angles of displacement.

A human being standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The human's acceleration of 32'/second/second is proportional to that distinct rotation's characteristic angles of displacement.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;n&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work:
&lt;blockquote&gt;The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}&lt;/blockquote&gt;

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in the Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space which is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the direct model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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      <text bytes="110283" sha1="904dzi66x1n6kugboyn91609lmci0rw" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation is a simple rotation in which the characteristic angle of each rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration of the object) is proportional to the distinct rotation's characteristic angles of displacement.

A human being standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The human's acceleration of 32'/second/second is proportional to that distinct rotation's characteristic angles of displacement.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;n&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work:
&lt;blockquote&gt;The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}&lt;/blockquote&gt;

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean &lt;math&gt;n&lt;/math&gt;-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in the Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space which is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the direct model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
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      <text bytes="110278" sha1="j2h8yruqu6kfdx0uctuzf41keriwds4" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation is a simple rotation in which the characteristic angle of each rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration of the object) is proportional to the distinct rotation's characteristic angles of displacement.

A human being standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The human's acceleration of 32'/second/second is proportional to that distinct rotation's characteristic angles of displacement.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;n&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work:
&lt;blockquote&gt;The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}&lt;/blockquote&gt;

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean &lt;math&gt;n&lt;/math&gt;-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in the Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space which is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the direct model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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        <username>Dc.samizdat</username>
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      <text bytes="110274" sha1="caeqeuax8rr70591hd6a2vboyz386g4" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation is a simple rotation in which the characteristic angle of each rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration of the object) is proportional to the distinct rotation's characteristic angles of displacement.

A human being standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The human's acceleration of 32'/second/second is proportional to that distinct rotation's characteristic angles of displacement.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;n&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work:
&lt;blockquote&gt;The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}&lt;/blockquote&gt;

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean &lt;math&gt;n&lt;/math&gt;-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in the Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space which is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the direct model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
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        <username>Dc.samizdat</username>
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      </contributor>
      <comment>/* Origins of the theory */</comment>
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      <text bytes="110288" sha1="ri2lpi0n1m6bsc4faso9083k3tikr9h" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation is a simple rotation in which the characteristic angle of each rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration of the object) is proportional to the distinct rotation's characteristic angles of displacement.

A human being standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The human's acceleration of 32'/second/second is proportional to that distinct rotation's characteristic angles of displacement.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;n&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work:
&lt;blockquote&gt;The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}&lt;/blockquote&gt;

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean &lt;math&gt;n&lt;/math&gt;-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in the Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space which is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the direct model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
      <sha1>ri2lpi0n1m6bsc4faso9083k3tikr9h</sha1>
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    <revision>
      <id>2841344</id>
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      <timestamp>2026-10-18T18:56:13Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
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      <comment>/* Origins of the theory */</comment>
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      <text bytes="110287" sha1="rgg9v7akq57fj2ip30uhbq9yuv9whxp" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation is a simple rotation in which the characteristic angle of each rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration of the object) is proportional to the distinct rotation's characteristic angles of displacement.

A human being standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The human's acceleration of 32'/second/second is proportional to that distinct rotation's characteristic angles of displacement.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;n&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work:
&lt;blockquote&gt;The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}&lt;/blockquote&gt;

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean &lt;math&gt;n&lt;/math&gt;-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space, which is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the direct model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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        <username>Dc.samizdat</username>
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      <comment>/* Origins of the theory */</comment>
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      <text bytes="110347" sha1="i1aogykm1submwbotmg3gsl9l3xoiug" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation is a simple rotation in which the characteristic angle of each rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration of the object) is proportional to the distinct rotation's characteristic angles of displacement.

A human being standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The human's acceleration of 32'/second/second is proportional to that distinct rotation's characteristic angles of displacement.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;n&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work:
&lt;blockquote&gt;The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}&lt;/blockquote&gt;

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean &lt;math&gt;n&lt;/math&gt;-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that &lt;math&gt;\mathbb{R}^4&lt;/math&gt; is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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      <id>2841347</id>
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      <text bytes="110357" sha1="8yywx8cgxfmcefb99h4le4k7jhktoy9" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation is a simple rotation in which the characteristic angle of each rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration of the object) is proportional to the distinct rotation's characteristic angles of displacement.

A human being standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The human's acceleration of 32'/second/second is proportional to that distinct rotation's characteristic angles of displacement.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;n&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work:
&lt;blockquote&gt;The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}&lt;/blockquote&gt;

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean &lt;math&gt;n&lt;/math&gt;-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that &lt;math&gt;\mathbb{R}^4&lt;/math&gt; is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
      <sha1>8yywx8cgxfmcefb99h4le4k7jhktoy9</sha1>
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        <username>Dc.samizdat</username>
        <id>2856930</id>
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      <text bytes="110394" sha1="smdv1n61ua3p047nq8nxg0ueeqgkt5a" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation &lt;math&gt;T&lt;/math&gt; is a distinct simple rotation &lt;math&gt;Q&lt;/math&gt; in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the rate of acceleration of the object) is a function of &lt;math&gt;c&lt;/math&gt; and the distinct rotation's unique conservation law.

A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is proportional to that distinct rotation's characteristic angles of displacement.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;n&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work:
&lt;blockquote&gt;The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}&lt;/blockquote&gt;

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean &lt;math&gt;n&lt;/math&gt;-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that &lt;math&gt;\mathbb{R}^4&lt;/math&gt; is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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    <revision>
      <id>2841431</id>
      <parentid>2841430</parentid>
      <timestamp>2026-10-19T02:51:43Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
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      <comment>/* General relativity is special relativity in a Euclidean space of four orthogonal dimensions */</comment>
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      <text bytes="110483" sha1="8s4qtihhofvj9beysk8pvhm6lom4cm5" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation &lt;math&gt;T&lt;/math&gt; is a distinct simple rotation &lt;math&gt;Q&lt;/math&gt; in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the acceleration of the object) is a function of &lt;math&gt;c&lt;/math&gt; and the distinct rotation's unique conservation law.

A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of &lt;math&gt;c&lt;/math&gt; and the distinct rotation's unique conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;n&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work:
&lt;blockquote&gt;The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}&lt;/blockquote&gt;

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean &lt;math&gt;n&lt;/math&gt;-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that &lt;math&gt;\mathbb{R}^4&lt;/math&gt; is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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    <revision>
      <id>2841438</id>
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      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
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      <comment>/* General relativity is special relativity in a Euclidean space of four orthogonal dimensions */</comment>
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      <text bytes="110512" sha1="midws5418i53z4amn1aoicyytvm7ink" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated upwards away from the center of the earth at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic integer number of rotational displacements during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, is a function of the distinct rotation it is performing. However, it is not a simple function of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation &lt;math&gt;T&lt;/math&gt; is the distinct simple rotation &lt;math&gt;Q&lt;/math&gt; in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the acceleration of the object) is a function of &lt;math&gt;c&lt;/math&gt; and the distinct rotation's unique conservation law.

A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of &lt;math&gt;c&lt;/math&gt; and the distinct rotation's unique conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;n&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work:
&lt;blockquote&gt;The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}&lt;/blockquote&gt;

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean &lt;math&gt;n&lt;/math&gt;-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that &lt;math&gt;\mathbb{R}^4&lt;/math&gt; is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
      <sha1>midws5418i53z4amn1aoicyytvm7ink</sha1>
    </revision>
    <revision>
      <id>2841449</id>
      <parentid>2841438</parentid>
      <timestamp>2026-10-19T04:05:16Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
      </contributor>
      <comment>/* General relativity is special relativity in a Euclidean space of four orthogonal dimensions */</comment>
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      <text bytes="110506" sha1="1s1saj8sv7vt4ksrvsdxyxv0px7ehii" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic number of its characteristic rotational displacement during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant &lt;math&gt;c&lt;/math&gt; for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation &lt;math&gt;T&lt;/math&gt; is the distinct simple rotation &lt;math&gt;Q&lt;/math&gt; in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the acceleration of the object) is a function of &lt;math&gt;c&lt;/math&gt; and the distinct rotation's unique conservation law.

A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of &lt;math&gt;c&lt;/math&gt; and the distinct rotation's unique conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;n&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work:
&lt;blockquote&gt;The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}&lt;/blockquote&gt;

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean &lt;math&gt;n&lt;/math&gt;-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that &lt;math&gt;\mathbb{R}^4&lt;/math&gt; is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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    <revision>
      <id>2841450</id>
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      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
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      <comment>/* General relativity is special relativity in a Euclidean space of four orthogonal dimensions */</comment>
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      <text bytes="110492" sha1="ggoz0kzfaac5yv317s2b4u2abdfdvkk" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|June 2023 - October 2026}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.&lt;/blockquote&gt;

== Summary ==
We observe that:
* Physical space has four perpendicular dimensions, not just three.
* Atoms are [[W:4-polytope|4-polytopes]].
* The sun is a [[W:4-ball|4-ball]] that is round in four dimensions.
* Everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space.
* Our entire 3-space manifold is moving through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions.
* Special relativity describes the linear motion of objects and light signals in four-dimensional Euclidean space.
* General relativity describes the rotational motion of objects with mass in four-dimensional Euclidean space.

== A theory of the Euclidean cosmos ==
The physical universe is properly visualized as [[w:Four-dimensional_space|real Euclidean space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;]] of four orthogonal spatial dimensions. Space itself has a fourth perpendicular dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are [[W:4-ball|4-balls]] of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. 

All objects with mass move inertially through Euclidean 4-space at constant velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt; is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space.

A typical galaxy such as ours occupies a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our spiral galaxy appear from our accustomed point of view to occupy a disk-like region of 3-dimensional space, with a denser ball-like center, but they are not so confined: they are distributed within a region of 4-dimensional space. The disk and ball have thickness not only in the third dimension, but in the fourth spatial dimension as well. 

Light from stars and galaxies reaches us on straight lines through Euclidean 4-space, so from our viewpoint, in what we have always imagined to be a 3-space universe, we look into the surrounding 4-space. Although we are physically confined within a 3-dimensional hyperplane by the inertia of our motion through 4-space at constant velocity &lt;math&gt;c&lt;/math&gt;, light signals are not so confined, so we observe all the cosmological objects surrounding us, both in and above or below our hyperplane, without perceiving their separation in our fourth orthogonal dimension, the direction of our motion. We may perceive a galaxy as elliptical when it is actually spherical, because that is how its image projects from its 4-ball shape into a 3-ball region in our hyperplane, where we measure it with our 3-dimensional bodies. More generally, orbits are circular in 4-space, but elliptical in the 3-space of their elliptic hyperplane.

The galaxy as a whole, or more properly its orbital barycenter, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity &lt;math&gt;c&lt;/math&gt; in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy 4-ball occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity &lt;math&gt;c&lt;/math&gt;. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the 4-cylinder; their trajectories are screw-translations through 4-space, the compound of a simple rotation and a completely orthogonal linear translation. 

The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis of motion. It is the tremendous inertial force of stars in translational motion at velocity &lt;math&gt;c&lt;/math&gt; that holds the cylinder of motion together, not some invisible dark matter.

The observed universe as a whole appears to be a [[W:3-sphere|3-sphere]] expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. A 3-sphere is a hypersphere in Euclidean 4-space, but the enclosing surface of a 3-sphere is a curved, finite 3-space, dimensionally analogous to the surface of the earth which is a curved, finite 2-space. This 3-sphere could be the domain of our visible cosmos, but of course we do not know for certain that all the cosmological objects we observe lie near the surface of our expanding 3-sphere, since it is only our assumption that they must all have originated in the same big bang long ago. Possibly some of the more distant objects we observe did not, and lie elsewhere, outside our big-bang's 3-sphere of outflying matter or even inside its 3-sphere, below its surface. We cannot assume that all objects in the 4-space universe lie near the surface of the same expanding 3-sphere. 

For all observers, the conjectured big-bang of their origin corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space: the same point in the same Euclidean 4-space for all observers with the same origin. Our big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. 

The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity &lt;math&gt;c&lt;/math&gt;. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold, and have only the thickness of an atom in their direction-of-motion fourth dimension. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. 

A spherical region of 4-space is called a [[W:4-ball|4-ball]]. The enclosing surface of a 4-ball of any size is a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. Our entire big-bang-origin universe appears to be the largest 3-sphere we observe, but each of the cosmological objects within it (including our galaxy and our sun) is contained in a smaller 3-sphere shell of its own, lying (we assume) on the largest 3-sphere embedded in its surface, like a soap bubble on the surface of a larger soap bubble. All the 3-dimensional surfaces are expanding, as the largest 3-sphere inflates at radial velocity &lt;math&gt;c&lt;/math&gt;. We ourselves live within such an expanding 3-dimensional surface, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our solar system occupies a small patch on a filmy 4-dimensional soap-bubble of galactic size rounded by gravity, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. 

Our 3-manifold of ordinary space, as a surface within our moving 4-ball galaxy, is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt; with the galaxy, in a distinct direction orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of individual objects through Euclidean space by the actions of their symmetry groups. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. 

Any moving 3-dimensional manifold such as ours is an evolving surface boundary that is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a 3-dimensional smear of atoms no thicker than one atom in its fourth dimension, the direction of its linear translation through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be &quot;heaped up&quot; into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to such 4-dimensional lumps of matter as atomic plasma, and have little experimental knowledge of their internal geometry or processes. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know almost nothing about its interior 4-ball, a dimensionally rounder enclosed space whose existence we did not suspect.

Every moving surface boundary of matter in the observed universe is evolving in four dimensions at velocity &lt;math&gt;c&lt;/math&gt;. The current location in 4-space of any of its material objects corresponds to the present moment in the proper time of that object's inertial reference frame. The object's direction of movement at velocity &lt;math&gt;c&lt;/math&gt; corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from subatomic particles to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, in two completely orthogonal inertial motions each at the constant universal rate of transformation &lt;math&gt;c&lt;/math&gt;. Every object with mass moves relative to universal 4-coordinate Euclidean space on its own distinct geodesic spiral, a screw displacement trajectory that is the compound of its two completely orthogonal inertial motions, a rotation and a translation.  

Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity &lt;math&gt;c&lt;/math&gt; through all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c\prime = 2c&lt;/math&gt;, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity &lt;math&gt;c&lt;/math&gt;. For example, we can look across the center of the mostly-empty 4-ball containing our galaxy and see stars in the opposite sides of its concentric 3-sphere orbital surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity &lt;math&gt;c&lt;/math&gt;. They move in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper 3-space, and generally the farther they are from us the greater the divergence of their direction of motion from our direction of motion: the greater the relative motion between us and their Hubble redshift. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. 

This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space.

== Symmetries ==

It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel &amp; Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let &lt;math&gt;\mathrm{Q}&lt;/math&gt; denote a rotation, &lt;math&gt;\mathrm{R}&lt;/math&gt; a reflection, &lt;math&gt;\mathrm{T}&lt;/math&gt; a translation, and let &lt;math&gt;\mathrm{Q}^q \mathrm{R}^r\mathrm{T}&lt;/math&gt; denote a product of several such transformations, all commutative with one another. Then &lt;math&gt;\mathrm{RT}&lt;/math&gt; is a glide-reflection (in two or three dimensions), &lt;math&gt;\mathrm{QR}&lt;/math&gt; is a rotary-reflection, &lt;math&gt;\mathrm{QT}&lt;/math&gt; is a screw-displacement, and &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r \le n)&lt;/math&gt;, the number of dimensions.&lt;br&gt;
Transformations involving a translation are also expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + 1 \le n)&lt;/math&gt;.&lt;br&gt;
For &lt;math&gt;(n = 4)&lt;/math&gt; in particular, every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;
If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; or a &lt;math&gt;\mathrm{QT}&lt;/math&gt;, because we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;. By the same principle, we can view any &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; as an isoclinic (equi-angled) &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) for ''one'' of the two rotations (&lt;math&gt;\mathrm{Q}&lt;/math&gt;). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;) up to uncertainty, and can always distinguish the direction of their own proper time translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;).

As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group &lt;math&gt;SO(4)&lt;/math&gt; [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic &lt;math&gt;SO(4)&lt;/math&gt; rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, atoms exhibit &lt;math&gt;SO(4)&lt;/math&gt; symmetries of the discrete isoclinic (equi-angled) double rotations (&lt;math&gt;\mathrm{Q^2}&lt;/math&gt;) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]].

== Special relativity describes Euclidean 4-space ==

&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.&lt;ref&gt;{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}&lt;/ref&gt;&lt;/blockquote&gt;

Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional space because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign as the three space coordinates so spacetime is hyperbolic, not a Euclidean (flat) 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was [[#Origins of the theory|imagined by Einstein]] himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction.

Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some non-Euclidean 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity &lt;math&gt;c&lt;/math&gt;, in some 4-space direction.{{Sfn|Yamashita|2023}}

This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a Euclidean four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always &lt;math&gt;c&lt;/math&gt;, as measured by all observers from any inertial reference frame.{{Efn|Each observer is stationary in space in their own proper reference frame, while they move at maximum velocity {{Math|c}} through their own proper time. Observed from another reference frame in relative motion, they appear foreshortened in space in their direction of motion, and their clocks appear to be slowed to less than the maximum velocity {{Math|c}}.}} This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source.{{Efn|
...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity {{Math|c}} through space and proper time.}} But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity &lt;math&gt;c&lt;/math&gt;. In physics as it has been universally understood, observers are not supposed to be able to move at velocity &lt;math&gt;c&lt;/math&gt;. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four.

In the Euclidean relativity alternative view, however, every observer is always moving at velocity &lt;math&gt;c&lt;/math&gt; through the universe, which is real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity &lt;math&gt;c&lt;/math&gt;. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your ordinary proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and ordinary proper 3-space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity &lt;math&gt;c&lt;/math&gt;, in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper Euclidean 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;. Lorentz transformations are required only to convert between your respective proper Minkowski spacetime coordinate systems.

So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity &lt;math&gt;c&lt;/math&gt; through Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the &quot;speed of light&quot; &lt;math&gt;c&lt;/math&gt;, although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity &lt;math&gt;c&lt;/math&gt;, but in at least slightly different directions.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity {{Math|c}} relative to universal Cartesian 4-coordinate space, so the maximum relative velocity between two observers is {{Math|2c}} when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to {{Math|c}}, it is the same measurement in different units. Special relativity measures all velocities in Minkowski spacetime (in a non-Euclidean 3-space). Euclidean relativity measures all velocities in Euclidean 4-space.}} In Einstein's relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of light through 3-space. In Euclidean relativity, the invariant &lt;math&gt;c&lt;/math&gt; is the speed of matter through 4-space! The speed of light through 3-space is also perceived as &lt;math&gt;c&lt;/math&gt; by all observers, because they are each living in a moving 3-manifold that is translating through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same special relativity predictions of how observers in different inertial reference frames will perceive each other's motions in time and space. It is beyond the scope of this present paper to show how they also agree on the predictions of general relativity, but it is important to understand that our formulation of Euclidean relativity requires our acceptance of the experimentally verified findings of special relativity, general relativity and quantum mechanics. Our model and the standard model both describe the same geometric relations of space and time based on the same evidence, but as embedded in two very different universal host spaces: Euclidean 4-space versus Minkowski spacetime. In some instances our model provides a geometric explanation for physical phenomena where the standard model has none, as yet. An example is the two models' differing explanations for the gravitational coherence of galaxies: either their inertial motion at velocity &lt;math&gt;c&lt;/math&gt;, or their possession of experimentally undetected dark matter. A more central example is our use of Coxeter's kinematics to explain the laws of relativistic motion geometrically. {{Efn|More generally, our model is concerned with group-theoretic properties of number elucidated by Coxeter and other geometers.
...cite Kappraff &amp; Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff &amp; Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff &amp; Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords.}}

Euclidean relativity is not even a fringe theory; no physicists or astronomers have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could &quot;catch up&quot; with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at &lt;math&gt;c&lt;/math&gt; (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than &lt;math&gt;c&lt;/math&gt;. Euclidean relativity is a revolutionary theory indeed, in which &lt;math&gt;c&lt;/math&gt; cannot possibly be the speed of light!

We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for &lt;math&gt;\mathbb{R}^4&lt;/math&gt; to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be &lt;math&gt;c\prime = 2c&lt;/math&gt;, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate inertially along the edge (or the radius) of a unit 4-hypercube. This is conceivable in Euclidean 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number &lt;math&gt;\sqrt{4}&lt;/math&gt;.

== An object's motion in space is the product of its discrete self-reflections ==
Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a number of discrete self-reflections. Any action of a polytope that transforms its position and orientation in space may be measured as a distinct sequence of self-reflections of the object in its own surfaces. Therefore any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete sequence of local self-reflections. This is a purely kinematic description of motion which does not give any account of forces acting on the object that cause it to move.

Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which intersect each other. When a  object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality.

Coxeter's laws of kinematics are a geometric counterpart to Newton's algebraic laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures, which may help us to visualize the relationships between translation and rotation in classic Newtonian physics problems, such as the [[W:Kepler problem|Kepler problem]] of the motion of the planets.&lt;ref&gt;{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton &amp; Company|isbn=978-0393039184}}&lt;/ref&gt; But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. In particular, they give us geometric pictures of all the possible motions of objects in 4-dimensional Euclidean space:

&lt;blockquote&gt;Every orthogonal transformation in 4-space is expressible as:&lt;br&gt;
:&lt;math&gt;\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t&lt;/math&gt;&lt;br&gt;
where &lt;math&gt;(2^q + r + t \le 4)&lt;/math&gt;. Every displacement is either a double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, or a screw-displacement &lt;math&gt;\mathrm{QT}&lt;/math&gt; [where the rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt; is a simple rotation, but the &lt;math&gt;\mathrm{QT}&lt;/math&gt; is chiral like a &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;]. Every enantiomorphous transformation in 4-space (reversing chirality) is a &lt;math&gt;\mathrm{QRT}&lt;/math&gt;.&lt;/blockquote&gt;

While this description should be understood as geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (&lt;math&gt;\mathrm{Q}&lt;/math&gt;), reflection (&lt;math&gt;\mathrm{R}&lt;/math&gt;) and translation (&lt;math&gt;\mathrm{T}&lt;/math&gt;) are obvious analogues of what they are in three-dimensional space, but double rotation (&lt;math&gt;\mathrm{Q}^2&lt;/math&gt;) is something new and unprecedented in our physical experience, because double rotations cannot occur until there are four or more dimensions of space in which to rotate.

A point in 4-space may be in motion on two circles in two completely orthogonal rotation planes simultaneously. Nothing constrains the two circles to be of the same radius, or constrains either circle from being of infinite radius such that the point moves in a straight line within its rotation plane: a translation &lt;math&gt;\mathrm{T}&lt;/math&gt; rather than a rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;. The motion of a rigid object defined by multiple points is constrained by its rigidity, such that the radii of both circles may approach infinity, but only one of the two radii may actually reach infinity. For a rigid object, only one of the two rotations may actually be a translation. 

Four dimensional Euclidean space can accomodate no such thing as a &lt;math&gt;\mathrm{Q}^2\mathrm{T}&lt;/math&gt;. A translating double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt;, like a translating simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt;, is simply a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt;. That is the essence of the way the principle of relativity operates in Euclidean 4-space. An object which is double-rotating in its own proper inertial reference frame may be seen to be performing nothing more mysterious than a screw translation, when observed from an inertial reference frame from which the object is in relative translational motion. Of course, it is a screw translation in 4-space, which is more mysterious than a screw translation in our ordinary 3-space. In 3-space the orbit of a screw translation (or any &lt;math&gt;\mathrm{Q}&lt;/math&gt;) lies on a great circle of an ordinary sphere (a 2-sphere). In 4-space the orbit of a screw translation &lt;math&gt;\mathrm{QT}&lt;/math&gt; or double rotation &lt;math&gt;\mathrm{Q}^2&lt;/math&gt; lies on a great circle of a hypersphere (a 3-sphere). Such 4-dimensional great circles are inherently more complex than the ordinary circles we experience in 3-space. They do not lie in a single plane, but bend through all four dimensions, in either a left or right hand direction of curvature. Unlike ordinary circles they are inherently chiral, and their circumference is not &lt;math&gt;2\pi r&lt;/math&gt;, but like ordinary circles they are truly circular, geodesic circles. In 4-space they might even be said to be more circular than ordinary circles, which bend in only two dimensions. We refer to such 4-dimensional great circles as ''isoclines'', to distinguish them from ordinary 2-dimensional great circles in the plane. Their name comes from the fact that a point on a rigid 4-dimensional object undergoing [[W:SO(4)#Isoclinic rotations|isoclinic rotation]] traverses an isocline circle.

In a universe which is real Euclidean four-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, wherein these motions occur only at the constant velocity &lt;math&gt;c&lt;/math&gt;, there is a universal Cartesian 4-coordinate reference frame in which every rigid object is translating on a &lt;math&gt;\mathrm{QT}&lt;/math&gt; at velocity &lt;math&gt;c&lt;/math&gt;. That universal inertial reference frame is not the proper reference frame of any object or observer, wherein the object or observer is stationary, but it is the common reference frame of all observers.

== Light propagates through 4-space at twice its apparent velocity &lt;math&gt;c&lt;/math&gt;==
Coxeter's laws of kinematics in 4-dimensional Euclidean space apply to all objects with mass, but we find there is an additional kind of displacement which applies only to massless particles such as photons, considered as single point objects. Light quanta (photons) translate through 4-space by 4-dimensional reflection &lt;math&gt;\mathrm{R}^4&lt;/math&gt;, which may be termed a double translation &lt;math&gt;\mathrm{T}^2&lt;/math&gt;, a pure translation via two pairs of parallel reflections without any rotation component &lt;math&gt;\mathrm{Q}&lt;/math&gt;.

Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by &lt;math&gt;\mathrm{QT}&lt;/math&gt;, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic &lt;math&gt;\mathrm{Q^2}&lt;/math&gt;, an isoclinically rotating object such as an atom. A simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; or simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; is a double reflection &lt;math&gt;\mathrm{R^2}&lt;/math&gt;, so a &lt;math&gt;\mathrm{QT}&lt;/math&gt; or &lt;math&gt;\mathrm{Q^2}&lt;/math&gt; is an &lt;math&gt;\mathrm{R^4}&lt;/math&gt;, but not with the same group of reflection angles as a light signal &lt;math&gt;\mathrm{R^4}&lt;/math&gt;. A translation &lt;math&gt;\mathrm{T = R^2}&lt;/math&gt; is a double reflection in two parallel planes, and a rotation &lt;math&gt;\mathrm{Q = R^2}&lt;/math&gt; is a double reflection in two intersecting planes, as in a &lt;math&gt;\mathrm{QT = R^4}&lt;/math&gt; which is both at once. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is two double reflections in pairs of parallel planes at once, a reflection in four non-intersecting parallel planes; it is all translation and no rotation. In a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; all the motion goes to translation, so the translation goes twice as far as the simple translation &lt;math&gt;\mathrm{T}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. A double translation &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; is the opposite of a double rotation &lt;math&gt;\mathrm{Q^2 = R^4}&lt;/math&gt;, which is stationary but rotates twice as far as the simple rotation &lt;math&gt;\mathrm{Q}&lt;/math&gt; in a &lt;math&gt;\mathrm{QT}&lt;/math&gt;. 

The product of the two translations in a &lt;math&gt;\mathrm{T^2}&lt;/math&gt; is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple &lt;math&gt;\mathrm{T}&lt;/math&gt; over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double the unit-distance translation, but without any rotation component, so it cannot carry any mass with it. A &lt;math&gt;\mathrm{T^2}&lt;/math&gt; cannot reposition a 4-polytope the way a &lt;math&gt;\mathrm{QT}&lt;/math&gt; does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter.{{Efn|
...lensing of double translations &lt;math&gt;\mathrm{T^2 = R^4}&lt;/math&gt; in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet...}}

== Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions ==

{{Efn|...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here...}}

Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are in 4-space).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. 

It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in a spatial dimension. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (However in general relativity, discussed below, the actual rate of physical processes varies from place to place, and reference frame differences predicted by the theory are neither reciprocal nor illusory.)

None of these Lorentz effects are beyond geometric explanation or paradoxical.  The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. 

The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, Euclidean spaces of successive dimensions are analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature including all of physics, is an exact expression of intrinsic group-theoretic symmetries: that is Nother's great discovery.

== General relativity is special relativity in a Euclidean space of four orthogonal dimensions ==

The statement that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames is known as the [[W:Equivalence principle|Einstein equivalence principle]].

The weight experienced by an observer standing on the floor in a building on the surface of the earth is the same as the weight experienced by an observer standing on the floor in a spaceship in interstellar space accelerating at a rate of 32'/second/second. Both observers are experiencing an upwards acceleration at the same rate, which in their respective proper reference frames is measured as the weight of gravity, rather than as an accelerating motion (they are stationary in their proper reference frames).

Einstein used this equivalence principle as the basis for his general theory of relativity, in much the same way he had used the constant velocity of light as the basis for his special theory of relativity. In general relativity the two accelerating observers occupy scenes which are relativistically equivalent, which means that although they can be distinguished (they have different measurements) in any reference frame from which they may both be observed, they have the same invariant geometry in all reference frames (they are the same phenomena), implying that there exists, for either scene, another reference frame from which it measures exactly like the other scene. 

Relativistically equivalent does not imply that there exists a single reference frame in which the two scenes are congruent (have the same measurements). It only means that they can be transformed into each other by a shift in point of view, because their invariant geometries (their measurements which are independent of point of view) are the same.

Einstein's general theory of relativity describes that invariant geometry, for scenes in general, in spacetime. 

Our formulation of Euclidean relativity describes that invariant geometry, for scenes in general, in real Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;.

An observer standing on the surface of the earth is accelerated at the rate of 32'/second/second. If we neglect for the moment the rotation of the earth, the observer and the earth are both stationary in their common inertial reference frame, so this accelerating motion cannot be perceived as motion in that reference frame; it is perceptible there as the force of gravity. It is only perceptible as motion in some other reference frame in which the earth and the observer are both in motion, such as the universal common reference frame of Euclidean 4-coordinate space in which they are both in motion at velocity &lt;math&gt;c&lt;/math&gt; on their respective screw translations &lt;math&gt;QT&lt;/math&gt;. In that universal common reference frame the observer's acceleration of 32'/second/second is the rate of change in the direction of his vector of translation through 4-space. The velocity of his vector of translation &lt;math&gt;T&lt;/math&gt; through 4-space remains the constant &lt;math&gt;c&lt;/math&gt; throughout; only his direction is changing. A change in the direction of a vector is a rotation &lt;math&gt;Q&lt;/math&gt; of a translation &lt;math&gt;T&lt;/math&gt;: a screw translation &lt;math&gt;QT&lt;/math&gt;.

A change in the direction of a vector is a rotation which is an acceleration. We can be precise about the units of measurement of this acceleration at atomic scale. In Coxeter's kinematics rotations of geometric objects occur in discrete increments called rotational displacements, with each distinct kind of rotation performing a characteristic number of its characteristic rotational displacement during a full revolution that returns the object to its starting orientation. There are many distinct kinds of rotation, each with its characteristic rotational displacement and number of displacements per revolution.

The general rotation in 4-space is a double rotation &lt;math&gt;Q^2&lt;/math&gt; distinguished by two distinct completely orthogonal angles through which the object turns in each rotational displacement. The angles determine not only the distance through which the object turns, but the characteristic trajectory of each point on the surface of the rotating object, including the length of that trajectory before it closes into a circle when the object returns to its starting orientation. For any distinct kind of rotation, the circular trajectory is always an integer multiple of the characteristic rotational displacement, but the full circle may be greater than 360°. In 4-space rotational circles are not ordinary 2-dimensional circles that lie in the plane and have a 360° circumference. Many distinct 4-space rotations of interest have a circumference of 720°, and many are larger. 

In 4-space every object with mass moves on its distinct &lt;math&gt;QT&lt;/math&gt; trajectory. Each rotational displacement &lt;math&gt;Q&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which intersect each other, at angles related to a distinct star polygon. Each translational displacement &lt;math&gt;T&lt;/math&gt; is equivalent to a pair of reflection displacements in two surfaces which lie parallel to each other. In both kinds of motion (rotation and translation) it is the rate at which these double-reflection displacements occur which is constant and which we measure as the velocity &lt;math&gt;c&lt;/math&gt;. Every atom translates at velocity &lt;math&gt;c&lt;/math&gt;, performing a large number of atomic scale translational displacements per second. Concurrently, the atom rotates at velocity &lt;math&gt;c&lt;/math&gt;, performing the same large number of atomic scale rotational displacements per second.

Although the number of displacements at atomic scale per unit time is the same universal constant &lt;math&gt;c&lt;/math&gt; for all rotations and translations, distinct kinds of rotation revolve at distinct rates, because the number of rotational displacements per complete revolution and the circumference of the complete revolution are distinct characteristics of each kind of rotation. The velocity at which each point on the surface of a rotating object moves, and the frequency of its rotational circling, are functions of the distinct rotation it is performing. However, they are not simple functions of &lt;math&gt;c&lt;/math&gt; and the two defining angle parameters of the rotation. Distinct rotations arise from distinct symmetry groups and each is its own mystery with a unique conservation law. The relationships between those distinct conservation laws are even more mysterious, and have been shown to be chaotic. Steinbach{{Sfn|Steinbach|1997}} discovered the Golden Fields family of ratios which govern distinct rotational displacements related to the regular star polygons at least up to the hendecagon {11}. Kappraff and Adamson{{Sfn|Kappraff|Adamson|2004}} further characterized the families of rotation functions and showed that they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator.

The inertial tendency of mass is to follow a geodesic. The inertial conservation law of gravity applies to all motions of objects with mass, rotations as well as translations. A translation &lt;math&gt;T&lt;/math&gt; is the distinct simple rotation &lt;math&gt;Q&lt;/math&gt; in which the characteristic angle of rotational displacement is zero. Inertia is the tendency of objects with mass to conserve their angles of rotational displacement. In 4-space each object has two completely orthogonal angles of rotational displacement which are characteristic of the distinct rotation the object is performing. Inertia is the conservation of this distinct double rotation. In 4-coordinate Euclidean space the acceleration of an object with mass is a rotation of the object, a change to its direction, not a change to its constant velocity. Because the rate of atomic scale displacements is the universal constant &lt;math&gt;c&lt;/math&gt;, the rate of change of direction (the acceleration of the object) is a function of &lt;math&gt;c&lt;/math&gt; and the distinct rotation's conservation law.

A observer standing on the surface of the earth is performing a distinct double rotation characterized by two completely orthogonal angles of rotational displacement. The observer's acceleration of 32'/second/second is a function of &lt;math&gt;c&lt;/math&gt; and the distinct rotation's conservation law, and a measurement of the rate of change of the observer's direction of motion through 4-space at velocity &lt;math&gt;c&lt;/math&gt;.

...

== Dimensional relativity ==
The formulation of Euclidean relativity based on Coxeter's kinetic law of &lt;math&gt;n&lt;/math&gt;-dimensional congruent transformations in Euclidean space may be called ''dimensional relativity'', since it captures the theories of special and general relativity, and has its roots in dimensional analogy.

Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessible by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated, and by algebraic methods after [[W:William Kingdon Clifford|Clifford]].

By analogy to the surface of the earth, the bounding surface of a spherical region of &lt;math&gt;n&lt;/math&gt;-dimensional Euclidean space is an &lt;math&gt;(n-1)&lt;/math&gt;-sphere, a spherical space of one fewer dimensions than the &lt;math&gt;n&lt;/math&gt;-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean &lt;math&gt;n&lt;/math&gt;-spaces of increasing &lt;math&gt;n&lt;/math&gt;, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating &lt;math&gt;n&lt;/math&gt;-spaces. By the capacity for dimensional analogy which they possess, some observers see deeper into &lt;math&gt;n&lt;/math&gt;-dimensional space than others.

== Polycentric spherical relativity ==

An intelligent observer equipped with the principle of dimensional relativity may perceive the universe from any inertial reference frame, not only from their own proper stationary reference frame in the Euclidean &lt;math&gt;n&lt;/math&gt;-space universe in which they physically locate themself. We see that every observer may also properly view themself as stationary and the universe as an &lt;math&gt;n&lt;/math&gt;-sphere with themself at the center observing it, perceptually equidistant from all points on its &lt;math&gt;n&lt;/math&gt;-space surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything.

This ''polycentric model'' of the universe is a further restatement of the principle of relativity, and of the [[W:Copernican principle|Copernican principle]] that observation is democratic: observers occupy representative viewpoints, not privileged monocentric positions. The polycentric model is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. 

The polycentric model should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849, contemporaneous with and independent of Schlafli's work:
&lt;blockquote&gt;The universe is a sphere whose center is wherever there is intelligence.{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}}&lt;/blockquote&gt;

== Revolutions ==

The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In 1600 [[W:Giordano Bruno|Giordano Bruno]] who first openly advocated these views was burned at the stake in Rome's [[W:Campo de' Fiori|Campo de' Fiori]] by the Catholic inquisition.

In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity &lt;math&gt;c&lt;/math&gt;, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may not all have the same origin in space and time.

As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment observers beginning with Bruno dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a geometry related to time, at least, it must be 4-dimensional. In the present work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space.

Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we have now learned to observe them, any more than they all lie in our local 3-space.

When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us primarily by virtue of how long it takes their light to reach us. We can measure their distribution around us in 3-space or 4-space, but that is simply how we choose to measure their positions, not an actual finding of how they are distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean &lt;math&gt;n&lt;/math&gt;-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity &lt;math&gt;c&lt;/math&gt;, on more or less divergent paths from each other. But only closer observation will reveal evidence of whether everything we see lies in the same Euclidean 4-space, or if it is distributed in five or more dimensions, and how it is moving there. 

To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw translations), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw translation has two [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity &lt;math&gt;c&lt;/math&gt; in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that the 3-sphere enclosing each galaxy is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. 

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to light speed long ago, in whatever big bang our atoms emerged from, and have never slowed down since.

== Origins of the theory ==

Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of a Euclidean 4-space universe, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] introduces (in 1843) the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not quite conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and he did not describe our ordinary 3-space as embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal to that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified non-Euclidean spacetime of four dimensions. 

Anco and Maghadam found that &lt;math&gt;SO(4)&lt;/math&gt; breaks to &lt;math&gt;\mathbb{S}^3&lt;/math&gt; (the 3-sphere) if the energy in a Kepler orbit is negative (an elliptical orbit), and to &lt;math&gt;H^3&lt;/math&gt; (Minkowski spacetime) if the energy is positive (a hyperbolic orbit). Therefore the fact that the planets orbit on ellipses in our 3-space suggests that they orbit on a 3-sphere embedded in Euclidean 4-space. Thus we can conclude that &lt;math&gt;\mathbb{R}^4&lt;/math&gt; is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the more direct physical model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position as our exclusive conception of our place in space.{{Efn|
...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others.}}

The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.&lt;ref&gt;{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}&lt;/ref&gt;}}

== Boundaries ==

&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our 3-sphere surface in our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? What is the nature of the boundary which confines us to just three dimensions?

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined objects and motions. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. An inertial boundary is a proper explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that we live in real space, which is Schläfli's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover, first in imagination and then to explore physically, each an astonishing new enlightenment.&lt;ref&gt;{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}&lt;blockquote&gt;
:We shall not cease from exploration
:And the end of all our exploring
:Will be to arrive where we started
:And know the place for the first time.
:Through the unknown, remembered gate
:When the last of earth left to discover
:Is that which was the beginning;
:At the source of the longest river
:The voice of the hidden waterfall
:And the children in the apple-tree
:Not known, because not looked for
:But heard, half-heard, in the stillness
:Between two waves of the sea.
&lt;/blockquote&gt;&lt;/ref&gt;

Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. That project is forever beginning anew. Coxeter discovered that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether discovered all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, and just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions in which all objects with mass move ceaselessly at the constant velocity &lt;math&gt;c&lt;/math&gt;, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. 

I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity to Kepler. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== ... ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|name=radially equilateral}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}({{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|5}}(–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}},–{{sfrac|1|2}}){{spaces|3}}(–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}},–{{sfrac|1|2}},{{spaces|2}}{{sfrac|1|2}})
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Sfn|Mamone, Pileio &amp; Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

==Notes==
{{Regular convex 4-polytopes Notelist|wiki=W:}}

==Citations==
{{Regular convex 4-polytopes Reflist|wiki=W:}}

==References==
{{Refbegin}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1|ref={{SfnRef|Yamashita|2023}}}}
* {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}}

=== [[Polyscheme|Polyschemes]] ===
{{Regular convex 4-polytopes Refs|wiki=W:}}
{{Refend}}</text>
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    <title>Motivation and emotion/Assessment/Using generative AI</title>
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      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <comment>+ * [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Self-concept_and_motivation&amp;action=history Self-concept and motivation] (Book chapter, 2026)</comment>
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__TOC__
&lt;noinclude&gt;==In a nutshell==&lt;/noinclude&gt;
[[File:Astrocyte (NIH BioArt 40 - 627579).png|80px|right]]
* '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Permitted]''' - ethical use of GenAI is allowed in completing the [[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]].
* '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Restricted]''' - use of GenAI is NOT allowed in completing the [[Motivation and emotion/Assessment/Exam|exam]].

To use genAI appropriately:
* Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|
Wikiversity edit summaries]].
* [[w:Fact-checking|Fact-check]].
* Only cite sources you consult.
* Human-rewrite to enhance quality.&lt;includeonly&gt; * [[Motivation and emotion/Assessment/Using generative AI|More detail ...]]&lt;/includeonly&gt;&lt;noinclude&gt;

==Summary==
[[w:Generative AI|Generative artificial intelligence]] (genAI) use is '''permitted''' for the [[Motivation and emotion/Assessment/Major project|major project]] (topic development and book chapter) and '''restricted''' for the [[Motivation and emotion/Assessment/Exam|exam]].

GenAI tools can help brainstorm, explain concepts, develop a structure, synthesise ideas, and improve the quality of written expression. GenAI tools can aid, but should not replace, independent thinking and reading of primary sources.

Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]]. Academia is based on transparency. Follow the principle that &quot;''more acknowledgment is better than less''&quot;. However, acknowledgement is not required for using the {{Motivation emotion/Generator}} (Cogniti),  Studiosity Writing Feedback+, or for low-level tasks such as improving spelling and grammar.

You are responsible for content you submit. Be aware of limitations of genAI tools such as inaccuracies, biases, and incomplete content. Fact-check all claims and only cite peer-reviewed citations which you consulted.

The best results are obtained from genAI tools through carefully crafted prompting based on reading of primary sources, with human rewriting to enhance quality. 

If you are unsure, post to [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together.

==Detailed guidelines==
[[File:Deeply engrossed in puzzle.png|thumb|220x220px|'''Figure 1'''. &lt;!-- An image of an elderly woman deeply engrossed in her daily crossword puzzle. --&gt;This image was generated by [[Motivation and emotion|Motivation and Emotion]] student [[User:JorjaFive|JorjaFive]] using [[w:Midjourney|Midjourney]] and uploaded to [[commons:|Wikimedia Commons]] for use in the [[Motivation and emotion/Book/2023/Flourishing in the elderly|flourishing in the elderly]] chapter.]]

===Use ethically, with caution===
Learning to use genAI tools (such as [[w:ChatGPT|ChatGPT]], [[w:Claude (language model)|Claude]],
[[w:Gemini (chatbot)|Gemini]], and [[w:Microsoft Copilot|Microsoft Copilot]]) responsibly and ethically is an emerging skill. GenAI tools can be used to enhance academic work, but should be used judiciously, as a supplementary tool, rather than as a replacement for independent thinking and academic inquiry.

GenAI tools may be used to assist in preparation of the major project ([[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]). These tools can include the Cogniti book chapter topic generator, Studiosity Writing Feedback+, and frontier models.

===How to use===
Recommended uses of genAI tools include:
* brainstorming
* explaining key concepts
* developing a structure
* synthesising complex ideas
* rephrasing to improve [[Motivation and emotion/Assessment/Chapter/Readability|readability]] and quality of written expression
* correcting spelling and grammar
* image generation (e.g., see Figure 1)
* scenario development
* critical feedback and suggestions for improvement

===How to acknowledge===
[[File:Wikipedia Edit Summary dialog in VisualEditor.png|thumb|450px|'''Figure 2'''. If contributing genAI content, include the tool and prompt details in the edit summary, with a link to the conversation]]

[[File:Edit summary for genAI content.png|thumb|450px|'''Figure 3'''. Example page history which demonstrates best practice edit summaries for contributing and revising genAI content]]

Use of GenAI tools must be clearly acknowledged in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] (e.g., see Figure 2), otherwise it is a violation of academic integrity.

Best practice is to include a publicly accessible link to the chatbot conversation (e.g., [https://help.openai.com/en/articles/7925741-chatgpt-shared-links-faq ChatGPT shared links FAQ]). If a link can't be shared, then provide details about the tool and the prompt in the [[Wikiversity:FAQ/Editing/Edit summary|edit summary]], (e.g., &quot;ChatGPT May 24 2025 Version. ''Prompt detail or summary''&quot;) (see Figure 3). The chatbot conversation should ''not'' be used as a citation and listed in the references because it is not a reliable, primary, peer-reviewed source.

These practices help to ensure that the use of genAI is clear. Transparency is key to good practice in academia. If in doubt, err on the side of providing acknowledgement. However, there is no need to acknowledge genAI use of the Cogniti book chapter topic generator, Studiosity Writing Feedback+, or for low-level tasks such as fixing grammar and spelling.

===Limitations===
Be aware of the limitations of genAI tools. Content they generate may be inaccurate, biased, incomplete, or otherwise problematic. Minimal effort reading and prompting will yield low quality results. Refine prompts based on critical reading and thinking to get better outcomes. You are entirely responsible for the accuracy and quality of any content you submit.

===Fact-check and cite===
Always fact-check. Regardless of whether genAI has been used, all claims need to be supported by verified peer-reviewed citations which you have consulted. Guide and craft genAI responses based on your reading of peer-reviewed theory and research. Low-energy or unreflective reuse of genAI text without further investigation and human-writing based on reviewing primary, peer-reviewed academic literature is likely to lead to a poor quality result. [https://www.seangoedecke.com/llms-reward-expertise GenAI tools work best for topics which you already understand].

==Learning and sharing==
* Despite these warnings, you are encouraged to explore use of genAI tools to help enhance your knowledge, skills, and develop higher quality work.
* Using genAI in academia and education is rapidly evolving. Expect to experiment, make mistakes, and learn along the way.
* If you are unsure about how to use genAI effectively or how to acknowledge its use appropriately, ask in [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together.
* One way of making [[Motivation and emotion/Wikiversity/Social contributions|social contributions]] is to help others by sharing your comments, questions, experiences, tools, prompts, outputs, and so on, in [[Motivation and emotion/About/Discussion|discussions]].

==Example==
* [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Affiliation_motivation_across_cultures&amp;action=history Affiliation and motivation] (Book chapter, 2025)
* [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Self-concept_and_motivation&amp;action=history Self-concept and motivation] (Book chapter, 2026)

==See also==
* [[b:Wikibooks:Artificial Intelligence|Wikibooks:Artificial Intelligence]] (policy)
* [[w:Wikipedia:Large language models|Wikipedia:Large language models]] (information page)
* [[Wikiversity:Artificial intelligence|Wikiversity:Artificial intelligence]] (policy)

==External links==
* [https://canberra.libguides.com/genai GenAI for students] (University of Canberra Library)
* [https://techcrunch.com/2024/06/01/what-is-ai-how-does-ai-work/ WTF is AI?] provides a useful introduction and non-technical overview about how genAI works, what it is capable of, limitations, and issues

[[Category:Motivation and emotion/Assessment]]
[[Category:Generative artificial intelligence]]
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__TOC__
&lt;noinclude&gt;==In a nutshell==&lt;/noinclude&gt;
[[File:Astrocyte (NIH BioArt 40 - 627579).png|80px|right]]
* '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Permitted]''' - ethical use of GenAI is allowed in completing the [[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]].
* '''[https://www.canberra.edu.au/about-uc/l-and-t/genai-and-assessment-at-uc Restricted]''' - use of GenAI is NOT allowed in completing the [[Motivation and emotion/Assessment/Exam|exam]].

To use genAI appropriately:
* Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|
Wikiversity edit summaries]].
* [[w:Fact-checking|Fact-check]].
* Only cite sources you consult.
* Human-rewrite to enhance quality.&lt;includeonly&gt; * [[Motivation and emotion/Assessment/Using generative AI|More detail ...]]&lt;/includeonly&gt;&lt;noinclude&gt;

==Summary==
[[w:Generative AI|Generative artificial intelligence]] (genAI) use is '''permitted''' for the [[Motivation and emotion/Assessment/Major project|major project]] (topic development and book chapter) and '''restricted''' for the [[Motivation and emotion/Assessment/Exam|exam]].

GenAI tools can help brainstorm, explain concepts, develop a structure, synthesise ideas, and improve the quality of written expression. GenAI tools can aid, but should not replace, independent thinking and reading of primary sources.

Acknowledge genAI use in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]]. Academia is based on transparency. Follow the principle that &quot;''more acknowledgment is better than less''&quot;. However, acknowledgement is not required for using the {{Motivation emotion/Generator}} (Cogniti),  Studiosity Writing Feedback+, or for low-level tasks such as improving spelling and grammar.

You are responsible for content you submit. Be aware of limitations of genAI tools such as inaccuracies, biases, and incomplete content. Fact-check all claims and only cite peer-reviewed citations which you consulted.

The best results are obtained from genAI tools through carefully crafted prompting based on reading of primary sources, with human rewriting to enhance quality. 

If you are unsure, post to [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together.

==Detailed guidelines==
[[File:Deeply engrossed in puzzle.png|thumb|220x220px|'''Figure 1'''. &lt;!-- An image of an elderly woman deeply engrossed in her daily crossword puzzle. --&gt;This image was generated by [[Motivation and emotion|Motivation and Emotion]] student [[User:JorjaFive|JorjaFive]] using [[w:Midjourney|Midjourney]] and uploaded to [[commons:|Wikimedia Commons]] for use in the [[Motivation and emotion/Book/2023/Flourishing in the elderly|flourishing in the elderly]] chapter.]]

===Use ethically, with caution===
Learning to use genAI tools (such as [[w:ChatGPT|ChatGPT]], [[w:Claude (language model)|Claude]],
[[w:Gemini (chatbot)|Gemini]], and [[w:Microsoft Copilot|Microsoft Copilot]]) responsibly and ethically is an emerging skill. GenAI tools can be used to enhance academic work, but should be used judiciously, as a supplementary tool, rather than as a replacement for independent thinking and academic inquiry.

GenAI tools may be used to assist in preparation of the major project ([[Motivation and emotion/Assessment/Topic|topic development]] and [[Motivation and emotion/Assessment/Chapter|book chapter]]). These tools can include the Cogniti book chapter topic generator, Studiosity Writing Feedback+, and frontier models.

===How to use===
Recommended uses of genAI tools include:
* brainstorming
* explaining key concepts
* developing a structure
* synthesising complex ideas
* rephrasing to improve [[Motivation and emotion/Assessment/Chapter/Readability|readability]] and quality of written expression
* correcting spelling and grammar
* image generation (e.g., see Figure 1)
* scenario development
* critical feedback and suggestions for improvement

===How to acknowledge===
[[File:Wikipedia Edit Summary dialog in VisualEditor.png|thumb|450px|'''Figure 2'''. If contributing genAI content, include the tool and prompt details in the edit summary, with a link to the conversation]]

[[File:Edit summary for genAI content.png|thumb|450px|'''Figure 3'''. Example page history which demonstrates best practice edit summaries for contributing and revising genAI content]]

Use of GenAI tools must be clearly acknowledged in [[Wikiversity:FAQ/Editing/Edit summary|Wikiversity edit summaries]] (e.g., see Figure 2), otherwise it is a violation of academic integrity.

Best practice is to include a publicly accessible link to the chatbot conversation (e.g., [https://help.openai.com/en/articles/7925741-chatgpt-shared-links-faq ChatGPT shared links FAQ]). If a link can't be shared, then provide details about the tool and the prompt in the [[Wikiversity:FAQ/Editing/Edit summary|edit summary]], (e.g., &quot;ChatGPT May 24 2025 Version. ''Prompt detail or summary''&quot;) (see Figure 3). The chatbot conversation should ''not'' be used as a citation and listed in the references because it is not a reliable, primary, peer-reviewed source.

These practices help to ensure that the use of genAI is clear. Transparency is key to good practice in academia. If in doubt, err on the side of providing acknowledgement. However, there is no need to acknowledge genAI use of the Cogniti book chapter topic generator, Studiosity Writing Feedback+, or for low-level tasks such as fixing grammar and spelling.

===Limitations===
Be aware of the limitations of genAI tools. Content they generate may be inaccurate, biased, incomplete, or otherwise problematic. Minimal effort reading and prompting will yield low quality results. Refine prompts based on critical reading and thinking to get better outcomes. You are entirely responsible for the accuracy and quality of any content you submit.

===Fact-check and cite===
Always fact-check. Regardless of whether genAI has been used, all claims need to be supported by verified peer-reviewed citations which you have consulted. Guide and craft genAI responses based on your reading of peer-reviewed theory and research. Low-energy or unreflective reuse of genAI text without further investigation and human-writing based on reviewing primary, peer-reviewed academic literature is likely to lead to a poor quality result. [https://www.seangoedecke.com/llms-reward-expertise GenAI tools work best for topics which you already understand].

==Learning and sharing==
* Despite these warnings, you are encouraged to explore use of genAI tools to help enhance your knowledge, skills, and develop higher quality work.
* Using genAI in academia and education is rapidly evolving. Expect to experiment, make mistakes, and learn along the way.
* If you are unsure about how to use genAI effectively or how to acknowledge its use appropriately, ask in [[Motivation and emotion/About/Discussion|discussions]], so we can all learn together.
* One way of making [[Motivation and emotion/Wikiversity/Social contributions|social contributions]] is to help others by sharing your comments, questions, experiences, tools, prompts, outputs, and so on, in [[Motivation and emotion/About/Discussion|discussions]].

==Examples==
* [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Affiliation_motivation_across_cultures&amp;action=history Affiliation and motivation] (Book chapter, 2025)
* [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Self-concept_and_motivation&amp;action=history Self-concept and motivation] (Book chapter, 2026)

==See also==
* [[b:Wikibooks:Artificial Intelligence|Wikibooks:Artificial Intelligence]] (policy)
* [[w:Wikipedia:Large language models|Wikipedia:Large language models]] (information page)
* [[Wikiversity:Artificial intelligence|Wikiversity:Artificial intelligence]] (policy)

==External links==
* [https://canberra.libguides.com/genai GenAI for students] (University of Canberra Library)
* [https://techcrunch.com/2024/06/01/what-is-ai-how-does-ai-work/ WTF is AI?] provides a useful introduction and non-technical overview about how genAI works, what it is capable of, limitations, and issues

[[Category:Motivation and emotion/Assessment]]
[[Category:Generative artificial intelligence]]
&lt;/noinclude&gt;</text>
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__TOC__
==Overview==
{{RoundBoxTop|theme=10}}
'''Case study of Joel'''

[[File:Hand washing man.jpg|right|thumb|150px|'''Figure 1'''. Washing hands to prevent contracting COVID-19.]]

Joel is a 19-year-old university student who lives in on-campus accommodation. While he understands it is a good idea to wash his hands, he often skips the practice after taking the bus, touching shared surfaces, and before eating. He finds the practice to be inconvenient, especially when he is in a rush, and believes he is unlikely to become ill because he is young and healthy. 

Recently, several students have become sick with COVID-19. One of Joel’s peers missed a week of classes and found it challenging to catch up due to the illness. Joel realised how easily infections can spread in shared spaces, becoming increasingly concerned.

Due to the spread of COVID-19, the university launched a health promotion campaign. Posters around the campus explained how germs are spread from person to person and outlined the role of handwashing in preventing illness. Along with this, hand sanitiser stations were installed at the entrances to all buildings on campus, including the lobby of campus accommodations. 

After seeing other students on campus engage with the health initiative, Joel began to utilise the hand sanitiser provided on campus. After a few weeks, Joel noticed that he felt more confident about protecting himself from illness, becoming stricter about maintaining the practice of washing his hands before eating and after being in tight shared spaces, such as public transport.

{{RoundBoxBottom}}
Personal [[wikipedia:Hygiene|hygiene]] is a fundamental feature of day-to-day life that influences one’s health, interactions with others, and overall wellbeing. While hygiene behaviours such as handwashing, bathing, and brushing teeth are seen as routine [[wikipedia:Habit|habits]], people are motivated to maintain them for different reasons. [https://www.cdc.gov/hygiene/about/index.html The Centre for Disease Control and Prevention (CDC)] explains that hygiene can prevent disease, influence social acceptance, and bring personal comfort. Understanding the [[wikipedia:Motivation|motivation]] behind the maintenance of personal hygiene is vital in encouraging long-term health behaviours and developing successful health promotion interventions.

{{RoundBoxTop|theme=5}}
'''Focus questions'''

# What are the core motivators for personal hygiene?
# How did the COVID-19 pandemic influence motivation to maintain personal hygiene?
# How can the health belief model explain motivation to maintain personal hygiene behaviours?
# How does the maintenance of personal hygiene differ across cultural and economical contexts?
{{RoundBoxBottom}}

== What is personal hygiene? ==
[https://www.healthdirect.gov.au/personal-hygiene Health Direct] describes personal hygiene as the practice of maintaining the cleanliness of your external body to prevent the spread of germs and stay healthy. These hygiene practices are often seen in day to day life, such as brushing teeth or washing hands, and are instilled in people from a young age by their parents or caregivers. Hygiene behaviours ultimately become habits over time, and are not given much afterthought. There are many kinds of personal hygiene behaviours people engage with.  

'''Table 1.''' 

Personal hygiene behaviours 
{| class=&quot;wikitable&quot;
!Hygiene practice
!Examples
|-
|Oral hygiene
|Keeping teeth clean by brushing with toothpaste for two minutes twice daily, flossing daily, and using mouthwash. 
|-
|Hand hygiene
|Washing hands with warm water and soap for 20 seconds prior to eating, after using the toilet, and after petting animals. 
|-
|Body hygiene
|Washing body daily using soap and warm water to remove sweat, oils, and dirt from body. 
|-
|Menstrual hygiene
|Changing sanitary items regularly, washing hands before and after use, and disposing of these items appropriately. 
|-
|Personal grooming
|Washing clothing regularly, trimming fingernails, not sharing personal items with others, and washing and keeping hair clean. 
|-
|Symptom etiquette
|Covering mouth when coughing or sneezing to prevent the spread of germs, and wearing a mask in public when feeling unwell.
|}

== Core motivators of personal hygiene ==
There are a multitude of factors that can influence the maintenance of personal hygiene. Research regarding hygiene behaviour identifies core motivators as societal expectations, education, and emotions. Through analysing these motivators related to the [[wikipedia:COVID-19_pandemic|COVID-19 pandemic]], an understanding of why people maintain their personal hygiene can be established.  

=== Societal expectations ===
[[wikipedia:Social_norm|Societal expectations]] are explored by Laursen and Faur (2022), describing two distinct sources of [[wikipedia:Conformity|conformity]]; stable individual differences and impermanent individual differences. Stable individual differences are the long-term, ingrained, and consistent traits of the individual who is being influenced. Impermanent individual differences describe how the person is feeling in the situation where the behaviour is being influenced. The concept of impermanent individual differences provides a foundation for societal expectations as a motivator for maintaining hygiene behaviours.  

A systematic review examines how social relationships can influence people's healthcare decisions. It found strong influence in friends, family members, general practitioners, and specialist practitioners on real world health choices (Pilli et al., 2024). This can provide some context as to why people feel pressure to have clean smelling breath or a lack of body odour, because generally the people surrounding them encourage or hold value to these behaviours. There are different forms of input provided in these social relationships; informational, prescriptive, instrumental, and emotional. Prescriptive and informational inputs were found to be the most influential in motivating others to maintain a practice such as personal hygiene (Pilli et al., 2024). 

'''Table 2.''' 

Types of input in social relationships (Pilli et al., 2024)
{| class=&quot;wikitable&quot;
|Informational
|Provides advice and useful facts on the behaviour or practice.
|-
|Prescriptive
|Provides a personal or professional opinion on the behaviour or practice.
|-
|Instrumental
|Provide assistance and resources to support the behaviour or practice.
|-
|Emotional
|Provide encouragement to partake in the behaviour or practice. 
|}
The COVID-19 pandemic increased societal expectations surrounding specific hygiene behaviours, such as handwashing, sanitising, social distancing and wearing masks. Government mandates implementing quarantine and isolation increased the collective responsibility of the community, increasing motivation to maintain hygiene behaviours to prevent the spread of germs (Miller et al., 2020). The motivational factor of societal expectations can be observed in the COVID-19 pandemic, where the majority of people engaged in protocols and influenced others to do the same.  

{{Robelbox|theme=10|title=Case study quiz}}
&lt;quiz display=simple&gt; 
What hygiene behaviour does Joel engage with due to impermanent individual differences?
|type=&quot;()&quot;} 
- Making his bed
- Taking a shower
+ Utilising hand sanitiser stations on campus
- Not washing his hands before eating
&lt;/quiz&gt;

&lt;quiz display=simple&gt;
What input does the university provide in response to the spread of COVID-19?
|type=&quot;()&quot;} 
+ Instrumental
- Informational
- Emotional
- Prescriptive
&lt;/quiz&gt;
{{Robelbox/close}}

=== Education and understanding of hygiene practices ===
Long-term maintenance of hygiene behaviours rely on a strong comprehension of their effectiveness and impact. Bloomfield and Ackerly suggest that understanding the purpose of hygiene practices is key to develop hygiene behaviour change in everyday life. In many cases, people can understand how germs spread, but struggle to determine when to practice correct hygiene behaviours (2023).   

The study asked people what hygiene practices they implemented with a threat of COVID-19. Participants selected correct and effective hygiene behaviours to prevent contracting the disease, such as washing their hands after coughing and sneezing. However a large amount of participants also selected behaviours that were not effective, such as deep cleaning bedrooms (Bloomfield &amp; Ackerly, 2023). The '[https://ifhpath.arizona.edu/targeted-hygiene/9-moments-hygiene-home Nine Moments for Targeted Hygiene]' approach is promoted by the study as an educational risk management tool to motivate the maintenance of good personal hygiene. The goal is to help people understand why hygiene is needed, where risks occur, how infection spreads, and why the hygiene behaviour is important (Bloomfield and Ackerly, 2023).  
[[File:A woman wearing a protective face mask.jpg|thumb|'''Figure 2.''' Woman wearing face mask on pubic transport.]]
Ali and colleagues investigated how targeted educational interventions, similar to the approach promoted by Bloomfield and Ackerly, can motivate the maintenance of personal hygiene. It was found increased awareness and education surrounding disease transmission provided to individuals during the COVID-19 pandemic was a strong motivator for personal hygiene, with 95% of respondents indicating as such (Ali et al., 2023). This provides a strong indicator that education acts as a core motivator in maintaining personal hygiene behaviours.    

Public health campaigns informing the public about the risk of infections also acted as a motivator. Campaigns increased not only the engagement in personal hygiene behaviours, but the maintenance of them post-pandemic due to the insights people gained surrounding the spread of illnesses (Ali et al., 2023). This can be observed in communities today, where hand sanitiser stations remain in many populated and busy areas and people are inclined to wear masks if going out in public when unwell, as seen in Figure 2.   

=== Emotions ===
[[wikipedia:Emotion|Emotions]] are an important factor when discussing the motivation to maintain personal hygiene. While societal expectations and education are important motivators for personal hygiene, they are not substantial enough to independently motivate behaviours. Competing priorities such as workload pressures, time constraints, or lack of resources can derail the motivation to perform hygiene behaviours, however emotions can increase the importance of these behaviours (McCay, 2015).  

It is discussed that fear and disgust are common drivers of personal hygiene behaviours. Similarly, nurture and care for others also increases motivation to maintain personal hygiene practices, with a goal to protect loved ones from contracting an illness (McCay, 2015). This concept is assessed in a meta-analysis exploring the effect of fear on attitudes, behavioural intentions, and actual behaviours. It was found that fear appeals produce more preventative behaviours, such as personal hygiene. When a threat was communicated as serious and individuals felt they were at risk, they were more likely to engage and maintain that behaviour over the long-term (Tannenbaum et al., 2018). 

A similar concept is discussed by Wu and Lau, assessing how emotions during the COVID-19 pandemic increased the importance of personal hygiene. The threat of COVID-19 was appraised, leading to negative emotions, creating a value change in hygiene behaviours being engaged with more frequently (Wu and Lau, 2022). This suggests when survival driven emotions, such as fear and disgust, are provoked, people become more motivated to engage with protective behaviours. 

A review on 25 publications found that while some mental health disorders can motivate engagement with hygiene behaviours, such as [[wikipedia:Anxiety|anxiety]] and [[wikipedia:Obsessive–compulsive_disorder|obsessive-compulsive disorder]] (OCD), other disorders such as [[wikipedia:Depression_(mood)|depression]] and [[wikipedia:Post-traumatic_stress_disorder|post-traumatic stress disorder]] (PTSD) can act as barriers to these behaviours (Ghassemi et al., 2023). Depression is linked to poor personal hygiene due to a lack of energy, cognitive fatigue, and loss of motivation. As a result, individuals with depression generally are not motivated to maintain personal hygiene behaviours because their symptoms cause these practices to feel overwhelming, both physically and emotionally (Ghassemi et al., 2023; Stewart et al., 2021).

{{Robelbox|theme=10|title=Case study link}}
Emotions can be seen as a motivator in Joel's case when he becomes concerned at how easily COVID-19 can be spread after seeing one of his classmates become sick and fall behind. This fear is a factor to what motivates him to engage in personal hygiene behaviours to prevent him from contracting the illness. 
{{Robelbox/close}}

== Personal hygiene motivation and the health belief model ==
The [[wikipedia:Health_belief_model|health belief model]] is a psychological framework used to explain and predict health-related behaviours. The model was first developed in the 1950s by social psychologists working in the [https://www.usphs.gov/ United States Public Health Service], proposing that an individual's willingness to change their behaviour depends on their perceptions (Alyafei &amp; Easton-Carr, 2024). The health belief model can provide context into why people may maintain their personal hygiene behaviours through cognitive evaluations related to benefits and risks in engaging with hygiene behaviours. 

=== '''Cognitive evaluations''' ===
The health belief model relies on six core constructs, or cognitive evaluations, which can influence a person's perspective when deciding what behaviours to engage with. These constructs are defined in Table 3.  

'''Table 3.''' 

Core constructs of the health belief model 
{| class=&quot;wikitable&quot;
|Perceived susceptibility
|Assessment of the risk.
|-
|Perceived severity
|Assessment of the danger of a condition and what the emotional, physical, and social consequences may be. 
|-
|Perceived benefits
|Belief in the effectiveness of an action to reduce the perceived severity.
|-
|Perceived barriers
|Tangible and psychological obstacles in taking action.
|-
|Cues to action
|External and/or internal triggers that encourage people to change their behaviour. 
|-
|Self-efficacy
|Confidence in the ability to perform the behaviour successfully.
|}
Relative to personal hygiene, these core constructs explain behaviours by suggesting individuals are more likely to engage in hygiene practices when a health threat is perceived, believing these practices will effectively reduce the threat of infection (Alyafei &amp; Easton-Carr, 2024). 

{{Robelbox|theme=10|title=Case study quiz}}
&lt;quiz display=simple&gt; 
Where can cues to action be seen in Joel's case?
|type=&quot;()&quot;} 
- Friend missing classes and having difficulties catching up
- Joel believing he is unlikely to become sick due to being young and healthy
+ University health campaign posters and hand sanitiser stations across campus
- Living in on-campus accommodation
&lt;/quiz&gt;
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=== '''Health belief model in practice''' ===
The health belief model has been applied to personal hygiene behaviours to assess the motivating factors behind them. Three studies will be explored to understand the health belief model when applied to hygiene; a meta-analysis of oral hygiene, a study on mothers with hospitalised children, and a study on hand hygiene in hospital settings. 

14 cross-sectional studies were reviewed to determine what health belief model constructs influence oral hygiene. It was determined that perceived susceptibility, perceived benefits, and self-efficacy were the strongest predictors for oral hygiene behaviours. Individuals believed they were at risk of oral health problems, saw the benefits of oral hygiene, and had confidence in their ability to practice oral care, displaying perceived susceptibility, perceived benefits, and self-efficacy, respectively. These factors contributed to a prediction that people were likely to stay motivated to maintain oral hygiene (Atmojo et al., 2026).

A study on mothers with hospitalised children applied the health belief model constructs to hygiene. High levels of perceived susceptibility in their children being vulnerable to infection, perceived severity in the consequences of infection, and perceived benefits in hygiene practices preventing infection, were noted. 44.3% of participants also reported high perceived barriers in a lack of resources and accessibility to engage in proper hygiene behaviours (Kamal et al., 2017). This suggests that while strong motivation can be observed, barriers can prevent the behaviour from being put into practice. These barriers were observed due to cultural and economic contexts, where social norms and poverty impact the ability to engage in certain hygiene behaviours (Kamal et al., 2017).  

The final study assessed hand hygiene behaviour in hospitals. Participants were more likely to maintain hygiene behaviours when they believed they were at risk, viewed the consequences as serious, believed hygiene was effective, felt capable, and had a lack of barriers displaying perceived susceptibility, severity, benefits, and self-efficacy (Walker and Jackson, 2025). This study supports the health belief model constructs in hand hygiene, similarly to the previous studies, suggesting the model can accurately predict and explain personal hygiene behaviours. 

The three studies collectively show perceived susceptibility, perceived severity, perceived barriers, and self-efficacy are prominent features of the health belief model that appear in the motivation and maintenance of hygiene behaviours. These findings can provide grounds for interventions for the motivation of personal hygiene, where the four popular constructs should be targeted as effective predictors and contributors to motivation of behaviours specific to hygiene.   

== Cultural and economic hygiene contexts ==
The maintenance of personal hygiene can be impacted by a range of economical and cultural factors which shape attitudes, behaviours, and access to hygiene practices. Personal hygiene is often viewed as an individual responsibility, however financial resources and cultural beliefs can significantly affect one's ability to maintain these behaviours. 

=== Economical contexts ===
Some personal hygiene behaviours, such as washing hands, brushing teeth, and menstrual care seem as though they are essential daily behaviours for many. However, these behaviours, like many others, rely on resources to maintain them. In developed countries, these resources are seen almost everywhere, with warm water and soap found in almost all public bathrooms, in many developing countries this is not the case as outlined by the [https://www.cdc.gov/global-water-sanitation-hygiene/about/about-global-sanitation.html CDC] and as observed in Figure 3.  

[[File:Washing hands kids.jpg|thumb|'''Figure 3.''' School children utilising an outdoor tap to wash their hands. ]]

Rossouw and Ross investigate this through a concept referred to as [[wikipedia:Period_poverty|period poverty]]. They observed 8 locations that lacked proper infrastructure to support menstrual hygiene, health, and dignity. The observations showed wealth related inequalities in access to sanitary items and the conditions of menstrual hygiene spaces. These inequalities mainly surrounded education, accessibility, and household factors (Rossouw and Ross, 2021). While individual's may have the motivation to maintain proper menstrual hygiene, their economic context may not provide them with the resources to do so. 

A similar concept is explored regarding general personal hygiene as a public health issue, where personal hygiene insecurity is discussed as a growing issue. Research suggests that many people view personal care products, such as soap, toothpaste, and shampoo, as luxury items, having to prioritise rent and food first (Rajotte, 2026). People may feel an initial motivation to practice these behaviours, but due to their financial status this motivation decreases greatly and the behaviours are not maintained (Rajotte, 2026). This can support the idea that motivation does not operate in isolation, where people can be motivated to practice hygiene but their lack of resources prevents them from implementing them.

=== Cultural contexts ===
Similar to period poverty as discussed in economical contexts, cultural views on menstrual hygiene are also explored in a study focusing on adolescent females in Zambia. It was observed that menstruation was seen as something that should be kept secret, influencing girls' understanding and experiences of menstrual hygiene (Lahme et al., 2016). With this in mind, it is important to consider how to foster education programs which can address the stigma while respecting culture. While there are prominent cultural differences regarding menstruation, the lack of education due to these perspectives can interfere with proper personal hygiene.  

Hygiene behaviours can be expected differently cross-culturally, which is observed across 56 countries in a study by Eriksson and colleagues. Three hygiene domains of handwashing, spitting, and tooth-brushing were explored, finding differing results dependent on culture. There were three competing explanations for these differences; the tightness-looseness theory, disease threat theory, and civilising process theory. The tightness-looseness theory states that stricter social rules generally have stricter hygiene norms, the disease threat theory states that places with more risk for infectious disease have stricter hygiene norms, and finally, civilising process theory states hygiene norms are stricter in societies that place greater value on self-control (Eriksson et al., 2021). This can be seen where cultures that do not align with these theories often hold the three domains to a lower standard, for instance spitting is seen as a sign of respect in Kenya and Tanzania, however is seen as a public health hazard in Western cultures (Eriksson et al., 2021). 

Cultural traditions and religious beliefs can shape how individuals view personal hygiene and the importance they put into maintaining it. These factors may determine what hygiene practices are viewed as necessary and appropriate within different cultures. Understanding this is critical to explore the factors that motivate individuals to maintain personal hygiene. 

== Conclusion ==
Motivation to maintain personal hygiene behaviours can be explored through a range of factors and contexts. Core motivators, including social expectations through conformity and values, awareness through education and public health campaigns, and emotions such as fear or disgust, contribute to an individual's desire to maintain hygiene behaviours. These motivators are not independent, and often hygiene practices are only maintained when they overlap, which can be seen by the expectations, spread of knowledge, and fear present during the COVID-19 pandemic. The health belief model explains motivation behind personal hygiene behaviours, suggesting that perceived susceptibility, severity, barriers, and self-efficacy are most fundamental in forming motivation to engage in hygiene behaviours. The motivation to maintain personal hygiene behaviours varies across economic and cultural contexts, with lack of resources, education, and differing views placing different values on personal hygiene behaviours and their importance. 

Implications for behavioural interventions to motivate the maintenance of personal hygiene in society can be noted throughout this book chapter. Core motivators of emotions are seen as most significant in motivating personal hygiene behaviours that can be maintained. The health belief model suggests that informing individuals of their risk, the consequences, providing resources, and promoting confidence surrounding personal hygiene behaviours will be more effective in creating behaviours which can be maintained in the long term. Intertwining both motivators and the health belief model with respect to economic and cultural differences can create actual behaviour changes in hygiene contexts.

== See also ==
* [[Motivation and emotion/Book/2024/Disgust and hygiene|Disgust and hygiene]] (Book chapter, 2024)
* [[Motivation and emotion/Book/2018/Conformity and emotion|Conformity and emotion]] (Book chapter, 2018)
* [[wikipedia:Public_health_mitigation_of_COVID-19|Public health mitigation of COVID-19]] (Wikipedia)

==References==
{{Hanging indent|1= 

Ali, A. S., Mekonen, Y., &amp; Tesfahun, T. (2023). Hygiene behavior and COVID-19 pandemic: Opportunities of COVID-19-Imposed changes in hygiene behavior. ''INQUIRY: The Journal of Health Care Organization, Provision, and Financing, 60''(1). https://doi.org/10.1177/00469580231218421

Alyafei, A., &amp; Carr, R. E. (2024). The health belief model of behavior change. StatPearls Publishing. ''National Library of Medicine.'' https://www.ncbi.nlm.nih.gov/books/NBK606120/

Atmojo, J. T., Handayani, A. F., Widiyanto, A., Kuntari, S., &amp; Anasulfalah, H. (2026). Health belief model construct associated with oral health behaviors: A meta-analysis. ''Journal of Health Promotion and Behavior, 11''(3), 389–404. https://doi.org/10.26911/thejhpb.2026.11.03.08

Bloomfield, S. F., &amp; Ackerley, L. (2023). Developing better understanding of hygiene is key to developing hygiene behaviour change in home and everyday life settings. ''Perspect Public Health, 144''(6). https://doi.org/10.1177/17579139231163734

Eriksson, K., Dickins, T. E., &amp; Strimling, P. (2021). Hygiene norms across 56 nations are predicted by self-control values and disease threat. ''Current Research in Ecological and Social Psychology, 2''(1). https://doi.org/10.1016/j.cresp.2021.100013

Ghassemi, E., Astrid Hasund Thorseth, Karine Le Roch, Heath, T., &amp; White, S. (2023). Mapping the association between mental health and people’s perceived and actual ability to practice hygiene-related behaviours in humanitarian and pandemic crises: A scoping review. ''PLOS ONE, 18''(12). https://doi.org/10.1371/journal.pone.0286494

Kamal, M., El-Borgy, M., &amp; Wahba, M. (2017). Application of health belief model for hygienic behavior of mothers of hospitalized children in Alexandria. ''Journal of High Institute of Public Health, 47''(1), 13–21. https://doi.org/10.21608/jhiph.2017.19973

Lahme, A. M., Stern, R., &amp; Cooper, D. (2016). Factors impacting on menstrual hygiene and their implications for health promotion. ''Global Health Promotion, 25''(1), 54–62. https://doi.org/10.1177/1757975916648301

Laursen, B., &amp; Faur, S. (2022). What does it mean to be susceptible to influence? A brief primer on peer conformity and developmental changes that affect it. ''International Journal of Behavioral Development, 46''(3), 222–237. https://doi.org/10.1177/01650254221084103

McCay, L. (2015). Emotional motivators might improve hand hygiene among healthcare workers. ''BMJ, 1''(1). https://doi.org/10.1136/bmj.h3968

Miller, G. J., Hartman, T. K., Levita, L., Martinez, A. P., Mason, L., McBride, O., McKay, R., Murphy, J., Shevlin, M., Stocks, T. V. A., Bennett, K. M., &amp; Bentall, R. P. (2020). Capability, opportunity, and motivation to enact hygienic practices in the early stages of the COVID‐19 outbreak in the United Kingdom. ''British Journal of Health Psychology, 25''(4), 856–864. https://doi.org/10.1111/bjhp.12426

Pilli, L., Veldwijk, J., Swait, J. D., Donkers, B., &amp; de Bekker-Grob, E. W. (2024). Sources and processes of social influence on health-related choices: A systematic review based on a social-interdependent choice paradigm. ''Social Science &amp; Medicine, 361''(1). https://doi.org/10.1016/j.socscimed.2024.117360

Rajotte, J. C. (2026). Health and personal hygiene: Five key strategies to improve population outcomes. ''Journal of Public Health Management &amp; Practice, 32''(4), 643–646. https://doi.org/10.1097/phh.0000000000002375

Rossouw, L., &amp; Ross, H. (2021). Understanding period poverty: Socio-economic inequalities in menstrual hygiene management in eight low- and middle-income countries. ''International Journal of Environmental Research and Public Health, 18''(5). https://doi.org/10.3390/ijerph18052571

Stewart, V., Judd, C., &amp; Wheeler, A. J. (2021). Practitioners’ experiences of deteriorating personal hygiene standards in people living with depression in Australia: A qualitative study. ''Health &amp; Social Care in the Community, 30''(4). https://doi.org/10.1111/hsc.13491

Tannenbaum, M. B., Hepler, J., Zimmerman, R. S., Saul, L., Jacobs, S., Wilson, K., &amp; Albarracín, D. (2015). Appealing to fear: A meta-analysis of fear appeal effectiveness and theories. ''Psychological Bulletin, 141''(6), 1178–1204. https://doi.org/10.1037/a0039729

Walker, K., &amp; Jackson, R. (2015). The health belief model and determinants of oral hygiene practices and beliefs in preteen children: A pilot study. ''Pediatric Dentistry, 37''(1), 40–45. https://pubmed.ncbi.nlm.nih.gov/25685972/

Wu, A. Q., &amp; Lau, V. M. C. (2022). COVID-19-induced negative emotions and the impacts on personal values and travel behaviors: A threat appraisal perspective. ''Journal of Hospitality and Tourism Management, 51''(1), 143–155. https://doi.org/10.1016/j.jhtm.2022.03.006

}}

==External links==
* [https://www.beyondblue.org.au/ Support if you are experiencing anxiety or depression] (Beyond Blue, n.d.)
* [https://open.spotify.com/show/5HG094bpiecqetNsvz0ELs Tips for good hygiene podcast] (Spotify, 2022)
* [https://hygieneforhealth.org.au/importance/ Why is hygiene so important?] (Hygiene for Health, n.d.)

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== Overview ==
{{RoundBoxTop|theme=3}}
[[File:Falun Dafa fifth meditation exercise.jpg|thumb|'''Figure 1.''' The practice of meditation which is often associated with controlled breathing and relaxation. |316x316px]]

It's extremely likely that in a moment of panic or upset you have been told to take a deep breath. Although it may seem pointless or silly in the moment, performing the simple action of taking in a deep breath does more than you think. Go back to a time you were stressed or anxious, and paused for a second to control your breathing. What did you feel in your body? Did you feel more relaxed? Using breathing exercises to promote relaxation is a practice that has been used for thousands of years (Bhargav et al., 2026). 
{{RoundBoxBottom}}
Knowing how to enter a state of relaxation is crucial in maintaining psychological and physiological wellbeing. This is especially important within the context of chronic stress and it's associated health outcomes. Despite the growing popularity of relaxation techniques, understanding the mechanisms behind relaxation remains important. The ability and knowledge required to enter a state of relaxation has significant implications for emotional regulation.  

One of the most relevant relaxation techniques are breathing exercises. Breathing exercises exist in many different forms and practices, often placing emphasis on long inhalations and exhalations. The physiological mechanisms produced by breathing exercises are a result of Parasympathetic Nervous System activation, which promotes 'rest and digest' activity. Once the body recognises it is no longer at risk of threat, relaxation can occur. 

This chapter will examine the theoretical concepts behind relaxation and their importance, the physiological responses of the Parasympathetic Nervous System, breathing exercise fundamentals and the current research. Overall this chapter aims to answer the question: &quot;how do breathing exercises make us feel relaxed?&quot;. 

{{RoundBoxTop|theme=6}}Focus Questions:
1. Why is relaxation important?

2. How do the body and mind interact to create relaxation?

3. What are breathing exercises?

4. How do breathing exercises promote relaxation?
{{RoundBoxBottom}}

== What is relaxation? ==
Although different theories of [[wikipedia:Relaxation_(psychology)|relaxation]] have different ideas about what actually defines relaxation, it can generally be described as a the absence of tension, anxiety and stress (Pagnini et al., 2013). Experiencing a frequent state of relaxation is important for wellbeing, especially when contrasted to frequent states of stress. [[Stress (psychological)|Stress]] is defined as a non-specific response of the body to a negative stimulus (Selye, 1950). The role stress plays in our day to day life is often overlooked and in some cultures praised (Maulik, 2017). However, the symptoms of stress include negative emotions, impaired cognitive ability, difficulty sleeping, changes in heart rate and feeling 'on edge'. Chronic stress can have significant implications for physiological and psychological wellbeing. This includes increased likelihood of developing stress-related conditions such as Major Depressive Disorder (Marin et al., 2011).  

=== ABC relaxation theory ===
Now that we know that relaxation is important, what types of relaxation are there? Smith's psychological relaxation theory (2012)  describes a set of learned psychological processes that counteract stress arousal. There are over 15 relaxation states (R-states) that one can reach that fall into these four categories:  

# Basic relaxation: disengaged, sleepy, physically and mentally rested
# [[File:Abctheorycollage.png|right|299x299px|'''Figure 1.''' ABC theory model]]Positive energy: happy, energised, optomistic
# Core mindfulness: awareness, acceptance, flow
# Transcendence: wonder, awe, reverence

These R-states can be reached via the [[w:Three-term contigency|ABC model]]. A stands for the activating event. This is any stimuli that elicits a stress response. B stands for beliefs. Your interpretation or ideas about the event. C stands for consequences. your previous interpretation of events contributes to your physiological, emotional and cognitive status. Smith proposed that relaxation techniques can intervene in this stress process and change how we respond to the stimulus (Matsumoto &amp; Smith, 2001).

=== Progressive relaxation theory ===
Progressive relaxation theory or progressive muscle relaxation was developed in the 1920s by Edward Jacobson. It takes the approach that mental stress and physical stress are interlinked, and that by reducing physical tension, mental relaxation will occur (Jacobson, 1987). Jacobson proposed that tensing a specific set of muscles for a few seconds, relaxing, and then repeating, would teach the individual to control tensions in the body, and therefore reduce build up of stress. Progressive Muscle Relaxation is now one of the most widely used stress-management models (McGuigan &amp; Lehrer, 2007). See this [https://www.youtube.com/watch?v=SNqYG95j_UQ video] by Therapy in a Nutshell for a brief audiovisual guide to progressive relaxation (2019). 

=== The relaxation response ===
The relaxation response was developed by Herbert Benson in the 1970s. This theory places an emphasis on the body's natural ability to counteract stress through relaxation. Benson proposed that practicing relaxation techniques produces a physiological state opposite to the 'fight or flight' state (Benson et al., 1974). This disengages the sympathetic nervous system (which we'll discuss further down below) and reduces tension and physiological arousal. The steps to elicit this response are as follows:

# Find a quiet environment where you won't be distracted
# Relax your muscles, letting go of any obvious tension in the body and closing your eyes
# Draw your focus to your breath, breathe slowly through the nose and out through the mouth
# Repeat a focus word or phrase such as 'calm' on each exhale
# Acknowledge any distracting thoughts before returning back to focus on the breath and word/phrase

Benson himself gives a guide on how to elicit the relaxation response in this [https://www.youtube.com/watch?v=nBCsFuoFRp8&amp;t=7s video] (MassDPH, 2016). 

=== Implications for emotional regulation ===
[[w:emotional_regulation|Emotional regulation]] describes our ability to influence our emotions to be helpful rather than harmful (Gross, 2015). One of the criteria for emotional regulation is having effective strategies to manage our emotions without assistance. Having the knowledge and ability to elicit relaxation is a form of emotional regulation. This can include strategies such as breathing exercises and meditation (Fu et al., 2026). Emotional regulation is important as it allows us to experience emotions without letting them overwhelm us. This has implications for many aspects of our lives including (Gross &amp; Jazaieri, 2014): 
[[File:Happy men.jpg|left|thumb|'''Figure 2.''' Having good emotional regulation skills is associated with positive outcomes for relationships.]]
* Decision making
* Relationships
* Stress management
* Concentration
* Sense of control


=== Quiz Time! ===
{{RoundBoxTop|theme=3}}&lt;quiz display=simple&gt;
{Millie is stressed after a long day at work. She wants to relax so she tenses different muscles in her body and then relaxes them. She repeats this until she feels there is no tension left in her body. What theory of relaxation is Millie following?
|type=&quot;()&quot;}
+ Progressive relaxation theory
- The relaxation response
- ABC relaxation theory
- Autonomic functioning theory
&lt;/quiz&gt;{{RoundBoxBottom}}

== Parasympathetic nervous system ==
The [[wikipedia:Parasympathetic_nervous_system|Parasympathetic Nervous System]] (PNS) is a division of the Autonomic Nervous System. Commonly known as the 'rest and digest' division, the Parasympathetic Nervous System promotes restful activity when the body is not threatened, allowing the recovery and maintenance of autonomic functions (Wehrwein et al., 2016). This includes functions such as digestion, urination and heart rate regulation. It's opposite is the [[wikipedia:Sympathetic_nervous_system|Sympathetic Nervous System]] (SNS), also known as the 'fight or flight' division. The Sympathetic Nervous System prepares the body for danger and stops unecessary autonomic functions. This includes increased heart rate, dilation of pupils and slowing digestion to redirect energy. Although these divisions have seperate functions, it is important to note that they work in tandem to ensure our survival (Ondicova &amp; Mravec, 2010). 

=== How is it stimulated? ===
[[File:2032 Automatic Innervation.fr.jpg|thumb|312x312px|'''Figure 3.''' Path of the Vagus nerve ]]
The PNS is not simply activated by an on and off switch, it actively adjusts according to messages from the brainstem and spinal cord. Sensory information from inside the body e.g changes in blood pressure, is transmitted to the brainstem through sacral nerves (nerves in the lower spine) and cranial nerves (nerves that originate in the brain) (Dampney, 2016). 

[[wikipedia:Vagus_nerve|The Vagus Nerve]] is the primary nerve associated with the PNS. It connects from part of the mouth, down the neck and chest and down to the abdomen. The vagus nerve makes up 75% of the PNS (McCorry, 2007). It carries outgoing signals to tell the body to slow down, and carries incoming sensory information back to the brain. The Vagus nerve plays a key part in promoting relaxation (which will be discussed more later on) (Yuan &amp; Silberstein, 2016).

The main neurotransmitter associated with the PNS is [[wikipedia:Acetylcholine|Acetylcholine]]. This allows the PNS nerves to communicate by transmitting signals to and from the brain. once it is released from a postganglionic neuron, acetylcholine binds to receptors on the target organ, causing a physiological change in the body e.g bladder muscle contraction (Kurhaluk et al., 2025). 

=== What happens when it is active? ===
Although there is always some degree of activation in both the SNS and PNS, there are some specific physiological and psychological changes that occur when the PNS is innervated (Yin et al., 2024): 

Physiological changes:

* Decreased heart rate
* Increased digestion
* Increased saliva production
* Constriction of pupils
* Promotion of bladder contraction
* Support of recovery


Psychological changes: 

* Increased feelings of relaxation
* Reduced feelings of stress
* Improved emotional regulation
* Changes in attention and awareness

{{RoundBoxTop|theme=6}}Imagine: 

You are in a haunted house and are about to turn the next corner. You're anticipating a 'jump scare'. Your heart rate increases, you breathe faster, and you start to sweat. What division of your Autonomic Nervous System do you think has been innervated? If you thought of the Parasympathetic Nervous System, you'd be correct!  


{{RoundBoxBottom}}
[[File:The Old Hall, Fairies by Moonlight.jpg|center|thumb|'''Figure 4.''' Haunted House]]


== What are breathing exercises? ==
[[wikipedia:Breathwork_(New_Age)|Breathing exercises]] are non-invasive, natural techniques to induce relaxation and calm anxiety (Miri et al., 2023). They involve conscious inhalation and exhalation in a rhythmic, controlled manner. There are many different types of breathing exercises, although the most common ones place an emphasis on breathing deeply from the stomach. They also place focus on the regular practice of breathwork, with the aim of reducing stress and improving overall wellbeing (Toussaint et al., 2021).  

=== Diaphragmatic breathing ===
One of the most popular breathing exercises is diaphragmatic breathing. This involves purposefully contracting the diaphragm, expanding the belly, and deepening one's inhalation. This decreases fast, shallow breaths and increases oxygen intake. Specifically trying to engage the diaphragm is meant to stop shallow breathing, which is often associated with anxiety and sympathetic nervous system arousal (Leyro et al., 2021). 

Diaphragmatic breathing lowers blood pressure, lowers heart rate and decreases the frequency of respiration; in other words it decreases SNS activity and increases PNS activity (Ma et al., 2017). 

Michelle Kenway (2023) provides a useful guide on diaphragmatic breathing in her video: [https://www.youtube.com/watch?v=9jpchJcKivk How to do Diaphragmatic Breathing Exercises for Beginners]

=== Box breathing ===
[[File:Square (geometry).svg|thumb|'''Figure 5.''' Box breathing mimics the four sides of a square (or box)]]
Another well known breathing exercise is Box breathing. It is a four-step cycle that mimics the sides of a square as shown in figure 5 (McAllister et al., 2026): 

# Four second inhale
# Four second pause
# Four second exhale
# Four second pause

Box breathing has been shown to reduce biomarkers of stress, as well as improve mood and composure (Dillard et al., 2023). This also includes variations of box breathing, e.g two second pauses. This video gives an audiovisual guide to box breathing: [https://www.youtube.com/watch?v=mPXy0974vu0 Box Breathing Tutorial | Reduces Anxiety &amp; Stress] (Marie, 2022). 

{{RoundBoxTop|theme=3}}
Learning Activity!

Pick a breathing exercise and use one of the guides provided to practice yourself.
{{RoundBoxBottom}}

== How do breathing exercises link to relaxation? ==
Breathing exercises are closely linked to relaxation as they can help regulate the body's physiological response to stress. As discussed above in the Relaxation Response Theory, purposefully focusing on breathing can have an influence on the Autonomic Nervous System. The changes that follow allow the body and mind to return to a relaxed state. Breathing exercises also have cardiorespiratory and respiratory effects, which have further implications for a relaxation response, including elements of emotional regulation. 

=== Parasympathetic stimulation ===
The way breathing exercises activate the parasympathetic nervous system directly aligns with Benson's relaxation response. They activate the body's natural responses to leave the 'fight or flight' state. By entering the 'rest and digest' state, relaxation is promoted through the absence of stress and tension (Pathan et al., 2023). This is also relates back to the physical aspects of tension in progressive relaxation theory. 
[[File:Human diaphragm.png|left|thumb|'''Figure 6.''' Diaphragm location in the stomach]]
When a deep breath is taken, the diaphragm is shifted up and down. This movement stimulates the vagus nerve which runs directly through from the neck to the abdomen. The vagus nerve is modulated by the breath, it is suppressed during inhalation and facilitated during exhalation and slowed breathing patterns (Chang et al., 2015). The Vagus nerve then carries that information up to the medulla in the brain, initiating physiological changes associated with relaxation. This includes decreased heart rate, suppressed inflammation, and information relayed from the heart, airways, liver and GI tract. Gerritsen &amp; Band (2018) also explored vagus nerve stimulation as a form of respiratory biofeedback. Slowed breathing along with extended exhalation could possibly activate the PNS via vagus nerve afferents in the airways. This would signal a state of relaxation by the vagus nerve, resulting in more vagus nerve activity and therefore further relaxation.  

=== Psychological response ===
So how do these physiological changes cause us to become relaxed? Our body is constantly monitoring and interpreting information about our internal state in a process called [[wikipedia:Interoception|interoception]] The physical changes in our body produced by the PNS are ones that we interpret as being associated with calmness and relaxation (Critchley &amp; Garfinkel, 2017). This makes it easier for our body to respond by returning to a relaxed state. It also means that our cognitive ability improves because we are no longer anticipating a threat. This is when the interpretation stage of the ABC relaxation theory occurs. This makes it easier for us to regulate our emotions. As we are able to focus on our breathing, we are also able to interrupt stressful thoughts and bring attention back to the present moment (Balban et al., 2023).  

=== Emotional Regulation ===
[[File:Emoticon angry-red.png|thumb|'''Figure 7.''' Depiction of a negative emotion]]
Practicing breathing exercises regularly has implications for our ability to self regulate our emotions. It provides us with a proven strategy to manage stress and influence emotional response. Practicing breathing exercises can assist us in responding to emotionally challenging situations in a logical way, rather than letting the negative emotions take over (Fincham et al., 2023).  

Consistent breathwork also has the potential to improve awareness of our own emotional state. By recognising the early signs of stress e.g muscle tension and increased heart rate, we are able to adapt and manage our emotions accordingly before they become overwhelming. This then becomes a useful [[wikipedia:Coping|coping strategy]] to negative emotional experiences (Rossi et al., 2026).  

== History and practice ==
Although breathing exercises are highly popular and relevant in the current day, they have been around for thousands of years. Different forms of breathing exercises have often existed throughout history in the forms of [[mindfulness]] practices. The goal of mindfulness practices is to bring attention to the present in a non-judgemental way (Kabat-Zinn, 2015). Some examples of mindfulness practices include meditation and yoga. Both of these examples place a focus on breath control. Although the link to the autonomic nervous system was not always known, practicing mindfulness techniques have been used to reduce stress and induce relaxation throughout history (Mandlik et al., 2024). 
{{RoundBoxTop|theme=6}}Focus Feature:

Pranayama is the ancient yoga practice originating from Hinduism. It aims to control the flow of prana (life force) through a self-directed technique. Controlling the flow of prana aims to provide mental clarity, emotional balance, and resilience. It typically involves Pūraka (inhalation), Antaḥ Kumbhaka (holding your breath after an inhale), Recaka (exhalation) and Bahiḥ Kumbhaka (holding your breath after an exhale). (Jayawardena et al., 2020). There are also different techniques within the practice of Pranayama, such as Bhramari or 'bee breath', which involves humming during exhalation with the fingers in the ears and eyes covered. Bhargav et al. (2026) found that Pranayama acted similarly to other more modern breathing techniques and stimulated the PNS.

{{RoundBoxBottom}}
[[File:A style of nadi suddhi 1.JPG|center|thumb|'''Figure 8.''' Pranayama in practice]]

== Research ==
Although the usefulness of breathing exercises on promoting relaxation has been heavily researched, there are some gaps in the current state of literature that would provide a fully comprehensible conclusion. 

In 2023, Bentley et, al. conducted a systematic review of all the current literature on breathing practices for stress and anxiety reduction. They found that out of the 72 interventions included across articles, 54 breathing exercises showed a significant reduction in stress and anxiety. They also found that in it's increasing popularity, many people have claimed to have the 'most effective' breath work technique. However, no singular technique has been established as the best. They also found that although breathing techniques are often recommended to induce relaxation, there is no specific framework for recommendation in individuals practicing at home compared to professionals and researchers. Stricter rules to seperate participants into further groups are needed to identify patterns in different contexts. 

Toussaint et, al. (2021) also found significant results for the effectiveness of breathing exercises on relaxation. However, they found that in research using electrodermal activity as a measure of arousal, physiological arousal actually increased when beginning breathing exercises. They suggest that focusing too much on inhaling can cause increased physiological arousal as opposed to exhalation, which promotes relaxation. This is a common mistake made in breathing exercises and was frequently observed when obtaining results from the review. This mistake can hinder the purpose of the breathing exercise.  

== Conclusion ==
{{RoundBoxTop|theme=3}}Imagine:

You have had a tough week and come home to your roommate. He sees that you are stressed and tells you to &quot;try and relax&quot;. Would you try out a breathing exercise? How do you know it would work?{{RoundBoxBottom}}
Relaxation is an important aspect of psychological and physiological health and wellbeing, especially in managing stress and supporting emotional regulation. This chapter has discussed the theoretical frameworks of relaxation, the role of the PNS on relaxation, and the way in which breathing exercises contribute to relaxation. The research explored demonstrates that relaxation involves a combination of both physiological and psychological processes. 

Breathing exercises provide accessible self-directed strategies for regulating stress and emotions. By influencing breathing patterns, the Vagus nerve is able to receive input, and send a message to the brain exciting the PNS to resume ‘rest and digest’ activities. Diaphragmatic breathing and box breathing contribute to psychological relaxation via interoception, letting the body know that it’s free to relax. Focusing attention on the breath can also bring attention back to the present moment and improve emotional regulation. These processes align with the relaxation response, progressive relaxation theory and ABC relaxation theory. 

Although research generally supports the theory that breathing exercises reduce stress and anxiety, their effectiveness cannot be considered universal. Mistakes in techniques, individual interpretations and the context in which the exercises are practiced may influence the outcome. Further research is needed to establish which breathing exercises are the most effective for different populations. 
{{RoundBoxTop|theme=6}}Key Takeaways:

1. Relaxation is essential for wellbeing

2. The body and mind work together to elicit relaxation

3. Breathing exercises can help regulate stress

4. Consistent practice of breathing exercises supports emotional regulation
{{RoundBoxBottom}}

== See also ==
[[doi:10.1007/978-3-031-56798-8_4.|Slow Breathing for Anxiety: A Critical Perspective Towards Personalization]] - Book Chapter, 2024 (Vlemincx et al., )

[[wikipedia:Pranayama|Pranyama]] (Wikipedia)

[https://www-taylorfrancis-com.ezproxy.canberra.edu.au/chapters/oa-edit/10.4324/9781003378969-7/restorative-techniques-nathalie-pattyn-deanna-beech-jenny-wilhelmsson-helen-kilding-adrianna-mendrek Restorative Techniques Mindfulness, Relaxation, Breathing, and Yoga] - Book Chapter, 2024 (Pattyn et al.,)

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Bhargav, H., Mehta, U. M., Kumar, A., Subramanian, S., &amp; Keshavan, M. S. (2026). Breathing and the brain: Pranayama, an ancient self-directed approach to neuromodulation. ''Asian Journal of Psychiatry'', ''115'', 104788. https://doi.org/https://doi.org/10.1016/j.ajp.2025.104788. 

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Ma, X., Yue, Z.-Q., Gong, Z.-Q., Zhang, H., Duan, N.-Y., Shi, Y.-T., Wei, G.-X., &amp; Li, Y.-F. (2017). The Effect of Diaphragmatic Breathing on Attention, Negative Affect and Stress in Healthy Adults [Original Research]. ''Frontiers in Psychology'', ''Volume 8 - 2017''. https://doi.org/10.3389/fpsyg.2017.00874. 

Mandlik, G. V., Siopis, G., Nguyen, B., Ding, D., &amp; Edwards, K. M. (2024). Effect of a single session of yoga and meditation on stress reactivity: A systematic review. ''Stress and Health'', ''40''(3), e3324. https://doi.org/https://doi.org/10.1002/smi.3324. 

Marie), B. Y. N. (2022, November 15). ''Box Breathing Tutorial | Reduces Anxiety &amp; Stress'' Youtube. https://www.youtube.com/watch?v=mPXy0974vu0. 

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Vlemincx, E., Cortez-Vázquez, G., Charis, C., &amp; Panayiotou, G. (2024). Slow Breathing for Anxiety:A Critical Perspective Towards Personalization. In. Springer Nature. https://doi.org/10.1007/978-3-031-56798-8_4.  

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== External links ==
[https://www.youtube.com/watch?v=SNqYG95j_UQ Progressive Muscle Relaxation: An Essential Anxiety Skill #27] (youtube video)

[https://www.youtube.com/watch?v=nBCsFuoFRp8&amp;t=7s Relaxation Response: Dr. Herbert Benson Teaches You The Basics]

[https://www.youtube.com/watch?v=9jpchJcKivk How to do Diaphragmatic Breathing Exercises for Beginners] (youtube video)

[https://www.youtube.com/watch?v=mPXy0974vu0 Box Breathing Tutorial | Reduces Anxiety &amp; Stress] (youtube video)
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      <text bytes="28117" sha1="6vqgbch7j0i5j1nhej1za58mgdy2a9p" xml:space="preserve">{{title|Social dominance and power motivation:&lt;br&gt;What is the relationship between social dominance and power motivation?}}
__TOC__
==Overview==
{{RoundBoxTop|theme=3}}
[[File:Noun Staff Management 4185.svg|Management chart right|thumb|200px|'''Figure 1'''. Power hierarchy in the workplace]]

'''Scenario: Raising up vs. pushing down.'''

Two graduates start the same week at a large firm. One quickly puts their hand up to lead every project going, coordinating people, chasing decisions, and making sure things get done — and uses that influence to actively mentor junior colleagues and push for flatter, fairer pay structures. The other has no interest in leading projects or managing anyone, yet defends the firm's steep hierarchy (see Figure 1) as natural and fair: &quot;some people are just better suited to being in charge, and the system reflects that.&quot; They also actively lobbies against a new scheme providing staff from under-represented backgrounds with better access to mentoring, training, and development opportunities, arguing certain groups should stay in junior roles &quot;where they belong&quot; and pushing to have the scheme scrapped. Both are equally competent. Why does one seem driven to personally influence the people around them, while the other — without wanting any personal authority — is instead driven to keep entire groups beneath others?

{{RoundBoxBottom}}
Human societies are fundamentally structured around social hierarchies, however the psychological factors that lead individuals to navigate, challenge, or enforce these hierarchies can vary significantly. Power motivation and social dominance are two distinct yet related psychological constructs that explain different aspects of hierarchy seeking behaviour in human societies. Social Dominance Orientation (SDO) is defined as a preference for one's ingroup to dominate outgroups viewed as lesser and a general desire for group-based inequality. In contrast, power motivation (nPower) represents an individuals personal drive to have influence, control, or psychological impact over specific individuals.

While these constructs frequently overlap in everyday social interactions, psychological science demonstrates that they operate at fundamentally different levels when it comes to analysis: group-based ideological preference versus interpersonal motivation. Clarifying the distinction between social dominance and power motivation is essential as both constructs can predict real world outcomes, including leadership emergence, support for discriminatory policies, workplace dynamics, and the specific influence and control tactics individuals choose to employ when power is attained. By examining frameworks such as Social Dominance Theory, McClelland's Need Theory, and modern neuroscientific findings, psychological science provides diagnostic tools such as SDO7 scales and implicit motive coding to evaluate why individuals seek status and how they exercise power once it is gained.{{RoundBoxTop|theme=3}}

'''Focus questions'''

* What is social dominance orientation, and how does it relate to broader group hierarchies?
* What is power motivation (nPower), and how is it expressed differently across different demographics and cultural contexts? 
* How do legitimising myths sustain or challenge social hierarchies?
* How do SDO and power motivation shape political attitudes, leadership styles, and intergroup behaviours?

{{RoundBoxBottom}}

==Social dominance orientation==
Social dominance orientation represents a core attitudinal personality variable within intergroup psychology, revealing an individuals stance regarding group-based equality versus group-based hierarchy. Understanding social dominance orientation requires an examination of its theoretical origins within Social Dominance Theory, it's sub-dimensional structures, and its broader predictive validity across societal domains.

=== Origins in social dominance theory ===
[[wikipedia:Social_dominance_orientation|Social dominance theory]] (SDT), developed by Jim Sidanius and Felicia Pratto, opens with the observation that all human societies producing an economic surplus naturally develop group-based social hierarchies. SDT identifies three distinct forms of trimorphic social hierarchies that form the structure of human societies. The age system, which grants adults disproportionate power and social status compared to children; patriarchy, referring to systems where men hold greater political, social, and economic authority than women; and the arbitrary-set system which encompasses culturally constructed social categories such as race, ethnicity, religion, social class, nationality, or caste, that are hierarchically ordered with unequal access to power, opportunity, and privileges.  

According to SDT, social institutions such as legal systems, criminal courts, educational systems, and corporations sustain these group hierarchies through institutional discrimination. Institutions maintain hierarchy by disproportionately allocating positive social value, such as wealth, healthcare, prestige, and educational access, to dominant groups. Additionally, institutions direct negative social value, including harsher criminal penalties, dangerous labour, and poverty, towards subordinate groups. 
* Key references: (Pratto et al., 1994), (Sidanius &amp; Pratto, 2001)

=== Measuring social dominance orientation and what it predicts ===

{| class=&quot;wikitable&quot; style=&quot;float:right; clear:right; width:400px; margin:0 0 1em 1.5em; text-align:center; background-color:#f9f9f9; border:1px solid #aaa;&quot;
|-
! colspan=&quot;2&quot; style=&quot;background-color:#f9f9f9; font-size:110%; padding:8px; border:none;&quot; | Figure 2. Dimensional structure of SDO7&lt;br&gt;&lt;small style=&quot;font-weight:normal;&quot;&gt;&lt;em&gt;Based on Ho et al. (2015)&lt;/em&gt;&lt;/small&gt;
|-
| colspan=&quot;2&quot; style=&quot;background-color:#eef; padding:10px; border:1px solid #aaa;&quot; | '''Social Dominance Orientation (SDO)'''&lt;br&gt;&lt;small&gt;(Preference for group inequality)&lt;/small&gt;
|-
| style=&quot;width:50%; vertical-align:top; background-color:#fff; padding:10px; border:1px solid #aaa; text-align:left;&quot; |
'''SDO-Dominance (SDO-D)'''
* Active group oppression
* Overt group superiority
* Direct intergroup action again outgorups
| style=&quot;width:50%; vertical-align:top; background-color:#fff; padding:10px; border:1px solid #aaa; text-align:left;&quot; |
'''SDO-Egalitarianism (SDO-E)'''
* Opposition to group equality
* Opposition to equity/social schemes
* Subtle institutional bias
|}
To evaluate individual differences in support for group-based hierarchy, researchers constructed the SDO scale, with the newer SDO7 scale dividing the construct into two sub-dimensions. The first dimension, SDO-Dominance (SDO-D) assesses support for active, explicit group oppression and the forced subjugation of outgroups. The second dimension, SDO-Egalitarianism (SDO-E) assesses generalised oppositon to group equality, manifesting as subtle resistance to social welfare, affirmative actions, and equality-promoting policies.

Empirical cross-cultural research confirms that high SDO scores predict intergroup prejudice, ethnocentrism, sexism, homophobia, and support for harsher criminal justice policies. Additionally, individuals selectively self-segregate into specific societal roles based on their SDO levels. High-SDO individuals gravitate towards heirarchy-enhancing roles that reinforce existing social stratification, such as executives, criminal prosecutors, and police officers. In comparison, low-SDO individuals seek out hierarchy-reducing roles that challenge systemic inequality, such as human rights lawyers, public defenders, and social workers.

The SD07 scale distinguished between two sub-dimensions: SDO-Dominance (SDO-D) which involves support for active group oppression and SDO-Egalitarianism (SDO-E) which reflects a preference for group inequality and is linked to more subtle forms of prejudice and inequality as well as opposition to equality-promoting policies.&lt;quiz display=&quot;simple&quot;&gt;
{Which form of hierarchy in Social Dominance Theory involves culturally defined categories like race, ethnicity, or religion?
|type=&quot;()&quot;}
- The age system
- Patriarchy
+ The arbitrary-set system

{High-SDO individuals are most likely to select which of the following career paths?
|type=&quot;()&quot;}
- Hierarchy-reducing roles like public defenders
+ Hierarchy-enhancing roles like corporate executives
&lt;/quiz&gt;
==Power motivation==
Power motivation, commonly referred to as the Need for Power (nPower) is a psychological construct describing an individuals drive to exert impact, control, or influence over others and their surrounding environment. First conceptualised by Henry Murray in taxonomy of fundamental human needs, and later expanded upon by David McClelland in his Three Needs Theory, power motivation represents a primary driver of status-seeking, interpersonal dynamics, and leadership emergence. Rather than representing a purely manipulative or antisocial trait, power motivation exists along a broad psychological spectrum. It ranges from personalised power (pPower), which is characterised by direct control, self-aggrandisement, and zero-sum competition, to socialised power (sPower) where influence is channeled towards supporting and empowering others, mentoring, and achieving collective goals. 

=== McClelland's need theory and measurement ===
McClelland proposed the Need for Power (nPpower) operates alongside the Need for Achievement (nAch) and the Need for Affiliation (nAff) as fundamental human motivators. 

Power motivation operates across two cognitive levels. Implicit power motivation respresents an unconscious motive that can be assessed via projective tests such as the Picture Story Exercise (PSE) or the Thematic Apperception Test (TAT) where spontaneously constructed narratives are coded for imagery of impact, control, and prestige. Explicit power motivation involves conscious self-conceptions evaluated through self-report questionnaires measuring specific desires for leadership roles, authority, or prestige.

Research in social neuroscience indicates that implicit power motivation is accompanied by distinct physiological correlates, with individuals with strong implicit nPower exhibiting heightened salivary cortisol and testosterone fluctuations, as well as distinct neural activation patterns in the amygdala and striatum, when confronting nonverbal social cues signaling rank competiton, social defeat, or interpersonal dominance.

that humans vary in the relative strength of three learned needs: achievement, affiliation, and power, with nPower reflecting a desire to have an impact on or control over other people.
* Key references: (McClelland, 1975), (Rybnicek et al., 2017), (Wirth et al., 2006)

=== Personalised vs socialised power across cultures ===
McClelland emphasises that power motivation is not inherently destructive, and distinguished between two distinct expressions or faces of power. Personalised power (pPower) is driven by direct personal domination and status acquisition, often ignoring the needs of those considered to be subordinates. In contrast, socialised pwoer (sPower) is expressed responsibly through empowering others, mentoring, and influencing others in order to meet collective goals and organisational wellbeing. 

Cultural values heavily shape how power motivation is channeled and expressed. In societies characterised by vertical individualism, power is primarily conceptualised as personalised dominance and personal status acquisition. Conversely, in societies characterised by horizontal collectivism, power motivation is more frequently channeled into socialised expressions, such as community leadership, nurturing, and collective helping. Frieze and Boneva further categorised these explicit power expressions into three distinct behavioural dimension: leadership, prominence, and helping.
* Key references: (Triandis &amp; Gelfand, 1998), (Magee &amp; Galinsky, 2008)

==Legitimising myths==
Social dominance theory proposes that group hierarchies are maintained not solely through physical coercion, but also through the widespread adoption of legitimising myths—cultural beliefs, values, and attitudes that provide moral and intellectual justification for intergroup relations.

=== Hierarchy-enhancing vs hierarchy-attenuating myths ===
Legitimising myths are categorised based on whether they reinforce or undermine inequality in society. Hierarchy-enhancing legitimising myths consist of ideologies that justify inequality by suggesting that existing group advantages are earned, natural, or just, such as meritocracy, racism, sexism, and caste systems. In comparison, hierarchy-attenuating legitimising myths include ideologies that challenge group inequality and advocate for systemic redistribution and equal rights. 

Individuals high in SDO selectively endorse hierarchy-enhancing myths to rationalise their groups privileged position. This endorsement allows them to dismiss societal inequalities as legitimate and understandable consequences of group differences in effort, talent, or intrinsic worth.
* Key references: (Sidanius &amp; Pratto, 2001)

=== Legitimising narratives in media and institutions ===
Legitimising myths are transmitted and continually reinforced through mainstream media narratives, television, educational curriculums, and social media. By embedding hierarchy-enhancing narratives in public discourse, institutions normalise privilege and make systemic inequality appear invisible or natural. Consequently, legitimising myths serve as the psychological mechanism through which abstract SDO translates into active public support for discriminatory laws, harsher sentencing, and opposition to equity programs.
* Key references: (Sidanius &amp; Pratto, 2001), (Pratto et al., 1994)

==The link between social dominance orientation and power motivation==
Although Social Dominance Orientation and power motivation both pertain to social rank and hierarchy, they represent distinct psychological constructs operating at different levels of analysis.
{| class=&quot;wikitable&quot;
|+Table 2. ''Conceptual comparison between Social Dominance Orientation and Power Motivation''
!Feature
!Social Dominance Orientation (SDO)
!Need for Power (nPower)
|-
|'''Primary focus'''
|Group-based social hierarchy and intergroup inequality.
|Interpersonal impact, control, and personal influence.
|-
|'''Level of analysis'''
|Societal / ideological / intergroup level
|Individual / interpersonal / dual levels
|-
|'''Key motivator'''
|Desire for ingroup superiority or systemic group hierarchy
|Desire to direct, control, or impact specific individuals
|-
|'''Behavioural outcome'''
|Endorsing hierarchy-enhancing policy and predudice.
|Leadership emergence, mentoring (sPower) or coercion (pPower)
|}
Social Dominance Orientation reflects a group-level ideological preference for systemic inequality, whereas nPower reflects an individual-level drive for personal impact. Additonally, having high nPower does not automatically equate to having a high SDO.kA leader who is driven by strong socialised power (sPower) may seek personal influence specifically to dismantle institutional barriers and promote equality, resulting in low SDO, as seen in the opening scenario. However, an individual with low personal leadership drive may hold high SDO, actively lobbying to protect group privileges and restrict subordinate group advancements without desiring a personal leadership role.

== Political and social behaviour ==
Individual differences in SDO and nPower heavily influence collective political attitudes, voting patterns, and intergroup conflicts. 

=== SDO, right-wing authoritarianism, and political ideology ===
In political psychology, SDO works alongside Right-Wing Authoritarianism (RWA) as dual motivational predictors of prejudice and political conservatism. Developed by Bob Altemeyer, RWA represents an attitudinal cluster defined by authoritarian submission, authoritarian aggression, and conventialism. SDO and right-wing authoritarianism (RWA) arise from different wordview based roots however both can connect and predict prejudice and political conservatism

(table)

* Key references: (Duckitt &amp; Sibley, 2010), (Ekehammar et al., 2004), (Ward, 1982)

== Power, leadership, and individual differences ==
Intro paragraph about how motivation can be linked to leadership outcomes and the individual differences that shape these outcomes

=== Prosocial vs. antisocial leadership ===

* Individuals with high SDO levels gravitate towards hierarchy-enhancing roles and are more likely to engage in unethical decision-making as leaders
* The same motive for a desire for influence or power can lead to vastly different social outcomes depending on whether it is channeled through egalitarian or dominating orientations

{{RoundBoxTop|theme=3}}
'''Case study: power and dominance in cult leadership'''

* Cult leaders often display extreme, personalised power motives combined with high SDO beliefs about their groups superiority, displaying how the two constructs can compound to produce highly coersive social structures

{{RoundBoxBottom}}

* Key references: (Magee &amp; Galinsky, 2008), (Denrich, 2024)

=== Biological basis, gender differences, and situation triggers ===
* Neuroimaging research suggests the brain processes social rank as a fundamental dimension of interpersonal context, with distinct neural responses to ones position in a status hierarchy
* Sex differences are commonly reported in SDO with men scoring higher on average
* Situation triggers are also linked with ingroup threat or competition ot resources being able to temporarily heighten both SDO and power-motivated behaviour
* Key references: (Zink et al., 2008), (Sidanius et al., 2000), (Sidanius et al., 2000)

== Conclusion ==

* Social dominance orientation and power motivation are related but distinct: SDO is a group-level ideological preference for hierarchy sustained by legitimising myths; power motivation is a personal, often implicit, drive to influence specific others.
* The two exist separately however, a person can want personal influence without wanting group-based dominance, or vice versa
* Both are influenced by biology, personality, culture, and situational triggers, and both feed into real-world outcomes such as political ideology, intergroup conflict, and either coercive or responsible leadership
* Recognising which construct is driving a persons behaviour and whether power is being expressed personally or socially has practical value for understanding leadership, workplace dynamics, and social conflict.

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* [[Motivation and emotion/Book/2024/Social dominance and power motivation|Social dominance and power motivation]] (Book chapter, 2024)

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Abou-Ismail, R., Cichocka, A., Phillips, J., &amp; Sengupta, N. K. (2025). Authoritarianism and social dominance as differential predictors of individuals’ support for collective violence. Psychology of Violence, 15(5), 634–644. https://doi.org/10.1037/vio0000580Anderson, 

C., &amp; Kilduff, G. J. (2009). The pursuit of status in social groups. Current Directions in Psychological Science, 18(5), 295–298. https://doi.org/10.1111/.1467-8721.2009.01655.x

Denrich, D. S. (2024). Charismatic leadership and vulnerability: A comprehensive study of cult dynamics. Psychology Presentations. https://digitalcommons.ursinus.edu/psych_pres/11/

Duckitt, J., &amp; Sibley, C. G. (2010). Personality, ideology, prejudice, and politics: A dual‐process motivational model. Journal of Personality, 78(6), 1861–1894. https://doi.org/10.1111/j.1467-6494.2010.00672.x

Ekehammar, B., Akrami, N., Gylje, M., &amp; Zakrisson, I. (2004). What matters most to prejudice: Big five personality, social dominance orientation, or right-wing authoritarianism? European Journal of Personality, 18(6), 463–482. https://doi.org/10.1002/per.526

Ho, A. K., Sidanius, J., Kteily, N., Sheehy-Skeffington, J., Pratto, F., Henkel, K. E., Foels, R., &amp; Stewart, A. L. (2015). The nature of social dominance orientation: Theorizing and measuring preferences for intergroup inequality using the new SDO₇ scale. Journal of Personality and Social Psychology, 109(6), 1003–1028. https://doi.org/10.1037/pspi0000033

Magee, J. C., &amp; Galinsky, A. D. (2008). Social hierarchy: The self‐reinforcing nature of power and status. The Academy of Management Annals, 2(1), 351–398. https://doi.org/10.1080/19416520802211628

McClelland, D. C. (1975). Power : The inner experience. Irvington Publishers.Pratto, F., Sidanius, J., Stallworth, L. M., &amp; Malle, B. F. (1994). Social dominance orientation: A personality variable predicting social and political attitudes. Journal of Personality and Social Psychology, 67(4), 741–763. https://doi.org/10.1037/0022-3514.67.4.741

Rybnicek, R., Bergner, S., &amp; Gutschelhofer, A. (2017). How individual needs influence motivation effects: A neuroscientific study on McClelland’s need theory. Review of Managerial Science, 13(2), 443–482. springer. https://doi.org/10.1007/s11846-017-0252-1

Sidanius, J., Levin, S., Liu, J., &amp; Pratto, F. (2000). Social dominance orientation, anti-egalitarianism and the political psychology of gender: An extension and cross-cultural replication. European Journal of Social Psychology, 30(1), 41–67. https://doi.org/10.1002/(sici)1099-0992(200001/02)30:1&lt;41::aid-ejsp976&gt;3.0.co;2-o

Sidanius, J., &amp; Pratto, F. (2001). Social dominance: An intergroup theory of social hierarchy and oppression. Contemporary Sociology, 30(2), 120. https://doi.org/10.2307/2655372

Son Hing, L. S., Bobocel, D. R., Zanna, M. P., &amp; McBride, M. V. (2007). Authoritarian dynamics and unethical decision making: High social dominance orientation leaders and high right-wing authoritarianism followers. Journal of Personality and Social Psychology, 92(1), 67–81. https://doi.org/10.1037/0022-3514.92.1.67

Triandis, H. C., &amp; Gelfand, M. J. (1998). Converging measurement of horizontal and vertical individualism and collectivism. Journal of Personality and Social Psychology, 74(1), 118–128. https://doi.org/10.1037/0022-3514.74.1.118

Ward, D. (1982). Right-wing authoritarianism. . American Political Science Review, 76(3), 737–738. https://doi.org/10.2307/1963836

Wilson, M. S., &amp; Liu, J. H. (2003). Social dominance orientation and gender: The moderating role of gender identity. British Journal of Social Psychology, 42(2), 187–198. https://doi.org/10.1348/014466603322127175

Wirth, M. M., Welsh, K. M., &amp; Schultheiss, O. C. (2006). Salivary cortisol changes in humans after winning or losing a dominance contest depend on implicit power motivation. Hormones and Behavior, 49(3), 346–352. https://doi.org/10.1016/j.yhbeh.2005.08.013

Zink, C. F., Tong, Y., Chen, Q., Bassett, D. S., Stein, J. L., &amp; Meyer-Lindenberg, A. (2008). Know your place: Neural processing of social hierarchy in humans. Neuron, 58(2), 273–283. https://doi.org/10.1016/j.neuron.2008.01.025

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[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Dominance]]
[[Category:Motivation and emotion/Book/Power motivation]]
[[Category:Motivation and emotion/Book/Social]]</text>
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__TOC__
==Overview==
{{RoundBoxTop|theme=3}}
[[File:Noun Staff Management 4185.svg|Management chart right|thumb|200px|'''Figure 1'''. Power hierarchy in the workplace]]

'''Scenario: Raising up vs. pushing down.'''

Two graduates start the same week at a large firm. One quickly puts their hand up to lead every project going, coordinating people, chasing decisions, and making sure things get done — and uses that influence to actively mentor junior colleagues and push for flatter, fairer pay structures. The other has no interest in leading projects or managing anyone, yet defends the firm's steep hierarchy (see Figure 1) as natural and fair: &quot;some people are just better suited to being in charge, and the system reflects that.&quot; They also actively lobbies against a new scheme providing staff from under-represented backgrounds with better access to mentoring, training, and development opportunities, arguing certain groups should stay in junior roles &quot;where they belong&quot; and pushing to have the scheme scrapped. Both are equally competent. Why does one seem driven to personally influence the people around them, while the other — without wanting any personal authority — is instead driven to keep entire groups beneath others?

{{RoundBoxBottom}}
Human societies are fundamentally structured around social hierarchies, however the psychological factors that lead individuals to navigate, challenge, or enforce these hierarchies can vary significantly. Power motivation and social dominance are two distinct yet related psychological constructs that explain different aspects of hierarchy seeking behaviour in human societies. Social Dominance Orientation (SDO) is defined as a preference for one's ingroup to dominate outgroups viewed as lesser and a general desire for group-based inequality. In contrast, power motivation (nPower) represents an individuals personal drive to have influence, control, or psychological impact over specific individuals.

While these constructs frequently overlap in everyday social interactions, psychological science demonstrates that they operate at fundamentally different levels when it comes to analysis: group-based ideological preference versus interpersonal motivation. Clarifying the distinction between social dominance and power motivation is essential as both constructs can predict real world outcomes, including leadership emergence, support for discriminatory policies, workplace dynamics, and the specific influence and control tactics individuals choose to employ when power is attained. By examining frameworks such as Social Dominance Theory, McClelland's Need Theory, and modern neuroscientific findings, psychological science provides diagnostic tools such as SDO7 scales and implicit motive coding to evaluate why individuals seek status and how they exercise power once it is gained.{{RoundBoxTop|theme=3}}

'''Focus questions'''

* What is social dominance orientation, and how does it relate to broader group hierarchies?
* What is power motivation (nPower), and how is it expressed differently across different demographics and cultural contexts? 
* How do legitimising myths sustain or challenge social hierarchies?
* How do SDO and power motivation shape political attitudes, leadership styles, and intergroup behaviours?

{{RoundBoxBottom}}

==Social dominance orientation==
Social dominance orientation represents a core attitudinal personality variable within intergroup psychology, revealing an individuals stance regarding group-based equality versus group-based hierarchy. Understanding social dominance orientation requires an examination of its theoretical origins within Social Dominance Theory, it's sub-dimensional structures, and its broader predictive validity across societal domains.

=== Origins in social dominance theory ===
[[wikipedia:Social_dominance_orientation|Social dominance theory]] (SDT), developed by Jim Sidanius and Felicia Pratto, opens with the observation that all human societies producing an economic surplus naturally develop group-based social hierarchies. SDT identifies three distinct forms of trimorphic social hierarchies that form the structure of human societies. The age system, which grants adults disproportionate power and social status compared to children; patriarchy, referring to systems where men hold greater political, social, and economic authority than women; and the arbitrary-set system which encompasses culturally constructed social categories such as race, ethnicity, religion, social class, nationality, or caste, that are hierarchically ordered with unequal access to power, opportunity, and privileges.  

According to SDT, social institutions such as legal systems, criminal courts, educational systems, and corporations sustain these group hierarchies through institutional discrimination. Institutions maintain hierarchy by disproportionately allocating positive social value, such as wealth, healthcare, prestige, and educational access, to dominant groups. Additionally, institutions direct negative social value, including harsher criminal penalties, dangerous labour, and poverty, towards subordinate groups. 
* Key references: (Pratto et al., 1994), (Sidanius &amp; Pratto, 2001)

=== Measuring social dominance orientation and what it predicts ===

{| class=&quot;wikitable&quot; style=&quot;float:right; clear:right; width:400px; margin:0 0 1em 1.5em; text-align:center; background-color:#f9f9f9; border:1px solid #aaa;&quot;
|-
! colspan=&quot;2&quot; style=&quot;background-color:#f9f9f9; font-size:110%; padding:8px; border:none;&quot; | Figure 2. Dimensional structure of SDO7&lt;br&gt;&lt;small style=&quot;font-weight:normal;&quot;&gt;&lt;em&gt;Based on Ho et al. (2015)&lt;/em&gt;&lt;/small&gt;
|-
| colspan=&quot;2&quot; style=&quot;background-color:#eef; padding:10px; border:1px solid #aaa;&quot; | '''Social Dominance Orientation (SDO)'''&lt;br&gt;&lt;small&gt;(Preference for group inequality)&lt;/small&gt;
|-
| style=&quot;width:50%; vertical-align:top; background-color:#fff; padding:10px; border:1px solid #aaa; text-align:left;&quot; |
'''SDO-Dominance (SDO-D)'''
* Active group oppression
* Overt group superiority
* Direct intergroup action again outgorups
| style=&quot;width:50%; vertical-align:top; background-color:#fff; padding:10px; border:1px solid #aaa; text-align:left;&quot; |
'''SDO-Egalitarianism (SDO-E)'''
* Opposition to group equality
* Opposition to equity/social schemes
* Subtle institutional bias
|}
To evaluate individual differences in support for group-based hierarchy, researchers constructed the SDO scale, with the newer SDO7 scale dividing the construct into two sub-dimensions. The first dimension, SDO-Dominance (SDO-D) assesses support for active, explicit group oppression and the forced subjugation of outgroups. The second dimension, SDO-Egalitarianism (SDO-E) assesses generalised oppositon to group equality, manifesting as subtle resistance to social welfare, affirmative actions, and equality-promoting policies.

Empirical cross-cultural research confirms that high SDO scores predict intergroup prejudice, ethnocentrism, sexism, homophobia, and support for harsher criminal justice policies. Additionally, individuals selectively self-segregate into specific societal roles based on their SDO levels. High-SDO individuals gravitate towards heirarchy-enhancing roles that reinforce existing social stratification, such as executives, criminal prosecutors, and police officers. In comparison, low-SDO individuals seek out hierarchy-reducing roles that challenge systemic inequality, such as human rights lawyers, public defenders, and social workers.

The SD07 scale distinguished between two sub-dimensions: SDO-Dominance (SDO-D) which involves support for active group oppression and SDO-Egalitarianism (SDO-E) which reflects a preference for group inequality and is linked to more subtle forms of prejudice and inequality as well as opposition to equality-promoting policies.&lt;quiz display=&quot;simple&quot;&gt;
{Which form of hierarchy in Social Dominance Theory involves culturally defined categories like race, ethnicity, or religion?
|type=&quot;()&quot;}
- The age system
- Patriarchy
+ The arbitrary-set system

{High-SDO individuals are most likely to select which of the following career paths?
|type=&quot;()&quot;}
- Hierarchy-reducing roles like public defenders
+ Hierarchy-enhancing roles like corporate executives
&lt;/quiz&gt;
==Power motivation==
Power motivation, commonly referred to as the Need for Power (nPower) is a psychological construct describing an individuals drive to exert impact, control, or influence over others and their surrounding environment. First conceptualised by Henry Murray in taxonomy of fundamental human needs, and later expanded upon by David McClelland in his Three Needs Theory, power motivation represents a primary driver of status-seeking, interpersonal dynamics, and leadership emergence. Rather than representing a purely manipulative or antisocial trait, power motivation exists along a broad psychological spectrum. It ranges from personalised power (pPower), which is characterised by direct control, self-aggrandisement, and zero-sum competition, to socialised power (sPower) where influence is channeled towards supporting and empowering others, mentoring, and achieving collective goals. 

=== McClelland's need theory and measurement ===
McClelland proposed the Need for Power (nPpower) operates alongside the Need for Achievement (nAch) and the Need for Affiliation (nAff) as fundamental human motivators. 

Power motivation operates across two cognitive levels. Implicit power motivation respresents an unconscious motive that can be assessed via projective tests such as the Picture Story Exercise (PSE) or the Thematic Apperception Test (TAT) where spontaneously constructed narratives are coded for imagery of impact, control, and prestige. Explicit power motivation involves conscious self-conceptions evaluated through self-report questionnaires measuring specific desires for leadership roles, authority, or prestige.

Research in social neuroscience indicates that implicit power motivation is accompanied by distinct physiological correlates, with individuals with strong implicit nPower exhibiting heightened salivary cortisol and testosterone fluctuations, as well as distinct neural activation patterns in the amygdala and striatum, when confronting nonverbal social cues signaling rank competiton, social defeat, or interpersonal dominance.

that humans vary in the relative strength of three learned needs: achievement, affiliation, and power, with nPower reflecting a desire to have an impact on or control over other people.
* Key references: (McClelland, 1975), (Rybnicek et al., 2017), (Wirth et al., 2006)

=== Personalised vs socialised power across cultures ===
McClelland emphasises that power motivation is not inherently destructive, and distinguished between two distinct expressions or faces of power. Personalised power (pPower) is driven by direct personal domination and status acquisition, often ignoring the needs of those considered to be subordinates. In contrast, socialised pwoer (sPower) is expressed responsibly through empowering others, mentoring, and influencing others in order to meet collective goals and organisational wellbeing. 

Cultural values heavily shape how power motivation is channeled and expressed. In societies characterised by vertical individualism, power is primarily conceptualised as personalised dominance and personal status acquisition. Conversely, in societies characterised by horizontal collectivism, power motivation is more frequently channeled into socialised expressions, such as community leadership, nurturing, and collective helping. Frieze and Boneva further categorised these explicit power expressions into three distinct behavioural dimension: leadership, prominence, and helping.
* Key references: (Triandis &amp; Gelfand, 1998), (Magee &amp; Galinsky, 2008)

==Legitimising myths==
Social dominance theory proposes that group hierarchies are maintained not solely through physical coercion, but also through the widespread adoption of legitimising myths—cultural beliefs, values, and attitudes that provide moral and intellectual justification for intergroup relations.

=== Hierarchy-enhancing vs hierarchy-attenuating myths ===
Legitimising myths are categorised based on whether they reinforce or undermine inequality in society. Hierarchy-enhancing legitimising myths consist of ideologies that justify inequality by suggesting that existing group advantages are earned, natural, or just, such as meritocracy, racism, sexism, and caste systems. In comparison, hierarchy-attenuating legitimising myths include ideologies that challenge group inequality and advocate for systemic redistribution and equal rights. 

Individuals high in SDO selectively endorse hierarchy-enhancing myths to rationalise their groups privileged position. This endorsement allows them to dismiss societal inequalities as legitimate and understandable consequences of group differences in effort, talent, or intrinsic worth.
* Key references: (Sidanius &amp; Pratto, 2001)

=== Legitimising narratives in media and institutions ===
Legitimising myths are transmitted and continually reinforced through mainstream media narratives, television, educational curriculums, and social media. By embedding hierarchy-enhancing narratives in public discourse, institutions normalise privilege and make systemic inequality appear invisible or natural. Consequently, legitimising myths serve as the psychological mechanism through which abstract SDO translates into active public support for discriminatory laws, harsher sentencing, and opposition to equity programs.
* Key references: (Sidanius &amp; Pratto, 2001), (Pratto et al., 1994)

==The link between social dominance orientation and power motivation==
Although Social Dominance Orientation and power motivation both pertain to social rank and hierarchy, they represent distinct psychological constructs operating at different levels of analysis.
{| class=&quot;wikitable&quot;
|+Table 2. ''Conceptual comparison between Social Dominance Orientation and Power Motivation''
!Feature
!Social Dominance Orientation (SDO)
!Need for Power (nPower)
|-
|'''Primary focus'''
|Group-based social hierarchy and intergroup inequality.
|Interpersonal impact, control, and personal influence.
|-
|'''Level of analysis'''
|Societal / ideological / intergroup level
|Individual / interpersonal / dual levels
|-
|'''Key motivator'''
|Desire for ingroup superiority or systemic group hierarchy
|Desire to direct, control, or impact specific individuals
|-
|'''Behavioural outcome'''
|Endorsing hierarchy-enhancing policy and predudice.
|Leadership emergence, mentoring (sPower) or coercion (pPower)
|}
Social Dominance Orientation reflects a group-level ideological preference for systemic inequality, whereas nPower reflects an individual-level drive for personal impact. Additonally, having high nPower does not automatically equate to having a high SDO.kA leader who is driven by strong socialised power (sPower) may seek personal influence specifically to dismantle institutional barriers and promote equality, resulting in low SDO, as seen in the opening scenario. However, an individual with low personal leadership drive may hold high SDO, actively lobbying to protect group privileges and restrict subordinate group advancements without desiring a personal leadership role.

== Political and social behaviour ==
Individual differences in SDO and nPower heavily influence collective political attitudes, voting patterns, and intergroup conflicts. 

=== SDO, right-wing authoritarianism, and political ideology ===
In political psychology, SDO works alongside Right-Wing Authoritarianism (RWA) as dual motivational predictors of prejudice and political conservatism. Developed by Bob Altemeyer, RWA represents an attitudinal cluster defined by authoritarian submission, authoritarian aggression, and conventialism. SDO and right-wing authoritarianism (RWA) arise from different wordview based roots however both can connect and predict prejudice and political conservatism

(table)

John Duckitt's dual-process model shows that SDO and RWA arise from fundamentally different worldview roots. SDO stems from viewing the world as a &quot;competitive jungle&quot; where force and dominance determine success, driving a desire for group superiority. in contrast, RWA stems from viewing the world as a &quot;dangerous unstable place&quot; driving a desire for social order, sohesion, and strict conformity to authority. Together, high SDO and high RWA interact to predict strong support for anti-egalitarian political parties, opposition to environmental protection, harsh policies towards immigrants, and endorsement of ingroup violence. &lt;quiz display=&quot;simple&quot;&gt;
{According to the dual-process model, Right Wing Authoritarianism (RWA) is primarily motivated by which worldview?
|type=&quot;()&quot;}
- The world as a competitive jungle 
+ The world as a dangerous chaotic place needing order
- The world as an inherently egalitarian community
&lt;/quiz&gt;
* Key references: (Duckitt &amp; Sibley, 2010), (Ekehammar et al., 2004), (Ward, 1982)

== Power, leadership, and individual differences ==
The interactions between power motivation, social dominance, and biological mechanisms provide a predictor of leadership styles, ethical decision making, and organisational health.

=== Prosocial vs. antisocial leadership ===
Leadership based research demonstrates that identical positions of authority yield starkly different organisational outcomes depending on the leader's underlying motives. Leaders high in personalised power (pPower) and high in SDO are significantly more liekly to employ coercive influence tactics, engage in unethical pro-organisational behaviour, and view subordinates as instruments for self-aggrandisement. Conversely, leaders high in prestige motivation or socialised power (sPower) adopt empowering leadership styles that foster team cohesion, psychological safety, and collective innovation.
{{RoundBoxTop|theme=3}}
'''Case study: power and dominance in cult leadership'''

High personalised power motivation and extreme Social Dominance Orientation can compound to produce destructive, coercive, social structures. In cult environments, charismatic leaders combine intense personal impact with rigid hierarchy enhancing legitimising myths regarding their own absolute superiority.

By stripping followers of autonomy, enforcing strict behavioural conformity, and casting all outside groups as inherently inferior, cult leaders exercise extreme personalised dominance. Psychological analysis reveals that such destructive dynamics occur when personal authority (pPower) is unchecked by socialised accountability (sPower), and is reinforced by ideological beliefs in absolute group hierarchy (SDO).{{RoundBoxBottom}}

* Key references: (Magee &amp; Galinsky, 2008), (Denrich, 2024)

=== Biological basis, gender differences, and situation triggers ===
Neuroimaging and biological studies reveal that human brains posess dedicated neural pathways for processing social rank, territory, and status hierarchies. Brain regions such as the [[wikipedia:Amygdala|amygdala]], the [[wikipedia:Striatum|striatum]], the anterior [[wikipedia:Insular_cortex|insula]], and the [[wikipedia:Intraparietal_sulcus|intraparietal sulcus]], activate during social encounters. 

Across samples, gender differences in SDO are consistently observed, with men scoring higher on average than women/ This phenomenon is explained by SDT's subordinate male target hypothesis and evolutionary bargaining models regarding physical formidability and resource defense. Additionally, situational triggers such as acute intergroup competiton, economic scarcity, or percieved threats to ingroup status can temporarily heighten SDO levels and activate aggressive power-seeking behaviours in individuals who are otherwise egalitarian.
* Key references: (Zink et al., 2008), (Sidanius et al., 2000), (Sidanius et al., 2000)

== Conclusion ==

* Social dominance orientation and power motivation are related but distinct: SDO is a group-level ideological preference for hierarchy sustained by legitimising myths; power motivation is a personal, often implicit, drive to influence specific others.
* The two exist separately however, a person can want personal influence without wanting group-based dominance, or vice versa
* Both are influenced by biology, personality, culture, and situational triggers, and both feed into real-world outcomes such as political ideology, intergroup conflict, and either coercive or responsible leadership
* Recognising which construct is driving a persons behaviour and whether power is being expressed personally or socially has practical value for understanding leadership, workplace dynamics, and social conflict.

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* [[Motivation and emotion/Book/2024/Social dominance and power motivation|Social dominance and power motivation]] (Book chapter, 2024)

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==References==
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Abou-Ismail, R., Cichocka, A., Phillips, J., &amp; Sengupta, N. K. (2025). Authoritarianism and social dominance as differential predictors of individuals’ support for collective violence. Psychology of Violence, 15(5), 634–644. https://doi.org/10.1037/vio0000580Anderson, 

C., &amp; Kilduff, G. J. (2009). The pursuit of status in social groups. Current Directions in Psychological Science, 18(5), 295–298. https://doi.org/10.1111/.1467-8721.2009.01655.x

Denrich, D. S. (2024). Charismatic leadership and vulnerability: A comprehensive study of cult dynamics. Psychology Presentations. https://digitalcommons.ursinus.edu/psych_pres/11/

Duckitt, J., &amp; Sibley, C. G. (2010). Personality, ideology, prejudice, and politics: A dual‐process motivational model. Journal of Personality, 78(6), 1861–1894. https://doi.org/10.1111/j.1467-6494.2010.00672.x

Ekehammar, B., Akrami, N., Gylje, M., &amp; Zakrisson, I. (2004). What matters most to prejudice: Big five personality, social dominance orientation, or right-wing authoritarianism? European Journal of Personality, 18(6), 463–482. https://doi.org/10.1002/per.526

Ho, A. K., Sidanius, J., Kteily, N., Sheehy-Skeffington, J., Pratto, F., Henkel, K. E., Foels, R., &amp; Stewart, A. L. (2015). The nature of social dominance orientation: Theorizing and measuring preferences for intergroup inequality using the new SDO₇ scale. Journal of Personality and Social Psychology, 109(6), 1003–1028. https://doi.org/10.1037/pspi0000033

Magee, J. C., &amp; Galinsky, A. D. (2008). Social hierarchy: The self‐reinforcing nature of power and status. The Academy of Management Annals, 2(1), 351–398. https://doi.org/10.1080/19416520802211628

McClelland, D. C. (1975). Power : The inner experience. Irvington Publishers.Pratto, F., Sidanius, J., Stallworth, L. M., &amp; Malle, B. F. (1994). Social dominance orientation: A personality variable predicting social and political attitudes. Journal of Personality and Social Psychology, 67(4), 741–763. https://doi.org/10.1037/0022-3514.67.4.741

Rybnicek, R., Bergner, S., &amp; Gutschelhofer, A. (2017). How individual needs influence motivation effects: A neuroscientific study on McClelland’s need theory. Review of Managerial Science, 13(2), 443–482. springer. https://doi.org/10.1007/s11846-017-0252-1

Sidanius, J., Levin, S., Liu, J., &amp; Pratto, F. (2000). Social dominance orientation, anti-egalitarianism and the political psychology of gender: An extension and cross-cultural replication. European Journal of Social Psychology, 30(1), 41–67. https://doi.org/10.1002/(sici)1099-0992(200001/02)30:1&lt;41::aid-ejsp976&gt;3.0.co;2-o

Sidanius, J., &amp; Pratto, F. (2001). Social dominance: An intergroup theory of social hierarchy and oppression. Contemporary Sociology, 30(2), 120. https://doi.org/10.2307/2655372

Son Hing, L. S., Bobocel, D. R., Zanna, M. P., &amp; McBride, M. V. (2007). Authoritarian dynamics and unethical decision making: High social dominance orientation leaders and high right-wing authoritarianism followers. Journal of Personality and Social Psychology, 92(1), 67–81. https://doi.org/10.1037/0022-3514.92.1.67

Triandis, H. C., &amp; Gelfand, M. J. (1998). Converging measurement of horizontal and vertical individualism and collectivism. Journal of Personality and Social Psychology, 74(1), 118–128. https://doi.org/10.1037/0022-3514.74.1.118

Ward, D. (1982). Right-wing authoritarianism. . American Political Science Review, 76(3), 737–738. https://doi.org/10.2307/1963836

Wilson, M. S., &amp; Liu, J. H. (2003). Social dominance orientation and gender: The moderating role of gender identity. British Journal of Social Psychology, 42(2), 187–198. https://doi.org/10.1348/014466603322127175

Wirth, M. M., Welsh, K. M., &amp; Schultheiss, O. C. (2006). Salivary cortisol changes in humans after winning or losing a dominance contest depend on implicit power motivation. Hormones and Behavior, 49(3), 346–352. https://doi.org/10.1016/j.yhbeh.2005.08.013

Zink, C. F., Tong, Y., Chen, Q., Bassett, D. S., Stein, J. L., &amp; Meyer-Lindenberg, A. (2008). Know your place: Neural processing of social hierarchy in humans. Neuron, 58(2), 273–283. https://doi.org/10.1016/j.neuron.2008.01.025

}}

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[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Dominance]]
[[Category:Motivation and emotion/Book/Power motivation]]
[[Category:Motivation and emotion/Book/Social]]</text>
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      <text bytes="30839" sha1="ovfjbhdhl916ugewelj9n31crqgrt0k" xml:space="preserve">{{title|Social dominance and power motivation:&lt;br&gt;What is the relationship between social dominance and power motivation?}}
__TOC__
==Overview==
{{RoundBoxTop|theme=3}}
[[File:Noun Staff Management 4185.svg|Management chart right|thumb|200px|'''Figure 1'''. Power hierarchy in the workplace]]

'''Scenario: Raising up vs. pushing down.'''

Two graduates start the same week at a large firm. One quickly puts their hand up to lead every project going, coordinating people, chasing decisions, and making sure things get done — and uses that influence to actively mentor junior colleagues and push for flatter, fairer pay structures. The other has no interest in leading projects or managing anyone, yet defends the firm's steep hierarchy (see Figure 1) as natural and fair: &quot;some people are just better suited to being in charge, and the system reflects that.&quot; They also actively lobbies against a new scheme providing staff from under-represented backgrounds with better access to mentoring, training, and development opportunities, arguing certain groups should stay in junior roles &quot;where they belong&quot; and pushing to have the scheme scrapped. Both are equally competent. Why does one seem driven to personally influence the people around them, while the other — without wanting any personal authority — is instead driven to keep entire groups beneath others?

{{RoundBoxBottom}}
Human societies are fundamentally structured around social hierarchies, however the psychological factors that lead individuals to navigate, challenge, or enforce these hierarchies can vary significantly. Power motivation and social dominance are two distinct yet related psychological constructs that explain different aspects of hierarchy seeking behaviour in human societies. Social Dominance Orientation (SDO) is defined as a preference for one's ingroup to dominate outgroups viewed as lesser and a general desire for group-based inequality. In contrast, power motivation (nPower) represents an individuals personal drive to have influence, control, or psychological impact over specific individuals.

While these constructs frequently overlap in everyday social interactions, psychological science demonstrates that they operate at fundamentally different levels when it comes to analysis: group-based ideological preference versus interpersonal motivation. Clarifying the distinction between social dominance and power motivation is essential as both constructs can predict real world outcomes, including leadership emergence, support for discriminatory policies, workplace dynamics, and the specific influence and control tactics individuals choose to employ when power is attained. By examining frameworks such as Social Dominance Theory, McClelland's Need Theory, and modern neuroscientific findings, psychological science provides diagnostic tools such as SDO7 scales and implicit motive coding to evaluate why individuals seek status and how they exercise power once it is gained.{{RoundBoxTop|theme=3}}

'''Focus questions'''

* What is social dominance orientation, and how does it relate to broader group hierarchies?
* What is power motivation (nPower), and how is it expressed differently across different demographics and cultural contexts? 
* How do legitimising myths sustain or challenge social hierarchies?
* How do SDO and power motivation shape political attitudes, leadership styles, and intergroup behaviours?

{{RoundBoxBottom}}

==Social dominance orientation==
Social dominance orientation represents a core attitudinal personality variable within intergroup psychology, revealing an individuals stance regarding group-based equality versus group-based hierarchy. Understanding social dominance orientation requires an examination of its theoretical origins within Social Dominance Theory, it's sub-dimensional structures, and its broader predictive validity across societal domains.

=== Origins in social dominance theory ===
[[wikipedia:Social_dominance_orientation|Social dominance theory]] (SDT), developed by Jim Sidanius and Felicia Pratto, opens with the observation that all human societies producing an economic surplus naturally develop group-based social hierarchies. SDT identifies three distinct forms of trimorphic social hierarchies that form the structure of human societies. The age system, which grants adults disproportionate power and social status compared to children; patriarchy, referring to systems where men hold greater political, social, and economic authority than women; and the arbitrary-set system which encompasses culturally constructed social categories such as race, ethnicity, religion, social class, nationality, or caste, that are hierarchically ordered with unequal access to power, opportunity, and privileges.  

According to SDT, social institutions such as legal systems, criminal courts, educational systems, and corporations sustain these group hierarchies through institutional discrimination. Institutions maintain hierarchy by disproportionately allocating positive social value, such as wealth, healthcare, prestige, and educational access, to dominant groups. Additionally, institutions direct negative social value, including harsher criminal penalties, dangerous labour, and poverty, towards subordinate groups. 
* Key references: (Pratto et al., 1994), (Sidanius &amp; Pratto, 2001)

=== Measuring social dominance orientation and what it predicts ===

{| class=&quot;wikitable&quot; style=&quot;float:right; clear:right; width:400px; margin:0 0 1em 1.5em; text-align:center; background-color:#f9f9f9; border:1px solid #aaa;&quot;
|-
! colspan=&quot;2&quot; style=&quot;background-color:#f9f9f9; font-size:110%; padding:8px; border:none;&quot; | Figure 2. Dimensional structure of SDO7&lt;br&gt;&lt;small style=&quot;font-weight:normal;&quot;&gt;&lt;em&gt;Based on Ho et al. (2015)&lt;/em&gt;&lt;/small&gt;
|-
| colspan=&quot;2&quot; style=&quot;background-color:#eef; padding:10px; border:1px solid #aaa;&quot; | '''Social Dominance Orientation (SDO)'''&lt;br&gt;&lt;small&gt;(Preference for group inequality)&lt;/small&gt;
|-
| style=&quot;width:50%; vertical-align:top; background-color:#fff; padding:10px; border:1px solid #aaa; text-align:left;&quot; |
'''SDO-Dominance (SDO-D)'''
* Active group oppression
* Overt group superiority
* Direct intergroup action again outgorups
| style=&quot;width:50%; vertical-align:top; background-color:#fff; padding:10px; border:1px solid #aaa; text-align:left;&quot; |
'''SDO-Egalitarianism (SDO-E)'''
* Opposition to group equality
* Opposition to equity/social schemes
* Subtle institutional bias
|}
To evaluate individual differences in support for group-based hierarchy, researchers constructed the SDO scale, with the newer SDO7 scale dividing the construct into two sub-dimensions. The first dimension, SDO-Dominance (SDO-D) assesses support for active, explicit group oppression and the forced subjugation of outgroups. The second dimension, SDO-Egalitarianism (SDO-E) assesses generalised oppositon to group equality, manifesting as subtle resistance to social welfare, affirmative actions, and equality-promoting policies.

Empirical cross-cultural research confirms that high SDO scores predict intergroup prejudice, ethnocentrism, sexism, homophobia, and support for harsher criminal justice policies. Additionally, individuals selectively self-segregate into specific societal roles based on their SDO levels. High-SDO individuals gravitate towards heirarchy-enhancing roles that reinforce existing social stratification, such as executives, criminal prosecutors, and police officers. In comparison, low-SDO individuals seek out hierarchy-reducing roles that challenge systemic inequality, such as human rights lawyers, public defenders, and social workers.

The SD07 scale distinguished between two sub-dimensions: SDO-Dominance (SDO-D) which involves support for active group oppression and SDO-Egalitarianism (SDO-E) which reflects a preference for group inequality and is linked to more subtle forms of prejudice and inequality as well as opposition to equality-promoting policies.&lt;quiz display=&quot;simple&quot;&gt;
{Which form of hierarchy in Social Dominance Theory involves culturally defined categories like race, ethnicity, or religion?
|type=&quot;()&quot;}
- The age system
- Patriarchy
+ The arbitrary-set system

{High-SDO individuals are most likely to select which of the following career paths?
|type=&quot;()&quot;}
- Hierarchy-reducing roles like public defenders
+ Hierarchy-enhancing roles like corporate executives
&lt;/quiz&gt;
==Power motivation==
Power motivation, commonly referred to as the Need for Power (nPower) is a psychological construct describing an individuals drive to exert impact, control, or influence over others and their surrounding environment. First conceptualised by Henry Murray in taxonomy of fundamental human needs, and later expanded upon by David McClelland in his Three Needs Theory, power motivation represents a primary driver of status-seeking, interpersonal dynamics, and leadership emergence. Rather than representing a purely manipulative or antisocial trait, power motivation exists along a broad psychological spectrum. It ranges from personalised power (pPower), which is characterised by direct control, self-aggrandisement, and zero-sum competition, to socialised power (sPower) where influence is channeled towards supporting and empowering others, mentoring, and achieving collective goals. 

=== McClelland's need theory and measurement ===
McClelland proposed the Need for Power (nPpower) operates alongside the Need for Achievement (nAch) and the Need for Affiliation (nAff) as fundamental human motivators. 

Power motivation operates across two cognitive levels. Implicit power motivation respresents an unconscious motive that can be assessed via projective tests such as the Picture Story Exercise (PSE) or the Thematic Apperception Test (TAT) where spontaneously constructed narratives are coded for imagery of impact, control, and prestige. Explicit power motivation involves conscious self-conceptions evaluated through self-report questionnaires measuring specific desires for leadership roles, authority, or prestige.

Research in social neuroscience indicates that implicit power motivation is accompanied by distinct physiological correlates, with individuals with strong implicit nPower exhibiting heightened salivary cortisol and testosterone fluctuations, as well as distinct neural activation patterns in the amygdala and striatum, when confronting nonverbal social cues signaling rank competiton, social defeat, or interpersonal dominance.

that humans vary in the relative strength of three learned needs: achievement, affiliation, and power, with nPower reflecting a desire to have an impact on or control over other people.
* Key references: (McClelland, 1975), (Rybnicek et al., 2017), (Wirth et al., 2006)

=== Personalised vs socialised power across cultures ===
McClelland emphasises that power motivation is not inherently destructive, and distinguished between two distinct expressions or faces of power. Personalised power (pPower) is driven by direct personal domination and status acquisition, often ignoring the needs of those considered to be subordinates. In contrast, socialised pwoer (sPower) is expressed responsibly through empowering others, mentoring, and influencing others in order to meet collective goals and organisational wellbeing. 

Cultural values heavily shape how power motivation is channeled and expressed. In societies characterised by vertical individualism, power is primarily conceptualised as personalised dominance and personal status acquisition. Conversely, in societies characterised by horizontal collectivism, power motivation is more frequently channeled into socialised expressions, such as community leadership, nurturing, and collective helping. Frieze and Boneva further categorised these explicit power expressions into three distinct behavioural dimension: leadership, prominence, and helping.
* Key references: (Triandis &amp; Gelfand, 1998), (Magee &amp; Galinsky, 2008)

==Legitimising myths==
Social dominance theory proposes that group hierarchies are maintained not solely through physical coercion, but also through the widespread adoption of legitimising myths—cultural beliefs, values, and attitudes that provide moral and intellectual justification for intergroup relations.

=== Hierarchy-enhancing vs hierarchy-attenuating myths ===
Legitimising myths are categorised based on whether they reinforce or undermine inequality in society. Hierarchy-enhancing legitimising myths consist of ideologies that justify inequality by suggesting that existing group advantages are earned, natural, or just, such as meritocracy, racism, sexism, and caste systems. In comparison, hierarchy-attenuating legitimising myths include ideologies that challenge group inequality and advocate for systemic redistribution and equal rights. 

Individuals high in SDO selectively endorse hierarchy-enhancing myths to rationalise their groups privileged position. This endorsement allows them to dismiss societal inequalities as legitimate and understandable consequences of group differences in effort, talent, or intrinsic worth.
* Key references: (Sidanius &amp; Pratto, 2001)

=== Legitimising narratives in media and institutions ===
Legitimising myths are transmitted and continually reinforced through mainstream media narratives, television, educational curriculums, and social media. By embedding hierarchy-enhancing narratives in public discourse, institutions normalise privilege and make systemic inequality appear invisible or natural. Consequently, legitimising myths serve as the psychological mechanism through which abstract SDO translates into active public support for discriminatory laws, harsher sentencing, and opposition to equity programs.
* Key references: (Sidanius &amp; Pratto, 2001), (Pratto et al., 1994)

==The link between social dominance orientation and power motivation==
Although Social Dominance Orientation and power motivation both pertain to social rank and hierarchy, they represent distinct psychological constructs operating at different levels of analysis.
{| class=&quot;wikitable&quot;
|+Table 2. ''Conceptual comparison between Social Dominance Orientation and Power Motivation''
!Feature
!Social Dominance Orientation (SDO)
!Need for Power (nPower)
|-
|'''Primary focus'''
|Group-based social hierarchy and intergroup inequality.
|Interpersonal impact, control, and personal influence.
|-
|'''Level of analysis'''
|Societal / ideological / intergroup level
|Individual / interpersonal / dual levels
|-
|'''Key motivator'''
|Desire for ingroup superiority or systemic group hierarchy
|Desire to direct, control, or impact specific individuals
|-
|'''Behavioural outcome'''
|Endorsing hierarchy-enhancing policy and predudice.
|Leadership emergence, mentoring (sPower) or coercion (pPower)
|}
Social Dominance Orientation reflects a group-level ideological preference for systemic inequality, whereas nPower reflects an individual-level drive for personal impact. Additonally, having high nPower does not automatically equate to having a high SDO.kA leader who is driven by strong socialised power (sPower) may seek personal influence specifically to dismantle institutional barriers and promote equality, resulting in low SDO, as seen in the opening scenario. However, an individual with low personal leadership drive may hold high SDO, actively lobbying to protect group privileges and restrict subordinate group advancements without desiring a personal leadership role.

== Political and social behaviour ==
Individual differences in SDO and nPower heavily influence collective political attitudes, voting patterns, and intergroup conflicts. 

=== SDO, right-wing authoritarianism, and political ideology ===
In political psychology, SDO works alongside Right-Wing Authoritarianism (RWA) as dual motivational predictors of prejudice and political conservatism. Developed by Bob Altemeyer, RWA represents an attitudinal cluster defined by authoritarian submission, authoritarian aggression, and conventialism. SDO and right-wing authoritarianism (RWA) arise from different wordview based roots however both can connect and predict prejudice and political conservatism

(table)

John Duckitt's dual-process model shows that SDO and RWA arise from fundamentally different worldview roots. SDO stems from viewing the world as a &quot;competitive jungle&quot; where force and dominance determine success, driving a desire for group superiority. in contrast, RWA stems from viewing the world as a &quot;dangerous unstable place&quot; driving a desire for social order, sohesion, and strict conformity to authority. Together, high SDO and high RWA interact to predict strong support for anti-egalitarian political parties, opposition to environmental protection, harsh policies towards immigrants, and endorsement of ingroup violence. &lt;quiz display=&quot;simple&quot;&gt;
{According to the dual-process model, Right Wing Authoritarianism (RWA) is primarily motivated by which worldview?
|type=&quot;()&quot;}
- The world as a competitive jungle 
+ The world as a dangerous chaotic place needing order
- The world as an inherently egalitarian community
&lt;/quiz&gt;
* Key references: (Duckitt &amp; Sibley, 2010), (Ekehammar et al., 2004), (Ward, 1982)

== Power, leadership, and individual differences ==
The interactions between power motivation, social dominance, and biological mechanisms provide a predictor of leadership styles, ethical decision making, and organisational health.

=== Prosocial vs. antisocial leadership ===
Leadership based research demonstrates that identical positions of authority yield starkly different organisational outcomes depending on the leader's underlying motives. Leaders high in personalised power (pPower) and high in SDO are significantly more liekly to employ coercive influence tactics, engage in unethical pro-organisational behaviour, and view subordinates as instruments for self-aggrandisement. Conversely, leaders high in prestige motivation or socialised power (sPower) adopt empowering leadership styles that foster team cohesion, psychological safety, and collective innovation.
{{RoundBoxTop|theme=3}}
'''Case study: power and dominance in cult leadership'''

High personalised power motivation and extreme Social Dominance Orientation can compound to produce destructive, coercive, social structures. In cult environments, charismatic leaders combine intense personal impact with rigid hierarchy enhancing legitimising myths regarding their own absolute superiority.

By stripping followers of autonomy, enforcing strict behavioural conformity, and casting all outside groups as inherently inferior, cult leaders exercise extreme personalised dominance. Psychological analysis reveals that such destructive dynamics occur when personal authority (pPower) is unchecked by socialised accountability (sPower), and is reinforced by ideological beliefs in absolute group hierarchy (SDO).{{RoundBoxBottom}}

* Key references: (Magee &amp; Galinsky, 2008), (Denrich, 2024)

=== Biological basis, gender differences, and situation triggers ===
Neuroimaging and biological studies reveal that human brains posess dedicated neural pathways for processing social rank, territory, and status hierarchies. Brain regions such as the [[wikipedia:Amygdala|amygdala]], the [[wikipedia:Striatum|striatum]], the anterior [[wikipedia:Insular_cortex|insula]], and the [[wikipedia:Intraparietal_sulcus|intraparietal sulcus]], activate during social encounters. 

Across samples, gender differences in SDO are consistently observed, with men scoring higher on average than women/ This phenomenon is explained by SDT's subordinate male target hypothesis and evolutionary bargaining models regarding physical formidability and resource defense. Additionally, situational triggers such as acute intergroup competiton, economic scarcity, or percieved threats to ingroup status can temporarily heighten SDO levels and activate aggressive power-seeking behaviours in individuals who are otherwise egalitarian.
* Key references: (Zink et al., 2008), (Sidanius et al., 2000), (Sidanius et al., 2000)

== Conclusion ==
Social dominance orientation and power motivation are distinct yet related psychological constructs that operate at different levels of analysis. SDO functions as a macro-level ideological preference for group-based hierarchy and intergroup inequality, whereas power motivation functions as a micro-level interpersonal drive for direct influence and control over individuals. 

SDO is rooted in Social Dominance Theory's trimorphic group systems and is evaluated via the SDO7 scale. power motivation manifests as either personalised power or socialised power and is heavily shaped by vertical versus horizontal cultural orientations. Legitimising myths serve as the crucial ideological bridge connecting abstract SDO preferences to real world policy support, whereas SDO and power motivation interact with Right-Wing Authoritarianism and neural rank-processing networks to shape political behaviour and leadership dynamics.

Distinguishing between personal leadership drive and group hierarchy defense provides practical value for organisation, political scientists, and community leaders. Recognising these underlying motives allows institutions to actively foster socialised power and prestige while dismantling coercive dominance and systemic group inequality.

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Abou-Ismail, R., Cichocka, A., Phillips, J., &amp; Sengupta, N. K. (2025). Authoritarianism and social dominance as differential predictors of individuals’ support for collective violence. Psychology of Violence, 15(5), 634–644. https://doi.org/10.1037/vio0000580Anderson, 

C., &amp; Kilduff, G. J. (2009). The pursuit of status in social groups. Current Directions in Psychological Science, 18(5), 295–298. https://doi.org/10.1111/.1467-8721.2009.01655.x

Denrich, D. S. (2024). Charismatic leadership and vulnerability: A comprehensive study of cult dynamics. Psychology Presentations. https://digitalcommons.ursinus.edu/psych_pres/11/

Duckitt, J., &amp; Sibley, C. G. (2010). Personality, ideology, prejudice, and politics: A dual‐process motivational model. Journal of Personality, 78(6), 1861–1894. https://doi.org/10.1111/j.1467-6494.2010.00672.x

Ekehammar, B., Akrami, N., Gylje, M., &amp; Zakrisson, I. (2004). What matters most to prejudice: Big five personality, social dominance orientation, or right-wing authoritarianism? European Journal of Personality, 18(6), 463–482. https://doi.org/10.1002/per.526

Ho, A. K., Sidanius, J., Kteily, N., Sheehy-Skeffington, J., Pratto, F., Henkel, K. E., Foels, R., &amp; Stewart, A. L. (2015). The nature of social dominance orientation: Theorizing and measuring preferences for intergroup inequality using the new SDO₇ scale. Journal of Personality and Social Psychology, 109(6), 1003–1028. https://doi.org/10.1037/pspi0000033

Magee, J. C., &amp; Galinsky, A. D. (2008). Social hierarchy: The self‐reinforcing nature of power and status. The Academy of Management Annals, 2(1), 351–398. https://doi.org/10.1080/19416520802211628

McClelland, D. C. (1975). Power : The inner experience. Irvington Publishers.Pratto, F., Sidanius, J., Stallworth, L. M., &amp; Malle, B. F. (1994). Social dominance orientation: A personality variable predicting social and political attitudes. Journal of Personality and Social Psychology, 67(4), 741–763. https://doi.org/10.1037/0022-3514.67.4.741

Rybnicek, R., Bergner, S., &amp; Gutschelhofer, A. (2017). How individual needs influence motivation effects: A neuroscientific study on McClelland’s need theory. Review of Managerial Science, 13(2), 443–482. springer. https://doi.org/10.1007/s11846-017-0252-1

Sidanius, J., Levin, S., Liu, J., &amp; Pratto, F. (2000). Social dominance orientation, anti-egalitarianism and the political psychology of gender: An extension and cross-cultural replication. European Journal of Social Psychology, 30(1), 41–67. https://doi.org/10.1002/(sici)1099-0992(200001/02)30:1&lt;41::aid-ejsp976&gt;3.0.co;2-o

Sidanius, J., &amp; Pratto, F. (2001). Social dominance: An intergroup theory of social hierarchy and oppression. Contemporary Sociology, 30(2), 120. https://doi.org/10.2307/2655372

Son Hing, L. S., Bobocel, D. R., Zanna, M. P., &amp; McBride, M. V. (2007). Authoritarian dynamics and unethical decision making: High social dominance orientation leaders and high right-wing authoritarianism followers. Journal of Personality and Social Psychology, 92(1), 67–81. https://doi.org/10.1037/0022-3514.92.1.67

Triandis, H. C., &amp; Gelfand, M. J. (1998). Converging measurement of horizontal and vertical individualism and collectivism. Journal of Personality and Social Psychology, 74(1), 118–128. https://doi.org/10.1037/0022-3514.74.1.118

Ward, D. (1982). Right-wing authoritarianism. . American Political Science Review, 76(3), 737–738. https://doi.org/10.2307/1963836

Wilson, M. S., &amp; Liu, J. H. (2003). Social dominance orientation and gender: The moderating role of gender identity. British Journal of Social Psychology, 42(2), 187–198. https://doi.org/10.1348/014466603322127175

Wirth, M. M., Welsh, K. M., &amp; Schultheiss, O. C. (2006). Salivary cortisol changes in humans after winning or losing a dominance contest depend on implicit power motivation. Hormones and Behavior, 49(3), 346–352. https://doi.org/10.1016/j.yhbeh.2005.08.013

Zink, C. F., Tong, Y., Chen, Q., Bassett, D. S., Stein, J. L., &amp; Meyer-Lindenberg, A. (2008). Know your place: Neural processing of social hierarchy in humans. Neuron, 58(2), 273–283. https://doi.org/10.1016/j.neuron.2008.01.025

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[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Dominance]]
[[Category:Motivation and emotion/Book/Power motivation]]
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__TOC__
==Overview==
{{RoundBoxTop|theme=3}}
[[File:Noun Staff Management 4185.svg|Management chart right|thumb|200px|'''Figure 1'''. Power hierarchy in the workplace]]

'''Scenario: Raising up vs. pushing down.'''

Two graduates start the same week at a large firm. One quickly puts their hand up to lead every project going, coordinating people, chasing decisions, and making sure things get done — and uses that influence to actively mentor junior colleagues and push for flatter, fairer pay structures. The other has no interest in leading projects or managing anyone, yet defends the firm's steep hierarchy (see Figure 1) as natural and fair: &quot;some people are just better suited to being in charge, and the system reflects that.&quot; They also actively lobbies against a new scheme providing staff from under-represented backgrounds with better access to mentoring, training, and development opportunities, arguing certain groups should stay in junior roles &quot;where they belong&quot; and pushing to have the scheme scrapped. Both are equally competent. Why does one seem driven to personally influence the people around them, while the other — without wanting any personal authority — is instead driven to keep entire groups beneath others?

{{RoundBoxBottom}}
Human societies are fundamentally structured around social hierarchies (Magee &amp; Galinsky, 2008; Sidanius &amp; Pratto, 1999), however the psychological factors that lead individuals to navigate, challenge, or enforce these hierarchies can vary significantly. Power motivation and social dominance are two distinct yet related psychological constructs that explain different aspects of hierarchy seeking behaviour in human societies. Social Dominance Orientation (SDO) is defined as a preference for one's ingroup to dominate outgroups viewed as lesser and a general desire for group-based inequality (Ho et al., 2015; Pratto et al., 1994). In contrast, power motivation (nPower) represents an individuals personal drive to have influence, control, or psychological impact over specific individuals (McClelland, 1975).

While these constructs frequently overlap in everyday social interactions, psychological science demonstrates that they operate at fundamentally different levels when it comes to analysis: group-based ideological preference versus interpersonal motivation (Ho et al., 2015; Suessenbach et al., 2018). Clarifying the distinction between social dominance and power motivation is essential as both constructs can predict real world outcomes, including leadership emergence, support for discriminatory policies, workplace dynamics, and the specific influence and control tactics individuals choose to employ when power is attained (Aiello et al., 2013; Cheng et al., 2013). By examining frameworks such as Social Dominance Theory, McClelland's Need Theory, and modern neuroscientific findings, psychological science provides diagnostic tools such as SDO7 scales and implicit motive coding to evaluate why individuals seek status and how they exercise power once it is gained (Ho et al., 2015; McClelland, 1975).

{{RoundBoxTop|theme=3}}

'''Focus questions'''

* What is social dominance orientation, and how does it relate to broader group hierarchies?
* What is power motivation (nPower), and how is it expressed differently across different demographics and cultural contexts? 
* How do legitimising myths sustain or challenge social hierarchies?
* How do SDO and power motivation shape political attitudes, leadership styles, and intergroup behaviours?

{{RoundBoxBottom}}

==Social dominance orientation==
Social dominance orientation represents a core attitudinal personality variable within intergroup psychology, revealing an individuals stance regarding group-based equality versus group-based hierarchy (Pratto et al., 1994). Understanding social dominance orientation requires an examination of its theoretical origins within Social Dominance Theory, it's sub-dimensional structures, and its broader predictive validity across societal domains.

=== Origins in social dominance theory ===
[[wikipedia:Social_dominance_orientation|Social dominance theory]] (SDT), developed by Jim Sidanius and Felicia Pratto, opens with the observation that all human societies producing an economic surplus naturally develop group-based social hierarchies (Sidanius &amp; Pratto, 1999). SDT identifies three distinct forms of trimorphic social hierarchies that form the structure of human societies. The age system, which grants adults disproportionate power and social status compared to children; patriarchy, referring to systems where men hold greater political, social, and economic authority than women; and the arbitrary-set system which encompasses culturally constructed social categories such as race, ethnicity, religion, social class, nationality, or caste, that are hierarchically ordered with unequal access to power, opportunity, and privileges (Sidanius &amp; Pratto, 1999).  

According to SDT, social institutions such as legal systems, criminal courts, educational systems, and corporations sustain these group hierarchies through institutional discrimination (Sidanius &amp; Pratto, 1999). Institutions maintain hierarchy by disproportionately allocating positive social value, such as wealth, healthcare, prestige, and educational access, to dominant groups. Additionally, institutions direct negative social value, including harsher criminal penalties, dangerous labour, and poverty, towards subordinate groups (Pratto et al., 1994; Sidanius &amp; Pratto, 1999). 

=== Measuring social dominance orientation and what it predicts ===

{| class=&quot;wikitable&quot; style=&quot;float:right; clear:right; width:400px; margin:0 0 1em 1.5em; text-align:center; background-color:#f9f9f9; border:1px solid #aaa;&quot;
|-
! colspan=&quot;2&quot; style=&quot;background-color:#f9f9f9; font-size:110%; padding:8px; border:none;&quot; | Figure 2. Dimensional structure of SDO7&lt;br&gt;&lt;small style=&quot;font-weight:normal;&quot;&gt;&lt;em&gt;Based on Ho et al. (2015)&lt;/em&gt;&lt;/small&gt;
|-
| colspan=&quot;2&quot; style=&quot;background-color:#eef; padding:10px; border:1px solid #aaa;&quot; | '''Social Dominance Orientation (SDO)'''&lt;br&gt;&lt;small&gt;(Preference for group inequality)&lt;/small&gt;
|-
| style=&quot;width:50%; vertical-align:top; background-color:#fff; padding:10px; border:1px solid #aaa; text-align:left;&quot; |
'''SDO-Dominance (SDO-D)'''
* Active group oppression
* Overt group superiority
* Direct intergroup action again outgorups
| style=&quot;width:50%; vertical-align:top; background-color:#fff; padding:10px; border:1px solid #aaa; text-align:left;&quot; |
'''SDO-Egalitarianism (SDO-E)'''
* Opposition to group equality
* Opposition to equity/social schemes
* Subtle institutional bias
|}
To evaluate individual differences in support for group-based hierarchy, researchers constructed the SDO scale, with the newer SDO7 scale dividing the construct into two sub-dimensions (Ho et al., 2015; see Figure 2). The first dimension, SDO-Dominance (SDO-D) assesses support for active, explicit group oppression and the forced subjugation of outgroups. The second dimension, SDO-Egalitarianism (SDO-E) assesses generalised oppositon to group equality, manifesting as subtle resistance to social welfare, affirmative actions, and equality-promoting policies (Ho et al., 2015, 2025).

Empirical cross-cultural research confirms that high SDO scores predict intergroup prejudice, ethnocentrism, sexism, homophobia, and support for harsher criminal justice policies (Pratto et al., 1994). Additionally, individuals selectively self-segregate into specific societal roles based on their SDO levels. High-SDO individuals gravitate towards heirarchy-enhancing roles that reinforce existing social stratification, such as executives, criminal prosecutors, and police officers. In comparison, low-SDO individuals seek out hierarchy-reducing roles that challenge systemic inequality, such as human rights lawyers, public defenders, and social workers (Pratto et al., 1994; Sidanius &amp; Pratto, 1999).


The SD07 scale distinguished between two sub-dimensions: SDO-Dominance (SDO-D) which involves support for active group oppression and SDO-Egalitarianism (SDO-E) which reflects a preference for group inequality and is linked to more subtle forms of prejudice and inequality as well as opposition to equality-promoting policies.&lt;quiz display=&quot;simple&quot;&gt;
{Which form of hierarchy in Social Dominance Theory involves culturally defined categories like race, ethnicity, or religion?
|type=&quot;()&quot;}
- The age system
- Patriarchy
+ The arbitrary-set system

{High-SDO individuals are most likely to select which of the following career paths?
|type=&quot;()&quot;}
- Hierarchy-reducing roles like public defenders
+ Hierarchy-enhancing roles like corporate executives
&lt;/quiz&gt;
==Power motivation==
Power motivation, commonly referred to as the Need for Power (nPower) is a psychological construct describing an individuals drive to exert impact, control, or influence over others and their surrounding environment (McClelland, 1975). First conceptualised by Henry Murray in taxonomy of fundamental human needs, and later expanded upon by David McClelland in his Three Needs Theory, power motivation represents a primary driver of status-seeking, interpersonal dynamics, and leadership emergence (McClelland, 1975; Suessenbach et al., 2018). Rather than representing a purely manipulative or antisocial trait, power motivation exists along a broad psychological spectrum. It ranges from personalised power (pPower), which is characterised by direct control, self-aggrandisement, and zero-sum competition, to socialised power (sPower) where influence is channelled towards supporting and empowering others, mentoring, and achieving collective goals (McClelland, 1975; Friederichs et al., 2023). 

=== McClelland's need theory and measurement ===
McClelland proposed vary in the relative strength of three learned needs: the Need for Power (nPower), the Need for Achievement (nAch) and the Need for Affiliation (nAff), with nPower reflecting a desire to have an impact on, or control over, others (McClelland, 1975).  

Power motivation operates across two cognitive levels. Implicit power motivation respresents an unconscious motive that can be assessed via projective tests such as the Picture Story Exercise (PSE) or the Thematic Apperception Test (TAT) where spontaneously constructed narratives are coded for imagery of impact, control, and prestige. Explicit power motivation involves conscious self-conceptions evaluated through self-report questionnaires measuring specific desires for leadership roles, authority, or prestige (Maliszewski et al., 2014; McClelland, 1975).

Research in social neuroscience indicates that implicit power motivation is accompanied by distinct physiological correlates, with individuals with strong implicit nPower exhibiting heightened salivary cortisol and testosterone fluctuations, as well as distinct neural activation patterns in the amygdala and striatum, when confronting nonverbal social cues signalling rank competiton, social defeat, or interpersonal dominance (Rybnicek et al., 2017; Wirth et al., 2006).

=== Personalised vs socialised power across cultures ===
McClelland emphasises that power motivation is not inherently destructive, and distinguished between two distinct expressions or faces of power (McClelland, 1975). Personalised power (pPower) is driven by direct personal domination and status acquisition, often ignoring the needs of those considered to be subordinates. In contrast, socialised pwoer (sPower) is expressed responsibly through empowering others, mentoring, and influencing others in order to meet collective goals and organisational wellbeing (Friederichs et al., 2023; McClelland, 1975). 

Cultural values heavily shape how power motivation is channeled and expressed. In societies characterised by vertical individualism, power is primarily conceptualised as personalised dominance and personal status acquisition. Conversely, in societies characterised by horizontal collectivism, power motivation is more frequently channeled into socialised expressions, such as community leadership, nurturing, and collective helping. Frieze and Boneva further categorised these explicit power expressions into three distinct behavioural dimension: leadership, prominence, and helping (Triandis &amp; Gelfand, 1998).

==Legitimising myths==
Social dominance theory proposes that group hierarchies are maintained not solely through physical coercion, but also through the widespread adoption of legitimising myths—cultural beliefs, values, and attitudes that provide moral and intellectual justification for intergroup relations (Sidanius &amp; Pratto, 1999).

=== Hierarchy-enhancing vs hierarchy-attenuating myths ===
Legitimising myths are categorised based on whether they reinforce or undermine inequality in society. Hierarchy-enhancing legitimising myths consist of ideologies that justify inequality by suggesting that existing group advantages are earned, natural, or just, such as meritocracy, racism, sexism, and caste systems. In comparison, hierarchy-attenuating legitimising myths include ideologies that challenge group inequality and advocate for systemic redistribution and equal rights (Pratto et al., 1994; Sidanius &amp; Pratto, 1999). 

Individuals high in SDO selectively endorse hierarchy-enhancing myths to rationalise their groups privileged position. This endorsement allows them to dismiss societal inequalities as legitimate and understandable consequences of group differences in effort, talent, or intrinsic worth (Pratto et al., 1994; Sidanius &amp; Pratto, 1999).

=== Legitimising narratives in media and institutions ===
Legitimising myths are transmitted and continually reinforced through mainstream media narratives, television, educational curriculums, and social media. By embedding hierarchy-enhancing narratives in public discourse, institutions normalise privilege and make systemic inequality appear invisible or natural. Consequently, legitimising myths serve as the psychological mechanism through which abstract SDO translates into active public support for discriminatory laws, harsher sentencing, and opposition to equity programs (Pratto et al., 1994; Sidanius &amp; Pratto, 1999).

==The link between social dominance orientation and power motivation==
Although Social Dominance Orientation and power motivation both pertain to social rank and hierarchy, they represent distinct psychological constructs operating at different levels of analysis (Ho et al., 2025; Suessenbach et al., 2018).
{| class=&quot;wikitable&quot;
|+Table 2. ''Conceptual comparison between Social Dominance Orientation and Power Motivation - Based on Ho et al. (2015) and McClelland (1975).''
!Feature
!Social Dominance Orientation (SDO)
!Need for Power (nPower)
|-
|'''Primary focus'''
|Group-based social hierarchy and intergroup inequality.
|Interpersonal impact, control, and personal influence.
|-
|'''Level of analysis'''
|Societal / ideological / intergroup level
|Individual / interpersonal / dual levels
|-
|'''Key motivator'''
|Desire for ingroup superiority or systemic group hierarchy
|Desire to direct, control, or impact specific individuals
|-
|'''Behavioural outcome'''
|Endorsing hierarchy-enhancing policy and predudice.
|Leadership emergence, mentoring (sPower) or coercion (pPower)
|}
Social Dominance Orientation reflects a group-level ideological preference for systemic inequality, whereas nPower reflects an individual-level drive for personal impact. Additonally, having high nPower does not automatically equate to having a high SDO.A leader who is driven by strong socialised power (sPower) may seek personal influence specifically to dismantle institutional barriers and promote equality, resulting in low SDO (Friederichs et al., 2023), as seen in the opening scenario. However, an individual with low personal leadership drive may hold high SDO, actively lobbying to protect group privileges and restrict subordinate group advancements without desiring a personal leadership role (Aiello et al., 2013; Ho et al., 2025).

== Political and social behaviour ==
Individual differences in SDO and nPower heavily influence collective political attitudes, voting patterns, and intergroup conflicts. 

=== SDO, right-wing authoritarianism, and political ideology ===
In political psychology, SDO works alongside Right-Wing Authoritarianism (RWA) as dual motivational predictors of prejudice and political conservatism (Duckitt &amp; Sibley, 2010; Perry &amp; Sibley, 2012). Developed by Bob Altemeyer, RWA represents an attitudinal cluster defined by authoritarian submission, authoritarian aggression, and conventionalism (Altemeyer, 1998). SDO and right-wing authoritarianism (RWA) arise from different wordview based roots however both can connect and predict prejudice and political conservatism

Duckitt's dual-process model shows that SDO and RWA arise from fundamentally different worldview roots. SDO stems from viewing the world as a &quot;competitive jungle&quot; where force and dominance determine success, driving a desire for group superiority. in contrast, RWA stems from viewing the world as a &quot;dangerous unstable place&quot; driving a desire for social order, cohesion, and strict conformity to authority (Duckitt &amp; Sibley, 2010). Together, high SDO and high RWA interact to predict strong support for anti-egalitarian political parties, opposition to environmental protection, harsh policies towards immigrants, and endorsement of ingroup violence (Abou-Ismail et al., 2025; Duckitt &amp; Sibley, 2010). &lt;quiz display=&quot;simple&quot;&gt;
{According to the dual-process model, Right Wing Authoritarianism (RWA) is primarily motivated by which worldview?
|type=&quot;()&quot;}
- The world as a competitive jungle 
+ The world as a dangerous chaotic place needing order
- The world as an inherently egalitarian community
&lt;/quiz&gt;
* Key references: (Duckitt &amp; Sibley, 2010), (Ekehammar et al., 2004), (Ward, 1982)

== Power, leadership, and individual differences ==
The interactions between power motivation, social dominance, and biological mechanisms provide a predictor of leadership styles, ethical decision making, and organisational health.

=== Prosocial vs. antisocial leadership ===
Leadership based research demonstrates that identical positions of authority yield starkly different organisational outcomes depending on the leader's underlying motives. Leaders high in personalised power (pPower) and high in SDO are significantly more liekly to employ coercive influence tactics, engage in unethical pro-organisational behaviour, and view subordinates as instruments for self-aggrandisement (Son Hing et al., 2007). In contrast, leaders high in prestige motivation or socialised power (sPower) adopt empowering leadership styles that foster team cohesion, psychological safety, and collective innovation (Cheong et al., 2019; Friederichs et al., 2023; Suessenbach et al., 2018).

{{RoundBoxTop|theme=3}}
'''Case study: power and dominance in cult leadership'''

High personalised power motivation and extreme Social Dominance Orientation can compound to produce destructive, coercive, social structures. In cult environments, charismatic leaders combine intense personal impact with rigid hierarchy enhancing legitimising myths regarding their own absolute superiority (Denrich, 2024; Magee &amp; Galinsky, 2008).

By stripping followers of autonomy, enforcing strict behavioural conformity, and casting all outside groups as inherently inferior, cult leaders exercise extreme personalised dominance. Psychological analysis reveals that such destructive dynamics occur when personal authority (pPower) is unchecked by socialised accountability (sPower), and is reinforced by ideological beliefs in absolute group hierarchy (SDO) (Denrich, 2024).{{RoundBoxBottom}}

* Key references: (Magee &amp; Galinsky, 2008), (Denrich, 2024)

=== Biological basis, gender differences, and situation triggers ===
Neuroimaging and biological studies reveal that human brains possess dedicated neural pathways for processing social rank, territory, and status hierarchies. Brain regions such as the [[wikipedia:Amygdala|amygdala]], the [[wikipedia:Striatum|striatum]], the anterior [[wikipedia:Insular_cortex|insula]], and the [[wikipedia:Intraparietal_sulcus|intraparietal sulcus]], activate during social encounters. 

Across samples, gender differences in SDO are consistently observed, with men scoring higher on average than women/ This phenomenon is explained by SDT's subordinate male target hypothesis and evolutionary bargaining models regarding physical formidability and resource defence. Additionally, situational triggers such as acute intergroup competiton, economic scarcity, or percieved threats to ingroup status can temporarily heighten SDO levels and activate aggressive power-seeking behaviours in individuals who are otherwise egalitarian.
* Key references: (Zink et al., 2008), (Sidanius et al., 2000), (Sidanius et al., 2000)

== Conclusion ==
Social dominance orientation and power motivation are distinct yet related psychological constructs that operate at different levels of analysis. SDO functions as a macro-level ideological preference for group-based hierarchy and intergroup inequality, whereas power motivation functions as a micro-level interpersonal drive for direct influence and control over individuals. 

SDO is rooted in Social Dominance Theory's trimorphic group systems and is evaluated via the SDO7 scale. power motivation manifests as either personalised power or socialised power and is heavily shaped by vertical versus horizontal cultural orientations. Legitimising myths serve as the crucial ideological bridge connecting abstract SDO preferences to real world policy support, whereas SDO and power motivation interact with Right-Wing Authoritarianism and neural rank-processing networks to shape political behaviour and leadership dynamics.

Distinguishing between personal leadership drive and group hierarchy defense provides practical value for organisation, political scientists, and community leaders. Recognising these underlying motives allows institutions to actively foster socialised power and prestige while dismantling coercive dominance and systemic group inequality.
==See also==
* [[wikipedia:Dominance_hierarchy|Dominance hierarchy]]
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] 
* [[wikipedia:Need_for_power|Need for power]] 
* [[wikipedia:Right-wing_authoritarianism|Right wing authoritarianism]] 
* [[w:Self determination theory|Self determination theory]] 
* [http://en.wikipedia.org/wiki/Social_dominance_orientation Social dominance orientation] 
* [[wikipedia:Social_dominance_theory|Social dominance theory]] 
* [[wikipedia:Social_identity_theory|Social identity theory]]

==References==
Provide the references for all citations in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. Alternatively, you can use wiki style (as used on Wikipedia), as long as the information is complete and the formatting is consistent.\

{{Hanging indent|1=

Abou-Ismail, R., Cichocka, A., Phillips, J., &amp; Sengupta, N. K. (2025). Authoritarianism and social dominance as differential predictors of individuals’ support for collective violence. Psychology of Violence, 15(5), 634–644. https://doi.org/10.1037/vio0000580Anderson, 

C., &amp; Kilduff, G. J. (2009). The pursuit of status in social groups. Current Directions in Psychological Science, 18(5), 295–298. https://doi.org/10.1111/.1467-8721.2009.01655.x

Denrich, D. S. (2024). Charismatic leadership and vulnerability: A comprehensive study of cult dynamics. Psychology Presentations. https://digitalcommons.ursinus.edu/psych_pres/11/

Duckitt, J., &amp; Sibley, C. G. (2010). Personality, ideology, prejudice, and politics: A dual‐process motivational model. Journal of Personality, 78(6), 1861–1894. https://doi.org/10.1111/j.1467-6494.2010.00672.x

Ekehammar, B., Akrami, N., Gylje, M., &amp; Zakrisson, I. (2004). What matters most to prejudice: Big five personality, social dominance orientation, or right-wing authoritarianism? European Journal of Personality, 18(6), 463–482. https://doi.org/10.1002/per.526

Ho, A. K., Sidanius, J., Kteily, N., Sheehy-Skeffington, J., Pratto, F., Henkel, K. E., Foels, R., &amp; Stewart, A. L. (2015). The nature of social dominance orientation: Theorizing and measuring preferences for intergroup inequality using the new SDO₇ scale. Journal of Personality and Social Psychology, 109(6), 1003–1028. https://doi.org/10.1037/pspi0000033

Magee, J. C., &amp; Galinsky, A. D. (2008). Social hierarchy: The self‐reinforcing nature of power and status. The Academy of Management Annals, 2(1), 351–398. https://doi.org/10.1080/19416520802211628

McClelland, D. C. (1975). Power : The inner experience. Irvington Publishers.Pratto, F., Sidanius, J., Stallworth, L. M., &amp; Malle, B. F. (1994). Social dominance orientation: A personality variable predicting social and political attitudes. Journal of Personality and Social Psychology, 67(4), 741–763. https://doi.org/10.1037/0022-3514.67.4.741

Rybnicek, R., Bergner, S., &amp; Gutschelhofer, A. (2017). How individual needs influence motivation effects: A neuroscientific study on McClelland’s need theory. Review of Managerial Science, 13(2), 443–482. springer. https://doi.org/10.1007/s11846-017-0252-1

Sidanius, J., Levin, S., Liu, J., &amp; Pratto, F. (2000). Social dominance orientation, anti-egalitarianism and the political psychology of gender: An extension and cross-cultural replication. European Journal of Social Psychology, 30(1), 41–67. https://doi.org/10.1002/(sici)1099-0992(200001/02)30:1&lt;41::aid-ejsp976&gt;3.0.co;2-o

Sidanius, J., &amp; Pratto, F. (2001). Social dominance: An intergroup theory of social hierarchy and oppression. Contemporary Sociology, 30(2), 120. https://doi.org/10.2307/2655372

Son Hing, L. S., Bobocel, D. R., Zanna, M. P., &amp; McBride, M. V. (2007). Authoritarian dynamics and unethical decision making: High social dominance orientation leaders and high right-wing authoritarianism followers. Journal of Personality and Social Psychology, 92(1), 67–81. https://doi.org/10.1037/0022-3514.92.1.67

Triandis, H. C., &amp; Gelfand, M. J. (1998). Converging measurement of horizontal and vertical individualism and collectivism. Journal of Personality and Social Psychology, 74(1), 118–128. https://doi.org/10.1037/0022-3514.74.1.118

Ward, D. (1982). Right-wing authoritarianism. . American Political Science Review, 76(3), 737–738. https://doi.org/10.2307/1963836

Wilson, M. S., &amp; Liu, J. H. (2003). Social dominance orientation and gender: The moderating role of gender identity. British Journal of Social Psychology, 42(2), 187–198. https://doi.org/10.1348/014466603322127175

Wirth, M. M., Welsh, K. M., &amp; Schultheiss, O. C. (2006). Salivary cortisol changes in humans after winning or losing a dominance contest depend on implicit power motivation. Hormones and Behavior, 49(3), 346–352. https://doi.org/10.1016/j.yhbeh.2005.08.013

Zink, C. F., Tong, Y., Chen, Q., Bassett, D. S., Stein, J. L., &amp; Meyer-Lindenberg, A. (2008). Know your place: Neural processing of social hierarchy in humans. Neuron, 58(2), 273–283. https://doi.org/10.1016/j.neuron.2008.01.025

}}

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[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Dominance]]
[[Category:Motivation and emotion/Book/Power motivation]]
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      <text bytes="31398" sha1="ax9y1imepj9e2a04ehl5kb9451plgqm" xml:space="preserve">{{title|Social dominance and power motivation:&lt;br&gt;What is the relationship between social dominance and power motivation?}}
__TOC__
==Overview==
{{RoundBoxTop|theme=3}}
[[File:Noun Staff Management 4185.svg|Management chart right|thumb|200px|'''Figure 1'''. Power hierarchy in the workplace]]

'''Scenario: Raising up vs. pushing down.'''

Two graduates start the same week at a large firm. One quickly puts their hand up to lead every project going, coordinating people, chasing decisions, and making sure things get done — and uses that influence to actively mentor junior colleagues and push for flatter, fairer pay structures. The other has no interest in leading projects or managing anyone, yet defends the firm's steep hierarchy (see Figure 1) as natural and fair: &quot;some people are just better suited to being in charge, and the system reflects that.&quot; They also actively lobbies against a new scheme providing staff from under-represented backgrounds with better access to mentoring, training, and development opportunities, arguing certain groups should stay in junior roles &quot;where they belong&quot; and pushing to have the scheme scrapped. Both are equally competent. Why does one seem driven to personally influence the people around them, while the other — without wanting any personal authority — is instead driven to keep entire groups beneath others?

{{RoundBoxBottom}}
Human societies are fundamentally structured around social hierarchies (Magee &amp; Galinsky, 2008; Sidanius &amp; Pratto, 1999), however the psychological factors that lead individuals to navigate, challenge, or enforce these hierarchies can vary significantly. Power motivation and social dominance are two distinct yet related psychological constructs that explain different aspects of hierarchy seeking behaviour in human societies. Social Dominance Orientation (SDO) is defined as a preference for one's ingroup to dominate outgroups viewed as lesser and a general desire for group-based inequality (Ho et al., 2015; Pratto et al., 1994). In contrast, power motivation (nPower) represents an individuals personal drive to have influence, control, or psychological impact over specific individuals (McClelland, 1975).

While these constructs frequently overlap in everyday social interactions, psychological science demonstrates that they operate at fundamentally different levels when it comes to analysis: group-based ideological preference versus interpersonal motivation (Ho et al., 2015; Suessenbach et al., 2018). Clarifying the distinction between social dominance and power motivation is essential as both constructs can predict real world outcomes, including leadership emergence, support for discriminatory policies, workplace dynamics, and the specific influence and control tactics individuals choose to employ when power is attained (Aiello et al., 2013; Cheng et al., 2013). By examining frameworks such as Social Dominance Theory, McClelland's Need Theory, and modern neuroscientific findings, psychological science provides diagnostic tools such as SDO7 scales and implicit motive coding to evaluate why individuals seek status and how they exercise power once it is gained (Ho et al., 2015; McClelland, 1975).

{{RoundBoxTop|theme=3}}

'''Focus questions'''

* What is social dominance orientation, and how does it relate to broader group hierarchies?
* What is power motivation (nPower), and how is it expressed differently across different demographics and cultural contexts? 
* How do legitimising myths sustain or challenge social hierarchies?
* How do SDO and power motivation shape political attitudes, leadership styles, and intergroup behaviours?

{{RoundBoxBottom}}

==Social dominance orientation==
Social dominance orientation represents a core attitudinal personality variable within intergroup psychology, revealing an individuals stance regarding group-based equality versus group-based hierarchy (Pratto et al., 1994). Understanding social dominance orientation requires an examination of its theoretical origins within Social Dominance Theory, it's sub-dimensional structures, and its broader predictive validity across societal domains.

=== Origins in social dominance theory ===
[[wikipedia:Social_dominance_orientation|Social dominance theory]] (SDT), developed by Jim Sidanius and Felicia Pratto, opens with the observation that all human societies producing an economic surplus naturally develop group-based social hierarchies (Sidanius &amp; Pratto, 1999). SDT identifies three distinct forms of trimorphic social hierarchies that form the structure of human societies. The age system, which grants adults disproportionate power and social status compared to children; patriarchy, referring to systems where men hold greater political, social, and economic authority than women; and the arbitrary-set system which encompasses culturally constructed social categories such as race, ethnicity, religion, social class, nationality, or caste, that are hierarchically ordered with unequal access to power, opportunity, and privileges (Sidanius &amp; Pratto, 1999).  

According to SDT, social institutions such as legal systems, criminal courts, educational systems, and corporations sustain these group hierarchies through institutional discrimination (Sidanius &amp; Pratto, 1999). Institutions maintain hierarchy by disproportionately allocating positive social value, such as wealth, healthcare, prestige, and educational access, to dominant groups. Additionally, institutions direct negative social value, including harsher criminal penalties, dangerous labour, and poverty, towards subordinate groups (Pratto et al., 1994; Sidanius &amp; Pratto, 1999). 

=== Measuring social dominance orientation and what it predicts ===

{| class=&quot;wikitable&quot; style=&quot;float:right; clear:right; width:400px; margin:0 0 1em 1.5em; text-align:center; background-color:#f9f9f9; border:1px solid #aaa;&quot;
|-
! colspan=&quot;2&quot; style=&quot;background-color:#f9f9f9; font-size:110%; padding:8px; border:none;&quot; | Figure 2. Dimensional structure of SDO7&lt;br&gt;&lt;small style=&quot;font-weight:normal;&quot;&gt;&lt;em&gt;Based on Ho et al. (2015)&lt;/em&gt;&lt;/small&gt;
|-
| colspan=&quot;2&quot; style=&quot;background-color:#eef; padding:10px; border:1px solid #aaa;&quot; | '''Social Dominance Orientation (SDO)'''&lt;br&gt;&lt;small&gt;(Preference for group inequality)&lt;/small&gt;
|-
| style=&quot;width:50%; vertical-align:top; background-color:#fff; padding:10px; border:1px solid #aaa; text-align:left;&quot; |
'''SDO-Dominance (SDO-D)'''
* Active group oppression
* Overt group superiority
* Direct intergroup action again outgorups
| style=&quot;width:50%; vertical-align:top; background-color:#fff; padding:10px; border:1px solid #aaa; text-align:left;&quot; |
'''SDO-Egalitarianism (SDO-E)'''
* Opposition to group equality
* Opposition to equity/social schemes
* Subtle institutional bias
|}
To evaluate individual differences in support for group-based hierarchy, researchers constructed the SDO scale, with the newer SDO7 scale dividing the construct into two sub-dimensions (Ho et al., 2015; see Figure 2). The first dimension, SDO-Dominance (SDO-D) assesses support for active, explicit group oppression and the forced subjugation of outgroups. The second dimension, SDO-Egalitarianism (SDO-E) assesses generalised oppositon to group equality, manifesting as subtle resistance to social welfare, affirmative actions, and equality-promoting policies (Ho et al., 2015, 2025).

Empirical cross-cultural research confirms that high SDO scores predict intergroup prejudice, ethnocentrism, sexism, homophobia, and support for harsher criminal justice policies (Pratto et al., 1994). Additionally, individuals selectively self-segregate into specific societal roles based on their SDO levels. High-SDO individuals gravitate towards heirarchy-enhancing roles that reinforce existing social stratification, such as executives, criminal prosecutors, and police officers. In comparison, low-SDO individuals seek out hierarchy-reducing roles that challenge systemic inequality, such as human rights lawyers, public defenders, and social workers (Pratto et al., 1994; Sidanius &amp; Pratto, 1999).


The SD07 scale distinguished between two sub-dimensions: SDO-Dominance (SDO-D) which involves support for active group oppression and SDO-Egalitarianism (SDO-E) which reflects a preference for group inequality and is linked to more subtle forms of prejudice and inequality as well as opposition to equality-promoting policies.&lt;quiz display=&quot;simple&quot;&gt;
{Which form of hierarchy in Social Dominance Theory involves culturally defined categories like race, ethnicity, or religion?
|type=&quot;()&quot;}
- The age system
- Patriarchy
+ The arbitrary-set system

{High-SDO individuals are most likely to select which of the following career paths?
|type=&quot;()&quot;}
- Hierarchy-reducing roles like public defenders
+ Hierarchy-enhancing roles like corporate executives
&lt;/quiz&gt;
==Power motivation==
Power motivation, commonly referred to as the Need for Power (nPower) is a psychological construct describing an individuals drive to exert impact, control, or influence over others and their surrounding environment (McClelland, 1975). First conceptualised by Henry Murray in taxonomy of fundamental human needs, and later expanded upon by David McClelland in his Three Needs Theory, power motivation represents a primary driver of status-seeking, interpersonal dynamics, and leadership emergence (McClelland, 1975; Suessenbach et al., 2018). Rather than representing a purely manipulative or antisocial trait, power motivation exists along a broad psychological spectrum. It ranges from personalised power (pPower), which is characterised by direct control, self-aggrandisement, and zero-sum competition, to socialised power (sPower) where influence is channelled towards supporting and empowering others, mentoring, and achieving collective goals (McClelland, 1975; Friederichs et al., 2023). 

=== McClelland's need theory and measurement ===
McClelland proposed vary in the relative strength of three learned needs: the Need for Power (nPower), the Need for Achievement (nAch) and the Need for Affiliation (nAff), with nPower reflecting a desire to have an impact on, or control over, others (McClelland, 1975).  

Power motivation operates across two cognitive levels. Implicit power motivation respresents an unconscious motive that can be assessed via projective tests such as the Picture Story Exercise (PSE) or the Thematic Apperception Test (TAT) where spontaneously constructed narratives are coded for imagery of impact, control, and prestige. Explicit power motivation involves conscious self-conceptions evaluated through self-report questionnaires measuring specific desires for leadership roles, authority, or prestige (Maliszewski et al., 2014; McClelland, 1975).

Research in social neuroscience indicates that implicit power motivation is accompanied by distinct physiological correlates, with individuals with strong implicit nPower exhibiting heightened salivary cortisol and testosterone fluctuations, as well as distinct neural activation patterns in the amygdala and striatum, when confronting nonverbal social cues signalling rank competiton, social defeat, or interpersonal dominance (Rybnicek et al., 2017; Wirth et al., 2006).

=== Personalised vs socialised power across cultures ===
McClelland emphasises that power motivation is not inherently destructive, and distinguished between two distinct expressions or faces of power (McClelland, 1975). Personalised power (pPower) is driven by direct personal domination and status acquisition, often ignoring the needs of those considered to be subordinates. In contrast, socialised pwoer (sPower) is expressed responsibly through empowering others, mentoring, and influencing others in order to meet collective goals and organisational wellbeing (Friederichs et al., 2023; McClelland, 1975). 

Cultural values heavily shape how power motivation is channeled and expressed. In societies characterised by vertical individualism, power is primarily conceptualised as personalised dominance and personal status acquisition. Conversely, in societies characterised by horizontal collectivism, power motivation is more frequently channeled into socialised expressions, such as community leadership, nurturing, and collective helping. Frieze and Boneva further categorised these explicit power expressions into three distinct behavioural dimension: leadership, prominence, and helping (Triandis &amp; Gelfand, 1998).

==Legitimising myths==
Social dominance theory proposes that group hierarchies are maintained not solely through physical coercion, but also through the widespread adoption of legitimising myths—cultural beliefs, values, and attitudes that provide moral and intellectual justification for intergroup relations (Sidanius &amp; Pratto, 1999).

=== Hierarchy-enhancing vs hierarchy-attenuating myths ===
Legitimising myths are categorised based on whether they reinforce or undermine inequality in society. Hierarchy-enhancing legitimising myths consist of ideologies that justify inequality by suggesting that existing group advantages are earned, natural, or just, such as meritocracy, racism, sexism, and caste systems. In comparison, hierarchy-attenuating legitimising myths include ideologies that challenge group inequality and advocate for systemic redistribution and equal rights (Pratto et al., 1994; Sidanius &amp; Pratto, 1999). 

Individuals high in SDO selectively endorse hierarchy-enhancing myths to rationalise their groups privileged position. This endorsement allows them to dismiss societal inequalities as legitimate and understandable consequences of group differences in effort, talent, or intrinsic worth (Pratto et al., 1994; Sidanius &amp; Pratto, 1999).

=== Legitimising narratives in media and institutions ===
Legitimising myths are transmitted and continually reinforced through mainstream media narratives, television, educational curriculums, and social media. By embedding hierarchy-enhancing narratives in public discourse, institutions normalise privilege and make systemic inequality appear invisible or natural. Consequently, legitimising myths serve as the psychological mechanism through which abstract SDO translates into active public support for discriminatory laws, harsher sentencing, and opposition to equity programs (Pratto et al., 1994; Sidanius &amp; Pratto, 1999).

==The link between social dominance orientation and power motivation==
Although Social Dominance Orientation and power motivation both pertain to social rank and hierarchy, they represent distinct psychological constructs operating at different levels of analysis (Ho et al., 2025; Suessenbach et al., 2018).
{| class=&quot;wikitable&quot;
|+Table 2. ''Conceptual comparison between Social Dominance Orientation and Power Motivation - Based on Ho et al. (2015) and McClelland (1975).''
!Feature
!Social Dominance Orientation (SDO)
!Need for Power (nPower)
|-
|'''Primary focus'''
|Group-based social hierarchy and intergroup inequality.
|Interpersonal impact, control, and personal influence.
|-
|'''Level of analysis'''
|Societal / ideological / intergroup level
|Individual / interpersonal / dual levels
|-
|'''Key motivator'''
|Desire for ingroup superiority or systemic group hierarchy
|Desire to direct, control, or impact specific individuals
|-
|'''Behavioural outcome'''
|Endorsing hierarchy-enhancing policy and predudice.
|Leadership emergence, mentoring (sPower) or coercion (pPower)
|}
Social Dominance Orientation reflects a group-level ideological preference for systemic inequality, whereas nPower reflects an individual-level drive for personal impact. Additonally, having high nPower does not automatically equate to having a high SDO.A leader who is driven by strong socialised power (sPower) may seek personal influence specifically to dismantle institutional barriers and promote equality, resulting in low SDO (Friederichs et al., 2023), as seen in the opening scenario. However, an individual with low personal leadership drive may hold high SDO, actively lobbying to protect group privileges and restrict subordinate group advancements without desiring a personal leadership role (Aiello et al., 2013; Ho et al., 2025).

== Political and social behaviour ==
Individual differences in SDO and nPower heavily influence collective political attitudes, voting patterns, and intergroup conflicts. 

=== SDO, right-wing authoritarianism, and political ideology ===
In political psychology, SDO works alongside Right-Wing Authoritarianism (RWA) as dual motivational predictors of prejudice and political conservatism (Duckitt &amp; Sibley, 2010; Perry &amp; Sibley, 2012). Developed by Bob Altemeyer, RWA represents an attitudinal cluster defined by authoritarian submission, authoritarian aggression, and conventionalism (Altemeyer, 1998). SDO and right-wing authoritarianism (RWA) arise from different wordview based roots however both can connect and predict prejudice and political conservatism

Duckitt's dual-process model shows that SDO and RWA arise from fundamentally different worldview roots. SDO stems from viewing the world as a &quot;competitive jungle&quot; where force and dominance determine success, driving a desire for group superiority. in contrast, RWA stems from viewing the world as a &quot;dangerous unstable place&quot; driving a desire for social order, cohesion, and strict conformity to authority (Duckitt &amp; Sibley, 2010). Together, high SDO and high RWA interact to predict strong support for anti-egalitarian political parties, opposition to environmental protection, harsh policies towards immigrants, and endorsement of ingroup violence (Abou-Ismail et al., 2025; Duckitt &amp; Sibley, 2010). &lt;quiz display=&quot;simple&quot;&gt;
{According to the dual-process model, Right Wing Authoritarianism (RWA) is primarily motivated by which worldview?
|type=&quot;()&quot;}
- The world as a competitive jungle 
+ The world as a dangerous chaotic place needing order
- The world as an inherently egalitarian community
&lt;/quiz&gt;
* Key references: (Duckitt &amp; Sibley, 2010), (Ekehammar et al., 2004), (Ward, 1982)

== Power, leadership, and individual differences ==
The interactions between power motivation, social dominance, and biological mechanisms provide a predictor of leadership styles, ethical decision making, and organisational health.

=== Prosocial vs. antisocial leadership ===
Leadership based research demonstrates that identical positions of authority yield starkly different organisational outcomes depending on the leader's underlying motives. Leaders high in personalised power (pPower) and high in SDO are significantly more liekly to employ coercive influence tactics, engage in unethical pro-organisational behaviour, and view subordinates as instruments for self-aggrandisement (Son Hing et al., 2007). In contrast, leaders high in prestige motivation or socialised power (sPower) adopt empowering leadership styles that foster team cohesion, psychological safety, and collective innovation (Cheong et al., 2019; Friederichs et al., 2023; Suessenbach et al., 2018).

{{RoundBoxTop|theme=3}}
'''Case study: power and dominance in cult leadership'''

High personalised power motivation and extreme Social Dominance Orientation can compound to produce destructive, coercive, social structures. In cult environments, charismatic leaders combine intense personal impact with rigid hierarchy enhancing legitimising myths regarding their own absolute superiority (Denrich, 2024; Magee &amp; Galinsky, 2008).

By stripping followers of autonomy, enforcing strict behavioural conformity, and casting all outside groups as inherently inferior, cult leaders exercise extreme personalised dominance. Psychological analysis reveals that such destructive dynamics occur when personal authority (pPower) is unchecked by socialised accountability (sPower), and is reinforced by ideological beliefs in absolute group hierarchy (SDO) (Denrich, 2024).{{RoundBoxBottom}}

=== Biological basis, gender differences, and situation triggers ===
Neuroimaging and biological studies reveal that human brains possess dedicated neural pathways for processing social rank, territory, and status hierarchies. Brain regions such as the [[wikipedia:Amygdala|amygdala]], the [[wikipedia:Striatum|striatum]], the anterior [[wikipedia:Insular_cortex|insula]], and the [[wikipedia:Intraparietal_sulcus|intraparietal sulcus]], activate during social encounters involving rank (Watanabe &amp; Yamamoto, 2015). Individual differences in SDO have also been linked to neural sensitivity (Adrián-Ventura et al., 2026; Ligneul et al., 2017)). 

Across samples, gender differences in SDO are consistently observed, with men scoring higher on average than women (Sidanius &amp; Pratto, 1999). This is explained by SDT's subordinate male target hypothesis and evolutionary bargaining models regarding physical formidability and resource defence (Sidanius &amp; Pratto, 1999). Additionally, situational triggers such as acute intergroup competition, economic scarcity, or percieved threats to ingroup status can temporarily heighten SDO levels and activate aggressive power-seeking behaviours in individuals who are otherwise egalitarian individuals (Ho et al., 2025).

== Conclusion ==
Social dominance orientation and power motivation are distinct yet related psychological constructs that operate at different levels of analysis. SDO functions as a macro-level ideological preference for group-based hierarchy and intergroup inequality, whereas power motivation functions as a micro-level interpersonal drive for direct influence and control over individuals (Ho et al., 2025; McClelland, 1975). 

SDO is rooted in Social Dominance Theory's trimorphic group systems and is evaluated via the SDO7 scale (Ho et al., 2015; Sidanius &amp; Pratto, 1999). Power motivation manifests as either personalised power or socialised power and is heavily shaped by vertical versus horizontal cultural orientations (McClelland, 1975; Triandis &amp; Gelfand, 1998). Legitimising myths serve as the crucial ideological bridge connecting abstract SDO preferences to real world policy support (Pratto et al., 1994), whereas SDO and power motivation interact with Right-Wing Authoritarianism and neural rank-processing networks to shape political behaviour and leadership dynamics (Duckitt &amp; Sibley, 2010).

Distinguishing between personal leadership drive and group hierarchy defense provides practical value for organisation, political scientists, and community leaders. Recognising these underlying motives allows institutions to actively foster socialised power and prestige while dismantling coercive dominance and systemic group inequality (Cheng, 2020; (Friederichs et al., 2023).

==See also==
* [[wikipedia:Dominance_hierarchy|Dominance hierarchy]]
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] 
* [[wikipedia:Need_for_power|Need for power]] 
* [[wikipedia:Right-wing_authoritarianism|Right wing authoritarianism]] 
* [[w:Self determination theory|Self determination theory]] 
* [http://en.wikipedia.org/wiki/Social_dominance_orientation Social dominance orientation] 
* [[wikipedia:Social_dominance_theory|Social dominance theory]] 
* [[wikipedia:Social_identity_theory|Social identity theory]]

==References==
Provide the references for all citations in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. Alternatively, you can use wiki style (as used on Wikipedia), as long as the information is complete and the formatting is consistent.\

{{Hanging indent|1=

Abou-Ismail, R., Cichocka, A., Phillips, J., &amp; Sengupta, N. K. (2025). Authoritarianism and social dominance as differential predictors of individuals’ support for collective violence. Psychology of Violence, 15(5), 634–644. https://doi.org/10.1037/vio0000580

Adrián-Ventura, J., Fasce, A., Miró-Padilla, A., Cherednichenko, A., Ávila, C., &amp; Avendaño, D. (2026). Neuroanatomical correlates of social dominance orientation and the contributing role of reward sensitivity. Current Psychology, 45(13), Article 1168. https://doi.org/10.1007/s12144-026-09740-z

Aiello, A., Pratto, F., &amp; Pierro, A. (2013). Framing social dominance orientation and power in organizational context. Basic and Applied Social Psychology, 35(5), 487–495. https://doi.org/10.1080/01973533.2013.823614

Altemeyer, B. (1998). The other “authoritarian personality”. Advances in Experimental Social Psychology, 30, 47–92. https://doi.org/10.1016/s0065-2601(08)60382-2

Cheng, J. T. (2020). Dominance, prestige, and the role of leveling in human social hierarchy and equality. Current Opinion in Psychology, 33, 238–244. https://doi.org/10.1016/j.copsyc.2019.10.004

Cheng, J. T., Tracy, J. L., Foulsham, T., Kingstone, A., &amp; Henrich, J. (2013). Two ways to the top: Evidence that dominance and prestige are distinct yet viable avenues to social rank and influence. Journal of Personality and Social Psychology, 104(1), 103–125. https://doi.org/10.1037/a0030398

Cheng, J. T., Tracy, J. L., &amp; Henrich, J. (2010). Pride, personality, and the evolutionary foundations of human social status. Evolution and Human Behavior, 31(5), 334–347. https://doi.org/10.1016/j.evolhumbehav.2010.02.004

Cheong, M., Yammarino, F. J., Dionne, S. D., Spain, S. M., &amp; Tsai, C.-Y. (2019). A review of the effectiveness of empowering leadership. The Leadership Quarterly, 30(1).

Denrich, D. S. (2024). Charismatic leadership and vulnerability: A comprehensive study of cult dynamics. Psychology Presentations. https://digitalcommons.ursinus.edu/psych_pres/11/

Duckitt, J., &amp; Sibley, C. G. (2010). Personality, ideology, prejudice, and politics: A dual‐process motivational model. Journal of Personality, 78(6), 1861–1894. https://doi.org/10.1111/j.1467-6494.2010.00672.x

Friederichs, K. M., Waldenmeier, K., &amp; Baumann, N. (2023). The benefits of prosocial power motivation in leadership: Action orientation fosters a win-win. Plos One, 18(7), e0287394–e0287394. https://doi.org/10.1371/journal.pone.0287394

Ho, A. K., Kteily, N. S., Sheehy-Skeffington, J., &amp; Thomsen, L. (2025). Social dominance orientation: The motivational basis of intergroup inequality. Advances in Experimental Social Psychology, 72, 125–208. https://doi.org/10.1016/bs.aesp.2025.04.003

Ho, A. K., Sidanius, J., Kteily, N., Sheehy-Skeffington, J., Pratto, F., Henkel, K. E., Foels, R., &amp; Stewart, A. L. (2015). The nature of social dominance orientation: Theorizing and measuring preferences for intergroup inequality using the new SDO₇ scale. Journal of Personality and Social Psychology, 109(6), 1003–1028. https://doi.org/10.1037/pspi0000033

Ligneul, R., Girard, R., &amp; Dreher, J.-C. (2017). Social brains and divides: The interplay between social dominance orientation and the neural sensitivity to hierarchical ranks. Scientific Reports, 7(1). https://doi.org/10.1038/srep45920

Magee, J. C., &amp; Galinsky, A. D. (2008). Social hierarchy: The self‐reinforcing nature of power and status. The Academy of Management Annals, 2(1), 351–398. https://doi.org/10.1080/19416520802211628

Maliszewski, N., Kuźmińska, A. O., Wieczorkowska-Wierzbińska, G., &amp; Werner-Maliszewska, A. (2014). The impact of explicit and implicit power motivation on educational choices. Polish Psychological Bulletin, 45(3), 275–285. https://doi.org/10.2478/ppb-2014-0034

McClelland, D. C. (1975). Power: The inner experience. American Journal of Sociology, 82(5). https://doi.org/10.1086/226461

Perry, R., &amp; Sibley, C. G. (2012). Big-five personality prospectively predicts social dominance orientation and right-wing authoritarianism. Personality and Individual Differences, 52(1), 3–8. https://doi.org/10.1016/j.paid.2011.08.009

Pratto, F., Sidanius, J., Stallworth, L. M., &amp; Malle, B. F. (1994). Social dominance orientation: A personality variable predicting social and political attitudes. Journal of Personality and Social Psychology, 67(4), 741–763. https://doi.org/10.1037/0022-3514.67.4.741

Rybnicek, R., Bergner, S., &amp; Gutschelhofer, A. (2017). How individual needs influence motivation effects: A neuroscientific study on mcclelland’s need theory. Review of Managerial Science, 13(2), 443–482. springer. https://doi.org/10.1007/s11846-017-0252-1

Sidanius, J., &amp; Pratto, F. (1999). Social dominance: An intergroup theory of social hierarchy and oppression. Cambridge University Press. https://doi.org/10.1017/cbo9781139175043

Son Hing, L. S., Bobocel, D. R., Zanna, M. P., &amp; McBride, M. V. (2007). Authoritarian dynamics and unethical decision making: High social dominance orientation leaders and high right-wing authoritarianism followers. Journal of Personality and Social Psychology, 92(1), 67–81. https://doi.org/10.1037/0022-3514.92.1.67

Suessenbach, F., Loughnan, S., Schönbrodt, F. D., &amp; Moore, A. B. (2018). The dominance, prestige, and leadership account of social power motives. European Journal of Personality, 33(1), 7–33. https://doi.org/10.1002/per.2184

Triandis, H. C., &amp; Gelfand, M. J. (1998). Converging measurement of horizontal and vertical individualism and collectivism. Journal of Personality and Social Psychology, 74(1), 118–128. https://doi.org/10.1037/0022-3514.74.1.118

Watanabe, N., &amp; Yamamoto, M. (2015). Neural mechanisms of social dominance. Frontiers in Neuroscience, 9. https://doi.org/10.3389/fnins.2015.00154

Wirth, M. M., Welsh, K. M., &amp; Schultheiss, O. C. (2006). Salivary cortisol changes in humans after winning or losing a dominance contest depend on implicit power motivation. Hormones and Behavior, 49(3), 346–352. https://doi.org/10.1016/j.yhbeh.2005.08.013

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[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Dominance]]
[[Category:Motivation and emotion/Book/Power motivation]]
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      <text bytes="31135" sha1="29y3bbpnghvq6wvdni7hqwvhsffmx73" xml:space="preserve">{{title|Social dominance and power motivation:&lt;br&gt;What is the relationship between social dominance and power motivation?}}
__TOC__
==Overview==
{{RoundBoxTop|theme=3}}
[[File:Noun Staff Management 4185.svg|Management chart right|thumb|200px|'''Figure 1'''. Power hierarchy in the workplace]]

'''Scenario: Raising up vs. pushing down.'''

Two graduates start the same week at a large firm. One quickly puts their hand up to lead every project going, coordinating people, chasing decisions, and making sure things get done — and uses that influence to actively mentor junior colleagues and push for flatter, fairer pay structures. The other has no interest in leading projects or managing anyone, yet defends the firm's steep hierarchy (see Figure 1) as natural and fair: &quot;some people are just better suited to being in charge, and the system reflects that.&quot; They also actively lobbies against a new scheme providing staff from under-represented backgrounds with better access to mentoring, training, and development opportunities, arguing certain groups should stay in junior roles &quot;where they belong&quot; and pushing to have the scheme scrapped. Both are equally competent. Why does one seem driven to personally influence the people around them, while the other — without wanting any personal authority — is instead driven to keep entire groups beneath others?

{{RoundBoxBottom}}
Human societies are fundamentally structured around social hierarchies (Magee &amp; Galinsky, 2008; Sidanius &amp; Pratto, 1999), however the psychological factors that lead individuals to navigate, challenge, or enforce these hierarchies can vary significantly. Power motivation and social dominance are two distinct yet related psychological constructs that explain different aspects of hierarchy seeking behaviour in human societies. Social Dominance Orientation (SDO) is defined as a preference for one's ingroup to dominate outgroups viewed as lesser and a general desire for group-based inequality (Ho et al., 2015; Pratto et al., 1994). In contrast, power motivation (nPower) represents an individuals personal drive to have influence, control, or psychological impact over specific individuals (McClelland, 1975).

While these constructs frequently overlap in everyday social interactions, psychological science demonstrates that they operate at fundamentally different levels when it comes to analysis: group-based ideological preference versus interpersonal motivation (Ho et al., 2015; Suessenbach et al., 2018). Clarifying the distinction between social dominance and power motivation is essential as both constructs can predict real world outcomes, including leadership emergence, support for discriminatory policies, workplace dynamics, and the specific influence and control tactics individuals choose to employ when power is attained (Aiello et al., 2013; Cheng et al., 2013). By examining frameworks such as Social Dominance Theory, McClelland's Need Theory, and modern neuroscientific findings, psychological science provides diagnostic tools such as SDO7 scales and implicit motive coding to evaluate why individuals seek status and how they exercise power once it is gained (Ho et al., 2015; McClelland, 1975).

{{RoundBoxTop|theme=3}}

'''Focus questions'''

* What is social dominance orientation, and how does it relate to broader group hierarchies?
* What is power motivation (nPower), and how is it expressed differently across different demographics and cultural contexts? 
* How do legitimising myths sustain or challenge social hierarchies?
* How do SDO and power motivation shape political attitudes, leadership styles, and intergroup behaviours?

{{RoundBoxBottom}}

==Social dominance orientation==
Social dominance orientation represents a core attitudinal personality variable within intergroup psychology, revealing an individuals stance regarding group-based equality versus group-based hierarchy (Pratto et al., 1994). Understanding social dominance orientation requires an examination of its theoretical origins within Social Dominance Theory, it's sub-dimensional structures, and its broader predictive validity across societal domains.

=== Origins in social dominance theory ===
[[wikipedia:Social_dominance_orientation|Social dominance theory]] (SDT), developed by Jim Sidanius and Felicia Pratto, opens with the observation that all human societies producing an economic surplus naturally develop group-based social hierarchies (Sidanius &amp; Pratto, 1999). SDT identifies three distinct forms of trimorphic social hierarchies that form the structure of human societies. The age system, which grants adults disproportionate power and social status compared to children; patriarchy, referring to systems where men hold greater political, social, and economic authority than women; and the arbitrary-set system which encompasses culturally constructed social categories such as race, ethnicity, religion, social class, nationality, or caste, that are hierarchically ordered with unequal access to power, opportunity, and privileges (Sidanius &amp; Pratto, 1999).  

According to SDT, social institutions such as legal systems, criminal courts, educational systems, and corporations sustain these group hierarchies through institutional discrimination (Sidanius &amp; Pratto, 1999). Institutions maintain hierarchy by disproportionately allocating positive social value, such as wealth, healthcare, prestige, and educational access, to dominant groups. Additionally, institutions direct negative social value, including harsher criminal penalties, dangerous labour, and poverty, towards subordinate groups (Pratto et al., 1994; Sidanius &amp; Pratto, 1999). 

=== Measuring social dominance orientation and what it predicts ===

{| class=&quot;wikitable&quot; style=&quot;float:right; clear:right; width:400px; margin:0 0 1em 1.5em; text-align:center; background-color:#f9f9f9; border:1px solid #aaa;&quot;
|-
! colspan=&quot;2&quot; style=&quot;background-color:#f9f9f9; font-size:110%; padding:8px; border:none;&quot; | Figure 2. Dimensional structure of SDO7&lt;br&gt;&lt;small style=&quot;font-weight:normal;&quot;&gt;&lt;em&gt;Based on Ho et al. (2015)&lt;/em&gt;&lt;/small&gt;
|-
| colspan=&quot;2&quot; style=&quot;background-color:#eef; padding:10px; border:1px solid #aaa;&quot; | '''Social Dominance Orientation (SDO)'''&lt;br&gt;&lt;small&gt;(Preference for group inequality)&lt;/small&gt;
|-
| style=&quot;width:50%; vertical-align:top; background-color:#fff; padding:10px; border:1px solid #aaa; text-align:left;&quot; |
'''SDO-Dominance (SDO-D)'''
* Active group oppression
* Overt group superiority
* Direct intergroup action again outgorups
| style=&quot;width:50%; vertical-align:top; background-color:#fff; padding:10px; border:1px solid #aaa; text-align:left;&quot; |
'''SDO-Egalitarianism (SDO-E)'''
* Opposition to group equality
* Opposition to equity/social schemes
* Subtle institutional bias
|}
To evaluate individual differences in support for group-based hierarchy, researchers constructed the SDO scale, with the newer SDO7 scale dividing the construct into two sub-dimensions (Ho et al., 2015; see Figure 2). The first dimension, SDO-Dominance (SDO-D) assesses support for active, explicit group oppression and the forced subjugation of outgroups. The second dimension, SDO-Egalitarianism (SDO-E) assesses generalised oppositon to group equality, manifesting as subtle resistance to social welfare, affirmative actions, and equality-promoting policies (Ho et al., 2015, 2025).

Empirical cross-cultural research confirms that high SDO scores predict intergroup prejudice, ethnocentrism, sexism, homophobia, and support for harsher criminal justice policies (Pratto et al., 1994). Additionally, individuals selectively self-segregate into specific societal roles based on their SDO levels. High-SDO individuals gravitate towards heirarchy-enhancing roles that reinforce existing social stratification, such as executives, criminal prosecutors, and police officers. In comparison, low-SDO individuals seek out hierarchy-reducing roles that challenge systemic inequality, such as human rights lawyers, public defenders, and social workers (Pratto et al., 1994; Sidanius &amp; Pratto, 1999).


The SD07 scale distinguished between two sub-dimensions: SDO-Dominance (SDO-D) which involves support for active group oppression and SDO-Egalitarianism (SDO-E) which reflects a preference for group inequality and is linked to more subtle forms of prejudice and inequality as well as opposition to equality-promoting policies.&lt;quiz display=&quot;simple&quot;&gt;
{Which form of hierarchy in Social Dominance Theory involves culturally defined categories like race, ethnicity, or religion?
|type=&quot;()&quot;}
- The age system
- Patriarchy
+ The arbitrary-set system

{High-SDO individuals are most likely to select which of the following career paths?
|type=&quot;()&quot;}
- Hierarchy-reducing roles like public defenders
+ Hierarchy-enhancing roles like corporate executives
&lt;/quiz&gt;
==Power motivation==
Power motivation, commonly referred to as the Need for Power (nPower) is a psychological construct describing an individuals drive to exert impact, control, or influence over others and their surrounding environment (McClelland, 1975). First conceptualised by Henry Murray in taxonomy of fundamental human needs, and later expanded upon by David McClelland in his Three Needs Theory, power motivation represents a primary driver of status-seeking, interpersonal dynamics, and leadership emergence (McClelland, 1975; Suessenbach et al., 2018). Rather than representing a purely manipulative or antisocial trait, power motivation exists along a broad psychological spectrum. It ranges from personalised power (pPower), which is characterised by direct control, self-aggrandisement, and zero-sum competition, to socialised power (sPower) where influence is channelled towards supporting and empowering others, mentoring, and achieving collective goals (McClelland, 1975; Friederichs et al., 2023). 

=== McClelland's need theory and measurement ===
McClelland proposed vary in the relative strength of three learned needs: the Need for Power (nPower), the Need for Achievement (nAch) and the Need for Affiliation (nAff), with nPower reflecting a desire to have an impact on, or control over, others (McClelland, 1975).  

Power motivation operates across two cognitive levels. Implicit power motivation respresents an unconscious motive that can be assessed via projective tests such as the Picture Story Exercise (PSE) or the Thematic Apperception Test (TAT) where spontaneously constructed narratives are coded for imagery of impact, control, and prestige. Explicit power motivation involves conscious self-conceptions evaluated through self-report questionnaires measuring specific desires for leadership roles, authority, or prestige (Maliszewski et al., 2014; McClelland, 1975).

Research in social neuroscience indicates that implicit power motivation is accompanied by distinct physiological correlates, with individuals with strong implicit nPower exhibiting heightened salivary cortisol and testosterone fluctuations, as well as distinct neural activation patterns in the amygdala and striatum, when confronting nonverbal social cues signalling rank competiton, social defeat, or interpersonal dominance (Rybnicek et al., 2017; Wirth et al., 2006).

=== Personalised vs socialised power across cultures ===
McClelland emphasises that power motivation is not inherently destructive, and distinguished between two distinct expressions or faces of power (McClelland, 1975). Personalised power (pPower) is driven by direct personal domination and status acquisition, often ignoring the needs of those considered to be subordinates. In contrast, socialised pwoer (sPower) is expressed responsibly through empowering others, mentoring, and influencing others in order to meet collective goals and organisational wellbeing (Friederichs et al., 2023; McClelland, 1975). 

Cultural values heavily shape how power motivation is channeled and expressed. In societies characterised by vertical individualism, power is primarily conceptualised as personalised dominance and personal status acquisition. Conversely, in societies characterised by horizontal collectivism, power motivation is more frequently channeled into socialised expressions, such as community leadership, nurturing, and collective helping. Frieze and Boneva further categorised these explicit power expressions into three distinct behavioural dimension: leadership, prominence, and helping (Triandis &amp; Gelfand, 1998).

==Legitimising myths==
Social dominance theory proposes that group hierarchies are maintained not solely through physical coercion, but also through the widespread adoption of legitimising myths—cultural beliefs, values, and attitudes that provide moral and intellectual justification for intergroup relations (Sidanius &amp; Pratto, 1999).

=== Hierarchy-enhancing vs hierarchy-attenuating myths ===
Legitimising myths are categorised based on whether they reinforce or undermine inequality in society. Hierarchy-enhancing legitimising myths consist of ideologies that justify inequality by suggesting that existing group advantages are earned, natural, or just, such as meritocracy, racism, sexism, and caste systems. In comparison, hierarchy-attenuating legitimising myths include ideologies that challenge group inequality and advocate for systemic redistribution and equal rights (Pratto et al., 1994; Sidanius &amp; Pratto, 1999). 

Individuals high in SDO selectively endorse hierarchy-enhancing myths to rationalise their groups privileged position. This endorsement allows them to dismiss societal inequalities as legitimate and understandable consequences of group differences in effort, talent, or intrinsic worth (Pratto et al., 1994; Sidanius &amp; Pratto, 1999).

=== Legitimising narratives in media and institutions ===
Legitimising myths are transmitted and continually reinforced through mainstream media narratives, television, educational curriculums, and social media. By embedding hierarchy-enhancing narratives in public discourse, institutions normalise privilege and make systemic inequality appear invisible or natural. Consequently, legitimising myths serve as the psychological mechanism through which abstract SDO translates into active public support for discriminatory laws, harsher sentencing, and opposition to equity programs (Pratto et al., 1994; Sidanius &amp; Pratto, 1999).

==The link between social dominance orientation and power motivation==
Although Social Dominance Orientation and power motivation both pertain to social rank and hierarchy, they represent distinct psychological constructs operating at different levels of analysis (Ho et al., 2025; Suessenbach et al., 2018).
{| class=&quot;wikitable&quot;
|+Table 2. ''Conceptual comparison between Social Dominance Orientation and Power Motivation - Based on Ho et al. (2015) and McClelland (1975).''
!Feature
!Social Dominance Orientation (SDO)
!Need for Power (nPower)
|-
|'''Primary focus'''
|Group-based social hierarchy and intergroup inequality.
|Interpersonal impact, control, and personal influence.
|-
|'''Level of analysis'''
|Societal / ideological / intergroup level
|Individual / interpersonal / dual levels
|-
|'''Key motivator'''
|Desire for ingroup superiority or systemic group hierarchy
|Desire to direct, control, or impact specific individuals
|-
|'''Behavioural outcome'''
|Endorsing hierarchy-enhancing policy and predudice.
|Leadership emergence, mentoring (sPower) or coercion (pPower)
|}
Social Dominance Orientation reflects a group-level ideological preference for systemic inequality, whereas nPower reflects an individual-level drive for personal impact. Additonally, having high nPower does not automatically equate to having a high SDO.A leader who is driven by strong socialised power (sPower) may seek personal influence specifically to dismantle institutional barriers and promote equality, resulting in low SDO (Friederichs et al., 2023), as seen in the opening scenario. However, an individual with low personal leadership drive may hold high SDO, actively lobbying to protect group privileges and restrict subordinate group advancements without desiring a personal leadership role (Aiello et al., 2013; Ho et al., 2025).

== Political and social behaviour ==
Individual differences in SDO and nPower heavily influence collective political attitudes, voting patterns, and intergroup conflicts. 

=== SDO, right-wing authoritarianism, and political ideology ===
In political psychology, SDO works alongside Right-Wing Authoritarianism (RWA) as dual motivational predictors of prejudice and political conservatism (Duckitt &amp; Sibley, 2010; Perry &amp; Sibley, 2012). Developed by Bob Altemeyer, RWA represents an attitudinal cluster defined by authoritarian submission, authoritarian aggression, and conventionalism (Altemeyer, 1998). SDO and right-wing authoritarianism (RWA) arise from different wordview based roots however both can connect and predict prejudice and political conservatism

Duckitt's dual-process model shows that SDO and RWA arise from fundamentally different worldview roots. SDO stems from viewing the world as a &quot;competitive jungle&quot; where force and dominance determine success, driving a desire for group superiority. in contrast, RWA stems from viewing the world as a &quot;dangerous unstable place&quot; driving a desire for social order, cohesion, and strict conformity to authority (Duckitt &amp; Sibley, 2010). Together, high SDO and high RWA interact to predict strong support for anti-egalitarian political parties, opposition to environmental protection, harsh policies towards immigrants, and endorsement of ingroup violence (Abou-Ismail et al., 2025; Duckitt &amp; Sibley, 2010). &lt;quiz display=&quot;simple&quot;&gt;
{According to the dual-process model, Right Wing Authoritarianism (RWA) is primarily motivated by which worldview?
|type=&quot;()&quot;}
- The world as a competitive jungle 
+ The world as a dangerous chaotic place needing order
- The world as an inherently egalitarian community
&lt;/quiz&gt;
* Key references: (Duckitt &amp; Sibley, 2010), (Ekehammar et al., 2004), (Ward, 1982)

== Power, leadership, and individual differences ==
The interactions between power motivation, social dominance, and biological mechanisms provide a predictor of leadership styles, ethical decision making, and organisational health.

=== Prosocial vs. antisocial leadership ===
Leadership based research demonstrates that identical positions of authority yield starkly different organisational outcomes depending on the leader's underlying motives. Leaders high in personalised power (pPower) and high in SDO are significantly more liekly to employ coercive influence tactics, engage in unethical pro-organisational behaviour, and view subordinates as instruments for self-aggrandisement (Son Hing et al., 2007). In contrast, leaders high in prestige motivation or socialised power (sPower) adopt empowering leadership styles that foster team cohesion, psychological safety, and collective innovation (Cheong et al., 2019; Friederichs et al., 2023; Suessenbach et al., 2018).

{{RoundBoxTop|theme=3}}
'''Case study: power and dominance in cult leadership'''

High personalised power motivation and extreme Social Dominance Orientation can compound to produce destructive, coercive, social structures. In cult environments, charismatic leaders combine intense personal impact with rigid hierarchy enhancing legitimising myths regarding their own absolute superiority (Denrich, 2024; Magee &amp; Galinsky, 2008).

By stripping followers of autonomy, enforcing strict behavioural conformity, and casting all outside groups as inherently inferior, cult leaders exercise extreme personalised dominance. Psychological analysis reveals that such destructive dynamics occur when personal authority (pPower) is unchecked by socialised accountability (sPower), and is reinforced by ideological beliefs in absolute group hierarchy (SDO) (Denrich, 2024).{{RoundBoxBottom}}

=== Biological basis, gender differences, and situation triggers ===
Neuroimaging and biological studies reveal that human brains possess dedicated neural pathways for processing social rank, territory, and status hierarchies. Brain regions such as the [[wikipedia:Amygdala|amygdala]], the [[wikipedia:Striatum|striatum]], the anterior [[wikipedia:Insular_cortex|insula]], and the [[wikipedia:Intraparietal_sulcus|intraparietal sulcus]], activate during social encounters involving rank (Watanabe &amp; Yamamoto, 2015). Individual differences in SDO have also been linked to neural sensitivity (Adrián-Ventura et al., 2026; Ligneul et al., 2017)). 

Across samples, gender differences in SDO are consistently observed, with men scoring higher on average than women (Sidanius &amp; Pratto, 1999). This is explained by SDT's subordinate male target hypothesis and evolutionary bargaining models regarding physical formidability and resource defence (Sidanius &amp; Pratto, 1999). Additionally, situational triggers such as acute intergroup competition, economic scarcity, or percieved threats to ingroup status can temporarily heighten SDO levels and activate aggressive power-seeking behaviours in individuals who are otherwise egalitarian individuals (Ho et al., 2025).

== Conclusion ==
Social dominance orientation and power motivation are distinct yet related psychological constructs that operate at different levels of analysis. SDO functions as a macro-level ideological preference for group-based hierarchy and intergroup inequality, whereas power motivation functions as a micro-level interpersonal drive for direct influence and control over individuals (Ho et al., 2025; McClelland, 1975). 

SDO is rooted in Social Dominance Theory's trimorphic group systems and is evaluated via the SDO7 scale (Ho et al., 2015; Sidanius &amp; Pratto, 1999). Power motivation manifests as either personalised power or socialised power and is heavily shaped by vertical versus horizontal cultural orientations (McClelland, 1975; Triandis &amp; Gelfand, 1998). Legitimising myths serve as the crucial ideological bridge connecting abstract SDO preferences to real world policy support (Pratto et al., 1994), whereas SDO and power motivation interact with Right-Wing Authoritarianism and neural rank-processing networks to shape political behaviour and leadership dynamics (Duckitt &amp; Sibley, 2010).

Distinguishing between personal leadership drive and group hierarchy defense provides practical value for organisation, political scientists, and community leaders. Recognising these underlying motives allows institutions to actively foster socialised power and prestige while dismantling coercive dominance and systemic group inequality (Cheng, 2020; (Friederichs et al., 2023).

==See also==
* [[wikipedia:Dominance_hierarchy|Dominance hierarchy]]
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] 
* [[wikipedia:Need_for_power|Need for power]] 
* [[wikipedia:Right-wing_authoritarianism|Right wing authoritarianism]] 
* [[w:Self determination theory|Self determination theory]] 
* [http://en.wikipedia.org/wiki/Social_dominance_orientation Social dominance orientation] 
* [[wikipedia:Social_dominance_theory|Social dominance theory]] 
* [[wikipedia:Social_identity_theory|Social identity theory]]

==References==
{{Hanging indent|1=

Abou-Ismail, R., Cichocka, A., Phillips, J., &amp; Sengupta, N. K. (2025). Authoritarianism and social dominance as differential predictors of individuals’ support for collective violence. Psychology of Violence, 15(5), 634–644. https://doi.org/10.1037/vio0000580

Adrián-Ventura, J., Fasce, A., Miró-Padilla, A., Cherednichenko, A., Ávila, C., &amp; Avendaño, D. (2026). Neuroanatomical correlates of social dominance orientation and the contributing role of reward sensitivity. Current Psychology, 45(13), Article 1168. https://doi.org/10.1007/s12144-026-09740-z

Aiello, A., Pratto, F., &amp; Pierro, A. (2013). Framing social dominance orientation and power in organizational context. Basic and Applied Social Psychology, 35(5), 487–495. https://doi.org/10.1080/01973533.2013.823614

Altemeyer, B. (1998). The other “authoritarian personality”. Advances in Experimental Social Psychology, 30, 47–92. https://doi.org/10.1016/s0065-2601(08)60382-2

Cheng, J. T. (2020). Dominance, prestige, and the role of leveling in human social hierarchy and equality. Current Opinion in Psychology, 33, 238–244. https://doi.org/10.1016/j.copsyc.2019.10.004

Cheng, J. T., Tracy, J. L., Foulsham, T., Kingstone, A., &amp; Henrich, J. (2013). Two ways to the top: Evidence that dominance and prestige are distinct yet viable avenues to social rank and influence. Journal of Personality and Social Psychology, 104(1), 103–125. https://doi.org/10.1037/a0030398

Cheng, J. T., Tracy, J. L., &amp; Henrich, J. (2010). Pride, personality, and the evolutionary foundations of human social status. Evolution and Human Behavior, 31(5), 334–347. https://doi.org/10.1016/j.evolhumbehav.2010.02.004

Cheong, M., Yammarino, F. J., Dionne, S. D., Spain, S. M., &amp; Tsai, C.-Y. (2019). A review of the effectiveness of empowering leadership. The Leadership Quarterly, 30(1).

Denrich, D. S. (2024). Charismatic leadership and vulnerability: A comprehensive study of cult dynamics. Psychology Presentations. https://digitalcommons.ursinus.edu/psych_pres/11/

Duckitt, J., &amp; Sibley, C. G. (2010). Personality, ideology, prejudice, and politics: A dual‐process motivational model. Journal of Personality, 78(6), 1861–1894. https://doi.org/10.1111/j.1467-6494.2010.00672.x

Friederichs, K. M., Waldenmeier, K., &amp; Baumann, N. (2023). The benefits of prosocial power motivation in leadership: Action orientation fosters a win-win. Plos One, 18(7), e0287394–e0287394. https://doi.org/10.1371/journal.pone.0287394

Ho, A. K., Kteily, N. S., Sheehy-Skeffington, J., &amp; Thomsen, L. (2025). Social dominance orientation: The motivational basis of intergroup inequality. Advances in Experimental Social Psychology, 72, 125–208. https://doi.org/10.1016/bs.aesp.2025.04.003

Ho, A. K., Sidanius, J., Kteily, N., Sheehy-Skeffington, J., Pratto, F., Henkel, K. E., Foels, R., &amp; Stewart, A. L. (2015). The nature of social dominance orientation: Theorizing and measuring preferences for intergroup inequality using the new SDO₇ scale. Journal of Personality and Social Psychology, 109(6), 1003–1028. https://doi.org/10.1037/pspi0000033

Ligneul, R., Girard, R., &amp; Dreher, J.-C. (2017). Social brains and divides: The interplay between social dominance orientation and the neural sensitivity to hierarchical ranks. Scientific Reports, 7(1). https://doi.org/10.1038/srep45920

Magee, J. C., &amp; Galinsky, A. D. (2008). Social hierarchy: The self‐reinforcing nature of power and status. The Academy of Management Annals, 2(1), 351–398. https://doi.org/10.1080/19416520802211628

Maliszewski, N., Kuźmińska, A. O., Wieczorkowska-Wierzbińska, G., &amp; Werner-Maliszewska, A. (2014). The impact of explicit and implicit power motivation on educational choices. Polish Psychological Bulletin, 45(3), 275–285. https://doi.org/10.2478/ppb-2014-0034

McClelland, D. C. (1975). Power: The inner experience. American Journal of Sociology, 82(5). https://doi.org/10.1086/226461

Perry, R., &amp; Sibley, C. G. (2012). Big-five personality prospectively predicts social dominance orientation and right-wing authoritarianism. Personality and Individual Differences, 52(1), 3–8. https://doi.org/10.1016/j.paid.2011.08.009

Pratto, F., Sidanius, J., Stallworth, L. M., &amp; Malle, B. F. (1994). Social dominance orientation: A personality variable predicting social and political attitudes. Journal of Personality and Social Psychology, 67(4), 741–763. https://doi.org/10.1037/0022-3514.67.4.741

Rybnicek, R., Bergner, S., &amp; Gutschelhofer, A. (2017). How individual needs influence motivation effects: A neuroscientific study on mcclelland’s need theory. Review of Managerial Science, 13(2), 443–482. springer. https://doi.org/10.1007/s11846-017-0252-1

Sidanius, J., &amp; Pratto, F. (1999). Social dominance: An intergroup theory of social hierarchy and oppression. Cambridge University Press. https://doi.org/10.1017/cbo9781139175043

Son Hing, L. S., Bobocel, D. R., Zanna, M. P., &amp; McBride, M. V. (2007). Authoritarian dynamics and unethical decision making: High social dominance orientation leaders and high right-wing authoritarianism followers. Journal of Personality and Social Psychology, 92(1), 67–81. https://doi.org/10.1037/0022-3514.92.1.67

Suessenbach, F., Loughnan, S., Schönbrodt, F. D., &amp; Moore, A. B. (2018). The dominance, prestige, and leadership account of social power motives. European Journal of Personality, 33(1), 7–33. https://doi.org/10.1002/per.2184

Triandis, H. C., &amp; Gelfand, M. J. (1998). Converging measurement of horizontal and vertical individualism and collectivism. Journal of Personality and Social Psychology, 74(1), 118–128. https://doi.org/10.1037/0022-3514.74.1.118

Watanabe, N., &amp; Yamamoto, M. (2015). Neural mechanisms of social dominance. Frontiers in Neuroscience, 9. https://doi.org/10.3389/fnins.2015.00154

Wirth, M. M., Welsh, K. M., &amp; Schultheiss, O. C. (2006). Salivary cortisol changes in humans after winning or losing a dominance contest depend on implicit power motivation. Hormones and Behavior, 49(3), 346–352. https://doi.org/10.1016/j.yhbeh.2005.08.013

}}

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[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Dominance]]
[[Category:Motivation and emotion/Book/Power motivation]]
[[Category:Motivation and emotion/Book/Social]]</text>
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      <text bytes="30084" sha1="3vswx3l46frusetu55lwbkp2yiwn4xg" xml:space="preserve">{{title|Social dominance and power motivation:&lt;br&gt;What is the relationship between social dominance and power motivation?}}
__TOC__
==Overview==
{{RoundBoxTop|theme=3}}
[[File:Noun Staff Management 4185.svg|Management chart right|thumb|200px|'''Figure 1'''. Power hierarchy in the workplace]]

'''Scenario: Raising up vs. pushing down.'''

Two graduates start the same week at a large firm. One quickly puts their hand up to lead every project going, coordinating people, chasing decisions, and making sure things get done — and uses that influence to actively mentor junior colleagues and push for flatter, fairer pay structures. The other has no interest in leading projects or managing anyone, yet defends the firm's steep hierarchy (see Figure 1) as natural and fair: &quot;some people are just better suited to being in charge, and the system reflects that.&quot; They also actively lobbies against a new scheme providing staff from under-represented backgrounds with better access to mentoring, training, and development opportunities, arguing certain groups should stay in junior roles &quot;where they belong&quot; and pushing to have the scheme scrapped. Both are equally competent. Why does one seem driven to personally influence the people around them, while the other — without wanting any personal authority — is instead driven to keep entire groups beneath others?

{{RoundBoxBottom}}
Human societies are fundamentally structured around social hierarchies (Magee &amp; Galinsky, 2008; Sidanius &amp; Pratto, 1999), however, the psychological factors that lead individuals to navigate, challenge, or enforce these hierarchies can vary significantly. Power motivation and social dominance are two distinct yet related psychological constructs that explain different aspects of hierarchy seeking behaviour in human societies. Social Dominance Orientation (SDO) is defined as a preference for one's ingroup to dominate outgroups viewed as lesser and a general desire for group-based inequality (Ho et al., 2015; Pratto et al., 1994). In contrast, power motivation (nPower) represents an individual's personal drive to have influence, control, or psychological impact over specific individuals (McClelland, 1975).

While these constructs frequently overlap in everyday social interactions, psychological science demonstrates that they operate at fundamentally different levels when it comes to analysis: group-based ideological preference versus interpersonal motivation (Ho et al., 2015; Suessenbach et al., 2018). Clarifying the distinction between social dominance and power motivation is essential as both constructs can predict real world outcomes, including leadership emergence, support for discriminatory policies, workplace dynamics, and the specific influence and control tactics individuals choose to employ when power is attained (Aiello et al., 2013; Cheng et al., 2013). By examining frameworks such as Social Dominance Theory, McClelland's Need Theory, and modern neuroscientific findings, psychological science provides diagnostic tools such as SDO7 scales and implicit motive coding to evaluate why individuals seek status and how they exercise power once it is gained (Ho et al., 2015; McClelland, 1975).

{{RoundBoxTop|theme=3}}

'''Focus questions'''

* What is social dominance orientation, and how does it relate to broader group hierarchies?
* What is power motivation (nPower), and how is it expressed differently across different demographics and cultural contexts? 
* How do legitimising myths sustain or challenge social hierarchies?
* How do SDO and power motivation shape political attitudes, leadership styles, and intergroup behaviours?

{{RoundBoxBottom}}

==Social dominance orientation==
Social dominance orientation represents a core attitudinal personality variable within intergroup psychology, revealing an individual's stance regarding group-based equality versus group-based hierarchy (Pratto et al., 1994). Understanding social dominance orientation requires an examination of it's theoretical origins within Social Dominance Theory, it's sub-dimensional structures, and it's broader predictive validity across societal domains.

=== Origins in social dominance theory ===
[[wikipedia:Social_dominance_orientation|Social dominance theory]] (SDT), developed by Jim Sidanius and Felicia Pratto, opens with the observation that all human societies producing an economic surplus naturally develop group-based social hierarchies (Sidanius &amp; Pratto, 1999). SDT identifies three distinct forms of trimorphic social hierarchies that form the structure of human societies. The age system, which grants adults disproportionate power and social status compared to children; patriarchy, referring to systems where men hold greater political, social, and economic authority than women; and the arbitrary-set system which encompasses culturally constructed social categories such as race, ethnicity, religion, social class, nationality, or caste, that are hierarchically ordered with unequal access to power, opportunity, and privileges (Sidanius &amp; Pratto, 1999).  

According to SDT, social institutions such as legal systems, criminal courts, educational systems, and corporations sustain these group hierarchies through institutional discrimination (Sidanius &amp; Pratto, 1999). Institutions maintain hierarchy by disproportionately allocating positive social value, such as wealth, healthcare, prestige, and educational access, to dominant groups. Additionally, institutions direct negative social value, including harsher criminal penalties, dangerous labour, and poverty, towards subordinate groups (Pratto et al., 1994; Sidanius &amp; Pratto, 1999). 

=== Measuring social dominance orientation and what it predicts ===

{| class=&quot;wikitable&quot; style=&quot;float:right; clear:right; width:400px; margin:0 0 1em 1.5em; text-align:center; background-color:#f9f9f9; border:1px solid #aaa;&quot;
|-
! colspan=&quot;2&quot; style=&quot;background-color:#f9f9f9; font-size:110%; padding:8px; border:none;&quot; | Figure 2. Dimensional structure of SDO7&lt;br&gt;&lt;small style=&quot;font-weight:normal;&quot;&gt;&lt;em&gt;Based on Ho et al. (2015)&lt;/em&gt;&lt;/small&gt;
|-
| colspan=&quot;2&quot; style=&quot;background-color:#eef; padding:10px; border:1px solid #aaa;&quot; | '''Social Dominance Orientation (SDO)'''&lt;br&gt;&lt;small&gt;(Preference for group inequality)&lt;/small&gt;
|-
| style=&quot;width:50%; vertical-align:top; background-color:#fff; padding:10px; border:1px solid #aaa; text-align:left;&quot; |
'''SDO-Dominance (SDO-D)'''
* Active group oppression
* Overt group superiority
* Direct intergroup action again outgroups
| style=&quot;width:50%; vertical-align:top; background-color:#fff; padding:10px; border:1px solid #aaa; text-align:left;&quot; |
'''SDO-Egalitarianism (SDO-E)'''
* Opposition to group equality
* Opposition to equity/social schemes
* Subtle institutional bias
|}
To evaluate individual differences in support for group-based hierarchy, researchers constructed the SDO scale, with the newer SDO7 scale dividing the construct into two sub-dimensions (Ho et al., 2015; see Figure 2). The first dimension, SDO-Dominance (SDO-D) assesses support for active, explicit group oppression and the forced subjugation of outgroups. The second dimension, SDO-Egalitarianism (SDO-E) assesses generalised opposition to group equality, manifesting as subtle resistance to social welfare, affirmative actions, and equality-promoting policies (Ho et al., 2015, 2025).

Empirical cross-cultural research confirms that high SDO scores predict intergroup prejudice, ethnocentrism, sexism, homophobia, and support for harsher criminal justice policies (Pratto et al., 1994). Additionally, individuals selectively self-segregate into specific societal roles based on their SDO levels. High-SDO individuals gravitate towards hierarchy-enhancing roles that reinforce existing social stratification, such as executives, criminal prosecutors, and police officers. In comparison, low-SDO individuals seek out hierarchy-reducing roles that challenge systemic inequality, such as human rights lawyers, public defenders, and social workers (Pratto et al., 1994; Sidanius &amp; Pratto, 1999).


The SDO7 scale distinguished between two sub-dimensions: SDO-Dominance (SDO-D) which involves support for active group oppression and SDO-Egalitarianism (SDO-E) which reflects a preference for group inequality and is linked to more subtle forms of prejudice and inequality as well as opposition to equality-promoting policies.&lt;quiz display=&quot;simple&quot;&gt;
{Which form of hierarchy in Social Dominance Theory involves culturally defined categories like race, ethnicity, or religion?
|type=&quot;()&quot;}
- The age system
- Patriarchy
+ The arbitrary-set system

{High-SDO individuals are most likely to select which of the following career paths?
|type=&quot;()&quot;}
- Hierarchy-reducing roles like public defenders
+ Hierarchy-enhancing roles like corporate executives
&lt;/quiz&gt;
==Power motivation==
Power motivation, commonly referred to as the Need for Power (nPower) is a psychological construct describing an individuals drive to exert impact, control, or influence over others and their surrounding environment (McClelland, 1975). First conceptualised by Henry Murray in taxonomy of fundamental human needs, and later expanded upon by David McClelland in his Three Needs Theory, power motivation represents a primary driver of status-seeking, interpersonal dynamics, and leadership emergence (McClelland, 1975; Suessenbach et al., 2018). Rather than representing a purely manipulative or antisocial trait, power motivation exists along a broad psychological spectrum. It ranges from personalised power (pPower), which is characterised by direct control, self-aggrandisement, and zero-sum competition, to socialised power (sPower) where influence is channelled towards supporting and empowering others, mentoring, and achieving collective goals (McClelland, 1975; Friederichs et al., 2023). 

=== McClelland's need theory and measurement ===
McClelland proposed that humans vary in the relative strength of three learned needs: the Need for Power (nPower), the Need for Achievement (nAch) and the Need for Affiliation (nAff), with nPower reflecting a desire to have an impact on, or control over, others (McClelland, 1975).  

Power motivation operates across two cognitive levels. Implicit power motivation represents an unconscious motive that can be assessed via projective tests such as the Picture Story Exercise (PSE) or the Thematic Apperception Test (TAT) where spontaneously constructed narratives are coded for imagery of impact, control, and prestige. Explicit power motivation involves conscious self-conceptions evaluated through self-report questionnaires measuring specific desires for leadership roles, authority, or prestige (Maliszewski et al., 2014; McClelland, 1975).

Research in social neuroscience indicates that implicit power motivation is accompanied by distinct physiological correlates, with individuals with strong implicit nPower exhibiting heightened salivary cortisol and testosterone fluctuations, as well as distinct neural activation patterns in the amygdala and striatum, when confronting nonverbal social cues signalling rank competition, social defeat, or interpersonal dominance (Rybnicek et al., 2017; Wirth et al., 2006).

=== Personalised vs socialised power across cultures ===
McClelland emphasises that power motivation is not inherently destructive, and distinguished between two distinct expressions or faces of power (McClelland, 1975). Personalised power (pPower) is driven by direct personal domination and status acquisition, often ignoring the needs of those considered to be subordinates. In contrast, socialised power (sPower) is expressed responsibly through empowering others, mentoring, and influencing others in order to meet collective goals and organisational wellbeing (Friederichs et al., 2023; McClelland, 1975). 

Cultural values heavily shape how power motivation is channelled and expressed. In societies characterised by vertical individualism, power is primarily conceptualised as personalised dominance and personal status acquisition. Conversely, in societies characterised by horizontal collectivism, power motivation is more frequently channelled into socialised expressions, such as community leadership, nurturing, and collective helping (Triandis &amp; Gelfand, 1998). These explicit power expressions were further categorised into three distinct behavioural dimensions: leadership, prominence, and helping (Triandis &amp; Gelfand, 1998).

==Legitimising myths==
Social dominance theory proposes that group hierarchies are maintained not solely through physical coercion, but also through the widespread adoption of legitimising myths—cultural beliefs, values, and attitudes that provide moral and intellectual justification for intergroup relations (Sidanius &amp; Pratto, 1999).

=== Hierarchy-enhancing vs hierarchy-attenuating myths ===
Legitimising myths are categorised based on whether they reinforce or undermine inequality in society. Hierarchy-enhancing legitimising myths consist of ideologies that justify inequality by suggesting that existing group advantages are earned, natural, or just, such as meritocracy, racism, sexism, and caste systems. In comparison, hierarchy-attenuating legitimising myths include ideologies that challenge group inequality and advocate for systemic redistribution and equal rights (Pratto et al., 1994; Sidanius &amp; Pratto, 1999). 

Individuals high in SDO selectively endorse hierarchy-enhancing myths to rationalise their groups privileged position. This endorsement allows them to dismiss societal inequalities as legitimate and understandable consequences of group differences in effort, talent, or intrinsic worth (Pratto et al., 1994; Sidanius &amp; Pratto, 1999).

=== Legitimising narratives in media and institutions ===
Legitimising myths are transmitted and continually reinforced through mainstream media narratives, television, educational curriculums, and social media. By embedding hierarchy-enhancing narratives in public discourse, institutions normalise privilege and make systemic inequality appear invisible or natural. Consequently, legitimising myths serve as the psychological mechanism through which abstract SDO translates into active public support for discriminatory laws, harsher sentencing, and opposition to equity programs (Pratto et al., 1994; Sidanius &amp; Pratto, 1999).

==The link between social dominance orientation and power motivation==
Although Social Dominance Orientation and power motivation both pertain to social rank and hierarchy, they represent distinct psychological constructs operating at different levels of analysis (Ho et al., 2025; Suessenbach et al., 2018).
{| class=&quot;wikitable&quot;
|+Table 1. ''Conceptual comparison between Social Dominance Orientation and Power Motivation - Based on Ho et al. (2015) and McClelland (1975).''
!Feature
!Social Dominance Orientation (SDO)
!Need for Power (nPower)
|-
|'''Primary focus'''
|Group-based social hierarchy and intergroup inequality.
|Interpersonal impact, control, and personal influence.
|-
|'''Level of analysis'''
|Societal / ideological / intergroup level
|Individual / interpersonal / dual levels
|-
|'''Key motivator'''
|Desire for ingroup superiority or systemic group hierarchy
|Desire to direct, control, or impact specific individuals
|-
|'''Behavioural outcome'''
|Endorsing hierarchy-enhancing policy and prejudice.
|Leadership emergence, mentoring (sPower) or coercion (pPower)
|}
As Table 1 shows Social Dominance Orientation reflects a group-level ideological preference for systemic inequality, whereas nPower reflects an individual-level drive for personal impact. Additonally, having high nPower does not automatically equate to having a high SDO. A leader who is driven by strong socialised power (sPower) may seek personal influence specifically to dismantle institutional barriers and promote equality, resulting in low SDO (Friederichs et al., 2023), as seen in the opening scenario. However, an individual with low personal leadership drive may hold high SDO, actively lobbying to protect group privileges and restrict subordinate group advancements without desiring a personal leadership role (Aiello et al., 2013; Ho et al., 2025).

== Political and social behaviour ==
Individual differences in SDO and nPower heavily influence collective political attitudes, voting patterns, and intergroup conflicts. 

=== SDO, right-wing authoritarianism, and political ideology ===
In political psychology, SDO works alongside Right-Wing Authoritarianism (RWA) as dual motivational predictors of prejudice and political conservatism (Duckitt &amp; Sibley, 2010; Perry &amp; Sibley, 2012). Developed by Bob Altemeyer, RWA represents an attitudinal cluster defined by authoritarian submission, authoritarian aggression, and conventionalism (Altemeyer, 1998). SDO and right-wing authoritarianism (RWA) arise from different worldview based roots however both can connect and predict prejudice and political conservatism

Duckitt's dual-process model shows that SDO and RWA arise from fundamentally different worldview roots. SDO stems from viewing the world as a &quot;competitive jungle&quot; where force and dominance determine success, driving a desire for group superiority. In contrast, RWA stems from viewing the world as a &quot;dangerous unstable place&quot; driving a desire for social order, cohesion, and strict conformity to authority (Duckitt &amp; Sibley, 2010). Together, high SDO and high RWA interact to predict strong support for anti-egalitarian political parties, opposition to environmental protection, harsh policies towards immigrants, and endorsement of ingroup violence (Abou-Ismail et al., 2025; Duckitt &amp; Sibley, 2010). &lt;quiz display=&quot;simple&quot;&gt;
{According to the dual-process model, Right Wing Authoritarianism (RWA) is primarily motivated by which worldview?
|type=&quot;()&quot;}
- The world as a competitive jungle 
+ The world as a dangerous chaotic place needing order
- The world as an inherently egalitarian community
&lt;/quiz&gt;
== Power, leadership, and individual differences ==
The interactions between power motivation, social dominance, and biological mechanisms provide a predictor of leadership styles, ethical decision making, and organisational health.

=== Prosocial vs. antisocial leadership ===
Leadership based research demonstrates that identical positions of authority yield starkly different organisational outcomes depending on the leader's underlying motives. Leaders high in personalised power (pPower) and high in SDO are significantly more likely to employ coercive influence tactics, engage in unethical pro-organisational behaviour, and view subordinates as instruments for self-aggrandisement (Son Hing et al., 2007). In contrast, leaders high in prestige motivation or socialised power (sPower) adopt empowering leadership styles that foster team cohesion, psychological safety, and collective innovation (Cheong et al., 2019; Friederichs et al., 2023; Suessenbach et al., 2018).

{{RoundBoxTop|theme=3}}
'''Case study: power and dominance in cult leadership'''

High personalised power motivation and extreme Social Dominance Orientation can compound to produce destructive, coercive, social structures. In cult environments, charismatic leaders combine intense personal impact with rigid hierarchy enhancing legitimising myths regarding their own absolute superiority (Denrich, 2024; Magee &amp; Galinsky, 2008).

By stripping followers of autonomy, enforcing strict behavioural conformity, and casting all outside groups as inherently inferior, cult leaders exercise extreme personalised dominance. Psychological analysis reveals that such destructive dynamics occur when personal authority (pPower) is unchecked by socialised accountability (sPower), and is reinforced by ideological beliefs in absolute group hierarchy (SDO) (Denrich, 2024).{{RoundBoxBottom}}

=== Biological basis, gender differences, and situational triggers ===
Neuroimaging and biological studies reveal that human brains possess dedicated neural pathways for processing social rank, territory, and status hierarchies. Brain regions such as the [[wikipedia:Amygdala|amygdala]], the [[wikipedia:Striatum|striatum]], the anterior [[wikipedia:Insular_cortex|insula]], and the [[wikipedia:Intraparietal_sulcus|intraparietal sulcus]], activate during social encounters involving rank (Watanabe &amp; Yamamoto, 2015). Individual differences in SDO have also been linked to neural sensitivity (Adrián-Ventura et al., 2026; Ligneul et al., 2017). 

Across samples, gender differences in SDO are consistently observed, with men scoring higher on average than women (Sidanius &amp; Pratto, 1999). This is explained by SDT's subordinate male target hypothesis and evolutionary bargaining models regarding physical formidability and resource defence (Sidanius &amp; Pratto, 1999). Additionally, situational triggers such as acute intergroup competition, economic scarcity, or perceived threats to ingroup status can temporarily heighten SDO levels and activate aggressive power-seeking behaviours in individuals who are otherwise egalitarian (Ho et al., 2025).

== Conclusion ==
Social dominance orientation and power motivation are distinct yet related psychological constructs that operate at different levels of analysis. SDO functions as a macro-level ideological preference for group-based hierarchy and intergroup inequality, whereas power motivation functions as a micro-level interpersonal drive for direct influence and control over individuals (Ho et al., 2025; McClelland, 1975). 

SDO is rooted in Social Dominance Theory's trimorphic group systems and is evaluated via the SDO7 scale (Ho et al., 2015; Sidanius &amp; Pratto, 1999). Power motivation manifests as either personalised power or socialised power and is heavily shaped by vertical versus horizontal cultural orientations (McClelland, 1975; Triandis &amp; Gelfand, 1998). Legitimising myths serve as the crucial ideological bridge connecting abstract SDO preferences to real world policy support (Pratto et al., 1994), whereas SDO and power motivation interact with Right-Wing Authoritarianism and neural rank-processing networks to shape political behaviour and leadership dynamics (Duckitt &amp; Sibley, 2010).

Distinguishing between personal leadership drive and group hierarchy defense provides practical value for organisations, political scientists, and community leaders. Recognising these underlying motives allows institutions to actively foster socialised power and prestige while dismantling coercive dominance and systemic group inequality (Cheng, 2020; Friederichs et al., 2023).

==See also==
* [[wikipedia:Dominance_hierarchy|Dominance hierarchy]]
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] 
* [[wikipedia:Need_for_power|Need for power]] 
* [[wikipedia:Right-wing_authoritarianism|Right wing authoritarianism]] 
* [[w:Self determination theory|Self determination theory]] 
* [http://en.wikipedia.org/wiki/Social_dominance_orientation Social dominance orientation] 
* [[wikipedia:Social_dominance_theory|Social dominance theory]] 
* [[wikipedia:Social_identity_theory|Social identity theory]]

==References==
{{Hanging indent|1=

Abou-Ismail, R., Cichocka, A., Phillips, J., &amp; Sengupta, N. K. (2025). Authoritarianism and social dominance as differential predictors of individuals’ support for collective violence. Psychology of Violence, 15(5), 634–644. https://doi.org/10.1037/vio0000580

Adrián-Ventura, J., Fasce, A., Miró-Padilla, A., Cherednichenko, A., Ávila, C., &amp; Avendaño, D. (2026). Neuroanatomical correlates of social dominance orientation and the contributing role of reward sensitivity. Current Psychology, 45(13), Article 1168. https://doi.org/10.1007/s12144-026-09740-z

Aiello, A., Pratto, F., &amp; Pierro, A. (2013). Framing social dominance orientation and power in organizational context. Basic and Applied Social Psychology, 35(5), 487–495. https://doi.org/10.1080/01973533.2013.823614

Altemeyer, B. (1998). The other “authoritarian personality”. Advances in Experimental Social Psychology, 30, 47–92. https://doi.org/10.1016/s0065-2601(08)60382-2

Cheng, J. T. (2020). Dominance, prestige, and the role of leveling in human social hierarchy and equality. Current Opinion in Psychology, 33, 238–244. https://doi.org/10.1016/j.copsyc.2019.10.004

Cheng, J. T., Tracy, J. L., Foulsham, T., Kingstone, A., &amp; Henrich, J. (2013). Two ways to the top: Evidence that dominance and prestige are distinct yet viable avenues to social rank and influence. Journal of Personality and Social Psychology, 104(1), 103–125. https://doi.org/10.1037/a0030398

Cheng, J. T., Tracy, J. L., &amp; Henrich, J. (2010). Pride, personality, and the evolutionary foundations of human social status. Evolution and Human Behavior, 31(5), 334–347. https://doi.org/10.1016/j.evolhumbehav.2010.02.004

Cheong, M., Yammarino, F. J., Dionne, S. D., Spain, S. M., &amp; Tsai, C.-Y. (2019). A review of the effectiveness of empowering leadership. The Leadership Quarterly, 30(1). https://www.sciencedirect.com/science/article/abs/pii/S1048984318301310

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Duckitt, J., &amp; Sibley, C. G. (2010). Personality, ideology, prejudice, and politics: A dual‐process motivational model. Journal of Personality, 78(6), 1861–1894. https://doi.org/10.1111/j.1467-6494.2010.00672.x

Friederichs, K. M., Waldenmeier, K., &amp; Baumann, N. (2023). The benefits of prosocial power motivation in leadership: Action orientation fosters a win-win. PLOS ONE, 18(7), e0287394–e0287394. https://doi.org/10.1371/journal.pone.0287394

Ho, A. K., Kteily, N. S., Sheehy-Skeffington, J., &amp; Thomsen, L. (2025). Social dominance orientation: The motivational basis of intergroup inequality. Advances in Experimental Social Psychology, 72, 125–208. https://doi.org/10.1016/bs.aesp.2025.04.003

Ho, A. K., Sidanius, J., Kteily, N., Sheehy-Skeffington, J., Pratto, F., Henkel, K. E., Foels, R., &amp; Stewart, A. L. (2015). The nature of social dominance orientation: Theorizing and measuring preferences for intergroup inequality using the new SDO₇ scale. Journal of Personality and Social Psychology, 109(6), 1003–1028. https://doi.org/10.1037/pspi0000033

Ligneul, R., Girard, R., &amp; Dreher, J.-C. (2017). Social brains and divides: The interplay between social dominance orientation and the neural sensitivity to hierarchical ranks. Scientific Reports, 7(1). https://doi.org/10.1038/srep45920

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Maliszewski, N., Kuźmińska, A. O., Wieczorkowska-Wierzbińska, G., &amp; Werner-Maliszewska, A. (2014). The impact of explicit and implicit power motivation on educational choices. Polish Psychological Bulletin, 45(3), 275–285. https://doi.org/10.2478/ppb-2014-0034

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}}

== External links ==
* [https://www.ebsco.com/research-starters/social-sciences-and-humanities/social-dominance-theory Social Dominance Theory Overview] (EBSCO)
* [https://online.ucpress.edu/collabra/article/7/1/28250/118714/Using-and-Understanding-Power-in-Psychological Using and Understanding Power in Psychological Research: A Survey Study] (University of California Press)
* [https://jspp.psychopen.eu/index.php/jspp/article/view/4745/4745.html When Inequality Fails: Power, Group Dominance, and Societal Change] (Journal of Social and Political Psychology)

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==Overview==
{{RoundBoxTop|theme=11}}
[[File:Donald Trump takes the oath of office (2025).jpg|thumb|President-elect Donald Trump takes the oath of office |'''Figure 1'''. Donald Trump's 2025 Inauguration surrounded by some of the world's wealthiest and most powerful individuals]]

Imagine a leader standing at their inauguration, surrounded by a concentration of wealthy and influential individuals. At first glance, this may reflect a preference for resources and influence. However, a closer look raises a psychological question: what motivates a leader to seek and exercise power, and how does this shape the way they lead?

This scenario reflects the leadership of United States President Donald Trump, whose 2025 administration includes a notable concentration of wealthy and influential individuals (Roeloffs, 2025). The individuals present at Trump's inauguration illustrate this concentration of political and economic power (see Figure 1). This provides a contemporary example for examining the relationship between power motivation and leadership.{{ic|[[w:Donald Trump|Second inauguration of Donald Trump]]}} Power is reflected not only in who a leader surrounds themselves with, but also in how they exercise their influence. For example, Trump uses social media as a political megaphone, bypassing traditional bureaucratic communication channels (Gambino, 2021). His public leadership style places considerable emphasis on personal image and the need of personal control with the disregard of external influences of power (Mobaseri &amp; Nosrat Kharazmi, Zohreh, 2025).

This raises the question: does the desire for power necessarily make someone an effective leader? Individuals seek leadership for various reasons, and how they use their influence shapes their interactions with followers, decision-making, and pursuit of goals. Psychology helps explain these differences by examining power motivation and how individual motives influence leadership behaviour.
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This chapter will explore [https://pmc.ncbi.nlm.nih.gov/articles/PMC10355387/ power motivation] (Friederichs et al., 2023), the desire to influence, control, and have the ability to impact others, influencing leadership styles, behaviour and effectiveness (McClelland, 1970). Being expressed via socialised or personalised power, determining the leader's behaviour and effectiveness, (Reeve, 2018; McClelland, 1970; Carvalho &amp; Conde, 2024).

Understanding power motivation provides a psychological framework for examining how leaders exercise authority and how followers respond. Psychological science can help explain why some power-motivated leaders use influence to control, while others use it to empower (Reeve, 2018).

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[[File:P psychology.png|right]]
'''Focus questions:'''

*What psychological theories explain power motivation in leaders?

*How does a leader's orientation towards power influence their specific leadership style?

*What is implicit motivation, and how does it differ from explicit power motivation in leaders?

*How does power motivation influence leadership effectiveness?
{{RoundBoxBottom}}

==Understanding power motivation through psychological theories==
'''Focus question:''' ''What psychological theories explain power motivation in leaders?''

The definition of motivation and power, one describes the push to act the other often associated with aggression, influence, authority and control, together they hold a heavy definition. In psychology, [[Motivation and emotion/Lectures/Introduction|motivation]] is the driving force that guides human behaviour; it is the use of will-power and self-discipline - channelling effort to achieve a goal. Certain individuals have predominant motive of power, being motivated by the internal urge to dominate, influence, or control (Kurt, 2021). Power motivation is the broad construct that refers to the desire for leadership, authority or status, it is built up of three characteristics: strong action, emotional impact, and concern for status, frame, and reputation, heavily influenced by cultural values and socialised experiences (McClelland,1970).

Power seekers can be effective, well-adjusted, and highly motivated. Power is a source of human control; only the mentally healthy can wield it successfully. Those with this form of nPower struggle to feel satisfied unless they are in a position that fulfils their power-hungry needs, such as making decisions, influencing an audience, or obtaining information to become influential. Such occupations are teachers, journalists, clergy, psychologists, diplomats, business executives, political leaders and advisors (Reeve, 2018). [[wikipedia:David_McClelland|David McClelland's]] is popular within the psychology community for his thoughts on power motivation, with the most well-known theories, the Three Need Theory and the Two Faces of Power theory. In studies done by McClelland, it was discovered that those with high nPower tended to drink more heavily, making a comment that nPower can either manifest through drinking or 'hold office.'

=== Three need theory ===
[[File:DavidMcClelland.jpg|thumb|'''Figure 2.''' David McClelland]]David McClelland, a Harvard psychologist who conducted extensive research into human motivation (seen in Figure 2.), proposed the [[wikipedia:Need_theory|Three Need Theory]]. The theory identifies three acquired motivational needs: the need for achievement, the need for affiliation, and the need for power (McClelland, 1970). Although individuals can experiences all three needs, the strength of each varies between individuals and can influence their behaviour. Table 1 summarises these needs and their defining characteristics being examined from high to low behaviour (Kurt, 2021).

Of special interest to leadership is the nPower, which involved the desire to influnence others and have an impact on thier behaviour. While a strong need for achievement may motivate individuals to pursue challenging goals, and a strong need for affilication may encrourage them to maintain psoitive interpersonal relatinoships, a strong need for power can motivate individuals to seek influence and positions of authoirty. However the need for power alone does not determine whether someone will be an effective leader; its expression and the way an individual exercises their influence matter. 

On an additional note, [[Motivation and emotion/Book/2019/Two-factor motivation theory|Herzberg's Two-Factor theory]] and [[Motivation and emotion/Book/2011/Maslow's hierarchy of needs|Maslow's theory of Hierarchy of Needs]] can be evaluated along with the Three Need Theory. Looking into how motivation affects health, as success impacts stress, blood pressure, and hormone levels (McClelland,1970). Individuals develop motivation at different degrees, influenced by personal experiences and exposure. When an experience causes a positive emotional response, the individual is more likely to seek that feeling out again through a similar experience (Reeve, 2018). Explained through the McClelland Acquired Needs Theory, positive emotional experiences develop acquired needs through the reinforcement of the behaviour (Kurt, 2021).
{| class=&quot;wikitable&quot;
|+Table 1: Three Need Theory
!Need
!Definition
!High Behaviour
!Low Behaviour
|-
|Need for Achievement 
|Situations that challenge individuals with explicit standards.
|Individual exhibits a need to win and receive recognition.
|Constant fear of failure, typically avoids responsibilities. 
|-
|Need for Affiliation 
|Situations that afford warm relationship opportunities.
|A desire within for control, typically exaggerates own position.
|A heavily dependent individual, tries to minimise own position and importance.
|-
|Need for Power 
|Situations that enable others to exert influence over others.
|Individual demands and expects loyalty and harmony.
|Individual remains 'aloof' and keeps social distance from influence over others. 
|}

==== Two faces of power ====
McClelland's [https://www.jstor.org/stable/pdf/24356663.pdf Two Faces of Power] framework distinguishes between two ways the need for power (nPower) can be expressed, splitting the nPower into two manner's, personalised power or socialised power, also referred to as ''pP''ower, and ''s''Power; which demonstrate contrasting nature between how power can be expressed(McClelland, 1970). Personalised power centres on personal control, it is seen as socially unacceptable way of expression, is is closely linked dominance and status. Those influenced by ''p''Power may tend to seek to strengthen their own position and influence, in a way it is the definition that power is sometimes thought as, aggressive, and self-desired, directly affecting collective goals (McClelland, 1970). While McClelland was doing his research of these mannerisms of power, he though that if those who has personalised power were in the atmosphere of international relations the consequences would be ''ominous''. While, socialised power, ''s''Power, is more socially acceptable form of expression, leaders are motivated through the idea of benefiting others, and feeling ambivalence about holding such power; it incorporates feelings of personal strength, and the known knowledge of being careful (Bargh &amp; Lee-Chai, 2002; Friederichs et al., 2023; Magee &amp; Langner, 2008; McClellad, 1970). 

McClelland's distinction between the two faces of power was interestingly enough informed through the research of how the need for power can be expressed in different ways. As an example, McClelland discussed findings linked to high n''P''ower with heavier alcohol consumption among some individuals, while other expressed their power through holding leadership positions in organisations (McClellad, 1970). This contrast illustrates that a strong power motive does not automatically lead to the same behaviour. Instead, the mannerism in which it is expressed can whole-heartedly depend on how the individual regulates and directs their desire for influence. 

These forms of expression are not necessarily mutually exclusive. Leaders may display elements of both; McClelland believes that a true leader can balance both. They can exercise personal dominance and socialised leadership (Bargh &amp; Lee-Chai, 2002). ''p''Power can become problematic when leaders become too absorbed by the maintenance of their position and influence, the ability to dominate, manipulate, and disagree. However, the issue isn't high-power motivation; it's how it is expressed (McClelland, 1970). 

=== The leadership motive pattern ===
McClelland and David Burnham (1975) proposed the idea that effective leadership is associated with a certain specific combination of motives known as the [[Motivation and emotion/Book/2015/Leadership motivation#Leadership Motive Pattern|Leadership Motive Pattern]] (LMP) (Spangler et al., 2014). This consists of three primary elements, high need for power (nPow), a low need for affiliation (nAff) and a high activity inhibition AI). This model demonstrated how motivation can work together to shape leadership behaviour (Reeve, 2018). 

Each component serves a different purpose, building characterises which McClelland agrued described the most effective leaders  within beucratic organisation (Spangler et al., 2014). High nPower, is the force to influence, direct and impact others, this has been well-established by now. Low nAff, is a reduced desire for friendly, close interpersonal relationships, which prevent the leaders from producing biased decision-making  or being overly lenient out of the desire to be liked. High AI is based on self-control, maturity, and the ability to channel power socially rather an impulsively (McClelland &amp; Boyatzis, 1982).

Research by McClelland and Burnhamd (1982) found that the LMP was associated with greater career advancement over eight-and sixteen-year periods among non-technical managers; however, the same relationship was not found for technical managers. This suggests the pattern may only hold value for specific roles in demonstrating leadership effectiveness. When relevant, it demonstrated that managers of this pattern typically generate higher morale in their subordinates; leadership styles such as those of nations that spend relatively more on military forces than private consumption, which McClelland described as a system's capacity to mobilise resources in the interest of the nation (McClelland &amp; Boyatzis, 1982; Spangler et al., 2014). 


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== Recap ==
&lt;quiz display=simple&gt;
{&amp;nbsp;
|type=&quot;{}&quot;}
What is the driving force that guides human behaviour?
{ Motivation }

{What is the key difference between personalised power and socialised power?}
- Personalised power focuses on achievement, and socialised power focuses on affiliation
+ Personalised power focuses on personal dominance and control, and socialised power focuses on benefiting others
- Personalised power is consistently associated with an effective leadership style, whereas socialised power is associated with an ineffective leadership style.

{Which combination of motives is associated with McClelland’s Leadership Motive Pattern in effective managers?}
- High need for achievement, high need for affiliation and low activity inhibition
+ High need for power, low need for affiliation and high activity inhibition
- Low need for power, high need for affiliation and high activity inhibition

{Which behaviour best fits an individual with a high need for power?}
- Avoiding situations where they might influence others
+ Seek opportunities to influence, control, or have an impact on others
- Avoid challenging tasks for fear of failure


&lt;/quiz&gt;

{{RoundBoxBottom}}

== Power motivation and leadership style ==
'''Focus question:''' ''How does a leader's orientation towards power influence their specific leadership style?''

An individual’s desire for power does not automatically determine their leadership style. How an individual in a position of authority understands and exercises power over others can shape their interactions, decision-making approaches, and the goals they prioritise. Examining power orientation alongside psychological characteristics provides a deeper understanding of why leaders may use their influence in various ways and how those differences are reflected in their leadership style. 

=== Power orientation and leadership behaviour ===
Power motivation is the drive to influence others, while power orientation is the how; it is the framework for how a leader becomes influential. A negative stereotype surrounds high power motivation, with the speculation that it automatically relates to undesirable behaviour, unlike prosocial power motivation, which is often associated with generosity. However, those with high power motivation can have different power orientations. Carbalho and Conde (2024) distinguish ego-power orientation and social-power orientations, highlighting that individuals can combine said orientations in different ways. Ego-power is associated with pursuing goals to satisfy the self and achieve a sense of self-fulfilment; this doesn't automatically result in harmful leadership, as it partly depends on the individual's position of influence and work. Social-power orientation links directing power to collective outcomes

=== Leadership trait analysis ===
Leadership Trait Analysis (LTA), developed by Margaret Hermann (2003), is a framework for analysing political leaders' psychological characteristics using interviews and public speeches. It examines seven traits across three dimensions: responsiveness to constraints, openness to information and motivation. The seven traits include the need for power, the belief that one can control what happens next, self-confidence, trust in others, conceptual complexity, the intensity of in-group bias or nationalism, and the need for affiliation. Together, these traits help researchers examine how leaders process information, respond to constraints and approach decision-making.

Trump illustrates how psychological frameworks can be applied to political leadership. Mobaseri and Nosrat Kharazmi (2025) examined Trump's leadership characteristics and political beliefs across different periods, including before his presidency and during his first term. The research explores how far his core beliefs influence his responses to political experiences and the COVID-19 crisis. The study highlights the value of examining leaders' beliefs and characteristics over time to understand their responses to the political climate.

The analysis found Trump low in need for power, perceived control, self-confidence, in-group bias, and trust in others, but high in conceptual complexity. These traits informed Mobaseri and Nosrat Kharazmi's (2025) account of his leadership: resistance to adaptation, disregard for policymaking, charisma, and sensitivity to context in decisions.

The findings show how leadership reflects the interaction between a leader's psychology and their situation. LTA offers a way to analyse individual differences that shape leadership style.

=== Leadership styles and effectiveness ===
Power orientation can be reflected in different leadership styles, which describe how leaders direct, influence and interact with followers. For example, a leader who prioritises complete personal control may favour a more autocratic approach, while a leader who values engagement may be more inclined towards a democratic leadership. However, while leadership styles reflect theoretical models, they can also be shaped by individual characteristics and techniques (Khajeh et al., 2018; &quot;What Are the Different Leadership Styles?&quot;, 2024). Different styles place varying emphasis on factors seen in Table 2 (Deakin University, 2024; Bwalya, 2023). 

Effective leadership involves more than holding a position of authority; it is about how leaders behave and interact. There are five essential characteristics of leadership: self-image, self-control, socialised power, sustained dialogue, and strategic intent, providing a practical framework for a successful leader (Power, 2026). Power, motivation, and leadership matter across contexts, from political leaders to supervisors, who need to build relationships with employees and an environment of trust if they want to do so. The characteristics emphasise the importance of authority, responsibility, communication, and directing efforts towards organisational goals (Power, 2026; Friederichs et al., 2023)

Research suggests that transformational leadership can produce positive outcomes by motivating and inspiring followers and benefiting the group rather than serving personal interests (Peyton et al., 2019). This shows how power can support group goals rather than simply reinforcing leadership status. Nevertheless, no single leadership style guarantees effectiveness; outcomes depend on how the leader behaves and responds to the situation at hand.

{| class=&quot;wikitable&quot;
|+Table 2. Leadership Styles
! colspan=&quot;3&quot; |Leadership styles
|-
|Style
|Description
|Example Leaders
|-
|Autocratic 
|Leader holds complete control over decision-making with no input from followers. Consistently exercises control over the decision-making process. Expects strict compliance with policies and procedures, and does not take input from followers. They micromanage and control subordinate work. They make quick decisions because they do not have to consult. There is a lack of creative innovation (Bwalya, 2023). 
|Adolf Hitler and  Kim Jong-un 
|-
|Democratic 
|Leader is involved in team members' decision-making process, continuously encourages communication, and seeks feedback on matters, valuing input and ideas, wanting followers to participate in shaping strategies and goals (Bwalya, 2023).
|Former President of South Africa, Nelson Mandela and Former Prime Minister of New Zealand Jacinda Ardern 
|-
|Laissex-faire
| The leader is distant and has minimal involvement in decisions, unlike autocratic leadership, as laissez-faire lets followers make decisions with little guidance or supervision, trusting their ability to manage responsibilities. They are comfortable with mistakes and take accountability for followers' mistakes. This empowers employees and enables faster decision-making. However, the lack of guidance can cause confusion and lack of coordination (Bwalya, 2023). 
|Former President Herbert Hoover and Mahatma Ghandi
|-
|Servant 
|Leader is prosocial and motivated by power, focusing on the needs and well-being of others. Aiming to support and empower followers, in hopes they reach their full potential (Bwalya, 2023). 
|Pope Francis
|-
|Transformational 
|Based on inspiration and motivation to achieve performance, with high expectations and focus on challenging others to exceed self-interest. Focuses on transforming followers through inspiration, motivation, and effective communication. They rely on the leader's influence; if the leader fails to provide proper guidance, it can impact followers (Bwalya, 2023). 
|Former President of South Africa Nelson Mandela and Former President of the United States Barack Obama 
|-
|Transactional
|Focuses on the exchange relationship between the leader and their followers. The leader maintains stability and achieves goals by providing rewards and punishments based on performance. Very goal-oriented, with clear expectations, and quick decision-making (Bwalya, 2023).  
|Bill Gates and Former Chancellor of Germany Angela Merkel
|}

{{RoundBoxTop|theme=8}}[[Image: Hand Gesture - Holding a Magnifying Glass.gif|right|128px]] 
==Quiz==
&lt;quiz display=simple&gt; 
Which statement best explains the relationship between a leader’s power motivation and their leadership style?
|type=&quot;()&quot;} 
- Leaders with high power motivation are more likely to adopt an autocratic style, regardless of their values or circumstances
+ A leader’s power motivation determines their leadership style, while their psychological characteristics have very little influence
- Power motivation can influence a leader’s behaviour, but their power orientation, psychological characteristics and circumstances also shape how they exercise influence
&lt;/quiz&gt;
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== Implicit and explicit power motivation ==
'''Focus question:''' ''What is implicit motivation, and how does it differ from explicit power motivation in leaders?''

Human motivation can operate through two systems: implicit and explicit motivation. Both influencing behaviour, but very different in the extent to which the individuals are consciously aware of their motives behind their behaviour. When looking at leadership, it is helpful to dissect the distinctions to understand why a leader's states goals may not fully reflect their underlying needs which influence their behaviour. 

=== Implicit and explicit power motivation in leadership ===
Implicit motive (nPow) is unconscious motivation outside an individual’s awareness, mind map below in Figure 3 illustrates it. McClelland identified three implicit motives that shape thoughts, feelings, and actions: achievement, affiliation, and power. Developed through early preverbal experiences, they remain dormant until activated by incentives. Their influence appears in recurring patterns of thought, emotion, and behaviour, even when people cannot identify their motives (Reeve, 2018). Unlike explicit motives, implicit motives are difficult to measure directly. Researchers use the Picture-Story Exercise (PSE), asking participants to create stories from images and analysing them for themes related to the three motives. 

[[File:Implicit_Motives_associations.png|thumb| '''Figure 3.''' Mind map of implicit motives]]Explicit motives are conscious, self-attributed motives people can describe through their goals, values, and preferences (Slabbinck &amp; Van Witteloostuijn, 2020). Often assessed with self-report questionnaires, explicit power motives reflect desires for influence, status, and leadership. Their dimensions, dominance, prestige, and leadership, can help explain how power motives relate to dark personality traits. Dominance involves controlling others and is associated with Machiavellianism and counterproductive work behaviour. Prestige involves gaining influence by displaying knowledge or status and is linked to narcissism. Leadership involves guiding groups toward shared goals and may predict organisational citizenship behaviour and align with transformational leadership.

A strong explicit power motive does not automatically lead to destructive leadership. It can support productive leadership, but may also overlap with dark traits such as narcissism, Machiavellianism, and psychopathy.

=== Congruence ===
When an individual’s implicit and explicit motives align, it is called motive congruence. Motive congruence can predict outcomes of strength, flow, and well-being; it is associated with higher empathy and forgiveness rather than incongruence. Additionally, high implicit or explicit motives lead to higher empathy and forgiveness (Ran et al., 2021). Furthermore, when an individual’s implicit and explicit motives are not aligned, incongruence creates internal friction, chronic stress, and burnout. This can occur when they pursue goals that do not fit their unconscious drivers (Thrash et al., 2012). 

Applying this to leadership styles highlights how a leader's effectiveness and well-being depend on whether their chosen leadership style aligns with their implicit motive. When a leader's leadership style conflicts with their implicit motive, they experience ''motive incongruence,'' which can lead to chronic stress, burnout, and friction, whereas alignment predicts greater flow, high energy, and effortless leadership (Ran et al., 2021; Thrash et al., 2012).

== Power motivation and leadership effectiveness ==
'''Focus question:''' ''How does power motivation influence leadership effectiveness?''

Power motivation can influence leadership effectiveness depending on how the motive is expressed and regulated. Two incentive types can be distinguished: social and activity. Social incentives are rewards, expectations, demands, and norms coming from other people. Activity incentives are rewards inherent in performing the activity itself; the activity reinforces the individual.

A high need for power can motivate individuals to seek authoritative roles to make decisions and direct others; the shape power motivation takes, i.e., personalised or socialised, directly indicates leadership effectiveness. Power motivation can develop through social and environmental experiences. Individuals who develop power-strivings may have grown up in environments where parents set demanding standards, potentially contributing to a desire for recognition and admiration. nPower has been associated with aggressive tendencies, although high power motivation doesn't automatically result in overt aggression. Social norms, laws, and consequences can constrain this expression, keeping that desire to control internal rather than manifesting as overt aggression (Reeve, 2018). Individuals high in the need for power may be attracted to occupations that offer career advancement; they are drawn to professions with influential opportunities (Reeve, 2018).

=== Destructive power dynamics and power abuse ===
There is a ''fickle'' relationship between aggression and the need or desire for power are closely linked. Studies have linked aggressive tendencies to dominance and the need for power (Verona et al., 2023). Verona et al. (2023) define human aggression as behaving with the intent to cause harm to another individual, and the target of the behaviour is driven to avoid it. Aggression can also take direct vs indirect and overt vs covert forms. That said, no concrete evidence links any level of ''feeling'' power to aggression. 

An individual with a high need for power may desire impact, control, or influence over another person or group, or even the world at large; aggression can be a means of satisfying those power needs. However, social norms, laws, and consequences can constrain this expression, causing that aggression to manifest in a more covert form. Individuals, both men and women, report more impulses to act aggressively than others; this behaviour would include yelling, throwing or destroying items and insulting others. Other factors of aggression and its link with high power-seeking individuals include finding a release through drinking, using this as a way to inflate their sense of control. Furthermore, men respond to stress and other setbacks with the behaviour of inflicting abuse on their partners, as well as an increased level of sexual misconduct (Reeve, 2018; Spanler et al., 2014). This indicates that a sense of power comes not only from leadership and reputation but can also be built through strategies of drinking, risk-taking, and posturing (Reeve, 2018).

Those who harbour inclinations that are both benevolent and malevolent towards others strive to improve the world while also influencing everyone else (Reeve, 2018). The ''dark side'' of implicit motive is the combination of opportunity to use power for personal benefit, which is the 'abuse of power.' Unrestrained affiliation can lead to favouritism and corruption in political and bureaucratic organisations. Achievement ignores political/interpersonal issues. High need for achievement: find it difficult working in groups, making decisions, and enforcing authority, ignoring interpersonal relationships (Spanier et al., 2014).[[File:The_Dark_Triad_Traits.jpg|thumb|'''Figure 4.''' The dark triad, and its associated personality traits]]

=== The dark triad traits ===
First proposed by Paulhus and Williams (2002), the &quot;Dark Triad&quot; traits- narcissism, Machiavellianism, and psychopathy, seen in Figure 4, are three overlapping personality traits that can strongly motivate individuals to seek and wield power. When an individual has these traits, it often means they restrain and fuel their ruthlessness and self-serving behaviour. Research has found that scoring high on these traits increases an individual’s likelihood of committing crimes, causing distress, and creating severe issues for organisations when in authoritative leadership positions (LeBreton et al., 2018).  

Findings on the dark triad suggest that leadership outcomes depend not only on a leader's desire for influence, but also on their personality and how they exercise authority. However, the dark triad should not be associated with high implicit power motivation, as a strong unconscious drive to influence or impact others is not the same as the dark triad traits. An individual can have a strong implicit need for power without dark personality traits. Dark triad traits are associated with excessive admiration-seeking behaviour, manipulation, and callousness; these traits can interfere with relationships and judgement calls. Specific characteristics of the traits are listed in Table 3. (LeBreton et al., 2018).
{| class=&quot;wikitable&quot;
|+Table 3. Dark triad characteristic defined (LeBreton et al., 2018). 
!Dark triad traits
!Characteristics
|-
|Machiavellianism
|Cynical, strategic, and manipulative
|-
|Psychopathy
|Erratic behaviour, interpersonal manipulation, callous affect and criminal tendencies
|-
|Narcissism
|Pride, aggression, envy, grandiosity, constant need for admiration, poor self-esteem
|} 

=== '''Key predictors of effective leadership''' ===
Power motivation can support effective leadership when regulated and directed toward collective rather than personal benefit. McClelland's research suggests effective leaders combine a strong need for power with high self-discipline, or “power under control,” which is linked to charismatic leadership and group morale (Reeve, 2018). However, a desire for influence alone does not ensure effectiveness. 

Self-regulation is especially important for leaders with potentially destructive personality tendencies. Stress, exhaustion, hunger, and cognitive overload can weaken willpower, making defensive reactions harder to control and potentially harming others. Strong motivation and self-awareness help leaders manage counterproductive tendencies and limit their disruptive effects.

Other motives also shape leadership. A strong need for affiliation can promote communication, respect, appreciation, and support, strengthening leader–follower relationships. Achievement motivation can encourage goal pursuit, but excessive striving may undermine effectiveness: highly active, achievement-oriented leaders can become frustrated when results fall short of expectations.

Moral identity also influences how leaders use power. Those with weaker moral identities may prioritize self-interest, while a prosocial approach uses influence to benefit others. This approach is associated with less power-related anxiety and greater well-being, suggesting that leaders’ purposes for exercising power affect their effectiveness.{{RoundBoxTop|theme=3}}[[File:John F. Kennedy speaks at Rice University.jpg|thumb|President John F. Kennedy speaking at Rice University |'''Figure 5.''' John F. Kennedy speaking at Rice University]]

== Case Study: John F. Kennedy ==

John F. Kennedy (JFK) is often recognised as an example of charismatic political leadership because of his optimistic public image, ambitious presidency, and compelling communication. Despite his relatively short time in office, Kennedy established a distinctive presidential identity by blending political leadership with popular culture and staying engaged with government and the public, which can be seen in Figure 5 (Reeve, 2018; McCann &amp; Mollan, 2023).
Kennedy's leadership aligns with McClelland's theory of motivational needs, with his profile characterised by a high need for power and a low need for affiliation (McCann &amp; Mollan, 2023). His charismatic communication also reflects transformational leadership, which emphasises inspiring followers to work towards shared goals. McClelland (1970) found that students who listened to Kennedy's inaugural address reported stronger feelings of inspiration and uplift, illustrating how a leader's communication can influence their audience.
Kennedy therefore shows how power motivation can support leadership by enabling individuals to influence, inspire, and mobilise others. However, effective leadership also depends on how that influence is exercised, particularly when responding to challenging political situations.
{{RoundBoxBottom}}

{{RoundBoxTop|theme=6}}
== Quiz Yourself ==
&lt;quiz display=simple&gt;
{Which combination of implicit motives is associated with effective leadership according to McClelland's leadership motive pattern?
|type=&quot;()&quot;}
- High power, high affiliation, and low inhibition
+ High power, low affiliation, and high inhibition
- Low power, high affiliation, and high inhibition
- High power, low affiliation, and low inhibition

{Does a high need for power necessarily result in aggressive behaviour?
|type=&quot;()&quot;}
- True
+ False

&lt;/quiz&gt;
{{RoundBoxBottom}}

==Conclusion==
Psychological theory and research suggest that power motivation influences leadership by shaping how individuals seek, maintain, and regulate influence. McClelland's Three Need Theory explains the individual differences in the needs for power, achievement, and affiliation, while the Two Faces of Power distinguishes between personalised power, which prioritises personal control and self-interest, and socialised power, the opportunity to influence and benefit others; this distinction helps explain why power motivation can produce drastically different leadership outcomes (McClelland, 1970; Carvalho &amp; Conde, 2024). The LMP further suggests that a high need for power, low need for affiliation and high activity inhibition can contribute to effective leadership by balancing influence with regulated self-control (Reeve, 2018).

Ultimately, power motivation is neither inherently positive nor negative. It effects depend on how leaders exercise their authority, regulate their behaviour and balance personal ambitions with the need of others. Effective leadership is not determined by how much power a person wants, but how they use it. Leaders who regulate their power motivation and direct their influence towards collective goals, fostering development and outcomes, are more likely to be well received by the public or their subordinates (Peyton et al., 2019; Friederichs et al., 2023). Understanding power motivation therefore helps explain both the emergence of effective leaders and the risks of power abuse, highlighting the importance of self-regulation and ethical exercise of influence.{{RoundBoxTop|theme=11}}[[Image:Nuvola_apps_filetypes.png|right|102px]]
;Reflection activity

Think of a time when you were in a leadership position or had to influence a group decision. This could be anything from university or work to a team sport. Reflect on the following questions:

*What was the situation, and did you take control, encourage collaboration, or take a different approach? 
*How did you influence others or make decisions? 
*What do you think motivated your behaviour? 
*How did your approach affect the group and its outcome? Now, looking back, would you lead differently?{{RoundBoxBottom}}

==See also==
* [[Motivation and emotion/Book/2018/Emotional intelligence and leadership effectiveness|Emotional intelligence and leadership effectiveness]] (Book chapter, 2018)
* [[Motivation and emotion/Book/2015/Leadership motivation#Leadership Motive Pattern|Leadership motivation]] (Book chapter, 2015)
* [[Motivation and emotion/Book/2011/Maslow's hierarchy of needs|Maslow's hierarchy of needs]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2019/Two-factor motivation theory|Two-factor motivation theory]] (Book chapter, 2019)

{{ic|Integrate these links; use alphabetical order}}
* [[wikipedia:Need_theory|Need theory]] (Wikipedia)
* [[wikipedia:Need_for_power|Need for power]] (Wikipedia)
* [[wikipedia:David_McClelland|David Clelland]] (Wikipedia)

==References==

{{Hanging indent|1=

Bargh, J. A., &amp; Lee-Chai, A. Y. (2002). The use and abuse of power : Multiple perspectives in the causes of corruption. Psychology.

Bwalya, A. (2023). Leadership styles. Article in Journal of Entrepreneurship, Management and Innovation, 11(8), 181–193. https://doi.org/10.6084/m9.figshare.23932113

Carvalho, J. M. S., &amp; Conde, A. (2024). Individual power in human motivation – review and theoretical perspective. Acta Psychologica, 249, 104452–104452. https://doi.org/10.1016/j.actpsy.2024.104452

Deakin University. (2024, December 5). What are the different leadership styles? Deakin.Edu.Au. https://leadership.deakin.edu.au/blog/different-leadership-styles

Friederichs, K. M., Waldenmeier, K., &amp; Baumann, N. (2023). The benefits of prosocial power motivation in leadership: Action orientation fosters a win-win. Plos One, 18(7), e0287394–e0287394. https://doi.org/10.1371/journal.pone.0287394

Khajeh, A., Abu, M., &amp; Asaari, H. (2018). Impact of leadership styles on organizational performance. Journal of Human Resources Management Research, 2018(2166–0018), 2166–2184. https://ibimapublishing.com/articles/JHRMR/2018/687849/687849-1.pdf

Kurt, D. S. (2021, May 23). McClelland’s Three Needs Theory: Power, Achievement, and Affiliation. Education Library. https://educationlibrary.org/mcclellands-three-needs-theory-power-achievement-and-affiliation/#1

McCann, L., &amp; Mollan, S. (2023, November 20). JFK 60 years on: His leadership style and the reality behind the myths. The Conversation. https://theconversation.com/jfk-60-years-on-his-leadership-style-and-the-reality-behind-the-myths-216477

McClelland, D. C. (1970). The two faces of power. Journal of International Affairs, 24(1), 29–47. JSTOR. https://www.jstor.org/stable/24356663

Peyton, T., Zigarmi, D., &amp; Fowler, S. N. (2019). Examining the relationship between leaders’ power use, followers’ motivational outlooks, and followers’ work intentions. Frontiers in Psychology, 9(2620). https://doi.org/10.3389/fpsyg.2018.02620

Power , D. P. G. (2026). The five essentials of leadership {{!}} APS. Psychology.Org.Au. https://psychology.org.au/inpsych/2017/august/power

Reeve, J. (2018). Understanding motivation and emotion (7th edn, pp. 152–176). John Wiley &amp; Sons, Inc.

Slabbinck, H., &amp; Van Witteloostuijn, A. (2020). Explicit and implicit basic human motives, and public service motivation. Frontiers in Psychology, 11(1542). https://doi.org/10.3389/fpsyg.2020.01542

Spanler, W. D., Tikhomirov, A., Lee Sotak, K., &amp; Palrecha, R. (2014). Leader motive profiles in eight types of organizations. ScienceDirect, 25(6). https://www-sciencedirect-com.ezproxy.canberra.edu.au/science/article/pii/S1048984314001040

}}

==External links==
{{ic|Move these links into References and cite; replace with links to the most relevant external non-academic resources}}

* [https://leadership.deakin.edu.au/blog/what-is-transformational-leadership Article on Transformational leadership style] (Deakin University, 2024)
* [https://pmc.ncbi.nlm.nih.gov/articles/PMC10355387/ Power motivation, the benefits of prosocial power] (Friederichs et al., 2023)
* [https://www.jstor.org/stable/pdf/24356663.pdf The Two Faces of Power Journal] (McClelland, 1970)

==See also==
* [[Motivation and emotion/Book/2024/Power motivation and leadership|Power motivation and leadership]] (Book chapter, 2024)

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__TOC__

==Overview==
{{RoundBoxTop|theme=11}}
[[File:Donald Trump takes the oath of office (2025).jpg|thumb|President-elect Donald Trump takes the oath of office |'''Figure 1'''. Donald Trump's 2025 Inauguration surrounded by some of the world's wealthiest and most powerful individuals]]

Imagine a leader standing at their inauguration, surrounded by a concentration of wealthy and influential individuals. At first glance, this may reflect a preference for resources and influence. However, a closer look raises a psychological question: what motivates a leader to seek and exercise power, and how does this shape the way they lead?

This scenario reflects the leadership of United States President Donald Trump, whose 2025 administration includes a notable concentration of wealthy and influential individuals (Roeloffs, 2025). The individuals present at Trump's inauguration illustrate this concentration of political and economic power (see Figure 1). This provides a contemporary example for examining the relationship between power motivation and leadership.{{ic|[[w:Donald Trump|Second inauguration of Donald Trump]]}} Power is reflected not only in who a leader surrounds themselves with, but also in how they exercise their influence. For example, Trump uses social media as a political megaphone, bypassing traditional bureaucratic communication channels (Gambino, 2021). His public leadership style places considerable emphasis on personal image and the need of personal control with the disregard of external influences of power (Mobaseri &amp; Nosrat Kharazmi, Zohreh, 2025).

This raises the question: does the desire for power necessarily make someone an effective leader? Individuals seek leadership for various reasons, and how they use their influence shapes their interactions with followers, decision-making, and pursuit of goals. Psychology helps explain these differences by examining power motivation and how individual motives influence leadership behaviour.
{{RoundBoxBottom}}

This chapter will explore [https://pmc.ncbi.nlm.nih.gov/articles/PMC10355387/ power motivation] (Friederichs et al., 2023), the desire to influence, control, and have the ability to impact others, influencing leadership styles, behaviour and effectiveness (McClelland, 1970). Being expressed via socialised or personalised power, determining the leader's behaviour and effectiveness, (Reeve, 2018; McClelland, 1970; Carvalho &amp; Conde, 2024).

Understanding power motivation provides a psychological framework for examining how leaders exercise authority and how followers respond. Psychological science can help explain why some power-motivated leaders use influence to control, while others use it to empower (Reeve, 2018).

{{RoundBoxTop|theme=11}}
[[File:P psychology.png|right]]
'''Focus questions:'''

*What psychological theories explain power motivation in leaders?

*How does a leader's orientation towards power influence their specific leadership style?

*What is implicit motivation, and how does it differ from explicit power motivation in leaders?

*How does power motivation influence leadership effectiveness?
{{RoundBoxBottom}}

==Understanding power motivation through psychological theories==
'''Focus question:''' ''What psychological theories explain power motivation in leaders?''

The definition of motivation and power, one describes the push to act the other often associated with aggression, influence, authority and control, together they hold a heavy definition. In psychology, [[Motivation and emotion/Lectures/Introduction|motivation]] is the driving force that guides human behaviour; it is the use of will-power and self-discipline - channelling effort to achieve a goal. Certain individuals have predominant motive of power, being motivated by the internal urge to dominate, influence, or control (Kurt, 2021). Power motivation is the broad construct that refers to the desire for leadership, authority or status, it is built up of three characteristics: strong action, emotional impact, and concern for status, frame, and reputation, heavily influenced by cultural values and socialised experiences (McClelland,1970).

Power seekers can be effective, well-adjusted, and highly motivated. Power is a source of human control; only the mentally healthy can wield it successfully. Those with this form of nPower struggle to feel satisfied unless they are in a position that fulfils their power-hungry needs, such as making decisions, influencing an audience, or obtaining information to become influential. Such occupations are teachers, journalists, clergy, psychologists, diplomats, business executives, political leaders and advisors (Reeve, 2018). [[wikipedia:David_McClelland|David McClelland's]] is popular within the psychology community for his thoughts on power motivation, with the most well-known theories, the Three Need Theory and the Two Faces of Power theory.

=== Three need theory ===
[[File:DavidMcClelland.jpg|thumb|'''Figure 2.''' David McClelland]]McClelland, a Harvard psychologist who conducted extensive research into human motivation (seen in Figure 2.), proposed the [[wikipedia:Need_theory|Three Need Theory]]. The theory identifies three acquired motivational needs: the need for achievement, the need for affiliation, and the need for power (McClelland, 1970). Although individuals can experiences all three needs, the strength of each varies between individuals and can influence their behaviour. Table 1 summarises these needs and their defining characteristics being examined from high to low behaviour (Kurt, 2021).

Of special interest to leadership is the nPower, which involved the desire to influnence others and have an impact on thier behaviour. While a strong need for achievement may motivate individuals to pursue challenging goals, and a strong need for affilication may encrourage them to maintain positive interpersonal relationships, a strong need for power can motivate individuals to seek positions of authoirty. However the nPower alone does not determine whether someone will be an effective leader; its expression and the way an individual exercises their influence matter 

 {| class=&quot;wikitable&quot;
|+Table 1: Three Need Theory
!Need
!Definition
!High Behaviour
!Low Behaviour
|-
|Need for Achievement 
|Situations that challenge individuals with explicit standards.
|Individual exhibits a need to win and receive recognition.
|Constant fear of failure, typically avoids responsibilities. 
|-
|Need for Affiliation 
|Situations that afford warm relationship opportunities.
|A desire within for control, typically exaggerates own position.
|A heavily dependent individual, tries to minimise own position and importance.
|-
|Need for Power 
|Situations that enable others to exert influence over others.
|Individual demands and expects loyalty and harmony.
|Individual remains 'aloof' and keeps social distance from influence over others. 
|}

==== Two faces of power ====
McClelland's [https://www.jstor.org/stable/pdf/24356663.pdf Two Faces of Power] framework distinguishes between two ways the nPower can be expressed, personalised power or socialised power, also referred to as ''pP''ower, and ''s''Power (McClelland, 1970). ''pP''ower centres on personal control, it is seen as socially unacceptable way of expression, is is closely linked dominance and status. Those influenced by ''p''Power may tend to seek to strengthen their own position and influence (McClelland, 1970). While McClelland was doing his research of these mannerisms of power, he though that if those who obtained ''pP''ower were in the environment of international relations the consequences would be ''ominous''. While, ''s''Power, is the more socially acceptable form of expression, with leaders being motivated through the benefit of others; it incorporates feelings of personal strength, and the known knowledge of being careful (Bargh &amp; Lee-Chai, 2002; Friederichs et al., 2023; Magee &amp; Langner, 2008; McClellad, 1970). 

These forms of expression are not necessarily mutually exclusive. Leaders may display elements of both; McClelland believes that a true leader can balance personal dominance and socialised leadership (Bargh &amp; Lee-Chai, 2002). ''p''Power can become problematic when leaders become too absorbed by the maintenance of their position and influence, the ability to dominate, manipulate, and disagree. However, the issue isn't high-power motivation; it's how it is expressed (McClelland, 1970). 

=== The leadership motive pattern ===
McClelland and David Burnham (1975) proposed the idea that effective leadership is associated with a certain specific combination of motives known as the [[Motivation and emotion/Book/2015/Leadership motivation#Leadership Motive Pattern|Leadership Motive Pattern]] (LMP) (Spangler et al., 2014). This consists of three primary elements, high need for power (nPow), a low need for affiliation (nAff) and a high activity inhibition AI). This model demonstrated how motivation can work together to shape leadership behaviour (Reeve, 2018). 

Each component serves as a different purpose, building characterises of the most effective leaders within bureaucratic organisation (Spangler et al., 2014). High nPow, is the force to influence, direct and impact others, this has been well-established by now. Low nAff, is a reduced desire for friendly interpersonal relationships, which prevent the leaders from producing biased decision-making. High AI is based on self-control, maturity, and the ability to channel power socially rather an impulsively (McClelland &amp; Boyatzis, 1982).

Research by McClelland and Burnhamd (1982) found that the LMP may only hold value for specific roles in demonstrating leadership effectiveness. When relevant, it demonstrated that managers of this pattern typically generate higher morale in their subordinates; leadership styles such as those of nations that spend relatively more on military forces than private consumption, which McClelland described as a system's capacity to mobilise resources in the interest of the nation (McClelland &amp; Boyatzis, 1982; Spangler et al., 2014). 


{{RoundBoxTop|theme=8}}
== Recap ==
&lt;quiz display=simple&gt;
{&amp;nbsp;
|type=&quot;{}&quot;}
What is the driving force that guides human behaviour?
{ Motivation }

{What is the key difference between personalised power and socialised power?}
- Personalised power focuses on achievement, and socialised power focuses on affiliation
+ Personalised power focuses on personal dominance and control, and socialised power focuses on benefiting others
- Personalised power is consistently associated with an effective leadership style, whereas socialised power is associated with an ineffective leadership style.

{Which combination of motives is associated with McClelland’s Leadership Motive Pattern in effective managers?}
- High need for achievement, high need for affiliation and low activity inhibition
+ High need for power, low need for affiliation and high activity inhibition
- Low need for power, high need for affiliation and high activity inhibition

{Which behaviour best fits an individual with a high need for power?}
- Avoiding situations where they might influence others
+ Seek opportunities to influence, control, or have an impact on others
- Avoid challenging tasks for fear of failure


&lt;/quiz&gt;

{{RoundBoxBottom}}

== Power motivation and leadership style ==
'''Focus question:''' ''How does a leader's orientation towards power influence their specific leadership style?''

An individual’s desire for power does not automatically determine their leadership style. How an individual in a position of authority understands and exercises power over others can shape their interactions, decision-making approaches, and the goals they prioritise. Examining power orientation alongside psychological characteristics provides a deeper understanding of why leaders may use their influence in various ways and how those differences are reflected in their leadership style. 

=== Power orientation and leadership behaviour ===
Power motivation is the drive to influence others, while power orientation is the how; it is the framework for how a leader becomes influential. A negative stereotype surrounds high power motivation, with the speculation that it automatically relates to undesirable behaviour, unlike prosocial power motivation, which is often associated with generosity. However, those with high power motivation can have different power orientations. Carbalho and Conde (2024) distinguish ego-power orientation and social-power orientations, highlighting that individuals can combine said orientations in different ways. Ego-power is associated with pursuing goals to satisfy the self and achieve a sense of self-fulfilment; this doesn't automatically result in harmful leadership, as it partly depends on the individual's position of influence and work. Social-power orientation links directing power to collective outcomes

=== Leadership trait analysis ===
Leadership Trait Analysis (LTA), developed by Margaret Hermann (2003), is a framework for analysing political leaders' psychological characteristics using interviews and public speeches. It examines seven traits across three dimensions: responsiveness to constraints, openness to information and motivation. The seven traits include the need for power, the belief that one can control what happens next, self-confidence, trust in others, conceptual complexity, the intensity of in-group bias or nationalism, and the need for affiliation. Together, these traits help researchers examine how leaders process information, respond to constraints and approach decision-making.

Trump illustrates how psychological frameworks such as the LTA apply to political leadership. Mobaseri and Nosrat Kharazmi (2025) examined Trump's leadership characteristics and political beliefs before his presidency and during his first term. The research explored how much his core beliefs influenced his responses to political events and the COVID-19 crisis. The study highlights the value of examining leaders' beliefs and characteristics over time to understand their responses to the political climate.

The analysis found Trump low in need for power, perceived control, self-confidence, in-group bias, and trust in others, but high in conceptual complexity. These traits informed Mobaseri and Nosrat Kharazmi's (2025) account of his leadership: resistance to adaptation, disregard for policymaking, charisma, and sensitivity to context in decisions.

The findings show how leadership reflects the interaction between a leader's psychology and their situation. LTA offers a way to analyse individual differences that shape leadership style.

=== Leadership styles and effectiveness ===
Power orientation can be reflected in different leadership styles, which describe how leaders direct, influence and interact with followers. For example, a leader who prioritises complete personal control may favour a more autocratic approach, while a leader who values engagement may be more inclined towards a democratic leadership. However, while leadership styles reflect theoretical models, they can also be shaped by individual characteristics and techniques (Khajeh et al., 2018; &quot;What Are the Different Leadership Styles?&quot;, 2024). Different styles place varying emphasis on factors seen in Table 2 (Deakin University, 2024; Bwalya, 2023). 

Effective leadership involves more than holding a position of authority; there are five essential characteristics of leadership: self-image, self-control, socialised power, sustained dialogue, and strategic intent, providing a practical framework for a successful leader (Power, 2026). Power, motivation, and leadership matter across contexts, from political leaders to supervisors, who need to build relationships with employees and an environment of trust if they want to do so. The characteristics emphasise the importance of authority, responsibility, communication, and directing efforts towards organisational goals (Power, 2026; Friederichs et al., 2023)

Research suggests that transformational leadership can produce positive outcomes by motivating and inspiring followers and benefiting the group rather than serving personal interests (Peyton et al., 2019). This shows how power can support group goals rather than simply reinforcing leadership status. Nevertheless, no single leadership style guarantees effectiveness; outcomes depend on how the leader behaves and responds to the situation at hand.

{| class=&quot;wikitable&quot;
|+Table 2. Leadership Styles  (Bwalya, 2023)
! colspan=&quot;3&quot; |Leadership styles
|-
|Style
|Description
|Example Leaders
|-
|Autocratic 
|Leader holds complete control over decision-making with no input from followers. Consistently exercises control over the decision-making process. Expects strict compliance with policies and procedures, and does not take input from followers. They micromanage and control subordinate work. They make quick decisions because they do not have to consult. There is a lack of creative innovation (Bwalya, 2023). 
|Adolf Hitler and  Kim Jong-un 
|-
|Democratic 
|Leader is involved in team members' decision-making process, continuously encourages communication, and seeks feedback on matters, valuing input and ideas, wanting followers to participate in shaping strategies and goals (Bwalya, 2023).
|Former President of South Africa, Nelson Mandela and Former Prime Minister of New Zealand Jacinda Ardern 
|-
|Laissex-faire
| The leader is distant and has minimal involvement in decisions, unlike autocratic leadership, as laissez-faire lets followers make decisions with little guidance or supervision, trusting their ability to manage responsibilities. They are comfortable with mistakes and take accountability for followers' mistakes. This empowers employees and enables faster decision-making. However, the lack of guidance can cause confusion and lack of coordination (Bwalya, 2023). 
|Former President Herbert Hoover and Mahatma Ghandi
|-
|Servant 
|Leader is prosocial and motivated by power, focusing on the needs and well-being of others. Aiming to support and empower followers, in hopes they reach their full potential (Bwalya, 2023). 
|Pope Francis
|-
|Transformational 
|Based on inspiration and motivation to achieve performance, with high expectations and focus on challenging others to exceed self-interest. Focuses on transforming followers through inspiration, motivation, and effective communication. They rely on the leader's influence; if the leader fails to provide proper guidance, it can impact followers (Bwalya, 2023). 
|Former President of South Africa Nelson Mandela and Former President of the United States Barack Obama 
|-
|Transactional
|Focuses on the exchange relationship between the leader and their followers. The leader maintains stability and achieves goals by providing rewards and punishments based on performance. Very goal-oriented, with clear expectations, and quick decision-making (Bwalya, 2023).  
|Bill Gates and Former Chancellor of Germany Angela Merkel
|}

{{RoundBoxTop|theme=8}}[[Image: Hand Gesture - Holding a Magnifying Glass.gif|right|128px]] 
==Quiz==
&lt;quiz display=simple&gt; 
Which statement best explains the relationship between a leader’s power motivation and their leadership style?
|type=&quot;()&quot;} 
- Leaders with high power motivation are more likely to adopt an autocratic style, regardless of their values or circumstances
+ A leader’s power motivation determines their leadership style, while their psychological characteristics have very little influence
- Power motivation can influence a leader’s behaviour, but their power orientation, psychological characteristics and circumstances also shape how they exercise influence
&lt;/quiz&gt;
{{RoundBoxBottom}}

== Implicit and explicit power motivation ==
'''Focus question:''' ''What is implicit motivation, and how does it differ from explicit power motivation in leaders?''

Human motivation can operate through two systems: implicit and explicit motivation. Both influencing behaviour, but very different in the extent to which the individuals are consciously aware of their motives behind their behaviour. When looking at leadership, it is helpful to dissect the distinctions to understand why a leader's states goals may not fully reflect their underlying needs which influence their behaviour. 

Implicit motive (nPow) is unconscious motivation outside an individual’s awareness, mind map below in Figure 3 illustrates it. McClelland identified three implicit motives that shape thoughts, feelings, and actions: achievement, affiliation, and power. Developed through early preverbal experiences, they remain dormant until activated by incentives. Their influence appears in recurring patterns of thought, emotion, and behaviour, even when people cannot identify their motives (Reeve, 2018). Unlike explicit motives, implicit motives are difficult to measure directly. Researchers use the Picture-Story Exercise (PSE), asking participants to create stories from images and analysing them for themes related to the three motives. 

[[File:Implicit_Motives_associations.png|thumb| '''Figure 3.''' Mind map of implicit motives]]Explicit motives are conscious, self-attributed motives people can describe through their goals, values, and preferences (Slabbinck &amp; Van Witteloostuijn, 2020). Often assessed with self-report questionnaires, explicit power motives reflect desires for influence, status, and leadership. Their dimensions, dominance, prestige, and leadership, can help explain how power motives relate to dark personality traits. Dominance involves controlling others and is associated with Machiavellianism and counterproductive work behaviour. Prestige involves gaining influence by displaying knowledge or status and is linked to narcissism. Leadership involves guiding groups toward shared goals and may predict organisational citizenship behaviour and align with transformational leadership.

A strong explicit power motive does not automatically lead to destructive leadership. It can support productive leadership, but may also overlap with dark traits such as narcissism, Machiavellianism, and psychopathy.

=== Congruence ===
When implicit and explicit motives align, congruence, individuals are more likely to experience greater well-being and engagement, whereas misalignment can contribute to stress and reduced well-being (Ran et al., 2021; Thrash et al., 2012)..

Applying this to leadership styles highlights how a leader's effectiveness and well-being depend on whether their chosen leadership style aligns with their implicit motive. When a leader's leadership style conflicts with their implicit motive, they experience ''motive incongruence,'' which can lead to chronic stress, burnout, and friction, whereas alignment predicts greater flow, high energy, and effortless leadership (Ran et al., 2021; Thrash et al., 2012).

== Power motivation and leadership effectiveness ==
'''Focus question:''' ''How does power motivation influence leadership effectiveness?''

Power motivation can influence leadership effectiveness depending on how the motive is expressed and regulated. Two incentive types can be distinguished: social and activity. Social incentives are rewards, expectations, demands, and norms coming from other people. Activity incentives are rewards inherent in performing the activity itself; the activity reinforces the individual.

A high need for power can motivate individuals to seek authoritative roles to make decisions and direct others; the shape power motivation takes, i.e., personalised or socialised, directly indicates leadership effectiveness. Power motivation can develop through social and environmental experiences. Individuals who develop power-strivings may have grown up in environments where parents set demanding standards, potentially contributing to a desire for recognition and admiration. nPower has been associated with aggressive tendencies, although high power motivation doesn't automatically result in overt aggression. Social norms, laws, and consequences can constrain this expression, keeping that desire to control internal rather than manifesting as overt aggression (Reeve, 2018). Individuals high in the need for power may be attracted to occupations that offer career advancement; they are drawn to professions with influential opportunities (Reeve, 2018).

=== Destructive power dynamics and power abuse ===
There is a ''fickle'' relationship between aggression and the need or desire for power are closely linked. Studies have linked aggressive tendencies to dominance and the need for power (Verona et al., 2023). Verona et al. (2023) define human aggression as behaving with the intent to cause harm to another individual, and the target of the behaviour is driven to avoid it. Aggression can also take direct vs indirect and overt vs covert forms. That said, no concrete evidence links any level of ''feeling'' power to aggression. 

An individual with a high need for power may desire impact, control, or influence over another person or group, or even the world at large; aggression can be a means of satisfying those power needs. However, social norms, laws, and consequences can constrain this expression, causing that aggression to manifest in a more covert form. Individuals, both men and women, report more impulses to act aggressively than others; this behaviour would include yelling, throwing or destroying items and insulting others. Other factors of aggression and its link with high power-seeking individuals include finding a release through drinking, using this as a way to inflate their sense of control. Furthermore, men respond to stress and other setbacks with the behaviour of inflicting abuse on their partners, as well as an increased level of sexual misconduct (Reeve, 2018; Spanler et al., 2014). This indicates that a sense of power comes not only from leadership and reputation but can also be built through strategies of drinking, risk-taking, and posturing (Reeve, 2018).

Those who harbour inclinations that are both benevolent and malevolent towards others strive to improve the world while also influencing everyone else (Reeve, 2018). The ''dark side'' of implicit motive is the combination of opportunity to use power for personal benefit, which is the 'abuse of power.' Unrestrained affiliation can lead to favouritism and corruption in political and bureaucratic organisations. Achievement ignores political/interpersonal issues. High need for achievement: find it difficult working in groups, making decisions, and enforcing authority, ignoring interpersonal relationships (Spanier et al., 2014).[[File:The_Dark_Triad_Traits.jpg|thumb|'''Figure 4.''' The dark triad, and its associated personality traits]]

=== The dark triad traits ===
First proposed by Paulhus and Williams (2002), the &quot;Dark Triad&quot; traits- narcissism, Machiavellianism, and psychopathy, seen in Figure 4, are three overlapping personality traits that can strongly motivate individuals to seek and wield power. When an individual has these traits, it often means they restrain and fuel their ruthlessness and self-serving behaviour. Research has found that scoring high on these traits increases an individual’s likelihood of committing crimes, causing distress, and creating severe issues for organisations when in authoritative leadership positions (LeBreton et al., 2018).  

Findings on the dark triad suggest that leadership outcomes depend not only on a leader's desire for influence, but also on their personality and how they exercise authority. However, the dark triad should not be associated with high implicit power motivation, as a strong unconscious drive to influence or impact others is not the same as the dark triad traits. An individual can have a strong implicit need for power without dark personality traits. Dark triad traits are associated with excessive admiration-seeking behaviour, manipulation, and callousness; these traits can interfere with relationships and judgement calls. Specific characteristics of the traits are listed in Table 3. (LeBreton et al., 2018).
{| class=&quot;wikitable&quot;
|+Table 3. Dark triad characteristic defined (LeBreton et al., 2018). 
!Dark triad traits
!Characteristics
|-
|Machiavellianism
|Cynical, strategic, and manipulative
|-
|Psychopathy
|Erratic behaviour, interpersonal manipulation, callous affect and criminal tendencies
|-
|Narcissism
|Pride, aggression, envy, grandiosity, constant need for admiration, poor self-esteem
|} 

=== '''Key predictors of effective leadership''' ===
Power motivation can support effective leadership when regulated and directed toward collective rather than personal benefit. McClelland's research suggests effective leaders combine a strong need for power with high self-discipline, or “power under control,” which is linked to charismatic leadership and group morale (Reeve, 2018). However, a desire for influence alone does not ensure effectiveness. 

Self-regulation is especially important for leaders with potentially destructive personality tendencies. Stress, exhaustion, hunger, and cognitive overload can weaken willpower, making defensive reactions harder to control and potentially harming others. Strong motivation and self-awareness help leaders manage counterproductive tendencies and limit their disruptive effects.

Other motives also shape leadership. A strong need for affiliation can promote communication, respect, appreciation, and support, strengthening leader–follower relationships. Achievement motivation can encourage goal pursuit, but excessive striving may undermine effectiveness: highly active, achievement-oriented leaders can become frustrated when results fall short of expectations.

Moral identity also influences how leaders use power. Those with weaker moral identities may prioritize self-interest, while a prosocial approach uses influence to benefit others. This approach is associated with less power-related anxiety and greater well-being, suggesting that leaders’ purposes for exercising power affect their effectiveness.{{RoundBoxTop|theme=3}}[[File:John F. Kennedy speaks at Rice University.jpg|thumb|President John F. Kennedy speaking at Rice University |'''Figure 5.''' John F. Kennedy speaking at Rice University]]

== Case Study: John F. Kennedy ==

John F. Kennedy (JFK) is often recognised as an example of charismatic political leadership because of his optimistic public image, ambitious presidency, and compelling communication. Despite his relatively short time in office, Kennedy established a distinctive presidential identity by blending political leadership with popular culture and staying engaged with government and the public, which can be seen in Figure 5 (Reeve, 2018; McCann &amp; Mollan, 2023).
Kennedy's leadership aligns with McClelland's theory of motivational needs, with his profile characterised by a high need for power and a low need for affiliation (McCann &amp; Mollan, 2023). His charismatic communication also reflects transformational leadership, which emphasises inspiring followers to work towards shared goals. McClelland (1970) found that students who listened to Kennedy's inaugural address reported stronger feelings of inspiration and uplift, illustrating how a leader's communication can influence their audience.
Kennedy therefore shows how power motivation can support leadership by enabling individuals to influence, inspire, and mobilise others. However, effective leadership also depends on how that influence is exercised, particularly when responding to challenging political situations.
{{RoundBoxBottom}}

{{RoundBoxTop|theme=6}}
== Quiz Yourself ==
&lt;quiz display=simple&gt;
{Which combination of implicit motives is associated with effective leadership according to McClelland's leadership motive pattern?
|type=&quot;()&quot;}
- High power, high affiliation, and low inhibition
+ High power, low affiliation, and high inhibition
- Low power, high affiliation, and high inhibition
- High power, low affiliation, and low inhibition

{Does a high need for power necessarily result in aggressive behaviour?
|type=&quot;()&quot;}
- True
+ False

&lt;/quiz&gt;
{{RoundBoxBottom}}

== Conclusion ==
Psychological theory and research suggest that power motivation shapes how individuals seek, maintain, and regulate influence. McClelland's Three Need Theory explains differences in needs for power, achievement, and affiliation. The Two Faces of Power distinguishes personalised power, focused on personal control and self-interest, from socialised power, which uses influence to benefit others. This distinction explains why power motivation can produce very different leadership outcomes (McClelland, 1970; Carvalho &amp; Conde, 2024). The LMP further suggests that a high need for power, low need for affiliation, and high activity inhibition can support effective leadership by balancing influence with self-control (Reeve, 2018).

Power motivation is neither inherently positive nor negative; its effects depend on how leaders exercise authority, regulate behaviour, and balance personal ambitions with others’ needs. Effective leadership depends not on how much power a person wants, but on how they use it. Leaders who regulate their power motivation and direct influence toward collective goals, development, and positive outcomes are more likely to be well received by the public and subordinates (Peyton et al., 2019; Friederichs et al., 2023). Understanding power motivation helps explain both effective leadership and the risks of abuse, underscoring the importance of self-regulation and ethical influence.

{{RoundBoxTop|theme=11}}[[Image:Nuvola_apps_filetypes.png|right|102px]]
;Reflection activity

Think of a time you influenced a group decision at university, work, or in a team sport. Reflect on:

* What was the situation, and how did you respond?
* How did you influence others or make decisions?
* What motivated your behaviour?
{{RoundBoxBottom}}

==See also==
* [[Motivation and emotion/Book/2018/Emotional intelligence and leadership effectiveness|Emotional intelligence and leadership effectiveness]] (Book chapter, 2018)
* [[Motivation and emotion/Book/2015/Leadership motivation#Leadership Motive Pattern|Leadership motivation]] (Book chapter, 2015)
* [[Motivation and emotion/Book/2011/Maslow's hierarchy of needs|Maslow's hierarchy of needs]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2019/Two-factor motivation theory|Two-factor motivation theory]] (Book chapter, 2019)

{{ic|Integrate these links; use alphabetical order}}
* [[wikipedia:Need_theory|Need theory]] (Wikipedia)
* [[wikipedia:Need_for_power|Need for power]] (Wikipedia)
* [[wikipedia:David_McClelland|David Clelland]] (Wikipedia)

==References==

{{Hanging indent|1=

Bargh, J. A., &amp; Lee-Chai, A. Y. (2002). The use and abuse of power : Multiple perspectives in the causes of corruption. Psychology.

Bwalya, A. (2023). Leadership styles. Article in Journal of Entrepreneurship, Management and Innovation, 11(8), 181–193. https://doi.org/10.6084/m9.figshare.23932113

Carvalho, J. M. S., &amp; Conde, A. (2024). Individual power in human motivation – review and theoretical perspective. Acta Psychologica, 249, 104452–104452. https://doi.org/10.1016/j.actpsy.2024.104452

Deakin University. (2024, December 5). What are the different leadership styles? Deakin.Edu.Au. https://leadership.deakin.edu.au/blog/different-leadership-styles

Friederichs, K. M., Waldenmeier, K., &amp; Baumann, N. (2023). The benefits of prosocial power motivation in leadership: Action orientation fosters a win-win. Plos One, 18(7), e0287394–e0287394. https://doi.org/10.1371/journal.pone.0287394

Khajeh, A., Abu, M., &amp; Asaari, H. (2018). Impact of leadership styles on organizational performance. Journal of Human Resources Management Research, 2018(2166–0018), 2166–2184. https://ibimapublishing.com/articles/JHRMR/2018/687849/687849-1.pdf

Kurt, D. S. (2021, May 23). McClelland’s Three Needs Theory: Power, Achievement, and Affiliation. Education Library. https://educationlibrary.org/mcclellands-three-needs-theory-power-achievement-and-affiliation/#1

McCann, L., &amp; Mollan, S. (2023, November 20). JFK 60 years on: His leadership style and the reality behind the myths. The Conversation. https://theconversation.com/jfk-60-years-on-his-leadership-style-and-the-reality-behind-the-myths-216477

McClelland, D. C. (1970). The two faces of power. Journal of International Affairs, 24(1), 29–47. JSTOR. https://www.jstor.org/stable/24356663

Peyton, T., Zigarmi, D., &amp; Fowler, S. N. (2019). Examining the relationship between leaders’ power use, followers’ motivational outlooks, and followers’ work intentions. Frontiers in Psychology, 9(2620). https://doi.org/10.3389/fpsyg.2018.02620

Power , D. P. G. (2026). The five essentials of leadership {{!}} APS. Psychology.Org.Au. https://psychology.org.au/inpsych/2017/august/power

Reeve, J. (2018). Understanding motivation and emotion (7th edn, pp. 152–176). John Wiley &amp; Sons, Inc.

Slabbinck, H., &amp; Van Witteloostuijn, A. (2020). Explicit and implicit basic human motives, and public service motivation. Frontiers in Psychology, 11(1542). https://doi.org/10.3389/fpsyg.2020.01542

Spanler, W. D., Tikhomirov, A., Lee Sotak, K., &amp; Palrecha, R. (2014). Leader motive profiles in eight types of organizations. ScienceDirect, 25(6). https://www-sciencedirect-com.ezproxy.canberra.edu.au/science/article/pii/S1048984314001040

}}

==External links==
{{ic|Move these links into References and cite; replace with links to the most relevant external non-academic resources}}

* [https://leadership.deakin.edu.au/blog/what-is-transformational-leadership Article on Transformational leadership style] (Deakin University, 2024)
* [https://pmc.ncbi.nlm.nih.gov/articles/PMC10355387/ Power motivation, the benefits of prosocial power] (Friederichs et al., 2023)
* [https://www.jstor.org/stable/pdf/24356663.pdf The Two Faces of Power Journal] (McClelland, 1970)

==See also==
* [[Motivation and emotion/Book/2024/Power motivation and leadership|Power motivation and leadership]] (Book chapter, 2024)

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__TOC__

==Overview==
{{RoundBoxTop|theme=11}}
[[File:Donald Trump takes the oath of office (2025).jpg|thumb|President-elect Donald Trump takes the oath of office |'''Figure 1'''. Donald Trump's 2025 Inauguration surrounded by some of the world's wealthiest and most powerful individuals]]

Imagine a leader standing at their inauguration, surrounded by a concentration of wealthy and influential individuals. At first glance, this may reflect a preference for resources and influence. However, a closer look raises a psychological question: what motivates a leader to seek and exercise power, and how does this shape the way they lead?

This scenario reflects the leadership of United States President Donald Trump, whose 2025 administration includes a notable concentration of wealthy and influential individuals (Roeloffs, 2025). The individuals present at Trump's inauguration illustrate this concentration of political and economic power (see Figure 1). This provides a contemporary example for examining the relationship between power motivation and leadership.{{ic|[[w:Donald Trump|Second inauguration of Donald Trump]]}} Power is reflected not only in who a leader surrounds themselves with, but also in how they exercise their influence. For example, Trump uses social media as a political megaphone, bypassing traditional bureaucratic communication channels (Gambino, 2021). His public leadership style places considerable emphasis on personal image and the need of personal control with the disregard of external influences of power (Mobaseri &amp; Nosrat Kharazmi, Zohreh, 2025).

This raises the question: does the desire for power necessarily make someone an effective leader? Individuals seek leadership for various reasons, and how they use their influence shapes their interactions with followers, decision-making, and pursuit of goals. Psychology helps explain these differences by examining power motivation and how individual motives influence leadership behaviour.
{{RoundBoxBottom}}

This chapter will explore [https://pmc.ncbi.nlm.nih.gov/articles/PMC10355387/ power motivation] (Friederichs et al., 2023), the desire to influence, control, and have the ability to impact others, influencing leadership styles, behaviour and effectiveness (McClelland, 1970). Being expressed via socialised or personalised power, determining the leader's behaviour and effectiveness, (Reeve, 2018; McClelland, 1970; Carvalho &amp; Conde, 2024).

Understanding power motivation provides a psychological framework for examining how leaders exercise authority and how followers respond. Psychological science can help explain why some power-motivated leaders use influence to control, while others use it to empower (Reeve, 2018).

{{RoundBoxTop|theme=11}}
[[File:P psychology.png|right]]
'''Focus questions:'''

*What psychological theories explain power motivation in leaders?

*How does a leader's orientation towards power influence their specific leadership style?

*What is implicit motivation, and how does it differ from explicit power motivation in leaders?

*How does power motivation influence leadership effectiveness?
{{RoundBoxBottom}}

==Understanding power motivation through psychological theories==
'''Focus question:''' ''What psychological theories explain power motivation in leaders?''

The definition of motivation and power, one describes the push to act the other often associated with aggression, influence, authority and control, together they hold a heavy definition. In psychology, [[Motivation and emotion/Lectures/Introduction|motivation]] is the driving force that guides human behaviour; it is the use of will-power and self-discipline - channelling effort to achieve a goal. Certain individuals have predominant motive of power, being motivated by the internal urge to dominate, influence, or control (Kurt, 2021). Power motivation is the broad construct that refers to the desire for leadership, authority or status, it is built up of three characteristics: strong action, emotional impact, and concern for status, frame, and reputation, heavily influenced by cultural values and socialised experiences (McClelland,1970).

Power seekers can be effective, well-adjusted, and highly motivated. Power is a source of human control; only the mentally healthy can wield it successfully. Those with this form of nPower struggle to feel satisfied unless they are in a position that fulfils their power-hungry needs, such as making decisions, influencing an audience, or obtaining information to become influential. Such occupations are teachers, journalists, clergy, psychologists, diplomats, business executives, political leaders and advisors (Reeve, 2018). [[wikipedia:David_McClelland|David McClelland's]] is popular within the psychology community for his thoughts on power motivation, with the most well-known theories, the Three Need Theory and the Two Faces of Power theory.

=== Three need theory ===
[[File:DavidMcClelland.jpg|thumb|'''Figure 2.''' David McClelland]]McClelland, a Harvard psychologist who conducted extensive research into human motivation (seen in Figure 2.), proposed the [[wikipedia:Need_theory|Three Need Theory]]. The theory identifies three acquired motivational needs: the need for achievement, the need for affiliation, and the need for power (McClelland, 1970). Although individuals can experiences all three needs, the strength of each varies between individuals and can influence their behaviour. Table 1 summarises these needs and their defining characteristics being examined from high to low behaviour (Kurt, 2021).

Of special interest to leadership is the nPower, which involved the desire to influnence others and have an impact on thier behaviour. While a strong need for achievement may motivate individuals to pursue challenging goals, and a strong need for affilication may encrourage them to maintain positive interpersonal relationships, a strong need for power can motivate individuals to seek positions of authoirty. However the nPower alone does not determine whether someone will be an effective leader; its expression and the way an individual exercises their influence matter 

 {| class=&quot;wikitable&quot;
|+Table 1: Three Need Theory
!Need
!Definition
!High Behaviour
!Low Behaviour
|-
|Need for Achievement 
|Situations that challenge individuals with explicit standards.
|Individual exhibits a need to win and receive recognition.
|Constant fear of failure, typically avoids responsibilities. 
|-
|Need for Affiliation 
|Situations that afford warm relationship opportunities.
|A desire within for control, typically exaggerates own position.
|A heavily dependent individual, tries to minimise own position and importance.
|-
|Need for Power 
|Situations that enable others to exert influence over others.
|Individual demands and expects loyalty and harmony.
|Individual remains 'aloof' and keeps social distance from influence over others. 
|}

==== Two faces of power ====
McClelland's [https://www.jstor.org/stable/pdf/24356663.pdf Two Faces of Power] framework distinguishes between two ways the nPower can be expressed, personalised power or socialised power, also referred to as ''pP''ower, and ''s''Power (McClelland, 1970). ''pP''ower centres on personal control, it is seen as socially unacceptable way of expression, is is closely linked dominance and status. Those influenced by ''p''Power may tend to seek to strengthen their own position and influence (McClelland, 1970). While McClelland was doing his research of these mannerisms of power, he though that if those who obtained ''pP''ower were in the environment of international relations the consequences would be ''ominous''. While, ''s''Power, is the more socially acceptable form of expression, with leaders being motivated through the benefit of others; it incorporates feelings of personal strength, and the known knowledge of being careful (Bargh &amp; Lee-Chai, 2002; Friederichs et al., 2023; Magee &amp; Langner, 2008; McClellad, 1970). 

These forms of expression are not necessarily mutually exclusive. Leaders may display elements of both; McClelland believes that a true leader can balance personal dominance and socialised leadership (Bargh &amp; Lee-Chai, 2002). ''p''Power can become problematic when leaders become too absorbed by the maintenance of their position and influence, the ability to dominate, manipulate, and disagree. However, the issue isn't high-power motivation; it's how it is expressed (McClelland, 1970). 

=== The leadership motive pattern ===
McClelland and David Burnham (1975) proposed the idea that effective leadership is associated with a certain specific combination of motives known as the [[Motivation and emotion/Book/2015/Leadership motivation#Leadership Motive Pattern|Leadership Motive Pattern]] (LMP) (Spangler et al., 2014). This consists of three primary elements, high need for power (nPow), a low need for affiliation (nAff) and a high activity inhibition AI). This model demonstrated how motivation can work together to shape leadership behaviour (Reeve, 2018). 

Each component serves as a different purpose, building characterises of the most effective leaders within bureaucratic organisation (Spangler et al., 2014). High nPow, is the force to influence, direct and impact others, this has been well-established by now. Low nAff, is a reduced desire for friendly interpersonal relationships, which prevent the leaders from producing biased decision-making. High AI is based on self-control, maturity, and the ability to channel power socially rather an impulsively (McClelland &amp; Boyatzis, 1982).

Research by McClelland and Burnhamd (1982) found that the LMP may only hold value for specific roles in demonstrating leadership effectiveness. When relevant, it demonstrated that managers of this pattern typically generate higher morale in their subordinates; leadership styles such as those of nations that spend relatively more on military forces than private consumption, which McClelland described as a system's capacity to mobilise resources in the interest of the nation (McClelland &amp; Boyatzis, 1982; Spangler et al., 2014). 


{{RoundBoxTop|theme=8}}
== Recap ==
&lt;quiz display=simple&gt;
{&amp;nbsp;
|type=&quot;{}&quot;}
What is the driving force that guides human behaviour?
{ Motivation }

{What is the key difference between personalised power and socialised power?}
- Personalised power focuses on achievement, and socialised power focuses on affiliation
+ Personalised power focuses on personal dominance and control, and socialised power focuses on benefiting others
- Personalised power is consistently associated with an effective leadership style, whereas socialised power is associated with an ineffective leadership style.

{Which combination of motives is associated with McClelland’s Leadership Motive Pattern in effective managers?}
- High need for achievement, high need for affiliation and low activity inhibition
+ High need for power, low need for affiliation and high activity inhibition
- Low need for power, high need for affiliation and high activity inhibition

{Which behaviour best fits an individual with a high need for power?}
- Avoiding situations where they might influence others
+ Seek opportunities to influence, control, or have an impact on others
- Avoid challenging tasks for fear of failure


&lt;/quiz&gt;

{{RoundBoxBottom}}

== Power motivation and leadership style ==
'''Focus question:''' ''How does a leader's orientation towards power influence their specific leadership style?''

An individual’s desire for power does not automatically determine their leadership style. How an individual in a position of authority understands and exercises power over others can shape their interactions, decision-making approaches, and the goals they prioritise. Examining power orientation alongside psychological characteristics provides a deeper understanding of why leaders may use their influence in various ways and how those differences are reflected in their leadership style. 

=== Power orientation and leadership behaviour ===
Power motivation is the drive to influence others, while power orientation is the how; it is the framework for how a leader becomes influential. A negative stereotype surrounds high power motivation, with the speculation that it automatically relates to undesirable behaviour, unlike prosocial power motivation, which is often associated with generosity. However, those with high power motivation can have different power orientations. Carbalho and Conde (2024) distinguish ego-power orientation and social-power orientations, highlighting that individuals can combine said orientations in different ways. Ego-power is associated with pursuing goals to satisfy the self and achieve a sense of self-fulfilment; this doesn't automatically result in harmful leadership, as it partly depends on the individual's position of influence and work. Social-power orientation links directing power to collective outcomes

=== Leadership trait analysis ===
Leadership Trait Analysis (LTA), developed by Margaret Hermann (2003), is a framework for analysing political leaders' psychological characteristics using interviews and public speeches. It examines seven traits across three dimensions: responsiveness to constraints, openness to information and motivation. The seven traits include the need for power, the belief that one can control what happens next, self-confidence, trust in others, conceptual complexity, the intensity of in-group bias or nationalism, and the need for affiliation. Together, these traits help researchers examine how leaders process information, respond to constraints and approach decision-making.

Trump illustrates how psychological frameworks such as the LTA apply to political leadership. Mobaseri and Nosrat Kharazmi (2025) examined Trump's leadership characteristics and political beliefs before his presidency and during his first term. The research explored how much his core beliefs influenced his responses to political events and the COVID-19 crisis. The study highlights the value of examining leaders' beliefs and characteristics over time to understand their responses to the political climate.

The analysis found Trump low in need for power, perceived control, self-confidence, in-group bias, and trust in others, but high in conceptual complexity. These traits informed Mobaseri and Nosrat Kharazmi's (2025) account of his leadership: resistance to adaptation, disregard for policymaking, charisma, and sensitivity to context in decisions.

The findings show how leadership reflects the interaction between a leader's psychology and their situation. LTA offers a way to analyse individual differences that shape leadership style.

=== Leadership styles and effectiveness ===
Power orientation can be reflected in different leadership styles, which describe how leaders direct, influence and interact with followers. For example, a leader who prioritises complete personal control may favour a more autocratic approach, while a leader who values engagement may be more inclined towards a democratic leadership. However, while leadership styles reflect theoretical models, they can also be shaped by individual characteristics and techniques (Khajeh et al., 2018; &quot;What Are the Different Leadership Styles?&quot;, 2024). Different styles place varying emphasis on factors seen in Table 2 (Deakin University, 2024; Bwalya, 2023). 

Effective leadership involves more than holding a position of authority; there are five essential characteristics of leadership: self-image, self-control, socialised power, sustained dialogue, and strategic intent, providing a practical framework for a successful leader (Power, 2026). Power, motivation, and leadership matter across contexts, from political leaders to supervisors, who need to build relationships with employees and an environment of trust if they want to do so. The characteristics emphasise the importance of authority, responsibility, communication, and directing efforts towards organisational goals (Power, 2026; Friederichs et al., 2023)

Research suggests that transformational leadership can produce positive outcomes by motivating and inspiring followers and benefiting the group rather than serving personal interests (Peyton et al., 2019). This shows how power can support group goals rather than simply reinforcing leadership status. Nevertheless, no single leadership style guarantees effectiveness; outcomes depend on how the leader behaves and responds to the situation at hand.

{| class=&quot;wikitable&quot;
|+Table 2. Leadership Styles  (Bwalya, 2023)
! colspan=&quot;3&quot; |Leadership styles
|-
|Style
|Description
|Example Leaders
|-
|Autocratic 
|Leader holds complete control over decision-making with no input from followers. Consistently exercises control over the decision-making process. Expects strict compliance with policies and procedures, and does not take input from followers. They micromanage and control subordinate work. They make quick decisions because they do not have to consult. There is a lack of creative innovation (Bwalya, 2023). 
|Adolf Hitler and  Kim Jong-un 
|-
|Democratic 
|Leader is involved in team members' decision-making process, continuously encourages communication, and seeks feedback on matters, valuing input and ideas, wanting followers to participate in shaping strategies and goals (Bwalya, 2023).
|Former President of South Africa, Nelson Mandela and Former Prime Minister of New Zealand Jacinda Ardern 
|-
|Laissex-faire
| The leader is distant and has minimal involvement in decisions, unlike autocratic leadership, as laissez-faire lets followers make decisions with little guidance or supervision, trusting their ability to manage responsibilities. They are comfortable with mistakes and take accountability for followers' mistakes. This empowers employees and enables faster decision-making. However, the lack of guidance can cause confusion and lack of coordination (Bwalya, 2023). 
|Former President Herbert Hoover and Mahatma Ghandi
|-
|Servant 
|Leader is prosocial and motivated by power, focusing on the needs and well-being of others. Aiming to support and empower followers, in hopes they reach their full potential (Bwalya, 2023). 
|Pope Francis
|-
|Transformational 
|Based on inspiration and motivation to achieve performance, with high expectations and focus on challenging others to exceed self-interest. Focuses on transforming followers through inspiration, motivation, and effective communication. They rely on the leader's influence; if the leader fails to provide proper guidance, it can impact followers (Bwalya, 2023). 
|Former President of South Africa Nelson Mandela and Former President of the United States Barack Obama 
|-
|Transactional
|Focuses on the exchange relationship between the leader and their followers. The leader maintains stability and achieves goals by providing rewards and punishments based on performance. Very goal-oriented, with clear expectations, and quick decision-making (Bwalya, 2023).  
|Bill Gates and Former Chancellor of Germany Angela Merkel
|}

{{RoundBoxTop|theme=8}}[[Image: Hand Gesture - Holding a Magnifying Glass.gif|right|128px]] 
==Quiz==
&lt;quiz display=simple&gt; 
Which statement best explains the relationship between a leader’s power motivation and their leadership style?
|type=&quot;()&quot;} 
- Leaders with high power motivation are more likely to adopt an autocratic style, regardless of their values or circumstances
+ A leader’s power motivation determines their leadership style, while their psychological characteristics have very little influence
- Power motivation can influence a leader’s behaviour, but their power orientation, psychological characteristics and circumstances also shape how they exercise influence
&lt;/quiz&gt;
{{RoundBoxBottom}}

== Implicit and explicit power motivation ==
'''Focus question:''' ''What is implicit motivation, and how does it differ from explicit power motivation in leaders?''

Human motivation can operate through two systems: implicit and explicit motivation. Both influencing behaviour, but very different in the extent to which the individuals are consciously aware of their motives behind their behaviour. When looking at leadership, it is helpful to dissect the distinctions to understand why a leader's states goals may not fully reflect their underlying needs which influence their behaviour. 

Implicit motive (nPow) is unconscious motivation outside an individual’s awareness, mind map below in Figure 3 illustrates it. McClelland identified three implicit motives that shape thoughts, feelings, and actions: achievement, affiliation, and power. Developed through early preverbal experiences, they remain dormant until activated by incentives. Their influence appears in recurring patterns of thought, emotion, and behaviour, even when people cannot identify their motives (Reeve, 2018). Unlike explicit motives, implicit motives are difficult to measure directly. Researchers use the Picture-Story Exercise (PSE), asking participants to create stories from images and analysing them for themes related to the three motives. 

[[File:Implicit_Motives_associations.png|thumb| '''Figure 3.''' Mind map of implicit motives]]Explicit motives are conscious, self-attributed motives people can describe through their goals, values, and preferences (Slabbinck &amp; Van Witteloostuijn, 2020). Often assessed with self-report questionnaires, explicit power motives reflect desires for influence, status, and leadership. Their dimensions, dominance, prestige, and leadership, can help explain how power motives relate to dark personality traits. Dominance involves controlling others and is associated with Machiavellianism and counterproductive work behaviour. Prestige involves gaining influence by displaying knowledge or status and is linked to narcissism. Leadership involves guiding groups toward shared goals and may predict organisational citizenship behaviour and align with transformational leadership.

A strong explicit power motive does not automatically lead to destructive leadership. It can support productive leadership, but may also overlap with dark traits such as narcissism, Machiavellianism, and psychopathy.

When implicit and explicit motives align, congruence, individuals are more likely to experience greater well-being and engagement, whereas misalignment can contribute to stress and reduced well-being (Ran et al., 2021; Thrash et al., 2012)..

Applying this to leadership styles highlights how a leader's effectiveness and well-being depend on whether their chosen leadership style aligns with their implicit motive. When a leader's leadership style conflicts with their implicit motive, they experience ''motive incongruence,'' which can lead to chronic stress, burnout, and friction, whereas alignment predicts greater flow, high energy, and effortless leadership (Ran et al., 2021; Thrash et al., 2012).

== Power motivation and leadership effectiveness ==
'''Focus question:''' ''How does power motivation influence leadership effectiveness?''

Power motivation influences leadership effectiveness through how it is expressed and regulated. Social incentives arise from others’ rewards, expectations, and norms, whereas activity incentives come from the activity itself. Individuals with high nPower may seek positions of authority and careers offering influence and advancement. Although power motivation can be associated with aggression, social norms, laws, and consequences can constrain its expression (Reeve, 2018).

=== Destructive power dynamics and power abuse ===
There is a ''fickle'' relationship between aggression and the need or desire for power are closely linked. Studies have linked aggressive tendencies to dominance and the need for power (Verona et al., 2023). Verona et al. (2023) define human aggression as behaving with the intent to cause harm to another individual, and the target of the behaviour is driven to avoid it. Aggression can also take direct vs indirect and overt vs covert forms. That said, no concrete evidence links any level of ''feeling'' power to aggression. 

An individual with a high need for power may desire impact, control, or influence over another person or group, or even the world at large; aggression can be a means of satisfying those power needs. However, social norms, laws, and consequences can constrain this expression, causing that aggression to manifest in a more covert form. Individuals, both men and women, report more impulses to act aggressively than others; this behaviour would include yelling, throwing or destroying items and insulting others. Other factors of aggression and its link with high power-seeking individuals include finding a release through drinking, using this as a way to inflate their sense of control. Furthermore, men respond to stress and other setbacks with the behaviour of inflicting abuse on their partners, as well as an increased level of sexual misconduct (Reeve, 2018; Spanler et al., 2014). This indicates that a sense of power comes not only from leadership and reputation but can also be built through strategies of drinking, risk-taking, and posturing (Reeve, 2018).

Those who harbour inclinations that are both benevolent and malevolent towards others strive to improve the world while also influencing everyone else (Reeve, 2018). The ''dark side'' of implicit motive is the combination of opportunity to use power for personal benefit, which is the 'abuse of power.' Unrestrained affiliation can lead to favouritism and corruption in political and bureaucratic organisations. Achievement ignores political/interpersonal issues. High need for achievement: find it difficult working in groups, making decisions, and enforcing authority, ignoring interpersonal relationships (Spanier et al., 2014).[[File:The_Dark_Triad_Traits.jpg|thumb|'''Figure 4.''' The dark triad, and its associated personality traits]]

=== The dark triad traits ===
First proposed by Paulhus and Williams (2002), the &quot;Dark Triad&quot; traits- narcissism, Machiavellianism, and psychopathy, seen in Figure 4, are three overlapping personality traits that can strongly motivate individuals to seek and wield power. When an individual has these traits, it often means they restrain and fuel their ruthlessness and self-serving behaviour. Research has found that scoring high on these traits increases an individual’s likelihood of committing crimes, causing distress, and creating severe issues for organisations when in authoritative leadership positions (LeBreton et al., 2018).  

Findings on the dark triad suggest that leadership outcomes depend not only on a leader's desire for influence, but also on their personality and how they exercise authority. However, the dark triad should not be associated with high implicit power motivation, as a strong unconscious drive to influence or impact others is not the same as the dark triad traits. An individual can have a strong implicit need for power without dark personality traits. Dark triad traits are associated with excessive admiration-seeking behaviour, manipulation, and callousness; these traits can interfere with relationships and judgement calls. Specific characteristics of the traits are listed in Table 3. (LeBreton et al., 2018).
{| class=&quot;wikitable&quot;
|+Table 3. Dark triad characteristic defined (LeBreton et al., 2018). 
!Dark triad traits
!Characteristics
|-
|Machiavellianism
|Cynical, strategic, and manipulative
|-
|Psychopathy
|Erratic behaviour, interpersonal manipulation, callous affect and criminal tendencies
|-
|Narcissism
|Pride, aggression, envy, grandiosity, constant need for admiration, poor self-esteem
|} 

=== '''Key predictors of effective leadership''' ===
Power motivation can support effective leadership when regulated and directed toward collective rather than personal benefit. McClelland's research suggests effective leaders combine a strong need for power with high self-discipline, or “power under control,” which is linked to charismatic leadership and group morale (Reeve, 2018). However, a desire for influence alone does not ensure effectiveness. 

Self-regulation is especially important for leaders with potentially destructive personality tendencies. Stress, exhaustion, hunger, and cognitive overload can weaken willpower, making defensive reactions harder to control and potentially harming others. Strong motivation and self-awareness help leaders manage counterproductive tendencies and limit their disruptive effects.

Other motives also shape leadership. A strong need for affiliation can promote communication, respect, appreciation, and support, strengthening leader–follower relationships. Achievement motivation can encourage goal pursuit, but excessive striving may undermine effectiveness: highly active, achievement-oriented leaders can become frustrated when results fall short of expectations.

Moral identity also influences how leaders use power. Those with weaker moral identities may prioritize self-interest, while a prosocial approach uses influence to benefit others. This approach is associated with less power-related anxiety and greater well-being, suggesting that leaders’ purposes for exercising power affect their effectiveness.{{RoundBoxTop|theme=3}}[[File:John F. Kennedy speaks at Rice University.jpg|thumb|President John F. Kennedy speaking at Rice University |'''Figure 5.''' John F. Kennedy speaking at Rice University]]

== Case Study: John F. Kennedy ==

John F. Kennedy (JFK) is often recognised as an example of charismatic political leadership because of his optimistic public image, ambitious presidency, and compelling communication. Despite his relatively short time in office, Kennedy established a distinctive presidential identity by blending political leadership with popular culture and staying engaged with government and the public, which can be seen in Figure 5 (Reeve, 2018; McCann &amp; Mollan, 2023).
Kennedy's leadership aligns with McClelland's theory of motivational needs, with his profile characterised by a high need for power and a low need for affiliation (McCann &amp; Mollan, 2023). His charismatic communication also reflects transformational leadership, which emphasises inspiring followers to work towards shared goals. McClelland (1970) found that students who listened to Kennedy's inaugural address reported stronger feelings of inspiration and uplift, illustrating how a leader's communication can influence their audience.
Kennedy therefore shows how power motivation can support leadership by enabling individuals to influence, inspire, and mobilise others. However, effective leadership also depends on how that influence is exercised, particularly when responding to challenging political situations.
{{RoundBoxBottom}}

{{RoundBoxTop|theme=6}}
== Quiz Yourself ==
&lt;quiz display=simple&gt;
{Which combination of implicit motives is associated with effective leadership according to McClelland's leadership motive pattern?
|type=&quot;()&quot;}
- High power, high affiliation, and low inhibition
+ High power, low affiliation, and high inhibition
- Low power, high affiliation, and high inhibition
- High power, low affiliation, and low inhibition

{Does a high need for power necessarily result in aggressive behaviour?
|type=&quot;()&quot;}
- True
+ False

&lt;/quiz&gt;
{{RoundBoxBottom}}

== Conclusion ==
Psychological theory and research suggest that power motivation shapes how individuals seek, maintain, and regulate influence. McClelland's Three Need Theory explains differences in needs for power, achievement, and affiliation. The Two Faces of Power distinguishes personalised power, focused on personal control and self-interest, from socialised power, which uses influence to benefit others. This distinction explains why power motivation can produce very different leadership outcomes (McClelland, 1970; Carvalho &amp; Conde, 2024). The LMP further suggests that a high need for power, low need for affiliation, and high activity inhibition can support effective leadership by balancing influence with self-control (Reeve, 2018).

Power motivation is neither inherently positive nor negative; its effects depend on how leaders exercise authority, regulate behaviour, and balance personal ambitions with others’ needs. Effective leadership depends not on how much power a person wants, but on how they use it. Leaders who regulate their power motivation and direct influence toward collective goals, development, and positive outcomes are more likely to be well received by the public and subordinates (Peyton et al., 2019; Friederichs et al., 2023). Understanding power motivation helps explain both effective leadership and the risks of abuse, underscoring the importance of self-regulation and ethical influence.

{{RoundBoxTop|theme=11}}[[Image:Nuvola_apps_filetypes.png|right|102px]]
;Reflection activity

Think of a time you influenced a group decision at university, work, or in a team sport. Reflect on:

* What was the situation, and how did you respond?
* How did you influence others or make decisions?
* What motivated your behaviour?
{{RoundBoxBottom}}

==See also==
* [[Motivation and emotion/Book/2018/Emotional intelligence and leadership effectiveness|Emotional intelligence and leadership effectiveness]] (Book chapter, 2018)
* [[Motivation and emotion/Book/2015/Leadership motivation#Leadership Motive Pattern|Leadership motivation]] (Book chapter, 2015)
* [[Motivation and emotion/Book/2011/Maslow's hierarchy of needs|Maslow's hierarchy of needs]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2019/Two-factor motivation theory|Two-factor motivation theory]] (Book chapter, 2019)

{{ic|Integrate these links; use alphabetical order}}
* [[wikipedia:Need_theory|Need theory]] (Wikipedia)
* [[wikipedia:Need_for_power|Need for power]] (Wikipedia)
* [[wikipedia:David_McClelland|David Clelland]] (Wikipedia)

==References==

{{Hanging indent|1=

Bargh, J. A., &amp; Lee-Chai, A. Y. (2002). The use and abuse of power : Multiple perspectives in the causes of corruption. Psychology.

Bwalya, A. (2023). Leadership styles. Article in Journal of Entrepreneurship, Management and Innovation, 11(8), 181–193. https://doi.org/10.6084/m9.figshare.23932113

Carvalho, J. M. S., &amp; Conde, A. (2024). Individual power in human motivation – review and theoretical perspective. Acta Psychologica, 249, 104452–104452. https://doi.org/10.1016/j.actpsy.2024.104452

Deakin University. (2024, December 5). What are the different leadership styles? Deakin.Edu.Au. https://leadership.deakin.edu.au/blog/different-leadership-styles

Friederichs, K. M., Waldenmeier, K., &amp; Baumann, N. (2023). The benefits of prosocial power motivation in leadership: Action orientation fosters a win-win. Plos One, 18(7), e0287394–e0287394. https://doi.org/10.1371/journal.pone.0287394

Khajeh, A., Abu, M., &amp; Asaari, H. (2018). Impact of leadership styles on organizational performance. Journal of Human Resources Management Research, 2018(2166–0018), 2166–2184. https://ibimapublishing.com/articles/JHRMR/2018/687849/687849-1.pdf

Kurt, D. S. (2021, May 23). McClelland’s Three Needs Theory: Power, Achievement, and Affiliation. Education Library. https://educationlibrary.org/mcclellands-three-needs-theory-power-achievement-and-affiliation/#1

McCann, L., &amp; Mollan, S. (2023, November 20). JFK 60 years on: His leadership style and the reality behind the myths. The Conversation. https://theconversation.com/jfk-60-years-on-his-leadership-style-and-the-reality-behind-the-myths-216477

McClelland, D. C. (1970). The two faces of power. Journal of International Affairs, 24(1), 29–47. JSTOR. https://www.jstor.org/stable/24356663

Peyton, T., Zigarmi, D., &amp; Fowler, S. N. (2019). Examining the relationship between leaders’ power use, followers’ motivational outlooks, and followers’ work intentions. Frontiers in Psychology, 9(2620). https://doi.org/10.3389/fpsyg.2018.02620

Power , D. P. G. (2026). The five essentials of leadership {{!}} APS. Psychology.Org.Au. https://psychology.org.au/inpsych/2017/august/power

Reeve, J. (2018). Understanding motivation and emotion (7th edn, pp. 152–176). John Wiley &amp; Sons, Inc.

Slabbinck, H., &amp; Van Witteloostuijn, A. (2020). Explicit and implicit basic human motives, and public service motivation. Frontiers in Psychology, 11(1542). https://doi.org/10.3389/fpsyg.2020.01542

Spanler, W. D., Tikhomirov, A., Lee Sotak, K., &amp; Palrecha, R. (2014). Leader motive profiles in eight types of organizations. ScienceDirect, 25(6). https://www-sciencedirect-com.ezproxy.canberra.edu.au/science/article/pii/S1048984314001040

}}

==External links==
{{ic|Move these links into References and cite; replace with links to the most relevant external non-academic resources}}

* [https://leadership.deakin.edu.au/blog/what-is-transformational-leadership Article on Transformational leadership style] (Deakin University, 2024)
* [https://pmc.ncbi.nlm.nih.gov/articles/PMC10355387/ Power motivation, the benefits of prosocial power] (Friederichs et al., 2023)
* [https://www.jstor.org/stable/pdf/24356663.pdf The Two Faces of Power Journal] (McClelland, 1970)

==See also==
* [[Motivation and emotion/Book/2024/Power motivation and leadership|Power motivation and leadership]] (Book chapter, 2024)

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__TOC__

==Overview==
{{RoundBoxTop|theme=11}}
[[File:Donald Trump takes the oath of office (2025).jpg|thumb|President-elect Donald Trump takes the oath of office |'''Figure 1'''. Donald Trump's 2025 Inauguration surrounded by some of the world's wealthiest and most powerful individuals]]

Imagine a leader standing at their inauguration, surrounded by a concentration of wealthy and influential individuals. At first glance, this may reflect a preference for resources and influence. However, a closer look raises a psychological question: what motivates a leader to seek and exercise power, and how does this shape the way they lead?

This scenario reflects the leadership of United States President Donald Trump, whose 2025 administration includes a notable concentration of wealthy and influential individuals (Roeloffs, 2025). The individuals present at Trump's inauguration illustrate this concentration of political and economic power (see Figure 1). This provides a contemporary example for examining the relationship between power motivation and leadership.{{ic|[[w:Donald Trump|Second inauguration of Donald Trump]]}} Power is reflected not only in who a leader surrounds themselves with, but also in how they exercise their influence. For example, Trump uses social media as a political megaphone, bypassing traditional bureaucratic communication channels (Gambino, 2021). His public leadership style places considerable emphasis on personal image and the need of personal control with the disregard of external influences of power (Mobaseri &amp; Nosrat Kharazmi, Zohreh, 2025).

This raises the question: does the desire for power necessarily make someone an effective leader? Individuals seek leadership for various reasons, and how they use their influence shapes their interactions with followers, decision-making, and pursuit of goals. Psychology helps explain these differences by examining power motivation and how individual motives influence leadership behaviour.
{{RoundBoxBottom}}

This chapter will explore [https://pmc.ncbi.nlm.nih.gov/articles/PMC10355387/ power motivation] (Friederichs et al., 2023), the desire to influence, control, and have the ability to impact others, influencing leadership styles, behaviour and effectiveness (McClelland, 1970). Being expressed via socialised or personalised power, determining the leader's behaviour and effectiveness, (Reeve, 2018; McClelland, 1970; Carvalho &amp; Conde, 2024).

Understanding power motivation provides a psychological framework for examining how leaders exercise authority and how followers respond. Psychological science can help explain why some power-motivated leaders use influence to control, while others use it to empower (Reeve, 2018).

{{RoundBoxTop|theme=11}}
[[File:P psychology.png|right]]
'''Focus questions:'''

*What psychological theories explain power motivation in leaders?

*How does a leader's orientation towards power influence their specific leadership style?

*What is implicit motivation, and how does it differ from explicit power motivation in leaders?

*How does power motivation influence leadership effectiveness?
{{RoundBoxBottom}}

==Understanding power motivation through psychological theories==
'''Focus question:''' ''What psychological theories explain power motivation in leaders?''

The definition of motivation and power, one describes the push to act the other often associated with aggression, influence, authority and control, together they hold a heavy definition. In psychology, [[Motivation and emotion/Lectures/Introduction|motivation]] is the driving force that guides human behaviour; it is the use of will-power and self-discipline - channelling effort to achieve a goal. Certain individuals have predominant motive of power, being motivated by the internal urge to dominate, influence, or control (Kurt, 2021). Power motivation is the broad construct that refers to the desire for leadership, authority or status, it is built up of three characteristics: strong action, emotional impact, and concern for status, frame, and reputation, heavily influenced by cultural values and socialised experiences (McClelland,1970).

Power seekers can be effective, well-adjusted, and highly motivated. Power is a source of human control; only the mentally healthy can wield it successfully. Those with this form of nPower struggle to feel satisfied unless they are in a position that fulfils their power-hungry needs, such as making decisions, influencing an audience, or obtaining information to become influential. Such occupations are teachers, journalists, clergy, psychologists, diplomats, business executives, political leaders and advisors (Reeve, 2018). [[wikipedia:David_McClelland|David McClelland's]] is popular within the psychology community for his thoughts on power motivation, with the most well-known theories, the Three Need Theory and the Two Faces of Power theory.

=== Three need theory ===
[[File:DavidMcClelland.jpg|thumb|'''Figure 2.''' David McClelland]]McClelland, a Harvard psychologist who conducted extensive research into human motivation (seen in Figure 2.), proposed the [[wikipedia:Need_theory|Three Need Theory]]. The theory identifies three acquired motivational needs: the need for achievement, the need for affiliation, and the need for power (McClelland, 1970). Although individuals can experiences all three needs, the strength of each varies between individuals and can influence their behaviour. Table 1 summarises these needs and their defining characteristics being examined from high to low behaviour (Kurt, 2021).

Of special interest to leadership is the nPower, which involved the desire to influnence others and have an impact on thier behaviour. While a strong need for achievement may motivate individuals to pursue challenging goals, and a strong need for affilication may encrourage them to maintain positive interpersonal relationships, a strong need for power can motivate individuals to seek positions of authoirty. However the nPower alone does not determine whether someone will be an effective leader; its expression and the way an individual exercises their influence matter 

 {| class=&quot;wikitable&quot;
|+Table 1: Three Need Theory
!Need
!Definition
!High Behaviour
!Low Behaviour
|-
|Need for Achievement 
|Situations that challenge individuals with explicit standards.
|Individual exhibits a need to win and receive recognition.
|Constant fear of failure, typically avoids responsibilities. 
|-
|Need for Affiliation 
|Situations that afford warm relationship opportunities.
|A desire within for control, typically exaggerates own position.
|A heavily dependent individual, tries to minimise own position and importance.
|-
|Need for Power 
|Situations that enable others to exert influence over others.
|Individual demands and expects loyalty and harmony.
|Individual remains 'aloof' and keeps social distance from influence over others. 
|}

==== Two faces of power ====
McClelland's [https://www.jstor.org/stable/pdf/24356663.pdf Two Faces of Power] framework distinguishes between two ways the nPower can be expressed, personalised power or socialised power, also referred to as ''pP''ower, and ''s''Power (McClelland, 1970). ''pP''ower centres on personal control, it is seen as socially unacceptable way of expression, is is closely linked dominance and status. Those influenced by ''p''Power may tend to seek to strengthen their own position and influence (McClelland, 1970). While McClelland was doing his research of these mannerisms of power, he though that if those who obtained ''pP''ower were in the environment of international relations the consequences would be ''ominous''. While, ''s''Power, is the more socially acceptable form of expression, with leaders being motivated through the benefit of others; it incorporates feelings of personal strength, and the known knowledge of being careful (Bargh &amp; Lee-Chai, 2002; Friederichs et al., 2023; Magee &amp; Langner, 2008; McClellad, 1970). 

These forms of expression are not necessarily mutually exclusive. Leaders may display elements of both; McClelland believes that a true leader can balance personal dominance and socialised leadership (Bargh &amp; Lee-Chai, 2002). ''p''Power can become problematic when leaders become too absorbed by the maintenance of their position and influence, the ability to dominate, manipulate, and disagree. However, the issue isn't high-power motivation; it's how it is expressed (McClelland, 1970). 

=== The leadership motive pattern ===
McClelland and David Burnham (1975) proposed the idea that effective leadership is associated with a certain specific combination of motives known as the [[Motivation and emotion/Book/2015/Leadership motivation#Leadership Motive Pattern|Leadership Motive Pattern]] (LMP) (Spangler et al., 2014). This consists of three primary elements, high need for power (nPow), a low need for affiliation (nAff) and a high activity inhibition AI). This model demonstrated how motivation can work together to shape leadership behaviour (Reeve, 2018). 

Each component serves as a different purpose, building characterises of the most effective leaders within bureaucratic organisation (Spangler et al., 2014). High nPow, is the force to influence, direct and impact others, this has been well-established by now. Low nAff, is a reduced desire for friendly interpersonal relationships, which prevent the leaders from producing biased decision-making. High AI is based on self-control, maturity, and the ability to channel power socially rather an impulsively (McClelland &amp; Boyatzis, 1982).

Research by McClelland and Burnhamd (1982) found that the LMP may only hold value for specific roles in demonstrating leadership effectiveness. When relevant, it demonstrated that managers of this pattern typically generate higher morale in their subordinates; leadership styles such as those of nations that spend relatively more on military forces than private consumption, which McClelland described as a system's capacity to mobilise resources in the interest of the nation (McClelland &amp; Boyatzis, 1982; Spangler et al., 2014). 


{{RoundBoxTop|theme=8}}
== Recap ==
&lt;quiz display=simple&gt;
{&amp;nbsp;
|type=&quot;{}&quot;}
What is the driving force that guides human behaviour?
{ Motivation }

{What is the key difference between personalised power and socialised power?}
- Personalised power focuses on achievement, and socialised power focuses on affiliation
+ Personalised power focuses on personal dominance and control, and socialised power focuses on benefiting others
- Personalised power is consistently associated with an effective leadership style, whereas socialised power is associated with an ineffective leadership style.

{Which combination of motives is associated with McClelland’s Leadership Motive Pattern in effective managers?}
- High need for achievement, high need for affiliation and low activity inhibition
+ High need for power, low need for affiliation and high activity inhibition
- Low need for power, high need for affiliation and high activity inhibition

{Which behaviour best fits an individual with a high need for power?}
- Avoiding situations where they might influence others
+ Seek opportunities to influence, control, or have an impact on others
- Avoid challenging tasks for fear of failure


&lt;/quiz&gt;

{{RoundBoxBottom}}

== Power motivation and leadership style ==
'''Focus question:''' ''How does a leader's orientation towards power influence their specific leadership style?''

An individual’s desire for power does not automatically determine their leadership style. How an individual in a position of authority understands and exercises power over others can shape their interactions, decision-making approaches, and the goals they prioritise. Examining power orientation alongside psychological characteristics provides a deeper understanding of why leaders may use their influence in various ways and how those differences are reflected in their leadership style. 

=== Power orientation and leadership behaviour ===
Power motivation is the drive to influence others, while power orientation is the how; it is the framework for how a leader becomes influential. A negative stereotype surrounds high power motivation, with the speculation that it automatically relates to undesirable behaviour, unlike prosocial power motivation, which is often associated with generosity. However, those with high power motivation can have different power orientations. Carbalho and Conde (2024) distinguish ego-power orientation and social-power orientations, highlighting that individuals can combine said orientations in different ways. Ego-power is associated with pursuing goals to satisfy the self and achieve a sense of self-fulfilment; this doesn't automatically result in harmful leadership, as it partly depends on the individual's position of influence and work. Social-power orientation links directing power to collective outcomes

=== Leadership trait analysis ===
Leadership Trait Analysis (LTA), developed by Margaret Hermann (2003), is a framework for analysing political leaders' psychological characteristics using interviews and public speeches. It examines seven traits across three dimensions: responsiveness to constraints, openness to information and motivation. The seven traits include the need for power, the belief that one can control what happens next, self-confidence, trust in others, conceptual complexity, the intensity of in-group bias or nationalism, and the need for affiliation. Together, these traits help researchers examine how leaders process information, respond to constraints and approach decision-making.

Trump illustrates how psychological frameworks such as the LTA apply to political leadership. Mobaseri and Nosrat Kharazmi (2025) examined Trump's leadership characteristics and political beliefs before his presidency and during his first term. The research explored how much his core beliefs influenced his responses to political events and the COVID-19 crisis. The study highlights the value of examining leaders' beliefs and characteristics over time to understand their responses to the political climate.

The analysis found Trump low in need for power, perceived control, self-confidence, in-group bias, and trust in others, but high in conceptual complexity. These traits informed Mobaseri and Nosrat Kharazmi's (2025) account of his leadership: resistance to adaptation, disregard for policymaking, charisma, and sensitivity to context in decisions.

The findings show how leadership reflects the interaction between a leader's psychology and their situation. LTA offers a way to analyse individual differences that shape leadership style.

=== Leadership styles and effectiveness ===
Power orientation can be reflected in different leadership styles, which describe how leaders direct, influence and interact with followers. For example, a leader who prioritises complete personal control may favour a more autocratic approach, while a leader who values engagement may be more inclined towards a democratic leadership. However, while leadership styles reflect theoretical models, they can also be shaped by individual characteristics and techniques (Khajeh et al., 2018; &quot;What Are the Different Leadership Styles?&quot;, 2024). Different styles place varying emphasis on factors seen in Table 2 (Deakin University, 2024; Bwalya, 2023). 

Effective leadership involves more than holding a position of authority; there are five essential characteristics of leadership: self-image, self-control, socialised power, sustained dialogue, and strategic intent, providing a practical framework for a successful leader (Power, 2026). Power, motivation, and leadership matter across contexts, from political leaders to supervisors, who need to build relationships with employees and an environment of trust if they want to do so. The characteristics emphasise the importance of authority, responsibility, communication, and directing efforts towards organisational goals (Power, 2026; Friederichs et al., 2023)

Research suggests that transformational leadership can produce positive outcomes by motivating and inspiring followers and benefiting the group rather than serving personal interests (Peyton et al., 2019). This shows how power can support group goals rather than simply reinforcing leadership status. Nevertheless, no single leadership style guarantees effectiveness; outcomes depend on how the leader behaves and responds to the situation at hand.

{| class=&quot;wikitable&quot;
|+Table 2. Leadership Styles  (Bwalya, 2023)
! colspan=&quot;3&quot; |Leadership styles
|-
|Style
|Description
|Example Leaders
|-
|Autocratic 
|Leader holds complete control over decision-making with no input from followers. Consistently exercises control over the decision-making process. Expects strict compliance with policies and procedures, and does not take input from followers. They micromanage and control subordinate work. They make quick decisions because they do not have to consult. There is a lack of creative innovation (Bwalya, 2023). 
|Adolf Hitler and  Kim Jong-un 
|-
|Democratic 
|Leader is involved in team members' decision-making process, continuously encourages communication, and seeks feedback on matters, valuing input and ideas, wanting followers to participate in shaping strategies and goals (Bwalya, 2023).
|Former President of South Africa, Nelson Mandela and Former Prime Minister of New Zealand Jacinda Ardern 
|-
|Laissex-faire
| The leader is distant and has minimal involvement in decisions, unlike autocratic leadership, as laissez-faire lets followers make decisions with little guidance or supervision, trusting their ability to manage responsibilities. They are comfortable with mistakes and take accountability for followers' mistakes. This empowers employees and enables faster decision-making. However, the lack of guidance can cause confusion and lack of coordination (Bwalya, 2023). 
|Former President Herbert Hoover and Mahatma Ghandi
|-
|Servant 
|Leader is prosocial and motivated by power, focusing on the needs and well-being of others. Aiming to support and empower followers, in hopes they reach their full potential (Bwalya, 2023). 
|Pope Francis
|-
|Transformational 
|Based on inspiration and motivation to achieve performance, with high expectations and focus on challenging others to exceed self-interest. Focuses on transforming followers through inspiration, motivation, and effective communication. They rely on the leader's influence; if the leader fails to provide proper guidance, it can impact followers (Bwalya, 2023). 
|Former President of South Africa Nelson Mandela and Former President of the United States Barack Obama 
|-
|Transactional
|Focuses on the exchange relationship between the leader and their followers. The leader maintains stability and achieves goals by providing rewards and punishments based on performance. Very goal-oriented, with clear expectations, and quick decision-making (Bwalya, 2023).  
|Bill Gates and Former Chancellor of Germany Angela Merkel
|}

{{RoundBoxTop|theme=8}}[[Image: Hand Gesture - Holding a Magnifying Glass.gif|right|128px]] 
==Quiz==
&lt;quiz display=simple&gt; 
Which statement best explains the relationship between a leader’s power motivation and their leadership style?
|type=&quot;()&quot;} 
- Leaders with high power motivation are more likely to adopt an autocratic style, regardless of their values or circumstances
+ A leader’s power motivation determines their leadership style, while their psychological characteristics have very little influence
- Power motivation can influence a leader’s behaviour, but their power orientation, psychological characteristics and circumstances also shape how they exercise influence
&lt;/quiz&gt;
{{RoundBoxBottom}}

== Implicit and explicit power motivation ==
'''Focus question:''' ''What is implicit motivation, and how does it differ from explicit power motivation in leaders?''

Human motivation can operate through two systems: implicit and explicit motivation. Both influencing behaviour, but very different in the extent to which the individuals are consciously aware of their motives behind their behaviour. When looking at leadership, it is helpful to dissect the distinctions to understand why a leader's states goals may not fully reflect their underlying needs which influence their behaviour. 

Implicit motive (nPow) is unconscious motivation outside an individual’s awareness, mind map below in Figure 3 illustrates it. McClelland identified three implicit motives that shape thoughts, feelings, and actions: achievement, affiliation, and power. Developed through early preverbal experiences, they remain dormant until activated by incentives. Their influence appears in recurring patterns of thought, emotion, and behaviour, even when people cannot identify their motives (Reeve, 2018). Unlike explicit motives, implicit motives are difficult to measure directly. Researchers use the Picture-Story Exercise (PSE), asking participants to create stories from images and analysing them for themes related to the three motives. 

[[File:Implicit_Motives_associations.png|thumb| '''Figure 3.''' Mind map of implicit motives]]Explicit motives are conscious, self-attributed motives people can describe through their goals, values, and preferences (Slabbinck &amp; Van Witteloostuijn, 2020). Often assessed with self-report questionnaires, explicit power motives reflect desires for influence, status, and leadership. Their dimensions, dominance, prestige, and leadership, can help explain how power motives relate to dark personality traits. Dominance involves controlling others and is associated with Machiavellianism and counterproductive work behaviour. Prestige involves gaining influence by displaying knowledge or status and is linked to narcissism. Leadership involves guiding groups toward shared goals and may predict organisational citizenship behaviour and align with transformational leadership.

A strong explicit power motive does not automatically lead to destructive leadership. It can support productive leadership, but may also overlap with dark traits such as narcissism, Machiavellianism, and psychopathy.

When implicit and explicit motives align, congruence, individuals are more likely to experience greater well-being and engagement, whereas misalignment can contribute to stress and reduced well-being (Ran et al., 2021; Thrash et al., 2012)..

Applying this to leadership styles highlights how a leader's effectiveness and well-being depend on whether their chosen leadership style aligns with their implicit motive. When a leader's leadership style conflicts with their implicit motive, they experience ''motive incongruence,'' which can lead to chronic stress, burnout, and friction, whereas alignment predicts greater flow, high energy, and effortless leadership (Ran et al., 2021; Thrash et al., 2012).

== Power motivation and leadership effectiveness ==
'''Focus question:''' ''How does power motivation influence leadership effectiveness?''

Power motivation influences leadership effectiveness through how it is expressed and regulated. Social incentives arise from others’ rewards, expectations, and norms, whereas activity incentives come from the activity itself. Individuals with high nPower may seek positions of authority and careers offering influence and advancement. Although power motivation can be associated with aggression, social norms, laws, and consequences can constrain its expression (Reeve, 2018).

=== Destructive power dynamics and power abuse ===
There is a ''fickle'' relationship between aggression and the need or desire for power are closely linked. Studies have linked aggressive tendencies to dominance and the need for power (Verona et al., 2023). Verona et al. (2023) define human aggression as behaving with the intent to cause harm to another individual, and the target of the behaviour is driven to avoid it. Aggression can also take direct vs indirect and overt vs covert forms. That said, no concrete evidence links any level of ''feeling'' power to aggression. 

An individual with a high need for power may desire impact, control, or influence over another person or group, or even the world at large; aggression can be a means of satisfying those power needs. However, social norms, laws, and consequences can constrain this expression, causing that aggression to manifest in a more covert form. Individuals, both men and women, report more impulses to act aggressively than others; this behaviour would include yelling, throwing or destroying items and insulting others. Other factors of aggression and its link with high power-seeking individuals include finding a release through drinking, using this as a way to inflate their sense of control. Furthermore, men respond to stress and other setbacks with the behaviour of inflicting abuse on their partners, as well as an increased level of sexual misconduct (Reeve, 2018; Spanler et al., 2014). This indicates that a sense of power comes not only from leadership and reputation but can also be built through strategies of drinking, risk-taking, and posturing (Reeve, 2018).

Those who harbour inclinations that are both benevolent and malevolent towards others strive to improve the world while also influencing everyone else (Reeve, 2018). The ''dark side'' of implicit motive is the combination of opportunity to use power for personal benefit, which is the 'abuse of power.' Unrestrained affiliation can lead to favouritism and corruption in political and bureaucratic organisations. Achievement ignores political/interpersonal issues. High need for achievement: find it difficult working in groups, making decisions, and enforcing authority, ignoring interpersonal relationships (Spanier et al., 2014).[[File:The_Dark_Triad_Traits.jpg|thumb|'''Figure 4.''' The dark triad, and its associated personality traits]]

=== The dark triad traits ===
First proposed by Paulhus and Williams (2002), the &quot;Dark Triad&quot; traits- narcissism, Machiavellianism, and psychopathy, seen in Figure 4, are three overlapping personality traits that can strongly motivate individuals to seek and wield power. When an individual has these traits, it often means they restrain and fuel their ruthlessness and self-serving behaviour. Research has found that scoring high on these traits increases an individual’s likelihood of committing crimes, causing distress, and creating severe issues for organisations when in authoritative leadership positions (LeBreton et al., 2018).  

Findings on the dark triad suggest that leadership outcomes depend not only on a leader's desire for influence, but also on their personality and how they exercise authority. However, the dark triad should not be associated with high implicit power motivation, as a strong unconscious drive to influence or impact others is not the same as the dark triad traits. An individual can have a strong implicit need for power without dark personality traits. Dark triad traits are associated with excessive admiration-seeking behaviour, manipulation, and callousness; these traits can interfere with relationships and judgement calls. Specific characteristics of the traits are listed in Table 3. (LeBreton et al., 2018).
{| class=&quot;wikitable&quot;
|+Table 3. Dark triad characteristic defined (LeBreton et al., 2018). 
!Dark triad traits
!Characteristics
|-
|Machiavellianism
|Cynical, strategic, and manipulative
|-
|Psychopathy
|Erratic behaviour, interpersonal manipulation, callous affect and criminal tendencies
|-
|Narcissism
|Pride, aggression, envy, grandiosity, constant need for admiration, poor self-esteem
|} 

=== '''Key predictors of effective leadership''' ===
Power motivation can support effective leadership when regulated and directed toward collective rather than personal benefit. McClelland's research suggests effective leaders combine a strong need for power with high self-discipline, or “power under control,” which is linked to charismatic leadership and group morale (Reeve, 2018). However, a desire for influence alone does not ensure effectiveness. 

Self-regulation is especially important for leaders with potentially destructive personality tendencies. Stress, exhaustion, hunger, and cognitive overload can weaken willpower, making defensive reactions harder to control and potentially harming others. Strong motivation and self-awareness help leaders manage counterproductive tendencies and limit their disruptive effects.

Other motives also shape leadership. A strong need for affiliation can promote communication, respect, appreciation, and support, strengthening leader–follower relationships. Achievement motivation can encourage goal pursuit, but excessive striving may undermine effectiveness: highly active, achievement-oriented leaders can become frustrated when results fall short of expectations.

Moral identity also influences how leaders use power. Those with weaker moral identities may prioritize self-interest, while a prosocial approach uses influence to benefit others. This approach is associated with less power-related anxiety and greater well-being, suggesting that leaders’ purposes for exercising power affect their effectiveness.{{RoundBoxTop|theme=3}}[[File:John F. Kennedy speaks at Rice University.jpg|thumb|President John F. Kennedy speaking at Rice University |'''Figure 5.''' John F. Kennedy speaking at Rice University]]

== Case Study: John F. Kennedy ==

John F. Kennedy (JFK) is often recognised as an example of charismatic political leadership because of his optimistic public image, ambitious presidency, and compelling communication. Despite his relatively short time in office, Kennedy established a distinctive presidential identity by blending political leadership with popular culture and staying engaged with government and the public, which can be seen in Figure 5 (Reeve, 2018; McCann &amp; Mollan, 2023).
Kennedy's leadership aligns with McClelland's theory of motivational needs, with his profile characterised by a high need for power and a low need for affiliation (McCann &amp; Mollan, 2023). His charismatic communication also reflects transformational leadership, which emphasises inspiring followers to work towards shared goals. McClelland (1970) found that students who listened to Kennedy's inaugural address reported stronger feelings of inspiration and uplift, illustrating how a leader's communication can influence their audience.
Kennedy therefore shows how power motivation can support leadership by enabling individuals to influence, inspire, and mobilise others. However, effective leadership also depends on how that influence is exercised, particularly when responding to challenging political situations.
{{RoundBoxBottom}}

{{RoundBoxTop|theme=6}}
== Quiz Yourself ==
&lt;quiz display=simple&gt;
{Which combination of implicit motives is associated with effective leadership according to McClelland's leadership motive pattern?
|type=&quot;()&quot;}
- High power, high affiliation, and low inhibition
+ High power, low affiliation, and high inhibition
- Low power, high affiliation, and high inhibition
- High power, low affiliation, and low inhibition

{Does a high need for power necessarily result in aggressive behaviour?
|type=&quot;()&quot;}
- True
+ False

&lt;/quiz&gt;
{{RoundBoxBottom}}

== Conclusion ==
Psychological theory and research suggest that power motivation shapes how individuals seek, maintain, and regulate influence. McClelland's Three Need Theory explains differences in needs for power, achievement, and affiliation. The Two Faces of Power distinguishes personalised power, focused on personal control and self-interest, from socialised power, which uses influence to benefit others. This distinction explains why power motivation can produce very different leadership outcomes (McClelland, 1970; Carvalho &amp; Conde, 2024). The LMP further suggests that a high need for power, low need for affiliation, and high activity inhibition can support effective leadership by balancing influence with self-control (Reeve, 2018).

Power motivation is neither inherently positive nor negative; its effects depend on how leaders exercise authority, regulate behaviour, and balance personal ambitions with others’ needs. Effective leadership depends not on how much power a person wants, but on how they use it. Leaders who regulate their power motivation and direct influence toward collective goals, development, and positive outcomes are more likely to be well received by the public and subordinates (Peyton et al., 2019; Friederichs et al., 2023). Understanding power motivation helps explain both effective leadership and the risks of abuse, underscoring the importance of self-regulation and ethical influence.

{{RoundBoxTop|theme=11}}[[Image:Nuvola_apps_filetypes.png|right|102px]]
;Reflection activity

Think of a time you influenced a group decision at university, work, or in a team sport. Reflect on:

* What was the situation, and how did you respond?
* How did you influence others or make decisions?
* What motivated your behaviour?
{{RoundBoxBottom}}

==See also==
* [[Motivation and emotion/Book/2018/Emotional intelligence and leadership effectiveness|Emotional intelligence and leadership effectiveness]] (Book chapter, 2018)
* [[Motivation and emotion/Book/2015/Leadership motivation#Leadership Motive Pattern|Leadership motivation]] (Book chapter, 2015)
* [[Motivation and emotion/Book/2011/Maslow's hierarchy of needs|Maslow's hierarchy of needs]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2019/Two-factor motivation theory|Two-factor motivation theory]] (Book chapter, 2019)

{{ic|Integrate these links; use alphabetical order}}
* [[wikipedia:Need_theory|Need theory]] (Wikipedia)
* [[wikipedia:Need_for_power|Need for power]] (Wikipedia)
* [[wikipedia:David_McClelland|David Clelland]] (Wikipedia)

==References==

{{Hanging indent|1=

Bargh, J. A., &amp; Lee-Chai, A. Y. (2002). The use and abuse of power : Multiple perspectives in the causes of corruption. Psychology.

Bwalya, A. (2023). Leadership styles. Article in Journal of Entrepreneurship, Management and Innovation, 11(8), 181–193. https://doi.org/10.6084/m9.figshare.23932113

Carvalho, J. M. S., &amp; Conde, A. (2024). Individual power in human motivation – review and theoretical perspective. Acta Psychologica, 249, 104452–104452. https://doi.org/10.1016/j.actpsy.2024.104452

Deakin University. (2024, December 5). What are the different leadership styles? Deakin.Edu.Au. https://leadership.deakin.edu.au/blog/different-leadership-styles

Friederichs, K. M., Waldenmeier, K., &amp; Baumann, N. (2023). The benefits of prosocial power motivation in leadership: Action orientation fosters a win-win. Plos One, 18(7), e0287394–e0287394. https://doi.org/10.1371/journal.pone.0287394

Gambino, L. (2021, January 9). Trump has lost Twitter, his biggest political megaphone. Now what? The Guardian. https://www.theguardian.com/us-news/2021/jan/08/trump-has-lost-twitter-his-biggest-political-megaphone-now-what

Khajeh, A., Abu, M., &amp; Asaari, H. (2018). Impact of leadership styles on organizational performance. Journal of Human Resources Management Research, 2018(2166–0018), 2166–2184. https://ibimapublishing.com/articles/JHRMR/2018/687849/687849-1.pdf

Kurt, D. S. (2021, May 23). McClelland’s Three Needs Theory: Power, Achievement, and Affiliation. Education Library. https://educationlibrary.org/mcclellands-three-needs-theory-power-achievement-and-affiliation/#1

LeBreton, J. M., Shiverdecker, L. K., &amp; Grimaldi, E. M. (2018). The dark triad and workplace behavior. Annual Review of Organizational Psychology and Organizational Behavior, 5(1), 387–414. https://doi.org/10.1146/annurev-orgpsych-032117-104451

Magee, J. C., &amp; Langner, C. A. (2008). How personalized and socialized power motivation facilitate antisocial and prosocial decision-making. Journal of Research in Personality, 42(6), 1547–1559. https://doi.org/10.1016/j.jrp.2008.07.009

McCann, L., &amp; Mollan, S. (2023, November 20). JFK 60 years on: His leadership style and the reality behind the myths. The Conversation. https://theconversation.com/jfk-60-years-on-his-leadership-style-and-the-reality-behind-the-myths-216477

McClelland, D. C. (1970). The two faces of power. Journal of International Affairs, 24(1), 29–47. JSTOR. https://www.jstor.org/stable/24356663

Mobaseri, Y., &amp; Nosrat Kharazmi, Zohreh. (2025). Cognitive characteristic and crisis behaviour: An analysis of Donald Trump’s leadership style and operational code in the time of crisis. Journal of World Sociopolitical Studies, 9(1), 87–115. https://doi.org/10.22059/wsps.2025.384855.1468

Peyton, T., Zigarmi, D., &amp; Fowler, S. N. (2019). Examining the relationship between leaders’ power use, followers’ motivational outlooks, and followers’ work intentions. Frontiers in Psychology, 9(2620). https://doi.org/10.3389/fpsyg.2018.02620

Power , D. P. G. (2026). The five essentials of leadership {{!}} APS. Psychology.Org.Au. https://psychology.org.au/inpsych/2017/august/power

Ran, Y., Liu, Q., Cheng, Q., &amp; Zhang, Y. (2021). Implicit-explicit power motives congruence and forgiveness in the workplace conflict: The mediating role of empathy. International Journal of Conflict Management, 32(3), 445–468. https://doi.org/10.1108/ijcma-06-2020-0116

Reeve, J. (2018). Understanding motivation and emotion (7th edn, pp. 152–176). John Wiley &amp; Sons, Inc.

Roeloffs, M. W. (2025, January 20). Billionaires worth a combined $1.2 trillion attended Trump’s inauguration: Here’s who was there—From musk to Bezos. Forbes. https://www.forbes.com/sites/maryroeloffs/2025/01/20/billionaires-worth-a-combined-12-trillion-attended-trumps-inauguration-heres-who-was-there-from-musk-to-bezos/

Slabbinck, H., &amp; Van Witteloostuijn, A. (2020). Explicit and implicit basic human motives, and public service motivation. Frontiers in Psychology, 11(1542). https://doi.org/10.3389/fpsyg.2020.01542

Spangler, W. D., Tikhomirov, A., Sotak, K. L., &amp; Palrecha, R. (2014). Leader motive profiles in eight types of organizations. The Leadership Quarterly, 25(6), 1080–1094. https://doi.org/10.1016/j.leaqua.2014.10.001

Spanler, W. D., Tikhomirov, A., Lee Sotak, K., &amp; Palrecha, R. (2014). Leader motive profiles in eight types of organizations. ScienceDirect, 25(6). https://www-sciencedirect-com.ezproxy.canberra.edu.au/science/article/pii/S1048984314001040

Thrash, T. M., Maruskin, L. A., &amp; Martin, C. C. (2012). Implicit–explicit motive congruence. In R. M. Ryan (Ed.), The oxford handbook of human motivation (pp. 141–156). Oxford University Press. https://psycnet.apa.org/record/2012-03687-009

Verona, E., McKinley, S. J., Hoffmann, A., Murphy, B. A., &amp; Watts, A. L. (2023). Psychopathy facets, perceived power, and forms of aggression. Personality Disorders: Theory, Research, and Treatment, 14(3), 259–273. https://doi.org/10.1037/per0000562

}}

==External links==
{{ic|Move these links into References and cite; replace with links to the most relevant external non-academic resources}}

* [https://leadership.deakin.edu.au/blog/what-is-transformational-leadership Article on Transformational leadership style] (Deakin University, 2024)
* [https://pmc.ncbi.nlm.nih.gov/articles/PMC10355387/ Power motivation, the benefits of prosocial power] (Friederichs et al., 2023)
* [https://www.jstor.org/stable/pdf/24356663.pdf The Two Faces of Power Journal] (McClelland, 1970)

==See also==
* [[Motivation and emotion/Book/2024/Power motivation and leadership|Power motivation and leadership]] (Book chapter, 2024)

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__TOC__

==Overview==
{{RoundBoxTop|theme=11}}
[[File:Donald Trump takes the oath of office (2025).jpg|thumb|President-elect Donald Trump takes the oath of office |'''Figure 1'''. Donald Trump's 2025 Inauguration surrounded by some of the world's wealthiest and most powerful individuals]]

Imagine a leader standing at their inauguration, surrounded by a concentration of wealthy and influential individuals. At first glance, this may reflect a preference for resources and influence. However, a closer look raises a psychological question: what motivates a leader to seek and exercise power, and how does this shape the way they lead?

This scenario reflects the leadership of United States President Donald Trump, whose 2025 administration includes a notable concentration of wealthy and influential individuals (Roeloffs, 2025). The individuals present at Trump's inauguration illustrate this concentration of political and economic power (see Figure 1). This provides a contemporary example for examining the relationship between power motivation and leadership.{{ic|[[w:Donald Trump|Second inauguration of Donald Trump]]}} Power is reflected not only in who a leader surrounds themselves with, but also in how they exercise their influence. For example, Trump uses social media as a political megaphone, bypassing traditional bureaucratic communication channels (Gambino, 2021). His public leadership style places considerable emphasis on personal image and the need of personal control with the disregard of external influences of power (Mobaseri &amp; Nosrat Kharazmi, Zohreh, 2025).

This raises the question: does the desire for power necessarily make someone an effective leader? Individuals seek leadership for various reasons, and how they use their influence shapes their interactions with followers, decision-making, and pursuit of goals. Psychology helps explain these differences by examining power motivation and how individual motives influence leadership behaviour.
{{RoundBoxBottom}}

This chapter will explore [https://pmc.ncbi.nlm.nih.gov/articles/PMC10355387/ power motivation] (Friederichs et al., 2023), the desire to [[wikipedia:Influence|influence]], [[wikipedia:Control|control]], and have the ability to impact others, influencing [[Motivation and emotion/Book/2015/Leadership motivation|leadership]] styles, behaviour and effectiveness (McClelland, 1970). Being expressed via socialised or personalised power, determining the leader's behaviour and effectiveness, (Reeve, 2018; McClelland, 1970; Carvalho &amp; Conde, 2024).

Understanding power motivation provides a psychological framework for examining how leaders exercise authority and how followers respond. Psychological science can help explain why some power-motivated leaders use influence to control, while others use it to empower (Reeve, 2018).

{{RoundBoxTop|theme=11}}
[[File:P psychology.png|right]]
'''Focus questions:'''

*What psychological theories explain power motivation in leaders?

*How does a leader's orientation towards power influence their specific leadership style?

*What is implicit motivation, and how does it differ from explicit power motivation in leaders?

*How does power motivation influence leadership effectiveness?
{{RoundBoxBottom}}

==Understanding power motivation through psychological theories==
'''Focus question:''' ''What psychological theories explain power motivation in leaders?''

The definition of motivation and power, one describes the push to act the other often associated with [[wikipedia:Aggression|aggression]], influence, [[wikipedia:Authority|authority]] and control, together they hold a heavy definition. In psychology, [[Motivation and emotion/Lectures/Introduction|motivation]] is the driving force that guides human behaviour; it is the use of will-power and self-discipline, channelling effort to achieve a [[wikipedia:Goal|goal]]. Certain individuals have predominant motive of power, being motivated by the internal urge to dominate, influence, or control (Kurt, 2021). Power motivation is the broad construct that refers to the desire for leadership, authority or status, it is built up of three characteristics: strong action, emotional impact, and concern for status, frame, and reputation, heavily influenced by cultural values and socialised experiences (McClelland,1970).

Power seekers can be effective, well-adjusted, and highly motivated. Power is a source of human control; only the mentally healthy can wield it successfully. Those with this form of nPower struggle to feel satisfied unless they are in a position that fulfils their power-hungry needs, such as making decisions, influencing an audience, or obtaining information to become influential. Such occupations are teachers, journalists, clergy, psychologists, diplomats, business executives, political leaders and advisors (Reeve, 2018). [[wikipedia:David_McClelland|David McClelland's]] is popular within the psychology community for his thoughts on power motivation, with the most well-known theories, the [[wikipedia:Need_theory|Three Need Theory]] and the [https://www.jstor.org/stable/pdf/24356663.pdf Two Faces of Power] theory.

=== Three need theory ===
[[File:DavidMcClelland.jpg|thumb|'''Figure 2.''' David McClelland]]McClelland, a Harvard psychologist who conducted extensive research into human motivation (seen in Figure 2.), proposed the Three Need Theory. The theory identifies three acquired motivational needs: the need for [[wikipedia:Need_for_achievement|achievement]], the need for [[wikipedia:Need_for_affiliation|affiliation]], and the need for power (McClelland, 1970). Although individuals can experiences all three needs, the strength of each varies between individuals and can influence their behaviour. Table 1 summarises these needs and their defining characteristics being examined from high to low behaviour (Kurt, 2021).

nPower in leadership involves the desire to influence others and have an impact on their behaviour. While a strong need for achievement may motivate individuals to pursue challenging goals, and a strong need for affliction may encourage them to maintain positive interpersonal relationships, a strong need for power can motivate individuals to seek positions of authority. However the nPower alone does not determine whether someone will be an effective leader; its expression and the way an individual exercises their influence matter   

 {| class=&quot;wikitable&quot;
|+Table 1: Three need theory
!Need
!Definition
!High behaviour
!Low behaviour
|-
|Need for Achievement 
|Situations that challenge individuals with explicit standards.
|Individual exhibits a need to win and receive recognition.
|Constant fear of failure, typically avoids responsibilities. 
|-
|Need for Affiliation 
|Situations that afford warm relationship opportunities.
|A desire within for control, typically exaggerates own position.
|A heavily dependent individual, tries to minimise own position and importance.
|-
|Need for Power 
|Situations that enable others to exert influence over others.
|Individual demands and expects loyalty and harmony.
|Individual remains 'aloof' and keeps social distance from influence over others. 
|}

==== Two faces of power ====
McClelland's Two Faces of Power framework distinguishes between two ways the nPower can be expressed, personalised power or socialised power, also referred to as ''pP''ower, and ''s''Power (McClelland, 1970). ''pP''ower centres on personal control, it is seen as socially unacceptable way of expression, is is closely linked dominance and status. Those influenced by ''p''Power may tend to seek to strengthen their own position and influence (McClelland, 1970). While McClelland was doing his research of these mannerisms of power, he though that if those who obtained ''pP''ower were in the environment of international relations the consequences would be ''ominous''. While, ''s''Power, is the more socially acceptable form of expression, with leaders being motivated through the benefit of others; it incorporates feelings of personal strength, and the known knowledge of being careful (Bargh &amp; Lee-Chai, 2002; Friederichs et al., 2023; Magee &amp; Langner, 2008; McClellad, 1970). 

These forms of expression are not necessarily mutually exclusive. Leaders may display elements of both; McClelland believes that a true leader can balance personal dominance and socialised leadership (Bargh &amp; Lee-Chai, 2002). ''p''Power can become problematic when leaders become too absorbed by the maintenance of their position and influence, the ability to dominate, manipulate, and disagree. However, the issue isn't high-power motivation; it's how it is expressed (McClelland, 1970). 

=== The leadership motive pattern ===
McClelland and David Burnham (1975) proposed the idea that effective leadership is associated with a certain specific combination of motives known as the [[Motivation and emotion/Book/2015/Leadership motivation#Leadership Motive Pattern|Leadership Motive Pattern]] (LMP) (Spangler et al., 2014). This consists of three primary elements, high need for power (nPow), a low need for affiliation (nAff) and a high activity inhibition (AI). This model demonstrated how motivation can work together to shape leadership behaviour (Reeve, 2018). 

Each component serves as a different purpose, building characterises of the most effective leaders within bureaucratic organisation (Spangler et al., 2014). High nPow, is the force to influence, direct and impact others, this has been well-established by now. Low nAff, is a reduced desire for friendly interpersonal relationships, which prevent the leaders from producing biased decision-making. High AI is based on [[wikipedia:Self-control|self-control]], maturity, and the ability to channel power socially rather an impulsively (McClelland &amp; Boyatzis, 1982).

Research by McClelland and Burnhamd (1982) found that the LMP may only hold value for specific roles in demonstrating leadership effectiveness. When relevant, it demonstrated that managers of this pattern typically generate higher morale in their subordinates; leadership styles such as those of nations that spend relatively more on military forces than private consumption, which McClelland described as a system's capacity to mobilise resources in the interest of the nation (McClelland &amp; Boyatzis, 1982; Spangler et al., 2014). 


{{RoundBoxTop|theme=8}}
== Recap ==
&lt;quiz display=simple&gt;
{&amp;nbsp;
|type=&quot;{}&quot;}
What is the driving force that guides human behaviour?
{ Motivation }

{What is the key difference between personalised power and socialised power?}
- Personalised power focuses on achievement, and socialised power focuses on affiliation
+ Personalised power focuses on personal dominance and control, and socialised power focuses on benefiting others
- Personalised power is consistently associated with an effective leadership style, whereas socialised power is associated with an ineffective leadership style.

{Which combination of motives is associated with McClelland’s Leadership Motive Pattern in effective managers?}
- High need for achievement, high need for affiliation and low activity inhibition
+ High need for power, low need for affiliation and high activity inhibition
- Low need for power, high need for affiliation and high activity inhibition

{Which behaviour best fits an individual with a high need for power?}
- Avoiding situations where they might influence others
+ Seek opportunities to influence, control, or have an impact on others
- Avoid challenging tasks for fear of failure


&lt;/quiz&gt;

{{RoundBoxBottom}}

== Power motivation and leadership style ==
'''Focus question:''' ''How does a leader's orientation towards power influence their specific leadership style?''

An individual’s desire for power does not automatically determine their leadership style. How an individual in a position of authority understands and exercises power over others can shape their interactions, decision-making approaches, and the goals they prioritise. Examining power orientation alongside psychological characteristics provides a deeper understanding of why leaders may use their influence in various ways and how those differences are reflected in their leadership style. 

=== Power orientation and leadership behaviour ===
Power motivation is the drive to influence others, while power orientation is the how; it is the framework for how a leader becomes influential. A negative stereotype surrounds high power motivation, with the speculation that it automatically relates to undesirable behaviour, unlike prosocial power motivation, which is often associated with generosity. However, those with high power motivation can have different power orientations. Carbalho and Conde (2024) distinguish ego-power orientation and social-power orientations, highlighting that individuals can combine said orientations in different ways. Ego-power is associated with pursuing goals to satisfy the self and achieve a sense of self-fulfilment; this doesn't automatically result in harmful leadership, as it partly depends on the individual's position of influence and work. Social-power orientation links directing power to collective outcomes

=== Leadership trait analysis ===
Leadership Trait Analysis (LTA), developed by Margaret Hermann (2003), is a framework for analysing political leaders' psychological characteristics using interviews and public speeches. It examines seven traits across three dimensions: responsiveness to constraints, openness to information and motivation. The seven traits include the need for power, the belief that one can control what happens next, self-confidence, trust in others, conceptual complexity, the intensity of in-group bias or nationalism, and the need for affiliation. Together, these traits help researchers examine how leaders process information, respond to constraints and approach decision-making.

Trump illustrates how psychological frameworks such as the LTA apply to political leadership. Mobaseri and Nosrat Kharazmi (2025) examined Trump's leadership characteristics and political beliefs before his presidency and during his first term. The research explored how much his core beliefs influenced his responses to political events and the COVID-19 crisis. The study highlights the value of examining leaders' beliefs and characteristics over time to understand their responses to the political climate.

The analysis found Trump low in need for power, perceived control, self-confidence, in-group bias, and trust in others, but high in conceptual complexity. These traits informed Mobaseri and Nosrat Kharazmi's (2025) account of his leadership: resistance to adaptation, disregard for policymaking, charisma, and sensitivity to context in decisions.

The findings show how leadership reflects the interaction between a leader's psychology and their situation. LTA offers a way to analyse individual differences that shape leadership style.

=== Leadership styles and effectiveness ===
Power orientation can be reflected in different leadership styles, which describe how leaders direct, influence and interact with followers. For example, a leader who prioritises complete personal control may favour a more autocratic approach, while a leader who values engagement may be more inclined towards a democratic leadership. However, while leadership styles reflect theoretical models, they can also be shaped by individual characteristics and techniques (Khajeh et al., 2018; &quot;What Are the Different Leadership Styles?&quot;, 2024). Different styles place varying emphasis on factors seen in Table 2 (Deakin University, 2024; Bwalya, 2023). 

Effective leadership involves more than holding a position of authority; there are five essential characteristics of leadership: self-image, self-control, socialised power, sustained dialogue, and strategic intent, providing a practical framework for a successful leader (Power, 2026). Power, motivation, and leadership matter across contexts, from political leaders to supervisors, who need to build relationships with employees and an environment of trust if they want to do so. The characteristics emphasise the importance of authority, responsibility, communication, and directing efforts towards organisational goals (Power, 2026; Friederichs et al., 2023)

Research suggests that transformational leadership can produce positive outcomes by motivating and inspiring followers and benefiting the group rather than serving personal interests (Peyton et al., 2019). This shows how power can support group goals rather than simply reinforcing leadership status. Nevertheless, no single leadership style guarantees effectiveness; outcomes depend on how the leader behaves and responds to the situation at hand.

{| class=&quot;wikitable&quot;
|+Table 2. Leadership styles  (Bwalya, 2023)
! colspan=&quot;3&quot; |Leadership styles
|-
|Style
|Description
|Example Leaders
|-
|Autocratic 
|Leader holds complete control over decision-making with no input from followers. Consistently exercises control over the decision-making process. Expects strict compliance with policies and procedures, and does not take input from followers. They micromanage and control subordinate work. They make quick decisions because they do not have to consult. There is a lack of creative innovation (Bwalya, 2023). 
|Adolf Hitler and  Kim Jong-un 
|-
|Democratic 
|Leader is involved in team members' decision-making process, continuously encourages communication, and seeks feedback on matters, valuing input and ideas, wanting followers to participate in shaping strategies and goals (Bwalya, 2023).
|Former President of South Africa, Nelson Mandela and Former Prime Minister of New Zealand Jacinda Ardern 
|-
|Laissex-faire
| The leader is distant and has minimal involvement in decisions, unlike autocratic leadership, as laissez-faire lets followers make decisions with little guidance or supervision, trusting their ability to manage responsibilities. They are comfortable with mistakes and take accountability for followers' mistakes. This empowers employees and enables faster decision-making. However, the lack of guidance can cause confusion and lack of coordination (Bwalya, 2023). 
|Former President Herbert Hoover and Mahatma Ghandi
|-
|Servant 
|Leader is prosocial and motivated by power, focusing on the needs and well-being of others. Aiming to support and empower followers, in hopes they reach their full potential (Bwalya, 2023). 
|Pope Francis
|-
|Transformational 
|Based on inspiration and motivation to achieve performance, with high expectations and focus on challenging others to exceed self-interest. Focuses on transforming followers through inspiration, motivation, and effective communication. They rely on the leader's influence; if the leader fails to provide proper guidance, it can impact followers (Bwalya, 2023). 
|Former President of South Africa Nelson Mandela and Former President of the United States Barack Obama 
|-
|Transactional
|Focuses on the exchange relationship between the leader and their followers. The leader maintains stability and achieves goals by providing rewards and punishments based on performance. Very goal-oriented, with clear expectations, and quick decision-making (Bwalya, 2023).  
|Bill Gates and Former Chancellor of Germany Angela Merkel
|}

{{RoundBoxTop|theme=8}}[[Image: Hand Gesture - Holding a Magnifying Glass.gif|right|128px]] 
==Quiz==
&lt;quiz display=simple&gt; 
Which statement best explains the relationship between a leader’s power motivation and their leadership style?
|type=&quot;()&quot;} 
- Leaders with high power motivation are more likely to adopt an autocratic style, regardless of their values or circumstances
+ A leader’s power motivation determines their leadership style, while their psychological characteristics have very little influence
- Power motivation can influence a leader’s behaviour, but their power orientation, psychological characteristics and circumstances also shape how they exercise influence
&lt;/quiz&gt;
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== Implicit and explicit power motivation ==
'''Focus question:''' ''What is implicit motivation, and how does it differ from explicit power motivation in leaders?''

Human motivation can operate through two systems: [[Motivation and emotion/Book/2020/Implicit motives|implicit and explicit motivation]]. Both influencing behaviour, but very different in the extent to which the individuals are consciously aware of their motives behind their behaviour. When looking at leadership, it is helpful to dissect the distinctions to understand why a leader's states goals may not fully reflect their underlying needs which influence their behaviour. 

Implicit motive (nPow) is [[wikipedia:Unconscious_mind|unconscious]] motivation outside an individual’s awareness, mind map below in Figure 3 illustrates it. McClelland identified three implicit motives that shape thoughts, feelings, and actions: achievement, affiliation, and power. Developed through early preverbal experiences, they remain dormant until activated by incentives. Their influence appears in recurring patterns of thought, [[wikipedia:Emotion|emotion]], and behaviour, even when people cannot identify their motives (Reeve, 2018). Unlike explicit motives, implicit motives are difficult to measure directly. Researchers use the Picture-Story Exercise (PSE), asking participants to create stories from images and analysing them for themes related to the three motives. 

[[File:Implicit_Motives_associations.png|thumb| '''Figure 3.''' Mind map of implicit motives]]Explicit motives are conscious, self-attributed motives people can describe through their goals, values, and preferences (Slabbinck &amp; Van Witteloostuijn, 2020). Often assessed with self-report questionnaires, explicit power motives reflect desires for influence, status, and leadership. Their dimensions, dominance, prestige, and leadership, can help explain how power motives relate to dark personality traits. Dominance involves controlling others and is associated with [[Motivation and emotion/Book/2024/Machiavellianism and power motivation|Machiavellianism]] and counterproductive work behaviour. Prestige involves gaining influence by displaying knowledge or status and is linked to [[Motivation and emotion/Book/2010/Narcissism|narcissism]]. Leadership involves guiding groups toward shared goals and may predict organisational citizenship behaviour and align with transformational leadership.

A strong explicit power motive does not automatically lead to destructive leadership. It can support productive leadership, but may also overlap with dark traits such as narcissism, Machiavellianism, and psychopathy.

When implicit and explicit motives align, congruence, individuals are more likely to experience greater well-being and engagement, whereas misalignment can contribute to stress and reduced well-being (Ran et al., 2021; Thrash et al., 2012).

Applying this to leadership styles highlights how a leader's effectiveness and well-being depend on whether their chosen leadership style aligns with their implicit motive. When a leader's leadership style conflicts with their implicit motive, they experience ''motive incongruence,'' which can lead to chronic stress, burnout, and friction, whereas alignment predicts greater flow, high energy, and effortless leadership (Ran et al., 2021; Thrash et al., 2012).

== Power motivation and leadership effectiveness ==
'''Focus question:''' ''How does power motivation influence leadership effectiveness?''

Power motivation influences leadership effectiveness through how it is expressed and regulated. Social incentives arise from others’ rewards, expectations, and norms, whereas activity incentives come from the activity itself. Individuals with high nPower may seek positions of authority and careers offering influence and advancement. Although power motivation can be associated with aggression, social norms, laws, and consequences can constrain its expression (Reeve, 2018).

=== Destructive power dynamics and power abuse ===
There is a ''fickle'' relationship between aggression and the need or desire for power are closely linked. Studies have linked aggressive tendencies to dominance and the need for power (Verona et al., 2023). Verona et al. (2023) define human aggression as behaving with the intent to cause harm to another individual, and the target of the behaviour is driven to avoid it. Aggression can also take direct vs indirect and overt vs covert forms. That said, no concrete evidence links any level of ''feeling'' power to aggression. 

An individual with a high need for power may desire impact, control, or influence over another person or group, or even the world at large; aggression can be a means of satisfying those power needs. However, social norms, laws, and consequences can constrain this expression, causing that aggression to manifest in a more covert form. Individuals, both men and women, report more impulses to act aggressively than others; this behaviour would include yelling, throwing or destroying items and insulting others. Other factors of aggression and its link with high power-seeking individuals include finding a release through drinking, using this as a way to inflate their sense of control. Furthermore, men respond to stress and other setbacks with the behaviour of inflicting abuse on their partners, as well as an increased level of sexual misconduct (Reeve, 2018; Spanler et al., 2014). This indicates that a sense of power comes not only from leadership and reputation but can also be built through strategies of drinking, risk-taking, and posturing (Reeve, 2018).

Those who harbour inclinations that are both benevolent and malevolent towards others strive to improve the world while also influencing everyone else (Reeve, 2018). The ''dark side'' of implicit motive is the combination of opportunity to use power for personal benefit, which is the 'abuse of power.' Unrestrained affiliation can lead to favouritism and corruption in political and bureaucratic organisations. Achievement ignores political/interpersonal issues. High need for achievement: find it difficult working in groups, making decisions, and enforcing authority, ignoring interpersonal relationships (Spanier et al., 2014).[[File:The_Dark_Triad_Traits.jpg|thumb|'''Figure 4.''' The dark triad, and its associated personality traits]]

=== The dark triad traits ===
First proposed by Paulhus and Williams (2002), the [[Motivation and emotion/Book/2021/Dark triad personality and motivation|&quot;Dark Triad&quot;]] traits- narcissism, Machiavellianism, and psychopathy, seen in Figure 4, are three overlapping personality traits that can strongly motivate individuals to seek and wield power. When an individual has these traits, it often means they restrain and fuel their ruthlessness and self-serving behaviour. Research has found that scoring high on these traits increases an individual’s likelihood of committing crimes, causing distress, and creating severe issues for organisations when in authoritative leadership positions (LeBreton et al., 2018).  

Findings on the dark triad suggest that leadership outcomes depend not only on a leader's desire for influence, but also on their personality and how they exercise authority. However, the dark triad should not be associated with high implicit power motivation, as a strong unconscious drive to influence or impact others is not the same as the dark triad traits. An individual can have a strong implicit need for power without dark personality traits. Dark triad traits are associated with excessive admiration-seeking behaviour, manipulation, and callousness; these traits can interfere with relationships and judgement calls. Specific characteristics of the traits are listed in Table 3. (LeBreton et al., 2018).
{| class=&quot;wikitable&quot;
|+Table 3. Dark triad characteristic defined (LeBreton et al., 2018). 
!Dark triad traits
!Characteristics
|-
|Machiavellianism
|Cynical, strategic, and manipulative
|-
|Psychopathy
|Erratic behaviour, interpersonal manipulation, callous affect and criminal tendencies
|-
|Narcissism
|Pride, aggression, envy, grandiosity, constant need for admiration, poor self-esteem
|} 

=== '''Key predictors of effective leadership''' ===
Power motivation can support effective leadership when regulated and directed toward collective rather than personal benefit. McClelland's research suggests effective leaders combine a strong need for power with high self-discipline, or “power under control,” which is linked to charismatic leadership and group morale (Reeve, 2018). However, a desire for influence alone does not ensure effectiveness. 

Self-regulation is especially important for leaders with potentially destructive personality tendencies. Stress, exhaustion, hunger, and cognitive overload can weaken willpower, making defensive reactions harder to control and potentially harming others. Strong motivation and self-awareness help leaders manage counterproductive tendencies and limit their disruptive effects.

Other motives also shape leadership. A strong need for affiliation can promote communication, respect, appreciation, and support, strengthening leader–follower relationships. Achievement motivation can encourage goal pursuit, but excessive striving may undermine effectiveness: highly active, achievement-oriented leaders can become frustrated when results fall short of expectations.

[[Motivation and emotion/Book/2018/Emotional intelligence and leadership effectiveness|Moral identity]] also influences how leaders use power. Those with weaker moral identities may prioritise [[wikipedia:Self-interest|self-interest,]] while a prosocial approach uses influence to benefit others. This approach is associated with less power-related anxiety and greater well-being, suggesting that leaders’ purposes for exercising power affect their effectiveness.

{{RoundBoxTop|theme=3}}[[File:John F. Kennedy speaks at Rice University.jpg|thumb|President John F. Kennedy speaking at Rice University |'''Figure 5.''' John F. Kennedy speaking at Rice University]]

== Case study: John F. Kennedy ==

John F. Kennedy (JFK) is often recognised as an example of charismatic political leadership because of his optimistic public image, ambitious presidency, and compelling communication. Despite his relatively short time in office, Kennedy established a distinctive presidential identity by blending political leadership with popular culture and staying engaged with government and the public, which can be seen in Figure 5 (Reeve, 2018; McCann &amp; Mollan, 2023).
Kennedy's leadership aligns with McClelland's theory of motivational needs, with his profile characterised by a high need for power and a low need for affiliation (McCann &amp; Mollan, 2023). His charismatic communication also reflects transformational leadership, which emphasises inspiring followers to work towards shared goals. McClelland (1970) found that students who listened to Kennedy's inaugural address reported stronger feelings of inspiration and uplift, illustrating how a leader's communication can influence their audience.
Kennedy therefore shows how power motivation can support leadership by enabling individuals to influence, inspire, and mobilise others. However, effective leadership also depends on how that influence is exercised, particularly when responding to challenging political situations.
{{RoundBoxBottom}}

{{RoundBoxTop|theme=6}}
== Quiz yourself ==
&lt;quiz display=simple&gt;
{Which combination of implicit motives is associated with effective leadership according to McClelland's leadership motive pattern?
|type=&quot;()&quot;}
- High power, high affiliation, and low inhibition
+ High power, low affiliation, and high inhibition
- Low power, high affiliation, and high inhibition
- High power, low affiliation, and low inhibition

{Does a high need for power necessarily result in aggressive behaviour?
|type=&quot;()&quot;}
- True
+ False

&lt;/quiz&gt;
{{RoundBoxBottom}}

== Conclusion ==
Psychological theory and research suggest that power motivation shapes how individuals seek, maintain, and regulate influence. McClelland's Three Need Theory explains differences in needs for power, achievement, and affiliation. The Two Faces of Power distinguishes personalised power, focused on personal control and self-interest, from socialised power, which uses influence to benefit others. This distinction explains why power motivation can produce very different leadership outcomes (McClelland, 1970; Carvalho &amp; Conde, 2024). The LMP further suggests that a high need for power, low need for affiliation, and high activity inhibition can support effective leadership by balancing influence with self-control (Reeve, 2018).

Power motivation is neither inherently positive nor negative; its effects depend on how leaders exercise authority, regulate behaviour, and balance personal ambitions with others’ needs. Effective leadership depends not on how much power a person wants, but on how they use it. Leaders who regulate their power motivation and direct influence toward collective goals, development, and positive outcomes are more likely to be well received by the public and subordinates (Peyton et al., 2019; Friederichs et al., 2023). Understanding power motivation helps explain both effective leadership and the risks of abuse, underscoring the importance of self-regulation and ethical influence.

{{RoundBoxTop|theme=11}}[[Image:Nuvola_apps_filetypes.png|right|102px]]
;Reflection activity

Think of a time you influenced a group decision at university, work, or in a team sport. Reflect on:

* What was the situation, and how did you respond?
* How did you influence others or make decisions?
* What motivated your behaviour?
{{RoundBoxBottom}}

==See also==
* [[Motivation and emotion/Book/2018/Emotional intelligence and leadership effectiveness|Emotional intelligence and leadership effectiveness]] (Book chapter, 2018)
* [[Motivation and emotion/Book/2015/Leadership motivation#Leadership Motive Pattern|Leadership motivation]] (Book chapter, 2015)
* [[Motivation and emotion/Book/2011/Maslow's hierarchy of needs|Maslow's hierarchy of needs]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2019/Two-factor motivation theory|Two-factor motivation theory]] (Book chapter, 2019)

{{ic|Integrate these links; use alphabetical order}}
* [[wikipedia:Need_theory|Need theory]] (Wikipedia)
* [[wikipedia:Need_for_power|Need for power]] (Wikipedia)
* [[wikipedia:David_McClelland|David Clelland]] (Wikipedia)

==References==

{{Hanging indent|1=

Bargh, J. A., &amp; Lee-Chai, A. Y. (2002). The use and abuse of power : Multiple perspectives in the causes of corruption. Psychology.

Bwalya, A. (2023). Leadership styles. Article in Journal of Entrepreneurship, Management and Innovation, 11(8), 181–193. https://doi.org/10.6084/m9.figshare.23932113

Carvalho, J. M. S., &amp; Conde, A. (2024). Individual power in human motivation – review and theoretical perspective. Acta Psychologica, 249, 104452–104452. https://doi.org/10.1016/j.actpsy.2024.104452

Deakin University. (2024, December 5). What are the different leadership styles? Deakin.Edu.Au. https://leadership.deakin.edu.au/blog/different-leadership-styles

Friederichs, K. M., Waldenmeier, K., &amp; Baumann, N. (2023). The benefits of prosocial power motivation in leadership: Action orientation fosters a win-win. Plos One, 18(7), e0287394–e0287394. https://doi.org/10.1371/journal.pone.0287394

Gambino, L. (2021, January 9). Trump has lost Twitter, his biggest political megaphone. Now what? The Guardian. https://www.theguardian.com/us-news/2021/jan/08/trump-has-lost-twitter-his-biggest-political-megaphone-now-what

Khajeh, A., Abu, M., &amp; Asaari, H. (2018). Impact of leadership styles on organizational performance. Journal of Human Resources Management Research, 2018(2166–0018), 2166–2184. https://ibimapublishing.com/articles/JHRMR/2018/687849/687849-1.pdf

Kurt, D. S. (2021, May 23). McClelland’s Three Needs Theory: Power, Achievement, and Affiliation. Education Library. https://educationlibrary.org/mcclellands-three-needs-theory-power-achievement-and-affiliation/#1

LeBreton, J. M., Shiverdecker, L. K., &amp; Grimaldi, E. M. (2018). The dark triad and workplace behavior. Annual Review of Organizational Psychology and Organizational Behavior, 5(1), 387–414. https://doi.org/10.1146/annurev-orgpsych-032117-104451

Magee, J. C., &amp; Langner, C. A. (2008). How personalized and socialized power motivation facilitate antisocial and prosocial decision-making. Journal of Research in Personality, 42(6), 1547–1559. https://doi.org/10.1016/j.jrp.2008.07.009

McCann, L., &amp; Mollan, S. (2023, November 20). JFK 60 years on: His leadership style and the reality behind the myths. The Conversation. https://theconversation.com/jfk-60-years-on-his-leadership-style-and-the-reality-behind-the-myths-216477

McClelland, D. C. (1970). The two faces of power. Journal of International Affairs, 24(1), 29–47. JSTOR. https://www.jstor.org/stable/24356663

Mobaseri, Y., &amp; Nosrat Kharazmi, Zohreh. (2025). Cognitive characteristic and crisis behaviour: An analysis of Donald Trump’s leadership style and operational code in the time of crisis. Journal of World Sociopolitical Studies, 9(1), 87–115. https://doi.org/10.22059/wsps.2025.384855.1468

Peyton, T., Zigarmi, D., &amp; Fowler, S. N. (2019). Examining the relationship between leaders’ power use, followers’ motivational outlooks, and followers’ work intentions. Frontiers in Psychology, 9(2620). https://doi.org/10.3389/fpsyg.2018.02620

Power , D. P. G. (2026). The five essentials of leadership {{!}} APS. Psychology.Org.Au. https://psychology.org.au/inpsych/2017/august/power

Ran, Y., Liu, Q., Cheng, Q., &amp; Zhang, Y. (2021). Implicit-explicit power motives congruence and forgiveness in the workplace conflict: The mediating role of empathy. International Journal of Conflict Management, 32(3), 445–468. https://doi.org/10.1108/ijcma-06-2020-0116

Reeve, J. (2018). Understanding motivation and emotion (7th edn, pp. 152–176). John Wiley &amp; Sons, Inc.

Roeloffs, M. W. (2025, January 20). Billionaires worth a combined $1.2 trillion attended Trump’s inauguration: Here’s who was there—From musk to Bezos. Forbes. https://www.forbes.com/sites/maryroeloffs/2025/01/20/billionaires-worth-a-combined-12-trillion-attended-trumps-inauguration-heres-who-was-there-from-musk-to-bezos/

Slabbinck, H., &amp; Van Witteloostuijn, A. (2020). Explicit and implicit basic human motives, and public service motivation. Frontiers in Psychology, 11(1542). https://doi.org/10.3389/fpsyg.2020.01542

Spangler, W. D., Tikhomirov, A., Sotak, K. L., &amp; Palrecha, R. (2014). Leader motive profiles in eight types of organizations. The Leadership Quarterly, 25(6), 1080–1094. https://doi.org/10.1016/j.leaqua.2014.10.001

Spanler, W. D., Tikhomirov, A., Lee Sotak, K., &amp; Palrecha, R. (2014). Leader motive profiles in eight types of organizations. ScienceDirect, 25(6). https://www-sciencedirect-com.ezproxy.canberra.edu.au/science/article/pii/S1048984314001040

Thrash, T. M., Maruskin, L. A., &amp; Martin, C. C. (2012). Implicit–explicit motive congruence. In R. M. Ryan (Ed.), The oxford handbook of human motivation (pp. 141–156). Oxford University Press. https://psycnet.apa.org/record/2012-03687-009

Verona, E., McKinley, S. J., Hoffmann, A., Murphy, B. A., &amp; Watts, A. L. (2023). Psychopathy facets, perceived power, and forms of aggression. Personality Disorders: Theory, Research, and Treatment, 14(3), 259–273. https://doi.org/10.1037/per0000562

}}

==External links==
{{ic|Move these links into References and cite; replace with links to the most relevant external non-academic resources}}

* [https://leadership.deakin.edu.au/blog/what-is-transformational-leadership Article on Transformational leadership style] (Deakin University, 2024)
* [https://pmc.ncbi.nlm.nih.gov/articles/PMC10355387/ Power motivation, the benefits of prosocial power] (Friederichs et al., 2023)
* [https://www.jstor.org/stable/pdf/24356663.pdf The Two Faces of Power Journal] (McClelland, 1970)

==See also==
* [[Motivation and emotion/Book/2024/Power motivation and leadership|Power motivation and leadership]] (Book chapter, 2024)

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==Overview==
{{RoundBoxTop|theme=11}}
[[File:Donald Trump takes the oath of office (2025).jpg|thumb|President-elect Donald Trump takes the oath of office |'''Figure 1'''. Donald Trump's 2025 Inauguration surrounded by some of the world's wealthiest and most powerful individuals]]

Imagine a leader standing at their inauguration, surrounded by a concentration of wealthy and influential individuals. At first glance, this may reflect a preference for resources and influence. However, a closer look raises a psychological question: what motivates a leader to seek and exercise power, and how does this shape the way they lead?

This scenario reflects the leadership of United States President Donald Trump, whose 2025 administration includes a notable concentration of wealthy and influential individuals (Roeloffs, 2025). The individuals present at Trump's inauguration illustrate this concentration of political and economic power (see Figure 1). This provides a contemporary example for examining the relationship between power motivation and leadership.{{ic|[[w:Donald Trump|Second inauguration of Donald Trump]]}} Power is reflected not only in who a leader surrounds themselves with, but also in how they exercise their influence. For example, Trump uses social media as a political megaphone, bypassing traditional bureaucratic communication channels (Gambino, 2021). His public leadership style places considerable emphasis on personal image and the need of personal control with the disregard of external influences of power (Mobaseri &amp; Nosrat Kharazmi, Zohreh, 2025).

This raises the question: does the desire for power necessarily make someone an effective leader? Individuals seek leadership for various reasons, and how they use their influence shapes their interactions with followers, decision-making, and pursuit of goals. Psychology helps explain these differences by examining power motivation and how individual motives influence leadership behaviour.
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This chapter will explore [https://pmc.ncbi.nlm.nih.gov/articles/PMC10355387/ power motivation] (Friederichs et al., 2023), the desire to [[wikipedia:Influence|influence]], [[wikipedia:Control|control]], and have the ability to impact others, influencing [[Motivation and emotion/Book/2015/Leadership motivation|leadership]] styles, behaviour and effectiveness (McClelland, 1970). Being expressed via socialised or personalised power, determining the leader's behaviour and effectiveness, (Reeve, 2018; McClelland, 1970; Carvalho &amp; Conde, 2024).

Understanding power motivation provides a psychological framework for examining how leaders exercise authority and how followers respond. Psychological science can help explain why some power-motivated leaders use influence to control, while others use it to empower (Reeve, 2018).

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[[File:P psychology.png|right]]
'''Focus questions:'''

*What psychological theories explain power motivation in leaders?

*How does a leader's orientation towards power influence their specific leadership style?

*What is implicit motivation, and how does it differ from explicit power motivation in leaders?

*How does power motivation influence leadership effectiveness?
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==Understanding power motivation through psychological theories==
'''Focus question:''' ''What psychological theories explain power motivation in leaders?''

The definition of motivation and power, one describes the push to act the other often associated with [[wikipedia:Aggression|aggression]], influence, [[wikipedia:Authority|authority]] and control, together they hold a heavy definition. In psychology, [[Motivation and emotion/Lectures/Introduction|motivation]] is the driving force that guides human behaviour; it is the use of will-power and self-discipline, channelling effort to achieve a [[wikipedia:Goal|goal]]. Certain individuals have predominant motive of power, being motivated by the internal urge to dominate, influence, or control (Kurt, 2021). Power motivation is the broad construct that refers to the desire for leadership, authority or status, it is built up of three characteristics: strong action, emotional impact, and concern for status, frame, and reputation, heavily influenced by cultural values and socialised experiences (McClelland,1970).

Power seekers can be effective, well-adjusted, and highly motivated. Power is a source of human control; only the mentally healthy can wield it successfully. Those with this form of need of power, [[wikipedia:Need_for_power|nPower]], struggle to feel satisfied unless they are in a position that fulfils their power-hungry needs, such as making decisions, influencing an audience, or obtaining information to become influential. Such occupations are teachers, journalists, clergy, psychologists, diplomats, business executives, political leaders and advisors (Reeve, 2018). [[wikipedia:David_McClelland|David McClelland's]] is popular within the psychology community for his thoughts on power motivation, with the most well-known theories, the [[wikipedia:Need_theory|Three Need Theory]] and the [https://www.jstor.org/stable/pdf/24356663.pdf Two Faces of Power] theory.

Other theories of motivation include the [[Motivation and emotion/Book/2011/Maslow's hierarchy of needs|Maslow's hierachy of need,]] and [[Motivation and emotion/Book/2019/Two-factor motivation theory|Herzberg's two-factor theory]]. These theories offer broader perspectives on the factors that drive human behaviour and motivation.

=== Three need theory ===
[[File:DavidMcClelland.jpg|thumb|'''Figure 2.''' David McClelland]]McClelland, a Harvard psychologist who conducted extensive research into human motivation (seen in Figure 2.), proposed the Three Need Theory. The theory identifies three acquired motivational needs: the need for [[wikipedia:Need_for_achievement|achievement]], the need for [[wikipedia:Need_for_affiliation|affiliation]], and the need for power (McClelland, 1970). Although individuals can experiences all three needs, the strength of each varies between individuals and can influence their behaviour. Table 1 summarises these needs and their defining characteristics being examined from high to low behaviour (Kurt, 2021).

nPower in leadership involves the desire to influence others and have an impact on their behaviour. While a strong need for achievement may motivate individuals to pursue challenging goals, and a strong need for affliction may encourage them to maintain positive interpersonal relationships, a strong need for power can motivate individuals to seek positions of authority. However the nPower alone does not determine whether someone will be an effective leader; its expression and the way an individual exercises their influence matter      

 {| class=&quot;wikitable&quot;
|+Table 1: Three need theory
!Need
!Definition
!High behaviour
!Low behaviour
|-
|Need for Achievement 
|Situations that challenge individuals with explicit standards.
|Individual exhibits a need to win and receive recognition.
|Constant fear of failure, typically avoids responsibilities. 
|-
|Need for Affiliation 
|Situations that afford warm relationship opportunities.
|A desire within for control, typically exaggerates own position.
|A heavily dependent individual, tries to minimise own position and importance.
|-
|Need for Power 
|Situations that enable others to exert influence over others.
|Individual demands and expects loyalty and harmony.
|Individual remains 'aloof' and keeps social distance from influence over others. 
|}

==== Two faces of power ====
McClelland's Two Faces of Power framework distinguishes between two ways the nPower can be expressed, personalised power or socialised power, also referred to as ''pP''ower, and ''s''Power (McClelland, 1970). ''pP''ower centres on personal control, it is seen as socially unacceptable way of expression, is is closely linked dominance and status. Those influenced by ''p''Power may tend to seek to strengthen their own position and influence (McClelland, 1970). While McClelland was doing his research of these mannerisms of power, he though that if those who obtained ''pP''ower were in the environment of international relations the consequences would be ''ominous''. While, ''s''Power, is the more socially acceptable form of expression, with leaders being motivated through the benefit of others; it incorporates feelings of personal strength, and the known knowledge of being careful (Bargh &amp; Lee-Chai, 2002; Friederichs et al., 2023; Magee &amp; Langner, 2008; McClellad, 1970). 

These forms of expression are not necessarily mutually exclusive. Leaders may display elements of both; McClelland believes that a true leader can balance personal dominance and socialised leadership (Bargh &amp; Lee-Chai, 2002). ''p''Power can become problematic when leaders become too absorbed by the maintenance of their position and influence, the ability to dominate, manipulate, and disagree. However, the issue isn't high-power motivation; it's how it is expressed (McClelland, 1970). 

=== The leadership motive pattern ===
McClelland and David Burnham (1975) proposed the idea that effective leadership is associated with a certain specific combination of motives known as the [[Motivation and emotion/Book/2015/Leadership motivation#Leadership Motive Pattern|Leadership Motive Pattern]] (LMP) (Spangler et al., 2014). This consists of three primary elements, high need for power (nPow), a low need for affiliation (nAff) and a high activity inhibition (AI). This model demonstrated how motivation can work together to shape leadership behaviour (Reeve, 2018). 

Each component serves as a different purpose, building characterises of the most effective leaders within bureaucratic organisation (Spangler et al., 2014). High nPow, is the force to influence, direct and impact others, this has been well-established by now. Low nAff, is a reduced desire for friendly interpersonal relationships, which prevent the leaders from producing biased decision-making. High AI is based on [[wikipedia:Self-control|self-control]], maturity, and the ability to channel power socially rather an impulsively (McClelland &amp; Boyatzis, 1982).

Research by McClelland and Burnhamd (1982) found that the LMP may only hold value for specific roles in demonstrating leadership effectiveness. When relevant, it demonstrated that managers of this pattern typically generate higher morale in their subordinates; leadership styles such as those of nations that spend relatively more on military forces than private consumption, which McClelland described as a system's capacity to mobilise resources in the interest of the nation (McClelland &amp; Boyatzis, 1982; Spangler et al., 2014). 


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== Recap ==
&lt;quiz display=simple&gt;
{&amp;nbsp;
|type=&quot;{}&quot;}
What is the driving force that guides human behaviour?
{ Motivation }

{What is the key difference between personalised power and socialised power?}
- Personalised power focuses on achievement, and socialised power focuses on affiliation
+ Personalised power focuses on personal dominance and control, and socialised power focuses on benefiting others
- Personalised power is consistently associated with an effective leadership style, whereas socialised power is associated with an ineffective leadership style.

{Which combination of motives is associated with McClelland’s Leadership Motive Pattern in effective managers?}
- High need for achievement, high need for affiliation and low activity inhibition
+ High need for power, low need for affiliation and high activity inhibition
- Low need for power, high need for affiliation and high activity inhibition

{Which behaviour best fits an individual with a high need for power?}
- Avoiding situations where they might influence others
+ Seek opportunities to influence, control, or have an impact on others
- Avoid challenging tasks for fear of failure


&lt;/quiz&gt;

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== Power motivation and leadership style ==
'''Focus question:''' ''How does a leader's orientation towards power influence their specific leadership style?''

An individual’s desire for power does not automatically determine their leadership style. How an individual in a position of authority understands and exercises power over others can shape their interactions, decision-making approaches, and the goals they prioritise. Examining power orientation alongside psychological characteristics provides a deeper understanding of why leaders may use their influence in various ways and how those differences are reflected in their leadership style. 

=== Power orientation and leadership behaviour ===
Power motivation is the drive to influence others, while power orientation is the how; it is the framework for how a leader becomes influential. A negative stereotype surrounds high power motivation, with the speculation that it automatically relates to undesirable behaviour, unlike prosocial power motivation, which is often associated with generosity. However, those with high power motivation can have different power orientations. Carbalho and Conde (2024) distinguish ego-power orientation and social-power orientations, highlighting that individuals can combine said orientations in different ways. Ego-power is associated with pursuing goals to satisfy the self and achieve a sense of self-fulfilment; this doesn't automatically result in harmful leadership, as it partly depends on the individual's position of influence and work. Social-power orientation links directing power to collective outcomes

=== Leadership trait analysis ===
[https://wsps.ut.ac.ir/article_101018.html Leadership Trait Analysis] (LTA), developed by Margaret Hermann (2003) (Mobaseri &amp; Nosrat Kharazmi, Zohreh, 2025), is a framework for analysing political leaders' psychological characteristics using interviews and public speeches. It examines seven traits across three dimensions: responsiveness to constraints, openness to information and motivation. The seven traits include the need for power, the belief that one can control what happens next, self-confidence, trust in others, conceptual complexity, the intensity of in-group bias or nationalism, and the need for affiliation. Together, these traits help researchers examine how leaders process information, respond to constraints and approach decision-making.

Trump illustrates how psychological frameworks such as the LTA apply to political leadership. Mobaseri and Nosrat Kharazmi (2025) examined Trump's leadership characteristics and political beliefs before his presidency and during his first term. The research explored how much his core beliefs influenced his responses to political events and the COVID-19 crisis. The study highlights the value of examining leaders' beliefs and characteristics over time to understand their responses to the political climate.

The analysis found Trump low in need for power, perceived control, self-confidence, in-group bias, and trust in others, but high in conceptual complexity. These traits informed Mobaseri and Nosrat Kharazmi's (2025) account of his leadership: resistance to adaptation, disregard for policymaking, charisma, and sensitivity to context in decisions.

The findings show how leadership reflects the interaction between a leader's psychology and their situation. LTA offers a way to analyse individual differences that shape leadership style.

=== Leadership styles and effectiveness ===
Power orientation can be reflected in different leadership styles, which describe how leaders direct, influence and interact with followers. For example, a leader who prioritises complete personal control may favour a more autocratic approach, while a leader who values engagement may be more inclined towards a democratic leadership. However, while leadership styles reflect theoretical models, they can also be shaped by individual characteristics and techniques (Khajeh et al., 2018; &quot;What Are the Different Leadership Styles?&quot;, 2024). Different styles place varying emphasis on factors seen in Table 2 (Deakin University, 2024; Bwalya, 2023). 

Effective leadership involves more than holding a position of authority; there are five essential characteristics of leadership: self-image, self-control, socialised power, sustained dialogue, and strategic intent, providing a practical framework for a successful leader (Power, 2026). Power, motivation, and leadership matter across contexts, from political leaders to supervisors, who need to build relationships with employees and an environment of trust if they want to do so. The characteristics emphasise the importance of authority, responsibility, communication, and directing efforts towards organisational goals (Power, 2026; Friederichs et al., 2023)

Research suggests that transformational leadership can produce positive outcomes by motivating and inspiring followers and benefiting the group rather than serving personal interests (Peyton et al., 2019). This shows how power can support group goals rather than simply reinforcing leadership status. Nevertheless, no single leadership style guarantees effectiveness; outcomes depend on how the leader behaves and responds to the situation at hand.

{| class=&quot;wikitable&quot;
|+Table 2. Leadership styles  (Bwalya, 2023)
! colspan=&quot;3&quot; |Leadership styles
|-
|Style
|Description
|Example Leaders
|-
|Autocratic 
|Leader holds complete control over decision-making with no input from followers. Consistently exercises control over the decision-making process. Expects strict compliance with policies and procedures, and does not take input from followers. They micromanage and control subordinate work. They make quick decisions because they do not have to consult. There is a lack of creative innovation (Bwalya, 2023). 
|Adolf Hitler and  Kim Jong-un 
|-
|Democratic 
|Leader is involved in team members' decision-making process, continuously encourages communication, and seeks feedback on matters, valuing input and ideas, wanting followers to participate in shaping strategies and goals (Bwalya, 2023).
|Former President of South Africa, Nelson Mandela and Former Prime Minister of New Zealand Jacinda Ardern 
|-
|Laissex-faire
| The leader is distant and has minimal involvement in decisions, unlike autocratic leadership, as laissez-faire lets followers make decisions with little guidance or supervision, trusting their ability to manage responsibilities. They are comfortable with mistakes and take accountability for followers' mistakes. This empowers employees and enables faster decision-making. However, the lack of guidance can cause confusion and lack of coordination (Bwalya, 2023). 
|Former President Herbert Hoover and Mahatma Ghandi
|-
|Servant 
|Leader is prosocial and motivated by power, focusing on the needs and well-being of others. Aiming to support and empower followers, in hopes they reach their full potential (Bwalya, 2023). 
|Pope Francis
|-
|Transformational 
|Based on inspiration and motivation to achieve performance, with high expectations and focus on challenging others to exceed self-interest. Focuses on transforming followers through inspiration, motivation, and effective communication. They rely on the leader's influence; if the leader fails to provide proper guidance, it can impact followers (Bwalya, 2023). 
|Former President of South Africa Nelson Mandela and Former President of the United States Barack Obama 
|-
|Transactional
|Focuses on the exchange relationship between the leader and their followers. The leader maintains stability and achieves goals by providing rewards and punishments based on performance. Very goal-oriented, with clear expectations, and quick decision-making (Bwalya, 2023).  
|Bill Gates and Former Chancellor of Germany Angela Merkel
|}

{{RoundBoxTop|theme=8}}[[Image: Hand Gesture - Holding a Magnifying Glass.gif|right|128px]] 
==Quiz==
&lt;quiz display=simple&gt; 
Which statement best explains the relationship between a leader’s power motivation and their leadership style?
|type=&quot;()&quot;} 
- Leaders with high power motivation are more likely to adopt an autocratic style, regardless of their values or circumstances
+ A leader’s power motivation determines their leadership style, while their psychological characteristics have very little influence
- Power motivation can influence a leader’s behaviour, but their power orientation, psychological characteristics and circumstances also shape how they exercise influence
&lt;/quiz&gt;
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== Implicit and explicit power motivation ==
'''Focus question:''' ''What is implicit motivation, and how does it differ from explicit power motivation in leaders?''

Human motivation can operate through two systems: [[Motivation and emotion/Book/2020/Implicit motives|implicit and explicit motivation]]. Both influencing behaviour, but very different in the extent to which the individuals are consciously aware of their motives behind their behaviour. When looking at leadership, it is helpful to dissect the distinctions to understand why a leader's states goals may not fully reflect their underlying needs which influence their behaviour. 

Implicit motive (nPow) is [[wikipedia:Unconscious_mind|unconscious]] motivation outside an individual’s awareness, mind map below in Figure 3 illustrates it. McClelland identified three implicit motives that shape thoughts, feelings, and actions: achievement, affiliation, and power. Developed through early preverbal experiences, they remain dormant until activated by incentives. Their influence appears in recurring patterns of thought, [[wikipedia:Emotion|emotion]], and behaviour, even when people cannot identify their motives (Reeve, 2018). Unlike explicit motives, implicit motives are difficult to measure directly. Researchers use the Picture-Story Exercise (PSE), asking participants to create stories from images and analysing them for themes related to the three motives. 

[[File:Implicit_Motives_associations.png|thumb| '''Figure 3.''' Mind map of implicit motives]]Explicit motives are conscious, self-attributed motives people can describe through their goals, values, and preferences (Slabbinck &amp; Van Witteloostuijn, 2020). Often assessed with self-report questionnaires, explicit power motives reflect desires for influence, status, and leadership. Their dimensions, dominance, prestige, and leadership, can help explain how power motives relate to dark personality traits. Dominance involves controlling others and is associated with [[Motivation and emotion/Book/2024/Machiavellianism and power motivation|Machiavellianism]] and counterproductive work behaviour. Prestige involves gaining influence by displaying knowledge or status and is linked to [[Motivation and emotion/Book/2010/Narcissism|narcissism]]. Leadership involves guiding groups toward shared goals and may predict organisational citizenship behaviour and align with transformational leadership.

A strong explicit power motive does not automatically lead to destructive leadership. It can support productive leadership, but may also overlap with dark traits such as narcissism, Machiavellianism, and psychopathy.

When implicit and explicit motives align, congruence, individuals are more likely to experience greater well-being and engagement, whereas misalignment can contribute to stress and reduced well-being (Ran et al., 2021; Thrash et al., 2012).

Applying this to leadership styles highlights how a leader's effectiveness and well-being depend on whether their chosen leadership style aligns with their implicit motive. When a leader's leadership style conflicts with their implicit motive, they experience ''motive incongruence,'' which can lead to chronic stress, burnout, and friction, whereas alignment predicts greater flow, high energy, and effortless leadership (Ran et al., 2021; Thrash et al., 2012).

== Power motivation and leadership effectiveness ==
'''Focus question:''' ''How does power motivation influence leadership effectiveness?''

Power motivation influences leadership effectiveness through how it is expressed and regulated. Social incentives arise from others’ rewards, expectations, and norms, whereas activity incentives come from the activity itself. Individuals with high nPower may seek positions of authority and careers offering influence and advancement. Although power motivation can be associated with aggression, social norms, laws, and consequences can constrain its expression (Reeve, 2018).

=== Destructive power dynamics and power abuse ===
There is a ''fickle'' relationship between aggression and the need or desire for power are closely linked. Studies have linked aggressive tendencies to dominance and the need for power (Verona et al., 2023). Verona et al. (2023) define human aggression as behaving with the intent to cause harm to another individual, and the target of the behaviour is driven to avoid it. Aggression can also take direct vs indirect and overt vs covert forms. That said, no concrete evidence links any level of ''feeling'' power to aggression. 

An individual with a high need for power may desire impact, control, or influence over another person or group, or even the world at large; aggression can be a means of satisfying those power needs. However, social norms, laws, and consequences can constrain this expression, causing that aggression to manifest in a more covert form. Individuals, both men and women, report more impulses to act aggressively than others; this behaviour would include yelling, throwing or destroying items and insulting others. Other factors of aggression and its link with high power-seeking individuals include finding a release through drinking, using this as a way to inflate their sense of control. Furthermore, men respond to stress and other setbacks with the behaviour of inflicting abuse on their partners, as well as an increased level of sexual misconduct (Reeve, 2018; Spanler et al., 2014). This indicates that a sense of power comes not only from leadership and reputation but can also be built through strategies of drinking, risk-taking, and posturing (Reeve, 2018).

Those who harbour inclinations that are both benevolent and malevolent towards others strive to improve the world while also influencing everyone else (Reeve, 2018). The ''dark side'' of implicit motive is the combination of opportunity to use power for personal benefit, which is the 'abuse of power.' Unrestrained affiliation can lead to favouritism and corruption in political and bureaucratic organisations. Achievement ignores political/interpersonal issues. High need for achievement: find it difficult working in groups, making decisions, and enforcing authority, ignoring interpersonal relationships (Spanier et al., 2014).[[File:The_Dark_Triad_Traits.jpg|thumb|'''Figure 4.''' The dark triad, and its associated personality traits]]

=== The dark triad traits ===
First proposed by Paulhus and Williams (2002), the [[Motivation and emotion/Book/2021/Dark triad personality and motivation|&quot;Dark Triad&quot;]] traits- narcissism, Machiavellianism, and psychopathy, seen in Figure 4, are three overlapping personality traits that can strongly motivate individuals to seek and wield power. When an individual has these traits, it often means they restrain and fuel their ruthlessness and self-serving behaviour. Research has found that scoring high on these traits increases an individual’s likelihood of committing crimes, causing distress, and creating severe issues for organisations when in authoritative leadership positions (LeBreton et al., 2018).  

Findings on the dark triad suggest that leadership outcomes depend not only on a leader's desire for influence, but also on their personality and how they exercise authority. However, the dark triad should not be associated with high implicit power motivation, as a strong unconscious drive to influence or impact others is not the same as the dark triad traits. An individual can have a strong implicit need for power without dark personality traits. Dark triad traits are associated with excessive admiration-seeking behaviour, manipulation, and callousness; these traits can interfere with relationships and judgement calls. Specific characteristics of the traits are listed in Table 3. (LeBreton et al., 2018).
{| class=&quot;wikitable&quot;
|+Table 3. Dark triad characteristic defined (LeBreton et al., 2018). 
!Dark triad traits
!Characteristics
|-
|Machiavellianism
|Cynical, strategic, and manipulative
|-
|Psychopathy
|Erratic behaviour, interpersonal manipulation, callous affect and criminal tendencies
|-
|Narcissism
|Pride, aggression, envy, grandiosity, constant need for admiration, poor self-esteem
|} 

=== '''Key predictors of effective leadership''' ===
Power motivation can support effective leadership when regulated and directed toward collective rather than personal benefit. McClelland's research suggests effective leaders combine a strong need for power with high self-discipline, or “power under control,” which is linked to charismatic leadership and group morale (Reeve, 2018). However, a desire for influence alone does not ensure effectiveness. 

Self-regulation is especially important for leaders with potentially destructive personality tendencies. Stress, exhaustion, hunger, and cognitive overload can weaken willpower, making defensive reactions harder to control and potentially harming others. Strong motivation and self-awareness help leaders manage counterproductive tendencies and limit their disruptive effects.

Other motives also shape leadership. A strong need for affiliation can promote communication, respect, appreciation, and support, strengthening leader–follower relationships. Achievement motivation can encourage goal pursuit, but excessive striving may undermine effectiveness: highly active, achievement-oriented leaders can become frustrated when results fall short of expectations.

[[Motivation and emotion/Book/2018/Emotional intelligence and leadership effectiveness|Moral identity]] also influences how leaders use power. Those with weaker moral identities may prioritise [[wikipedia:Self-interest|self-interest,]] while a prosocial approach uses influence to benefit others. This approach is associated with less power-related anxiety and greater well-being, suggesting that leaders’ purposes for exercising power affect their effectiveness.

{{RoundBoxTop|theme=3}}[[File:John F. Kennedy speaks at Rice University.jpg|thumb|President John F. Kennedy speaking at Rice University |'''Figure 5.''' John F. Kennedy speaking at Rice University]]

== Case study: John F. Kennedy ==

John F. Kennedy (JFK) is often recognised as an example of charismatic political leadership because of his optimistic public image, ambitious presidency, and compelling communication. Despite his relatively short time in office, Kennedy established a distinctive presidential identity by blending political leadership with popular culture and staying engaged with government and the public, which can be seen in Figure 5 (Reeve, 2018; McCann &amp; Mollan, 2023).
Kennedy's leadership aligns with McClelland's theory of motivational needs, with his profile characterised by a high need for power and a low need for affiliation (McCann &amp; Mollan, 2023). His charismatic communication also reflects transformational leadership, which emphasises inspiring followers to work towards shared goals. McClelland (1970) found that students who listened to Kennedy's inaugural address reported stronger feelings of inspiration and uplift, illustrating how a leader's communication can influence their audience.
Kennedy therefore shows how power motivation can support leadership by enabling individuals to influence, inspire, and mobilise others. However, effective leadership also depends on how that influence is exercised, particularly when responding to challenging political situations.
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== Quiz yourself ==
&lt;quiz display=simple&gt;
{Which combination of implicit motives is associated with effective leadership according to McClelland's leadership motive pattern?
|type=&quot;()&quot;}
- High power, high affiliation, and low inhibition
+ High power, low affiliation, and high inhibition
- Low power, high affiliation, and high inhibition
- High power, low affiliation, and low inhibition

{Does a high need for power necessarily result in aggressive behaviour?
|type=&quot;()&quot;}
- True
+ False

&lt;/quiz&gt;
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== Conclusion ==
Psychological theory and research suggest that power motivation shapes how individuals seek, maintain, and regulate influence. McClelland's Three Need Theory explains differences in needs for power, achievement, and affiliation. The Two Faces of Power distinguishes personalised power, focused on personal control and self-interest, from socialised power, which uses influence to benefit others. This distinction explains why power motivation can produce very different leadership outcomes (McClelland, 1970; Carvalho &amp; Conde, 2024). The LMP further suggests that a high need for power, low need for affiliation, and high activity inhibition can support effective leadership by balancing influence with self-control (Reeve, 2018).

Power motivation is neither inherently positive nor negative; its effects depend on how leaders exercise authority, regulate behaviour, and balance personal ambitions with others’ needs. Effective leadership depends not on how much power a person wants, but on how they use it. Leaders who regulate their power motivation and direct influence toward collective goals, development, and positive outcomes are more likely to be well received by the public and subordinates (Peyton et al., 2019; Friederichs et al., 2023). Understanding power motivation helps explain both effective leadership and the risks of abuse, underscoring the importance of self-regulation and ethical influence.

{{RoundBoxTop|theme=11}}[[Image:Nuvola_apps_filetypes.png|right|102px]]
;Reflection activity

Think of a time you influenced a group decision at university, work, or in a team sport. Reflect on:

* What was the situation, and how did you respond?
* How did you influence others or make decisions?
* What motivated your behaviour?
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==See also==
* [[Motivation and emotion/Book/2018/Emotional intelligence and leadership effectiveness|Emotional intelligence and leadership effectiveness]] (Book chapter, 2018)
* [[Motivation and emotion/Book/2015/Leadership motivation#Leadership Motive Pattern|Leadership motivation]] (Book chapter, 2015)
* [[Motivation and emotion/Book/2011/Maslow's hierarchy of needs|Maslow's hierarchy of needs]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2019/Two-factor motivation theory|Two-factor motivation theory]] (Book chapter, 2019)
* [[wikipedia:David_McClelland|David Clelland]] (Wikipedia)
* [[wikipedia:Need_for_power|Need for power]] (Wikipedia)
* [[wikipedia:Need_theory|Need theory]] (Wikipedia)

==References==

{{Hanging indent|1=

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Deakin University. (2024, December 5). What are the different leadership styles? Deakin.Edu.Au. https://leadership.deakin.edu.au/blog/different-leadership-styles

Friederichs, K. M., Waldenmeier, K., &amp; Baumann, N. (2023). The benefits of prosocial power motivation in leadership: Action orientation fosters a win-win. Plos One, 18(7), e0287394–e0287394. https://doi.org/10.1371/journal.pone.0287394

Gambino, L. (2021, January 9). Trump has lost Twitter, his biggest political megaphone. Now what? The Guardian. https://www.theguardian.com/us-news/2021/jan/08/trump-has-lost-twitter-his-biggest-political-megaphone-now-what

Khajeh, A., Abu, M., &amp; Asaari, H. (2018). Impact of leadership styles on organizational performance. Journal of Human Resources Management Research, 2018(2166–0018), 2166–2184. https://ibimapublishing.com/articles/JHRMR/2018/687849/687849-1.pdf

Kurt, D. S. (2021, May 23). McClelland’s Three Needs Theory: Power, Achievement, and Affiliation. Education Library. https://educationlibrary.org/mcclellands-three-needs-theory-power-achievement-and-affiliation/#1

LeBreton, J. M., Shiverdecker, L. K., &amp; Grimaldi, E. M. (2018). The dark triad and workplace behavior. Annual Review of Organizational Psychology and Organizational Behavior, 5(1), 387–414. https://doi.org/10.1146/annurev-orgpsych-032117-104451

Magee, J. C., &amp; Langner, C. A. (2008). How personalized and socialized power motivation facilitate antisocial and prosocial decision-making. Journal of Research in Personality, 42(6), 1547–1559. https://doi.org/10.1016/j.jrp.2008.07.009

McCann, L., &amp; Mollan, S. (2023, November 20). JFK 60 years on: His leadership style and the reality behind the myths. The Conversation. https://theconversation.com/jfk-60-years-on-his-leadership-style-and-the-reality-behind-the-myths-216477

McClelland, D. C. (1970). The two faces of power. Journal of International Affairs, 24(1), 29–47. JSTOR. https://www.jstor.org/stable/24356663

Mobaseri, Y., &amp; Nosrat Kharazmi, Zohreh. (2025). Cognitive characteristic and crisis behaviour: An analysis of Donald Trump’s leadership style and operational code in the time of crisis. Journal of World Sociopolitical Studies, 9(1), 87–115. https://doi.org/10.22059/wsps.2025.384855.1468

Peyton, T., Zigarmi, D., &amp; Fowler, S. N. (2019). Examining the relationship between leaders’ power use, followers’ motivational outlooks, and followers’ work intentions. Frontiers in Psychology, 9(2620). https://doi.org/10.3389/fpsyg.2018.02620

Power , D. P. G. (2026). The five essentials of leadership {{!}} APS. Psychology.Org.Au. https://psychology.org.au/inpsych/2017/august/power

Ran, Y., Liu, Q., Cheng, Q., &amp; Zhang, Y. (2021). Implicit-explicit power motives congruence and forgiveness in the workplace conflict: The mediating role of empathy. International Journal of Conflict Management, 32(3), 445–468. https://doi.org/10.1108/ijcma-06-2020-0116

Reeve, J. (2018). Understanding motivation and emotion (7th edn, pp. 152–176). John Wiley &amp; Sons, Inc.

Roeloffs, M. W. (2025, January 20). Billionaires worth a combined $1.2 trillion attended Trump’s inauguration: Here’s who was there—From musk to Bezos. Forbes. https://www.forbes.com/sites/maryroeloffs/2025/01/20/billionaires-worth-a-combined-12-trillion-attended-trumps-inauguration-heres-who-was-there-from-musk-to-bezos/

Slabbinck, H., &amp; Van Witteloostuijn, A. (2020). Explicit and implicit basic human motives, and public service motivation. Frontiers in Psychology, 11(1542). https://doi.org/10.3389/fpsyg.2020.01542

Spangler, W. D., Tikhomirov, A., Sotak, K. L., &amp; Palrecha, R. (2014). Leader motive profiles in eight types of organizations. The Leadership Quarterly, 25(6), 1080–1094. https://doi.org/10.1016/j.leaqua.2014.10.001

Spanler, W. D., Tikhomirov, A., Lee Sotak, K., &amp; Palrecha, R. (2014). Leader motive profiles in eight types of organizations. ScienceDirect, 25(6). https://www-sciencedirect-com.ezproxy.canberra.edu.au/science/article/pii/S1048984314001040

Thrash, T. M., Maruskin, L. A., &amp; Martin, C. C. (2012). Implicit–explicit motive congruence. In R. M. Ryan (Ed.), The oxford handbook of human motivation (pp. 141–156). Oxford University Press. https://psycnet.apa.org/record/2012-03687-009

Verona, E., McKinley, S. J., Hoffmann, A., Murphy, B. A., &amp; Watts, A. L. (2023). Psychopathy facets, perceived power, and forms of aggression. Personality Disorders: Theory, Research, and Treatment, 14(3), 259–273. https://doi.org/10.1037/per0000562

}}

==External links==
{{ic|Move these links into References and cite; replace with links to the most relevant external non-academic resources}}

* [https://leadership.deakin.edu.au/blog/what-is-transformational-leadership Article on Transformational leadership style] (Deakin University, 2024)
* [https://pmc.ncbi.nlm.nih.gov/articles/PMC10355387/ Power motivation, the benefits of prosocial power] (Friederichs et al., 2023)
* [https://www.jstor.org/stable/pdf/24356663.pdf The Two Faces of Power Journal] (McClelland, 1970)

==See also==
* [[Motivation and emotion/Book/2024/Power motivation and leadership|Power motivation and leadership]] (Book chapter, 2024)

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==Overview==
{{RoundBoxTop|theme=11}}
[[File:Donald Trump takes the oath of office (2025).jpg|thumb|President-elect Donald Trump takes the oath of office |'''Figure 1'''. Donald Trump's 2025 Inauguration surrounded by some of the world's wealthiest and most powerful individuals]]

Imagine a leader standing at their inauguration, surrounded by a concentration of wealthy and influential individuals. At first glance, this may reflect a preference for resources and influence. However, a closer look raises a psychological question: what motivates a leader to seek and exercise power, and how does this shape the way they lead?

This scenario reflects the leadership of United States President Donald Trump, whose 2025 administration includes a notable concentration of wealthy and influential individuals (Roeloffs, 2025). The individuals present at Trump's inauguration illustrate this concentration of political and economic power (see Figure 1). This provides a contemporary example for examining the relationship between power motivation and leadership.{{ic|[[w:Donald Trump|Second inauguration of Donald Trump]]}} Power is reflected not only in who a leader surrounds themselves with, but also in how they exercise their influence. For example, Trump uses social media as a political megaphone, bypassing traditional bureaucratic communication channels (Gambino, 2021). His public leadership style places considerable emphasis on personal image and the need of personal control with the disregard of external influences of power (Adubato, 2019; Mobaseri &amp; Nosrat Kharazmi, Zohreh, 2025).

This raises the question: does the desire for power necessarily make someone an effective leader? Individuals seek leadership for various reasons, and how they use their influence shapes their interactions with followers, decision-making, and pursuit of goals. Psychology helps explain these differences by examining power motivation and how individual motives influence leadership behaviour.
{{RoundBoxBottom}}

This chapter will explore [https://pmc.ncbi.nlm.nih.gov/articles/PMC10355387/ power motivation] (Friederichs et al., 2023), the desire to [[wikipedia:Influence|influence]], [[wikipedia:Control|control]], and have the ability to impact others, influencing [[Motivation and emotion/Book/2015/Leadership motivation|leadership]] styles, behaviour and effectiveness (McClelland, 1970). Being expressed via socialised or personalised power, determining the leader's behaviour and effectiveness, (Reeve, 2018; McClelland, 1970; Carvalho &amp; Conde, 2024).

Understanding power motivation provides a psychological framework for examining how leaders exercise authority and how followers respond. Psychological science can help explain why some power-motivated leaders use influence to control, while others use it to empower (Reeve, 2018).

{{RoundBoxTop|theme=11}}
[[File:P psychology.png|right]]
'''Focus questions:'''

*What psychological theories explain power motivation in leaders?

*How does a leader's orientation towards power influence their specific leadership style?

*What is implicit motivation, and how does it differ from explicit power motivation in leaders?

*How does power motivation influence leadership effectiveness?
{{RoundBoxBottom}}

==Understanding power motivation through psychological theories==
'''Focus question:''' ''What psychological theories explain power motivation in leaders?''

The definition of motivation and power, one describes the push to act the other often associated with [[wikipedia:Aggression|aggression]], influence, [[wikipedia:Authority|authority]] and control, together they hold a heavy definition. In psychology, [[Motivation and emotion/Lectures/Introduction|motivation]] is the driving force that guides human behaviour; it is the use of will-power and self-discipline, channelling effort to achieve a [[wikipedia:Goal|goal]]. Certain individuals have predominant motive of power, being motivated by the internal urge to dominate, influence, or control (Kurt, 2021). Power motivation is the broad construct that refers to the desire for leadership, authority or status, it is built up of three characteristics: strong action, emotional impact, and concern for status, frame, and reputation, heavily influenced by cultural values and socialised experiences (McClelland,1970).

Power seekers can be effective, well-adjusted, and highly motivated. Power is a source of human control; only the mentally healthy can wield it successfully. Those with this form of need of power, [[wikipedia:Need_for_power|nPower]], struggle to feel satisfied unless they are in a position that fulfils their power-hungry needs, such as making decisions, influencing an audience, or obtaining information to become influential. Such occupations are teachers, journalists, clergy, psychologists, diplomats, business executives, political leaders and advisors (Reeve, 2018). [[wikipedia:David_McClelland|David McClelland's]] is popular within the psychology community for his thoughts on power motivation, with the most well-known theories, the [[wikipedia:Need_theory|Three Need Theory]] and the [https://www.jstor.org/stable/pdf/24356663.pdf Two Faces of Power] theory.

Other theories of motivation include the [[Motivation and emotion/Book/2011/Maslow's hierarchy of needs|Maslow's hierachy of need,]] and [[Motivation and emotion/Book/2019/Two-factor motivation theory|Herzberg's two-factor theory]]. These theories offer broader perspectives on the factors that drive human behaviour and motivation.

=== Three need theory ===
[[File:DavidMcClelland.jpg|thumb|'''Figure 2.''' David McClelland]]McClelland, a Harvard psychologist who conducted extensive research into human motivation (seen in Figure 2.), proposed the Three Need Theory. The theory identifies three acquired motivational needs: the need for [[wikipedia:Need_for_achievement|achievement]], the need for [[wikipedia:Need_for_affiliation|affiliation]], and the need for power (McClelland, 1970). Although individuals can experiences all three needs, the strength of each varies between individuals and can influence their behaviour. Table 1 summarises these needs and their defining characteristics being examined from high to low behaviour (Kurt, 2021).

nPower in leadership involves the desire to influence others and have an impact on their behaviour. While a strong need for achievement may motivate individuals to pursue challenging goals, and a strong need for affliction may encourage them to maintain positive interpersonal relationships, a strong need for power can motivate individuals to seek positions of authority. However the nPower alone does not determine whether someone will be an effective leader; its expression and the way an individual exercises their influence matter      

 {| class=&quot;wikitable&quot;
|+Table 1: Three need theory
!Need
!Definition
!High behaviour
!Low behaviour
|-
|Need for Achievement 
|Situations that challenge individuals with explicit standards.
|Individual exhibits a need to win and receive recognition.
|Constant fear of failure, typically avoids responsibilities. 
|-
|Need for Affiliation 
|Situations that afford warm relationship opportunities.
|A desire within for control, typically exaggerates own position.
|A heavily dependent individual, tries to minimise own position and importance.
|-
|Need for Power 
|Situations that enable others to exert influence over others.
|Individual demands and expects loyalty and harmony.
|Individual remains 'aloof' and keeps social distance from influence over others. 
|}

==== Two faces of power ====
McClelland's Two Faces of Power framework distinguishes between two ways the nPower can be expressed, personalised power or socialised power, also referred to as ''pP''ower, and ''s''Power (McClelland, 1970). ''pP''ower centres on personal control, it is seen as socially unacceptable way of expression, is is closely linked dominance and status. Those influenced by ''p''Power may tend to seek to strengthen their own position and influence (McClelland, 1970). While McClelland was doing his research of these mannerisms of power, he though that if those who obtained ''pP''ower were in the environment of international relations the consequences would be ''ominous''. While, ''s''Power, is the more socially acceptable form of expression, with leaders being motivated through the benefit of others; it incorporates feelings of personal strength, and the known knowledge of being careful (Bargh &amp; Lee-Chai, 2002; Friederichs et al., 2023; Magee &amp; Langner, 2008; McClellad, 1970). 

These forms of expression are not necessarily mutually exclusive. Leaders may display elements of both; McClelland believes that a true leader can balance personal dominance and socialised leadership (Bargh &amp; Lee-Chai, 2002). ''p''Power can become problematic when leaders become too absorbed by the maintenance of their position and influence, the ability to dominate, manipulate, and disagree. However, the issue isn't high-power motivation; it's how it is expressed (McClelland, 1970). 

=== The leadership motive pattern ===
McClelland and David Burnham (1975) proposed the idea that effective leadership is associated with a certain specific combination of motives known as the [[Motivation and emotion/Book/2015/Leadership motivation#Leadership Motive Pattern|Leadership Motive Pattern]] (LMP) (Spangler et al., 2014). This consists of three primary elements, high need for power (nPow), a low need for affiliation (nAff) and a high activity inhibition (AI). This model demonstrated how motivation can work together to shape leadership behaviour (Reeve, 2018). 

Each component serves as a different purpose, building characterises of the most effective leaders within bureaucratic organisation (Spangler et al., 2014). High nPow, is the force to influence, direct and impact others, this has been well-established by now. Low nAff, is a reduced desire for friendly interpersonal relationships, which prevent the leaders from producing biased decision-making. High AI is based on [[wikipedia:Self-control|self-control]], maturity, and the ability to channel power socially rather an impulsively (McClelland &amp; Boyatzis, 1982).

Research by McClelland and Burnhamd (1982) found that the LMP may only hold value for specific roles in demonstrating leadership effectiveness. When relevant, it demonstrated that managers of this pattern typically generate higher morale in their subordinates; leadership styles such as those of nations that spend relatively more on military forces than private consumption, which McClelland described as a system's capacity to mobilise resources in the interest of the nation (McClelland &amp; Boyatzis, 1982; Spangler et al., 2014). 


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== Recap ==
&lt;quiz display=simple&gt;
{&amp;nbsp;
|type=&quot;{}&quot;}
What is the driving force that guides human behaviour?
{ Motivation }

{What is the key difference between personalised power and socialised power?}
- Personalised power focuses on achievement, and socialised power focuses on affiliation
+ Personalised power focuses on personal dominance and control, and socialised power focuses on benefiting others
- Personalised power is consistently associated with an effective leadership style, whereas socialised power is associated with an ineffective leadership style.

{Which combination of motives is associated with McClelland’s Leadership Motive Pattern in effective managers?}
- High need for achievement, high need for affiliation and low activity inhibition
+ High need for power, low need for affiliation and high activity inhibition
- Low need for power, high need for affiliation and high activity inhibition

{Which behaviour best fits an individual with a high need for power?}
- Avoiding situations where they might influence others
+ Seek opportunities to influence, control, or have an impact on others
- Avoid challenging tasks for fear of failure


&lt;/quiz&gt;

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== Power motivation and leadership style ==
'''Focus question:''' ''How does a leader's orientation towards power influence their specific leadership style?''

An individual’s desire for power does not automatically determine their leadership style. How an individual in a position of authority understands and exercises power over others can shape their interactions, decision-making approaches, and the goals they prioritise. Examining power orientation alongside psychological characteristics provides a deeper understanding of why leaders may use their influence in various ways and how those differences are reflected in their leadership style. 

=== Power orientation and leadership behaviour ===
Power motivation is the drive to influence others, while power orientation is the how; it is the framework for how a leader becomes influential. A negative stereotype surrounds high power motivation, with the speculation that it automatically relates to undesirable behaviour, unlike prosocial power motivation, which is often associated with generosity. However, those with high power motivation can have different power orientations. Carbalho and Conde (2024) distinguish ego-power orientation and social-power orientations, highlighting that individuals can combine said orientations in different ways. Ego-power is associated with pursuing goals to satisfy the self and achieve a sense of self-fulfilment; this doesn't automatically result in harmful leadership, as it partly depends on the individual's position of influence and work. Social-power orientation links directing power to collective outcomes

=== Leadership trait analysis ===
[https://wsps.ut.ac.ir/article_101018.html Leadership Trait Analysis] (LTA), developed by Margaret Hermann (2003) (Mobaseri &amp; Nosrat Kharazmi, Zohreh, 2025), is a framework for analysing political leaders' psychological characteristics using interviews and public speeches. It examines seven traits across three dimensions: responsiveness to constraints, openness to information and motivation. The seven traits include the need for power, the belief that one can control what happens next, self-confidence, trust in others, conceptual complexity, the intensity of in-group bias or nationalism, and the need for affiliation. Together, these traits help researchers examine how leaders process information, respond to constraints and approach decision-making.

Trump illustrates how psychological frameworks such as the LTA apply to political leadership. Mobaseri and Nosrat Kharazmi (2025) examined Trump's leadership characteristics and political beliefs before his presidency and during his first term. The research explored how much his core beliefs influenced his responses to political events and the COVID-19 crisis. The study highlights the value of examining leaders' beliefs and characteristics over time to understand their responses to the political climate.

The analysis found Trump low in need for power, perceived control, self-confidence, in-group bias, and trust in others, but high in conceptual complexity. These traits informed Mobaseri and Nosrat Kharazmi's (2025) account of his leadership: resistance to adaptation, disregard for policymaking, charisma, and sensitivity to context in decisions.

The findings show how leadership reflects the interaction between a leader's psychology and their situation. LTA offers a way to analyse individual differences that shape leadership style.

=== Leadership styles and effectiveness ===
Power orientation can be reflected in different leadership styles, which describe how leaders direct, influence and interact with followers. For example, a leader who prioritises complete personal control may favour a more autocratic approach, while a leader who values engagement may be more inclined towards a democratic leadership. However, while leadership styles reflect theoretical models, they can also be shaped by individual characteristics and techniques (Khajeh et al., 2018; &quot;What Are the Different Leadership Styles?&quot;, 2024). Different styles place varying emphasis on factors seen in Table 2 (Deakin University, 2024; Bwalya, 2023). 

Effective leadership involves more than holding a position of authority; there are five essential characteristics of leadership: self-image, self-control, socialised power, sustained dialogue, and strategic intent, providing a practical framework for a successful leader (Power, 2026). Power, motivation, and leadership matter across contexts, from political leaders to supervisors, who need to build relationships with employees and an environment of trust if they want to do so. The characteristics emphasise the importance of authority, responsibility, communication, and directing efforts towards organisational goals (Power, 2026; Friederichs et al., 2023)

Research suggests that transformational leadership can produce positive outcomes by motivating and inspiring followers and benefiting the group rather than serving personal interests (Peyton et al., 2019). This shows how power can support group goals rather than simply reinforcing leadership status. Nevertheless, no single leadership style guarantees effectiveness; outcomes depend on how the leader behaves and responds to the situation at hand.

{| class=&quot;wikitable&quot;
|+Table 2. Leadership styles  (Bwalya, 2023)
! colspan=&quot;3&quot; |Leadership styles
|-
|Style
|Description
|Example Leaders
|-
|Autocratic 
|Leader holds complete control over decision-making with no input from followers. Consistently exercises control over the decision-making process. Expects strict compliance with policies and procedures, and does not take input from followers. They micromanage and control subordinate work. They make quick decisions because they do not have to consult. There is a lack of creative innovation (Bwalya, 2023). 
|Adolf Hitler and  Kim Jong-un 
|-
|Democratic 
|Leader is involved in team members' decision-making process, continuously encourages communication, and seeks feedback on matters, valuing input and ideas, wanting followers to participate in shaping strategies and goals (Bwalya, 2023).
|Former President of South Africa, Nelson Mandela and Former Prime Minister of New Zealand Jacinda Ardern 
|-
|Laissex-faire
| The leader is distant and has minimal involvement in decisions, unlike autocratic leadership, as laissez-faire lets followers make decisions with little guidance or supervision, trusting their ability to manage responsibilities. They are comfortable with mistakes and take accountability for followers' mistakes. This empowers employees and enables faster decision-making. However, the lack of guidance can cause confusion and lack of coordination (Bwalya, 2023). 
|Former President Herbert Hoover and Mahatma Ghandi
|-
|Servant 
|Leader is prosocial and motivated by power, focusing on the needs and well-being of others. Aiming to support and empower followers, in hopes they reach their full potential (Bwalya, 2023). 
|Pope Francis
|-
|Transformational 
|Based on inspiration and motivation to achieve performance, with high expectations and focus on challenging others to exceed self-interest. Focuses on transforming followers through inspiration, motivation, and effective communication. They rely on the leader's influence; if the leader fails to provide proper guidance, it can impact followers (Bwalya, 2023). 
|Former President of South Africa Nelson Mandela and Former President of the United States Barack Obama 
|-
|Transactional
|Focuses on the exchange relationship between the leader and their followers. The leader maintains stability and achieves goals by providing rewards and punishments based on performance. Very goal-oriented, with clear expectations, and quick decision-making (Bwalya, 2023).  
|Bill Gates and Former Chancellor of Germany Angela Merkel
|}

{{RoundBoxTop|theme=8}}[[Image: Hand Gesture - Holding a Magnifying Glass.gif|right|128px]] 
==Quiz==
&lt;quiz display=simple&gt; 
Which statement best explains the relationship between a leader’s power motivation and their leadership style?
|type=&quot;()&quot;} 
- Leaders with high power motivation are more likely to adopt an autocratic style, regardless of their values or circumstances
+ A leader’s power motivation determines their leadership style, while their psychological characteristics have very little influence
- Power motivation can influence a leader’s behaviour, but their power orientation, psychological characteristics and circumstances also shape how they exercise influence
&lt;/quiz&gt;
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== Implicit and explicit power motivation ==
'''Focus question:''' ''What is implicit motivation, and how does it differ from explicit power motivation in leaders?''

Human motivation can operate through two systems: [[Motivation and emotion/Book/2020/Implicit motives|implicit and explicit motivation]]. Both influencing behaviour, but very different in the extent to which the individuals are consciously aware of their motives behind their behaviour. When looking at leadership, it is helpful to dissect the distinctions to understand why a leader's states goals may not fully reflect their underlying needs which influence their behaviour. 

Implicit motive (nPow) is [[wikipedia:Unconscious_mind|unconscious]] motivation outside an individual’s awareness, mind map below in Figure 3 illustrates it. McClelland identified three implicit motives that shape thoughts, feelings, and actions: achievement, affiliation, and power. Developed through early preverbal experiences, they remain dormant until activated by incentives. Their influence appears in recurring patterns of thought, [[wikipedia:Emotion|emotion]], and behaviour, even when people cannot identify their motives (Reeve, 2018). Unlike explicit motives, implicit motives are difficult to measure directly. Researchers use the Picture-Story Exercise (PSE), asking participants to create stories from images and analysing them for themes related to the three motives. 

[[File:Implicit_Motives_associations.png|thumb| '''Figure 3.''' Mind map of implicit motives]]Explicit motives are conscious, self-attributed motives people can describe through their goals, values, and preferences (Slabbinck &amp; Van Witteloostuijn, 2020). Often assessed with self-report questionnaires, explicit power motives reflect desires for influence, status, and leadership. Their dimensions, dominance, prestige, and leadership, can help explain how power motives relate to dark personality traits. Dominance involves controlling others and is associated with [[Motivation and emotion/Book/2024/Machiavellianism and power motivation|Machiavellianism]] and counterproductive work behaviour. Prestige involves gaining influence by displaying knowledge or status and is linked to [[Motivation and emotion/Book/2010/Narcissism|narcissism]]. Leadership involves guiding groups toward shared goals and may predict organisational citizenship behaviour and align with transformational leadership.

A strong explicit power motive does not automatically lead to destructive leadership. It can support productive leadership, but may also overlap with dark traits such as narcissism, Machiavellianism, and psychopathy.

When implicit and explicit motives align, congruence, individuals are more likely to experience greater well-being and engagement, whereas misalignment can contribute to stress and reduced well-being (Ran et al., 2021; Thrash et al., 2012).

Applying this to leadership styles highlights how a leader's effectiveness and well-being depend on whether their chosen leadership style aligns with their implicit motive. When a leader's leadership style conflicts with their implicit motive, they experience ''motive incongruence,'' which can lead to chronic stress, burnout, and friction, whereas alignment predicts greater flow, high energy, and effortless leadership (Ran et al., 2021; Thrash et al., 2012).

== Power motivation and leadership effectiveness ==
'''Focus question:''' ''How does power motivation influence leadership effectiveness?''

Power motivation influences leadership effectiveness through how it is expressed and regulated. Social incentives arise from others’ rewards, expectations, and norms, whereas activity incentives come from the activity itself. Individuals with high nPower may seek positions of authority and careers offering influence and advancement. Although power motivation can be associated with aggression, social norms, laws, and consequences can constrain its expression (Reeve, 2018).

=== Destructive power dynamics and power abuse ===
There is a ''fickle'' relationship between aggression and the need or desire for power are closely linked. Studies have linked aggressive tendencies to dominance and the need for power (Verona et al., 2023). Verona et al. (2023) define human aggression as behaving with the intent to cause harm to another individual, and the target of the behaviour is driven to avoid it. Aggression can also take direct vs indirect and overt vs covert forms. That said, no concrete evidence links any level of ''feeling'' power to aggression. 

An individual with a high need for power may desire impact, control, or influence over another person or group, or even the world at large; aggression can be a means of satisfying those power needs. However, social norms, laws, and consequences can constrain this expression, causing that aggression to manifest in a more covert form. Individuals, both men and women, report more impulses to act aggressively than others; this behaviour would include yelling, throwing or destroying items and insulting others. Other factors of aggression and its link with high power-seeking individuals include finding a release through drinking, using this as a way to inflate their sense of control. Furthermore, men respond to stress and other setbacks with the behaviour of inflicting abuse on their partners, as well as an increased level of sexual misconduct (Reeve, 2018; Spanler et al., 2014). This indicates that a sense of power comes not only from leadership and reputation but can also be built through strategies of drinking, risk-taking, and posturing (Reeve, 2018).

Those who harbour inclinations that are both benevolent and malevolent towards others strive to improve the world while also influencing everyone else (Reeve, 2018). The ''dark side'' of implicit motive is the combination of opportunity to use power for personal benefit, which is the 'abuse of power.' Unrestrained affiliation can lead to favouritism and corruption in political and bureaucratic organisations. Achievement ignores political/interpersonal issues. High need for achievement: find it difficult working in groups, making decisions, and enforcing authority, ignoring interpersonal relationships (Spanier et al., 2014).[[File:The_Dark_Triad_Traits.jpg|thumb|'''Figure 4.''' The dark triad, and its associated personality traits]]

=== The dark triad traits ===
First proposed by Paulhus and Williams (2002), the [[Motivation and emotion/Book/2021/Dark triad personality and motivation|&quot;Dark Triad&quot;]] traits- narcissism, Machiavellianism, and psychopathy, seen in Figure 4, are three overlapping personality traits that can strongly motivate individuals to seek and wield power. When an individual has these traits, it often means they restrain and fuel their ruthlessness and self-serving behaviour. Research has found that scoring high on these traits increases an individual’s likelihood of committing crimes, causing distress, and creating severe issues for organisations when in authoritative leadership positions (LeBreton et al., 2018).  

Findings on the dark triad suggest that leadership outcomes depend not only on a leader's desire for influence, but also on their personality and how they exercise authority. However, the dark triad should not be associated with high implicit power motivation, as a strong unconscious drive to influence or impact others is not the same as the dark triad traits. An individual can have a strong implicit need for power without dark personality traits. Dark triad traits are associated with excessive admiration-seeking behaviour, manipulation, and callousness; these traits can interfere with relationships and judgement calls. Specific characteristics of the traits are listed in Table 3. (LeBreton et al., 2018).
{| class=&quot;wikitable&quot;
|+Table 3. Dark triad characteristic defined (LeBreton et al., 2018). 
!Dark triad traits
!Characteristics
|-
|Machiavellianism
|Cynical, strategic, and manipulative
|-
|Psychopathy
|Erratic behaviour, interpersonal manipulation, callous affect and criminal tendencies
|-
|Narcissism
|Pride, aggression, envy, grandiosity, constant need for admiration, poor self-esteem
|} 

=== '''Key predictors of effective leadership''' ===
Power motivation can support effective leadership when regulated and directed toward collective rather than personal benefit. McClelland's research suggests effective leaders combine a strong need for power with high self-discipline, or “power under control,” which is linked to charismatic leadership and group morale (Reeve, 2018). However, a desire for influence alone does not ensure effectiveness. 

Self-regulation is especially important for leaders with potentially destructive personality tendencies. Stress, exhaustion, hunger, and cognitive overload can weaken willpower, making defensive reactions harder to control and potentially harming others. Strong motivation and self-awareness help leaders manage counterproductive tendencies and limit their disruptive effects.

Other motives also shape leadership. A strong need for affiliation can promote communication, respect, appreciation, and support, strengthening leader–follower relationships. Achievement motivation can encourage goal pursuit, but excessive striving may undermine effectiveness: highly active, achievement-oriented leaders can become frustrated when results fall short of expectations.

[[Motivation and emotion/Book/2018/Emotional intelligence and leadership effectiveness|Moral identity]] also influences how leaders use power. Those with weaker moral identities may prioritise [[wikipedia:Self-interest|self-interest,]] while a prosocial approach uses influence to benefit others. This approach is associated with less power-related anxiety and greater well-being, suggesting that leaders’ purposes for exercising power affect their effectiveness.

{{RoundBoxTop|theme=3}}[[File:John F. Kennedy speaks at Rice University.jpg|thumb|President John F. Kennedy speaking at Rice University |'''Figure 5.''' John F. Kennedy speaking at Rice University]]

== Case study: John F. Kennedy ==

John F. Kennedy (JFK) is often recognised as an example of charismatic political leadership because of his optimistic public image, ambitious presidency, and compelling communication. Despite his relatively short time in office, Kennedy established a distinctive presidential identity by blending political leadership with popular culture and staying engaged with government and the public, which can be seen in Figure 5 (Reeve, 2018; McCann &amp; Mollan, 2023).
Kennedy's leadership aligns with McClelland's theory of motivational needs, with his profile characterised by a high need for power and a low need for affiliation (McCann &amp; Mollan, 2023). His charismatic communication also reflects transformational leadership, which emphasises inspiring followers to work towards shared goals. McClelland (1970) found that students who listened to Kennedy's inaugural address reported stronger feelings of inspiration and uplift, illustrating how a leader's communication can influence their audience.
Kennedy therefore shows how power motivation can support leadership by enabling individuals to influence, inspire, and mobilise others. However, effective leadership also depends on how that influence is exercised, particularly when responding to challenging political situations.
{{RoundBoxBottom}}

{{RoundBoxTop|theme=6}}
== Quiz yourself ==
&lt;quiz display=simple&gt;
{Which combination of implicit motives is associated with effective leadership according to McClelland's leadership motive pattern?
|type=&quot;()&quot;}
- High power, high affiliation, and low inhibition
+ High power, low affiliation, and high inhibition
- Low power, high affiliation, and high inhibition
- High power, low affiliation, and low inhibition

{Does a high need for power necessarily result in aggressive behaviour?
|type=&quot;()&quot;}
- True
+ False

&lt;/quiz&gt;
{{RoundBoxBottom}}

== Conclusion ==
Psychological theory and research suggest that power motivation shapes how individuals seek, maintain, and regulate influence. McClelland's Three Need Theory explains differences in needs for power, achievement, and affiliation. The Two Faces of Power distinguishes personalised power, focused on personal control and self-interest, from socialised power, which uses influence to benefit others. This distinction explains why power motivation can produce very different leadership outcomes (McClelland, 1970; Carvalho &amp; Conde, 2024). The LMP further suggests that a high need for power, low need for affiliation, and high activity inhibition can support effective leadership by balancing influence with self-control (Reeve, 2018).

Power motivation is neither inherently positive nor negative; its effects depend on how leaders exercise authority, regulate behaviour, and balance personal ambitions with others’ needs. Effective leadership depends not on how much power a person wants, but on how they use it. Leaders who regulate their power motivation and direct influence toward collective goals, development, and positive outcomes are more likely to be well received by the public and subordinates (Peyton et al., 2019; Friederichs et al., 2023). Understanding power motivation helps explain both effective leadership and the risks of abuse, underscoring the importance of self-regulation and ethical influence.

{{RoundBoxTop|theme=11}}[[Image:Nuvola_apps_filetypes.png|right|102px]]
;Reflection activity

Think of a time you influenced a group decision at university, work, or in a team sport. Reflect on:

* What was the situation, and how did you respond?
* How did you influence others or make decisions?
* What motivated your behaviour?
{{RoundBoxBottom}}

==See also==
* [[Motivation and emotion/Book/2018/Emotional intelligence and leadership effectiveness|Emotional intelligence and leadership effectiveness]] (Book chapter, 2018)
* [[Motivation and emotion/Book/2015/Leadership motivation#Leadership Motive Pattern|Leadership motivation]] (Book chapter, 2015)
* [[Motivation and emotion/Book/2011/Maslow's hierarchy of needs|Maslow's hierarchy of needs]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2019/Two-factor motivation theory|Two-factor motivation theory]] (Book chapter, 2019)
* [[wikipedia:David_McClelland|David Clelland]] (Wikipedia)
* [[wikipedia:Need_for_power|Need for power]] (Wikipedia)
* [[wikipedia:Need_theory|Need theory]] (Wikipedia)

==References==

{{Hanging indent|1=

Bargh, J. A., &amp; Lee-Chai, A. Y. (2002). The use and abuse of power : Multiple perspectives in the causes of corruption. Psychology.

Bwalya, A. (2023). Leadership styles. Article in Journal of Entrepreneurship, Management and Innovation, 11(8), 181–193. https://doi.org/10.6084/m9.figshare.23932113

Carvalho, J. M. S., &amp; Conde, A. (2024). Individual power in human motivation – review and theoretical perspective. Acta Psychologica, 249, 104452–104452. https://doi.org/10.1016/j.actpsy.2024.104452

Deakin University. (2024, December 5). What are the different leadership styles? Deakin.Edu.Au. https://leadership.deakin.edu.au/blog/different-leadership-styles

Friederichs, K. M., Waldenmeier, K., &amp; Baumann, N. (2023). The benefits of prosocial power motivation in leadership: Action orientation fosters a win-win. Plos One, 18(7), e0287394–e0287394. https://doi.org/10.1371/journal.pone.0287394

Gambino, L. (2021, January 9). Trump has lost Twitter, his biggest political megaphone. Now what? The Guardian. https://www.theguardian.com/us-news/2021/jan/08/trump-has-lost-twitter-his-biggest-political-megaphone-now-what

Khajeh, A., Abu, M., &amp; Asaari, H. (2018). Impact of leadership styles on organizational performance. Journal of Human Resources Management Research, 2018(2166–0018), 2166–2184. https://ibimapublishing.com/articles/JHRMR/2018/687849/687849-1.pdf

Kurt, D. S. (2021, May 23). McClelland’s Three Needs Theory: Power, Achievement, and Affiliation. Education Library. https://educationlibrary.org/mcclellands-three-needs-theory-power-achievement-and-affiliation/#1

LeBreton, J. M., Shiverdecker, L. K., &amp; Grimaldi, E. M. (2018). The dark triad and workplace behavior. Annual Review of Organizational Psychology and Organizational Behavior, 5(1), 387–414. https://doi.org/10.1146/annurev-orgpsych-032117-104451

Magee, J. C., &amp; Langner, C. A. (2008). How personalized and socialized power motivation facilitate antisocial and prosocial decision-making. Journal of Research in Personality, 42(6), 1547–1559. https://doi.org/10.1016/j.jrp.2008.07.009

McCann, L., &amp; Mollan, S. (2023, November 20). JFK 60 years on: His leadership style and the reality behind the myths. The Conversation. https://theconversation.com/jfk-60-years-on-his-leadership-style-and-the-reality-behind-the-myths-216477

McClelland, D. C. (1970). The two faces of power. Journal of International Affairs, 24(1), 29–47. JSTOR. https://www.jstor.org/stable/24356663

Mobaseri, Y., &amp; Nosrat Kharazmi, Zohreh. (2025). Cognitive characteristic and crisis behaviour: An analysis of Donald Trump’s leadership style and operational code in the time of crisis. Journal of World Sociopolitical Studies, 9(1), 87–115. https://doi.org/10.22059/wsps.2025.384855.1468

Peyton, T., Zigarmi, D., &amp; Fowler, S. N. (2019). Examining the relationship between leaders’ power use, followers’ motivational outlooks, and followers’ work intentions. Frontiers in Psychology, 9(2620). https://doi.org/10.3389/fpsyg.2018.02620

Power , D. P. G. (2026). The five essentials of leadership {{!}} APS. Psychology.Org.Au. https://psychology.org.au/inpsych/2017/august/power

Ran, Y., Liu, Q., Cheng, Q., &amp; Zhang, Y. (2021). Implicit-explicit power motives congruence and forgiveness in the workplace conflict: The mediating role of empathy. International Journal of Conflict Management, 32(3), 445–468. https://doi.org/10.1108/ijcma-06-2020-0116

Reeve, J. (2018). Understanding motivation and emotion (7th edn, pp. 152–176). John Wiley &amp; Sons, Inc.

Roeloffs, M. W. (2025, January 20). Billionaires worth a combined $1.2 trillion attended Trump’s inauguration: Here’s who was there—From musk to Bezos. Forbes. https://www.forbes.com/sites/maryroeloffs/2025/01/20/billionaires-worth-a-combined-12-trillion-attended-trumps-inauguration-heres-who-was-there-from-musk-to-bezos/

Slabbinck, H., &amp; Van Witteloostuijn, A. (2020). Explicit and implicit basic human motives, and public service motivation. Frontiers in Psychology, 11(1542). https://doi.org/10.3389/fpsyg.2020.01542

Spangler, W. D., Tikhomirov, A., Sotak, K. L., &amp; Palrecha, R. (2014). Leader motive profiles in eight types of organizations. The Leadership Quarterly, 25(6), 1080–1094. https://doi.org/10.1016/j.leaqua.2014.10.001

Spanler, W. D., Tikhomirov, A., Lee Sotak, K., &amp; Palrecha, R. (2014). Leader motive profiles in eight types of organizations. ScienceDirect, 25(6). https://www-sciencedirect-com.ezproxy.canberra.edu.au/science/article/pii/S1048984314001040

Thrash, T. M., Maruskin, L. A., &amp; Martin, C. C. (2012). Implicit–explicit motive congruence. In R. M. Ryan (Ed.), The oxford handbook of human motivation (pp. 141–156). Oxford University Press. https://psycnet.apa.org/record/2012-03687-009

Verona, E., McKinley, S. J., Hoffmann, A., Murphy, B. A., &amp; Watts, A. L. (2023). Psychopathy facets, perceived power, and forms of aggression. Personality Disorders: Theory, Research, and Treatment, 14(3), 259–273. https://doi.org/10.1037/per0000562

}}

==External links==
* [https://www.forbes.com/sites/maryroeloffs/2025/01/20/billionaires-worth-a-combined-12-trillion-attended-trumps-inauguration-heres-who-was-there-from-musk-to-bezos/ Billionaires Worth A Combined $1.35 Trillion Attended Trump’s Inauguration: Here’s Who Was There—From Musk To Bezos] (Roeloffs, 2025)
* [https://www.stand-deliver.com/columns/leadership/1319-donald-trump-s-leadership-style-is-it-all-about-me.html Donald Trump’s Leadership Style: Is it all about “me”?] (Steve Adubato , 2019)
* [https://educationlibrary.org/mcclellands-three-needs-theory-power-achievement-and-affiliation/#1 McClelland’s Three Needs Theory: Power, Achievement, and Affiliation] (Kurt, 2021)
* [https://psychology.org.au/inpsych/2017/august/power The five essentials of leadership] (Power , 2026)
* [https://www.theguardian.com/us-news/2021/jan/08/trump-has-lost-twitter-his-biggest-political-megaphone-now-what Trump has lost Twitter, his biggest political megaphone. Now what?] (Gambino, 2021)
* [https://theconversation.com/jfk-60-years-on-his-leadership-style-and-the-reality-behind-the-myths-216477 JFK 60 years on: his leadership style and the reality behind the myths] (McCann &amp; Mollan, 2023)

==See also==
* [[Motivation and emotion/Book/2024/Power motivation and leadership|Power motivation and leadership]] (Book chapter, 2024)

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__TOC__

==Overview==
{{RoundBoxTop|theme=11}}
[[File:Donald Trump takes the oath of office (2025).jpg|thumb|President-elect Donald Trump takes the oath of office |'''Figure 1'''. Donald Trump's 2025 Inauguration surrounded by some of the world's wealthiest and most powerful individuals]]

Imagine a leader standing at their inauguration, surrounded by a concentration of wealthy and influential individuals. At first glance, this may reflect a preference for resources and influence. However, a closer look raises a psychological question: what motivates a leader to seek and exercise power, and how does this shape the way they lead?

This scenario reflects the leadership of United States President Donald Trump, whose 2025 administration includes a notable concentration of wealthy and influential individuals (Roeloffs, 2025). The individuals present at Trump's inauguration illustrate this concentration of political and economic power (see Figure 1). This provides a contemporary example for examining the relationship between power motivation and leadership.{{ic|[[w:Donald Trump|Second inauguration of Donald Trump]]}} Power is reflected not only in who a leader surrounds themselves with, but also in how they exercise their influence. For example, Trump uses social media as a political megaphone, bypassing traditional bureaucratic communication channels (Gambino, 2021). His public leadership style places considerable emphasis on personal image and the need of personal control with the disregard of external influences of power (Adubato, 2019; Mobaseri &amp; Nosrat Kharazmi, Zohreh, 2025).

This raises the question: does the desire for power necessarily make someone an effective leader? Individuals seek leadership for various reasons, and how they use their influence shapes their interactions with followers, decision-making, and pursuit of goals. Psychology helps explain these differences by examining power motivation and how individual motives influence leadership behaviour.
{{RoundBoxBottom}}

This chapter will explore [https://pmc.ncbi.nlm.nih.gov/articles/PMC10355387/ power motivation] (Friederichs et al., 2023), the desire to [[wikipedia:Influence|influence]], [[wikipedia:Control|control]], and have the ability to impact others, influencing [[Motivation and emotion/Book/2015/Leadership motivation|leadership]] styles, behaviour and effectiveness (McClelland, 1970). Being expressed via socialised or personalised power, determining the leader's behaviour and effectiveness, (Reeve, 2018; McClelland, 1970; Carvalho &amp; Conde, 2024).

Understanding power motivation provides a psychological framework for examining how leaders exercise authority and how followers respond. Psychological science can help explain why some power-motivated leaders use influence to control, while others use it to empower (Reeve, 2018).

{{RoundBoxTop|theme=11}}
[[File:P psychology.png|right]]
'''Focus questions:'''

*What psychological theories explain power motivation in leaders?

*How does a leader's orientation towards power influence their specific leadership style?

*What is implicit motivation, and how does it differ from explicit power motivation in leaders?

*How does power motivation influence leadership effectiveness?
{{RoundBoxBottom}}

==Understanding power motivation through psychological theories==
'''Focus question:''' ''What psychological theories explain power motivation in leaders?''

The definition of motivation and power, one describes the push to act the other often associated with [[wikipedia:Aggression|aggression]], influence, [[wikipedia:Authority|authority]] and control, together they hold a heavy definition. In psychology, [[Motivation and emotion/Lectures/Introduction|motivation]] is the driving force that guides human behaviour; it is the use of will-power and self-discipline, channelling effort to achieve a [[wikipedia:Goal|goal]]. Certain individuals have predominant motive of power, being motivated by the internal urge to dominate, influence, or control (Kurt, 2021). Power motivation is the broad construct that refers to the desire for leadership, authority or status, it is built up of three characteristics: strong action, emotional impact, and concern for status, frame, and reputation, heavily influenced by cultural values and socialised experiences (McClelland,1970).

Power seekers can be effective, well-adjusted, and highly motivated. Power is a source of human control; only the mentally healthy can wield it successfully. Those with this form of need of power, [[wikipedia:Need_for_power|nPower]], struggle to feel satisfied unless they are in a position that fulfils their power-hungry needs, such as making decisions, influencing an audience, or obtaining information to become influential. Such occupations are teachers, journalists, clergy, psychologists, diplomats, business executives, political leaders and advisors (Reeve, 2018). [[wikipedia:David_McClelland|David McClelland's]] is popular within the psychology community for his thoughts on power motivation, with the most well-known theories, the [[wikipedia:Need_theory|Three Need Theory]] and the [https://www.jstor.org/stable/pdf/24356663.pdf Two Faces of Power] theory.

Other theories of motivation include the [[Motivation and emotion/Book/2011/Maslow's hierarchy of needs|Maslow's hierachy of need,]] and [[Motivation and emotion/Book/2019/Two-factor motivation theory|Herzberg's two-factor theory]]. These theories offer broader perspectives on the factors that drive human behaviour and motivation.

=== Three need theory ===
[[File:DavidMcClelland.jpg|thumb|'''Figure 2.''' David McClelland]]McClelland, a Harvard psychologist who conducted extensive research into human motivation (seen in Figure 2.), proposed the Three Need Theory. The theory identifies three acquired motivational needs: the need for [[wikipedia:Need_for_achievement|achievement]], the need for [[wikipedia:Need_for_affiliation|affiliation]], and the need for power (McClelland, 1970). Although individuals can experiences all three needs, the strength of each varies between individuals and can influence their behaviour. Table 1 summarises these needs and their defining characteristics being examined from high to low behaviour (Kurt, 2021).

nPower in leadership involves the desire to influence others and have an impact on their behaviour. While a strong need for achievement may motivate individuals to pursue challenging goals, and a strong need for affliction may encourage them to maintain positive interpersonal relationships, a strong need for power can motivate individuals to seek positions of authority. However the nPower alone does not determine whether someone will be an effective leader; its expression and the way an individual exercises their influence matter      

 {| class=&quot;wikitable&quot;
|+Table 1: Three need theory
!Need
!Definition
!High behaviour
!Low behaviour
|-
|Need for Achievement 
|Situations that challenge individuals with explicit standards.
|Individual exhibits a need to win and receive recognition.
|Constant fear of failure, typically avoids responsibilities. 
|-
|Need for Affiliation 
|Situations that afford warm relationship opportunities.
|A desire within for control, typically exaggerates own position.
|A heavily dependent individual, tries to minimise own position and importance.
|-
|Need for Power 
|Situations that enable others to exert influence over others.
|Individual demands and expects loyalty and harmony.
|Individual remains 'aloof' and keeps social distance from influence over others. 
|}

==== Two faces of power ====
McClelland's Two Faces of Power framework distinguishes between two ways the nPower can be expressed, personalised power or socialised power, also referred to as ''pP''ower, and ''s''Power (McClelland, 1970). ''pP''ower centres on personal control, it is seen as socially unacceptable way of expression, is is closely linked dominance and status. Those influenced by ''p''Power may tend to seek to strengthen their own position and influence (McClelland, 1970). While McClelland was doing his research of these mannerisms of power, he though that if those who obtained ''pP''ower were in the environment of international relations the consequences would be ''ominous''. While, ''s''Power, is the more socially acceptable form of expression, with leaders being motivated through the benefit of others; it incorporates feelings of personal strength, and the known knowledge of being careful (Bargh &amp; Lee-Chai, 2002; Friederichs et al., 2023; Magee &amp; Langner, 2008; McClellad, 1970). 

These forms of expression are not necessarily mutually exclusive. Leaders may display elements of both; McClelland believes that a true leader can balance personal dominance and socialised leadership (Bargh &amp; Lee-Chai, 2002). ''p''Power can become problematic when leaders become too absorbed by the maintenance of their position and influence, the ability to dominate, manipulate, and disagree. However, the issue isn't high-power motivation; it's how it is expressed (McClelland, 1970). 

=== The leadership motive pattern ===
McClelland and David Burnham (1975) proposed the idea that effective leadership is associated with a certain specific combination of motives known as the [[Motivation and emotion/Book/2015/Leadership motivation#Leadership Motive Pattern|Leadership Motive Pattern]] (LMP) (Spangler et al., 2014). This consists of three primary elements, high need for power (nPow), a low need for affiliation (nAff) and a high activity inhibition (AI). This model demonstrated how motivation can work together to shape leadership behaviour (Reeve, 2018). 

Each component serves as a different purpose, building characterises of the most effective leaders within bureaucratic organisation (Spangler et al., 2014). High nPow, is the force to influence, direct and impact others, this has been well-established by now. Low nAff, is a reduced desire for friendly interpersonal relationships, which prevent the leaders from producing biased decision-making. High AI is based on [[wikipedia:Self-control|self-control]], maturity, and the ability to channel power socially rather an impulsively (McClelland &amp; Boyatzis, 1982).

Research by McClelland and Burnhamd (1982) found that the LMP may only hold value for specific roles in demonstrating leadership effectiveness. When relevant, it demonstrated that managers of this pattern typically generate higher morale in their subordinates; leadership styles such as those of nations that spend relatively more on military forces than private consumption, which McClelland described as a system's capacity to mobilise resources in the interest of the nation (McClelland &amp; Boyatzis, 1982; Spangler et al., 2014). 


{{RoundBoxTop|theme=8}}
== Recap ==
&lt;quiz display=simple&gt;
{&amp;nbsp;
|type=&quot;{}&quot;}
What is the driving force that guides human behaviour?
{ Motivation }

{What is the key difference between personalised power and socialised power?}
- Personalised power focuses on achievement, and socialised power focuses on affiliation
+ Personalised power focuses on personal dominance and control, and socialised power focuses on benefiting others
- Personalised power is consistently associated with an effective leadership style, whereas socialised power is associated with an ineffective leadership style.

{Which combination of motives is associated with McClelland’s Leadership Motive Pattern in effective managers?}
- High need for achievement, high need for affiliation and low activity inhibition
+ High need for power, low need for affiliation and high activity inhibition
- Low need for power, high need for affiliation and high activity inhibition

{Which behaviour best fits an individual with a high need for power?}
- Avoiding situations where they might influence others
+ Seek opportunities to influence, control, or have an impact on others
- Avoid challenging tasks for fear of failure


&lt;/quiz&gt;

{{RoundBoxBottom}}

== Power motivation and leadership style ==
'''Focus question:''' ''How does a leader's orientation towards power influence their specific leadership style?''

An individual’s desire for power does not automatically determine their leadership style. How an individual in a position of authority understands and exercises power over others can shape their interactions, decision-making approaches, and the goals they prioritise. Examining power orientation alongside psychological characteristics provides a deeper understanding of why leaders may use their influence in various ways and how those differences are reflected in their leadership style. 

=== Power orientation and leadership behaviour ===
Power motivation is the drive to influence others, while power orientation is the how; it is the framework for how a leader becomes influential. A negative stereotype surrounds high power motivation, with the speculation that it automatically relates to undesirable behaviour, unlike prosocial power motivation, which is often associated with generosity. However, those with high power motivation can have different power orientations. Carbalho and Conde (2024) distinguish ego-power orientation and social-power orientations, highlighting that individuals can combine said orientations in different ways. Ego-power is associated with pursuing goals to satisfy the self and achieve a sense of self-fulfilment; this doesn't automatically result in harmful leadership, as it partly depends on the individual's position of influence and work. Social-power orientation links directing power to collective outcomes

=== Leadership trait analysis ===
[https://wsps.ut.ac.ir/article_101018.html Leadership Trait Analysis] (LTA), developed by Margaret Hermann (2003) (Mobaseri &amp; Nosrat Kharazmi, Zohreh, 2025), is a framework for analysing political leaders' psychological characteristics using interviews and public speeches. It examines seven traits across three dimensions: responsiveness to constraints, openness to information and motivation. The seven traits include the need for power, the belief that one can control what happens next, self-confidence, trust in others, conceptual complexity, the intensity of in-group bias or nationalism, and the need for affiliation. Together, these traits help researchers examine how leaders process information, respond to constraints and approach decision-making.

Trump illustrates how psychological frameworks such as the LTA apply to political leadership. Mobaseri and Nosrat Kharazmi (2025) examined Trump's leadership characteristics and political beliefs before his presidency and during his first term. The research explored how much his core beliefs influenced his responses to political events and the COVID-19 crisis. The study highlights the value of examining leaders' beliefs and characteristics over time to understand their responses to the political climate.

The analysis found Trump low in need for power, perceived control, self-confidence, in-group bias, and trust in others, but high in conceptual complexity. These traits informed Mobaseri and Nosrat Kharazmi's (2025) account of his leadership: resistance to adaptation, disregard for policymaking, charisma, and sensitivity to context in decisions.

The findings show how leadership reflects the interaction between a leader's psychology and their situation. LTA offers a way to analyse individual differences that shape leadership style.

=== Leadership styles and effectiveness ===
Power orientation can be reflected in different leadership styles, which describe how leaders direct, influence and interact with followers. For example, a leader who prioritises complete personal control may favour a more autocratic approach, while a leader who values engagement may be more inclined towards a democratic leadership. However, while leadership styles reflect theoretical models, they can also be shaped by individual characteristics and techniques (Khajeh et al., 2018; &quot;What Are the Different Leadership Styles?&quot;, 2024). Different styles place varying emphasis on factors seen in Table 2 (Deakin University, 2024; Bwalya, 2023). 

Effective leadership involves more than holding a position of authority; there are five essential characteristics of leadership: self-image, self-control, socialised power, sustained dialogue, and strategic intent, providing a practical framework for a successful leader (Power, 2026). Power, motivation, and leadership matter across contexts, from political leaders to supervisors, who need to build relationships with employees and an environment of trust if they want to do so. The characteristics emphasise the importance of authority, responsibility, communication, and directing efforts towards organisational goals (Power, 2026; Friederichs et al., 2023)

Research suggests that transformational leadership can produce positive outcomes by motivating and inspiring followers and benefiting the group rather than serving personal interests (Peyton et al., 2019). This shows how power can support group goals rather than simply reinforcing leadership status. Nevertheless, no single leadership style guarantees effectiveness; outcomes depend on how the leader behaves and responds to the situation at hand.

{| class=&quot;wikitable&quot;
|+Table 2. Leadership styles  (Bwalya, 2023)
! colspan=&quot;3&quot; |Leadership styles
|-
|Style
|Description
|Example Leaders
|-
|Autocratic 
|Leader holds complete control over decision-making with no input from followers. Consistently exercises control over the decision-making process. Expects strict compliance with policies and procedures, and does not take input from followers. They micromanage and control subordinate work. They make quick decisions because they do not have to consult. There is a lack of creative innovation (Bwalya, 2023). 
|Adolf Hitler and  Kim Jong-un 
|-
|Democratic 
|Leader is involved in team members' decision-making process, continuously encourages communication, and seeks feedback on matters, valuing input and ideas, wanting followers to participate in shaping strategies and goals (Bwalya, 2023).
|Former President of South Africa, Nelson Mandela and Former Prime Minister of New Zealand Jacinda Ardern 
|-
|Laissex-faire
| The leader is distant and has minimal involvement in decisions, unlike autocratic leadership, as laissez-faire lets followers make decisions with little guidance or supervision, trusting their ability to manage responsibilities. They are comfortable with mistakes and take accountability for followers' mistakes. This empowers employees and enables faster decision-making. However, the lack of guidance can cause confusion and lack of coordination (Bwalya, 2023). 
|Former President Herbert Hoover and Mahatma Ghandi
|-
|Servant 
|Leader is prosocial and motivated by power, focusing on the needs and well-being of others. Aiming to support and empower followers, in hopes they reach their full potential (Bwalya, 2023). 
|Pope Francis
|-
|Transformational 
|Based on inspiration and motivation to achieve performance, with high expectations and focus on challenging others to exceed self-interest. Focuses on transforming followers through inspiration, motivation, and effective communication. They rely on the leader's influence; if the leader fails to provide proper guidance, it can impact followers (Bwalya, 2023). 
|Former President of South Africa Nelson Mandela and Former President of the United States Barack Obama 
|-
|Transactional
|Focuses on the exchange relationship between the leader and their followers. The leader maintains stability and achieves goals by providing rewards and punishments based on performance. Very goal-oriented, with clear expectations, and quick decision-making (Bwalya, 2023).  
|Bill Gates and Former Chancellor of Germany Angela Merkel
|}

{{RoundBoxTop|theme=8}}[[Image: Hand Gesture - Holding a Magnifying Glass.gif|right|128px]] 
==Quiz==
&lt;quiz display=simple&gt; 
Which statement best explains the relationship between a leader’s power motivation and their leadership style?
|type=&quot;()&quot;} 
- Leaders with high power motivation are more likely to adopt an autocratic style, regardless of their values or circumstances
+ A leader’s power motivation determines their leadership style, while their psychological characteristics have very little influence
- Power motivation can influence a leader’s behaviour, but their power orientation, psychological characteristics and circumstances also shape how they exercise influence
&lt;/quiz&gt;
{{RoundBoxBottom}}

== Implicit and explicit power motivation ==
'''Focus question:''' ''What is implicit motivation, and how does it differ from explicit power motivation in leaders?''

Human motivation can operate through two systems: [[Motivation and emotion/Book/2020/Implicit motives|implicit and explicit motivation]]. Both influencing behaviour, but very different in the extent to which the individuals are consciously aware of their motives behind their behaviour. When looking at leadership, it is helpful to dissect the distinctions to understand why a leader's states goals may not fully reflect their underlying needs which influence their behaviour. 

Implicit motive (nPow) is [[wikipedia:Unconscious_mind|unconscious]] motivation outside an individual’s awareness, mind map below in Figure 3 illustrates it. McClelland identified three implicit motives that shape thoughts, feelings, and actions: achievement, affiliation, and power. Developed through early preverbal experiences, they remain dormant until activated by incentives. Their influence appears in recurring patterns of thought, [[wikipedia:Emotion|emotion]], and behaviour, even when people cannot identify their motives (Reeve, 2018). Unlike explicit motives, implicit motives are difficult to measure directly. Researchers use the Picture-Story Exercise (PSE), asking participants to create stories from images and analysing them for themes related to the three motives. 

[[File:Implicit_Motives_associations.png|thumb| '''Figure 3.''' Mind map of implicit motives]]Explicit motives are conscious, self-attributed motives people can describe through their goals, values, and preferences (Slabbinck &amp; Van Witteloostuijn, 2020). Often assessed with self-report questionnaires, explicit power motives reflect desires for influence, status, and leadership. Their dimensions, dominance, prestige, and leadership, can help explain how power motives relate to dark personality traits. Dominance involves controlling others and is associated with [[Motivation and emotion/Book/2024/Machiavellianism and power motivation|Machiavellianism]] and counterproductive work behaviour. Prestige involves gaining influence by displaying knowledge or status and is linked to [[Motivation and emotion/Book/2010/Narcissism|narcissism]]. Leadership involves guiding groups toward shared goals and may predict organisational citizenship behaviour and align with transformational leadership.

A strong explicit power motive does not automatically lead to destructive leadership. It can support productive leadership, but may also overlap with dark traits such as narcissism, Machiavellianism, and psychopathy.

When implicit and explicit motives align, congruence, individuals are more likely to experience greater well-being and engagement, whereas misalignment can contribute to stress and reduced well-being (Ran et al., 2021; Thrash et al., 2012).

Applying this to leadership styles highlights how a leader's effectiveness and well-being depend on whether their chosen leadership style aligns with their implicit motive. When a leader's leadership style conflicts with their implicit motive, they experience ''motive incongruence,'' which can lead to chronic stress, burnout, and friction, whereas alignment predicts greater flow, high energy, and effortless leadership (Ran et al., 2021; Thrash et al., 2012).

== Power motivation and leadership effectiveness ==
'''Focus question:''' ''How does power motivation influence leadership effectiveness?''

Power motivation influences leadership effectiveness through how it is expressed and regulated. Social incentives arise from others’ rewards, expectations, and norms, whereas activity incentives come from the activity itself. Individuals with high nPower may seek positions of authority and careers offering influence and advancement. Although power motivation can be associated with aggression, social norms, laws, and consequences can constrain its expression (Reeve, 2018).

=== Destructive power dynamics and power abuse ===
There is a ''fickle'' relationship between aggression and the need or desire for power are closely linked. Studies have linked aggressive tendencies to dominance and the need for power (Verona et al., 2023). Verona et al. (2023) define human aggression as behaving with the intent to cause harm to another individual, and the target of the behaviour is driven to avoid it. Aggression can also take direct vs indirect and overt vs covert forms. That said, no concrete evidence links any level of ''feeling'' power to aggression. 

An individual with a high need for power may desire impact, control, or influence over another person or group, or even the world at large; aggression can be a means of satisfying those power needs. However, social norms, laws, and consequences can constrain this expression, causing that aggression to manifest in a more covert form. Individuals, both men and women, report more impulses to act aggressively than others; this behaviour would include yelling, throwing or destroying items and insulting others. Other factors of aggression and its link with high power-seeking individuals include finding a release through drinking, using this as a way to inflate their sense of control. Furthermore, men respond to stress and other setbacks with the behaviour of inflicting abuse on their partners, as well as an increased level of sexual misconduct (Reeve, 2018; Spanler et al., 2014). This indicates that a sense of power comes not only from leadership and reputation but can also be built through strategies of drinking, risk-taking, and posturing (Reeve, 2018).

Those who harbour inclinations that are both benevolent and malevolent towards others strive to improve the world while also influencing everyone else (Reeve, 2018). The ''dark side'' of implicit motive is the combination of opportunity to use power for personal benefit, which is the 'abuse of power.' Unrestrained affiliation can lead to favouritism and corruption in political and bureaucratic organisations. Achievement ignores political/interpersonal issues. High need for achievement: find it difficult working in groups, making decisions, and enforcing authority, ignoring interpersonal relationships (Spanier et al., 2014).[[File:The_Dark_Triad_Traits.jpg|thumb|'''Figure 4.''' The dark triad, and its associated personality traits]]

=== The dark triad traits ===
First proposed by Paulhus and Williams (2002), the [[Motivation and emotion/Book/2021/Dark triad personality and motivation|&quot;Dark Triad&quot;]] traits- narcissism, Machiavellianism, and psychopathy, seen in Figure 4, are three overlapping personality traits that can strongly motivate individuals to seek and wield power. When an individual has these traits, it often means they restrain and fuel their ruthlessness and self-serving behaviour. Research has found that scoring high on these traits increases an individual’s likelihood of committing crimes, causing distress, and creating severe issues for organisations when in authoritative leadership positions (LeBreton et al., 2018).  

Findings on the dark triad suggest that leadership outcomes depend not only on a leader's desire for influence, but also on their personality and how they exercise authority. However, the dark triad should not be associated with high implicit power motivation, as a strong unconscious drive to influence or impact others is not the same as the dark triad traits. An individual can have a strong implicit need for power without dark personality traits. Dark triad traits are associated with excessive admiration-seeking behaviour, manipulation, and callousness; these traits can interfere with relationships and judgement calls. Specific characteristics of the traits are listed in Table 3. (LeBreton et al., 2018).
{| class=&quot;wikitable&quot;
|+Table 3. Dark triad characteristic defined (LeBreton et al., 2018). 
!Dark triad traits
!Characteristics
|-
|Machiavellianism
|Cynical, strategic, and manipulative
|-
|Psychopathy
|Erratic behaviour, interpersonal manipulation, callous affect and criminal tendencies
|-
|Narcissism
|Pride, aggression, envy, grandiosity, constant need for admiration, poor self-esteem
|} 

=== '''Key predictors of effective leadership''' ===
Power motivation can support effective leadership when regulated and directed toward collective rather than personal benefit. McClelland's research suggests effective leaders combine a strong need for power with high self-discipline, or “power under control,” which is linked to charismatic leadership and group morale (Reeve, 2018). However, a desire for influence alone does not ensure effectiveness. 

Self-regulation is especially important for leaders with potentially destructive personality tendencies. Stress, exhaustion, hunger, and cognitive overload can weaken willpower, making defensive reactions harder to control and potentially harming others. Strong motivation and self-awareness help leaders manage counterproductive tendencies and limit their disruptive effects.

Other motives also shape leadership. A strong need for affiliation can promote communication, respect, appreciation, and support, strengthening leader–follower relationships. Achievement motivation can encourage goal pursuit, but excessive striving may undermine effectiveness: highly active, achievement-oriented leaders can become frustrated when results fall short of expectations.

[[Motivation and emotion/Book/2018/Emotional intelligence and leadership effectiveness|Moral identity]] also influences how leaders use power. Those with weaker moral identities may prioritise [[wikipedia:Self-interest|self-interest,]] while a prosocial approach uses influence to benefit others. This approach is associated with less power-related anxiety and greater well-being, suggesting that leaders’ purposes for exercising power affect their effectiveness.

{{RoundBoxTop|theme=3}}[[File:John F. Kennedy speaks at Rice University.jpg|thumb|President John F. Kennedy speaking at Rice University |'''Figure 5.''' John F. Kennedy speaking at Rice University]]

== Case study: John F. Kennedy ==

John F. Kennedy (JFK) is often recognised as an example of charismatic political leadership because of his optimistic public image, ambitious presidency, and compelling communication. Despite his relatively short time in office, Kennedy established a distinctive presidential identity by blending political leadership with popular culture and staying engaged with government and the public, which can be seen in Figure 5 (Reeve, 2018; McCann &amp; Mollan, 2023).
Kennedy's leadership aligns with McClelland's theory of motivational needs, with his profile characterised by a high need for power and a low need for affiliation (McCann &amp; Mollan, 2023). His charismatic communication also reflects transformational leadership, which emphasises inspiring followers to work towards shared goals. McClelland (1970) found that students who listened to Kennedy's inaugural address reported stronger feelings of inspiration and uplift, illustrating how a leader's communication can influence their audience.
Kennedy therefore shows how power motivation can support leadership by enabling individuals to influence, inspire, and mobilise others. However, effective leadership also depends on how that influence is exercised, particularly when responding to challenging political situations.
{{RoundBoxBottom}}

{{RoundBoxTop|theme=6}}
== Quiz yourself ==
&lt;quiz display=simple&gt;
{Which combination of implicit motives is associated with effective leadership according to McClelland's leadership motive pattern?
|type=&quot;()&quot;}
- High power, high affiliation, and low inhibition
+ High power, low affiliation, and high inhibition
- Low power, high affiliation, and high inhibition
- High power, low affiliation, and low inhibition

{Does a high need for power necessarily result in aggressive behaviour?
|type=&quot;()&quot;}
- True
+ False

&lt;/quiz&gt;
{{RoundBoxBottom}}

== Conclusion ==
Psychological theory and research suggest that power motivation shapes how individuals seek, maintain, and regulate influence. McClelland's Three Need Theory explains differences in needs for power, achievement, and affiliation. The Two Faces of Power distinguishes personalised power, focused on personal control and self-interest, from socialised power, which uses influence to benefit others. This distinction explains why power motivation can produce very different leadership outcomes (McClelland, 1970; Carvalho &amp; Conde, 2024). The LMP further suggests that a high need for power, low need for affiliation, and high activity inhibition can support effective leadership by balancing influence with self-control (Reeve, 2018).

Power motivation is neither inherently positive nor negative; its effects depend on how leaders exercise authority, regulate behaviour, and balance personal ambitions with others’ needs. Effective leadership depends not on how much power a person wants, but on how they use it. Leaders who regulate their power motivation and direct influence toward collective goals, development, and positive outcomes are more likely to be well received by the public and subordinates (Peyton et al., 2019; Friederichs et al., 2023). Understanding power motivation helps explain both effective leadership and the risks of abuse, underscoring the importance of self-regulation and ethical influence.

{{RoundBoxTop|theme=11}}[[Image:Nuvola_apps_filetypes.png|right|102px]]
;Reflection activity

Think of a time you influenced a group decision at university, work, or in a team sport. Reflect on:

* What was the situation, and how did you respond?
* How did you influence others or make decisions?
* What motivated your behaviour?
{{RoundBoxBottom}}

==See also==
* [[wikipedia:Donald_Trump|Donald Trump]] (Wikipedia)
* [[Motivation and emotion/Book/2018/Emotional intelligence and leadership effectiveness|Emotional intelligence and leadership effectiveness]] (Book chapter, 2018)
* [[Motivation and emotion/Book/2015/Leadership motivation#Leadership Motive Pattern|Leadership motivation]] (Book chapter, 2015)
* [[Motivation and emotion/Book/2011/Maslow's hierarchy of needs|Maslow's hierarchy of needs]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2019/Two-factor motivation theory|Two-factor motivation theory]] (Book chapter, 2019)
* [[wikipedia:David_McClelland|David Clelland]] (Wikipedia)
* [[wikipedia:Need_for_power|Need for power]] (Wikipedia)
* [[wikipedia:Need_theory|Need theory]] (Wikipedia)

==References==

{{Hanging indent|1=

Bargh, J. A., &amp; Lee-Chai, A. Y. (2002). The use and abuse of power : Multiple perspectives in the causes of corruption. Psychology.

Bwalya, A. (2023). Leadership styles. Article in Journal of Entrepreneurship, Management and Innovation, 11(8), 181–193. https://doi.org/10.6084/m9.figshare.23932113

Carvalho, J. M. S., &amp; Conde, A. (2024). Individual power in human motivation – review and theoretical perspective. Acta Psychologica, 249, 104452–104452. https://doi.org/10.1016/j.actpsy.2024.104452

Deakin University. (2024, December 5). What are the different leadership styles? Deakin.Edu.Au. https://leadership.deakin.edu.au/blog/different-leadership-styles

Friederichs, K. M., Waldenmeier, K., &amp; Baumann, N. (2023). The benefits of prosocial power motivation in leadership: Action orientation fosters a win-win. Plos One, 18(7), e0287394–e0287394. https://doi.org/10.1371/journal.pone.0287394

Gambino, L. (2021, January 9). Trump has lost Twitter, his biggest political megaphone. Now what? The Guardian. https://www.theguardian.com/us-news/2021/jan/08/trump-has-lost-twitter-his-biggest-political-megaphone-now-what

Khajeh, A., Abu, M., &amp; Asaari, H. (2018). Impact of leadership styles on organizational performance. Journal of Human Resources Management Research, 2018(2166–0018), 2166–2184. https://ibimapublishing.com/articles/JHRMR/2018/687849/687849-1.pdf

Kurt, D. S. (2021, May 23). McClelland’s Three Needs Theory: Power, Achievement, and Affiliation. Education Library. https://educationlibrary.org/mcclellands-three-needs-theory-power-achievement-and-affiliation/#1

LeBreton, J. M., Shiverdecker, L. K., &amp; Grimaldi, E. M. (2018). The dark triad and workplace behavior. Annual Review of Organizational Psychology and Organizational Behavior, 5(1), 387–414. https://doi.org/10.1146/annurev-orgpsych-032117-104451

Magee, J. C., &amp; Langner, C. A. (2008). How personalized and socialized power motivation facilitate antisocial and prosocial decision-making. Journal of Research in Personality, 42(6), 1547–1559. https://doi.org/10.1016/j.jrp.2008.07.009

McCann, L., &amp; Mollan, S. (2023, November 20). JFK 60 years on: His leadership style and the reality behind the myths. The Conversation. https://theconversation.com/jfk-60-years-on-his-leadership-style-and-the-reality-behind-the-myths-216477

McClelland, D. C. (1970). The two faces of power. Journal of International Affairs, 24(1), 29–47. JSTOR. https://www.jstor.org/stable/24356663

Mobaseri, Y., &amp; Nosrat Kharazmi, Zohreh. (2025). Cognitive characteristic and crisis behaviour: An analysis of Donald Trump’s leadership style and operational code in the time of crisis. Journal of World Sociopolitical Studies, 9(1), 87–115. https://doi.org/10.22059/wsps.2025.384855.1468

Peyton, T., Zigarmi, D., &amp; Fowler, S. N. (2019). Examining the relationship between leaders’ power use, followers’ motivational outlooks, and followers’ work intentions. Frontiers in Psychology, 9(2620). https://doi.org/10.3389/fpsyg.2018.02620

Power , D. P. G. (2026). The five essentials of leadership {{!}} APS. Psychology.Org.Au. https://psychology.org.au/inpsych/2017/august/power

Ran, Y., Liu, Q., Cheng, Q., &amp; Zhang, Y. (2021). Implicit-explicit power motives congruence and forgiveness in the workplace conflict: The mediating role of empathy. International Journal of Conflict Management, 32(3), 445–468. https://doi.org/10.1108/ijcma-06-2020-0116

Reeve, J. (2018). Understanding motivation and emotion (7th edn, pp. 152–176). John Wiley &amp; Sons, Inc.

Roeloffs, M. W. (2025, January 20). Billionaires worth a combined $1.2 trillion attended Trump’s inauguration: Here’s who was there—From musk to Bezos. Forbes. https://www.forbes.com/sites/maryroeloffs/2025/01/20/billionaires-worth-a-combined-12-trillion-attended-trumps-inauguration-heres-who-was-there-from-musk-to-bezos/

Slabbinck, H., &amp; Van Witteloostuijn, A. (2020). Explicit and implicit basic human motives, and public service motivation. Frontiers in Psychology, 11(1542). https://doi.org/10.3389/fpsyg.2020.01542

Spangler, W. D., Tikhomirov, A., Sotak, K. L., &amp; Palrecha, R. (2014). Leader motive profiles in eight types of organizations. The Leadership Quarterly, 25(6), 1080–1094. https://doi.org/10.1016/j.leaqua.2014.10.001

Spanler, W. D., Tikhomirov, A., Lee Sotak, K., &amp; Palrecha, R. (2014). Leader motive profiles in eight types of organizations. ScienceDirect, 25(6). https://www-sciencedirect-com.ezproxy.canberra.edu.au/science/article/pii/S1048984314001040

Thrash, T. M., Maruskin, L. A., &amp; Martin, C. C. (2012). Implicit–explicit motive congruence. In R. M. Ryan (Ed.), The oxford handbook of human motivation (pp. 141–156). Oxford University Press. https://psycnet.apa.org/record/2012-03687-009

Verona, E., McKinley, S. J., Hoffmann, A., Murphy, B. A., &amp; Watts, A. L. (2023). Psychopathy facets, perceived power, and forms of aggression. Personality Disorders: Theory, Research, and Treatment, 14(3), 259–273. https://doi.org/10.1037/per0000562

}}

==External links==
* [https://www.forbes.com/sites/maryroeloffs/2025/01/20/billionaires-worth-a-combined-12-trillion-attended-trumps-inauguration-heres-who-was-there-from-musk-to-bezos/ Billionaires Worth A Combined $1.35 Trillion Attended Trump’s Inauguration: Here’s Who Was There—From Musk To Bezos] (Roeloffs, 2025)
* [https://www.stand-deliver.com/columns/leadership/1319-donald-trump-s-leadership-style-is-it-all-about-me.html Donald Trump’s Leadership Style: Is it all about “me”?] (Steve Adubato , 2019)
* [https://educationlibrary.org/mcclellands-three-needs-theory-power-achievement-and-affiliation/#1 McClelland’s Three Needs Theory: Power, Achievement, and Affiliation] (Kurt, 2021)
* [https://psychology.org.au/inpsych/2017/august/power The five essentials of leadership] (Power , 2026)
* [https://www.theguardian.com/us-news/2021/jan/08/trump-has-lost-twitter-his-biggest-political-megaphone-now-what Trump has lost Twitter, his biggest political megaphone. Now what?] (Gambino, 2021)
* [https://theconversation.com/jfk-60-years-on-his-leadership-style-and-the-reality-behind-the-myths-216477 JFK 60 years on: his leadership style and the reality behind the myths] (McCann &amp; Mollan, 2023)

==See also==
* [[Motivation and emotion/Book/2024/Power motivation and leadership|Power motivation and leadership]] (Book chapter, 2024)

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__TOC__

==Overview==
{{RoundBoxTop|theme=11}}
[[File:Donald Trump takes the oath of office (2025).jpg|thumb|President-elect Donald Trump takes the oath of office |'''Figure 1'''. Donald Trump's 2025 Inauguration surrounded by some of the world's wealthiest and most powerful individuals]]

Imagine a leader standing at their inauguration, surrounded by a concentration of wealthy and influential individuals. At first glance, this may reflect a preference for resources and influence. However, a closer look raises a psychological question: what motivates a leader to seek and exercise power, and how does this shape the way they lead?

This scenario reflects the leadership of United States President Donald Trump, whose 2025 administration includes a notable concentration of wealthy and influential individuals (Roeloffs, 2025). The individuals present at Trump's inauguration illustrate this concentration of political and economic power (see Figure 1). This provides a contemporary example for examining the relationship between power motivation and leadership.{{ic|[[w:Donald Trump|Second inauguration of Donald Trump]]}} Power is reflected not only in who a leader surrounds themselves with, but also in how they exercise their influence. For example, Trump uses social media as a political megaphone, bypassing traditional bureaucratic communication channels (Gambino, 2021). His public leadership style places considerable emphasis on personal image and the need of personal control with the disregard of external influences of power (Adubato, 2019; Mobaseri &amp; Nosrat Kharazmi, Zohreh, 2025).

This raises the question: does the desire for power necessarily make someone an effective leader? Individuals seek leadership for various reasons, and how they use their influence shapes their interactions with followers, decision-making, and pursuit of goals. Psychology helps explain these differences by examining power motivation and how individual motives influence leadership behaviour.
{{RoundBoxBottom}}

This chapter will explore [https://pmc.ncbi.nlm.nih.gov/articles/PMC10355387/ power motivation] (Friederichs et al., 2023), the desire to [[wikipedia:Influence|influence]], [[wikipedia:Control|control]], and have the ability to impact others, influencing [[Motivation and emotion/Book/2015/Leadership motivation|leadership]] styles, behaviour and effectiveness (McClelland, 1970). Being expressed via socialised or personalised power, determining the leader's behaviour and effectiveness, (Reeve, 2018; McClelland, 1970; Carvalho &amp; Conde, 2024).

Understanding power motivation provides a psychological framework for examining how leaders exercise authority and how followers respond. Psychological science can help explain why some power-motivated leaders use influence to control, while others use it to empower (Reeve, 2018).

{{RoundBoxTop|theme=11}}
[[File:P psychology.png|right]]
'''Focus questions:'''

*What psychological theories explain power motivation in leaders?

*How does a leader's orientation towards power influence their specific leadership style?

*What is implicit motivation, and how does it differ from explicit power motivation in leaders?

*How does power motivation influence leadership effectiveness?
{{RoundBoxBottom}}

==Understanding power motivation through psychological theories==
'''Focus question:''' ''What psychological theories explain power motivation in leaders?''

The definition of motivation and power, one describes the push to act the other often associated with [[wikipedia:Aggression|aggression]], influence, [[wikipedia:Authority|authority]] and control, together they hold a heavy definition. In psychology, [[Motivation and emotion/Lectures/Introduction|motivation]] is the driving force that guides human behaviour; it is the use of will-power and self-discipline, channelling effort to achieve a [[wikipedia:Goal|goal]]. Certain individuals have predominant motive of power, being motivated by the internal urge to dominate, influence, or control (Kurt, 2021). Power motivation is the broad construct that refers to the desire for leadership, authority or status, it is built up of three characteristics: strong action, emotional impact, and concern for status, frame, and reputation, heavily influenced by cultural values and socialised experiences (McClelland,1970).

Power seekers can be effective, well-adjusted, and highly motivated. Power is a source of human control; only the mentally healthy can wield it successfully. Those with this form of need of power, [[wikipedia:Need_for_power|nPower]], struggle to feel satisfied unless they are in a position that fulfils their power-hungry needs, such as making decisions, influencing an audience, or obtaining information to become influential. Such occupations are teachers, journalists, clergy, psychologists, diplomats, business executives, political leaders and advisors (Reeve, 2018). [[wikipedia:David_McClelland|David McClelland's]] is popular within the psychology community for his thoughts on power motivation, with the most well-known theories, the [[wikipedia:Need_theory|Three Need Theory]] and the [https://www.jstor.org/stable/pdf/24356663.pdf Two Faces of Power] theory.

Other theories of motivation include the [[Motivation and emotion/Book/2011/Maslow's hierarchy of needs|Maslow's hierachy of need,]] and [[Motivation and emotion/Book/2019/Two-factor motivation theory|Herzberg's two-factor theory]]. These theories offer broader perspectives on the factors that drive human behaviour and motivation.

=== Three need theory ===
[[File:DavidMcClelland.jpg|thumb|'''Figure 2.''' David McClelland]]McClelland, a Harvard psychologist who conducted extensive research into human motivation (seen in Figure 2.), proposed the Three Need Theory. The theory identifies three acquired motivational needs: the need for [[wikipedia:Need_for_achievement|achievement]], the need for [[wikipedia:Need_for_affiliation|affiliation]], and the need for power (McClelland, 1970). Although individuals can experiences all three needs, the strength of each varies between individuals and can influence their behaviour. Table 1 summarises these needs and their defining characteristics being examined from high to low behaviour (Kurt, 2021).

nPower in leadership involves the desire to influence others and have an impact on their behaviour. While a strong need for achievement may motivate individuals to pursue challenging goals, and a strong need for affliction may encourage them to maintain positive interpersonal relationships, a strong need for power can motivate individuals to seek positions of authority. However the nPower alone does not determine whether someone will be an effective leader; its expression and the way an individual exercises their influence matter      

 {| class=&quot;wikitable&quot;
|+Table 1: Three need theory
!Need
!Definition
!High behaviour
!Low behaviour
|-
|Need for Achievement 
|Situations that challenge individuals with explicit standards.
|Individual exhibits a need to win and receive recognition.
|Constant fear of failure, typically avoids responsibilities. 
|-
|Need for Affiliation 
|Situations that afford warm relationship opportunities.
|A desire within for control, typically exaggerates own position.
|A heavily dependent individual, tries to minimise own position and importance.
|-
|Need for Power 
|Situations that enable others to exert influence over others.
|Individual demands and expects loyalty and harmony.
|Individual remains 'aloof' and keeps social distance from influence over others. 
|}

==== Two faces of power ====
McClelland's Two Faces of Power framework distinguishes between two ways the nPower can be expressed, personalised power or socialised power, also referred to as ''pP''ower, and ''s''Power (McClelland, 1970). ''pP''ower centres on personal control, it is seen as socially unacceptable way of expression, is is closely linked dominance and status. Those influenced by ''p''Power may tend to seek to strengthen their own position and influence (McClelland, 1970). While McClelland was doing his research of these mannerisms of power, he though that if those who obtained ''pP''ower were in the environment of international relations the consequences would be ''ominous''. While, ''s''Power, is the more socially acceptable form of expression, with leaders being motivated through the benefit of others; it incorporates feelings of personal strength, and the known knowledge of being careful (Bargh &amp; Lee-Chai, 2002; Friederichs et al., 2023; Magee &amp; Langner, 2008; McClellad, 1970). 

These forms of expression are not necessarily mutually exclusive. Leaders may display elements of both; McClelland believes that a true leader can balance personal dominance and socialised leadership (Bargh &amp; Lee-Chai, 2002). ''p''Power can become problematic when leaders become too absorbed by the maintenance of their position and influence, the ability to dominate, manipulate, and disagree. However, the issue isn't high-power motivation; it's how it is expressed (McClelland, 1970). 

=== The leadership motive pattern ===
McClelland and David Burnham (1975) proposed the idea that effective leadership is associated with a certain specific combination of motives known as the [[Motivation and emotion/Book/2015/Leadership motivation#Leadership Motive Pattern|Leadership Motive Pattern]] (LMP) (Spangler et al., 2014). This consists of three primary elements, high need for power (nPow), a low need for affiliation (nAff) and a high activity inhibition (AI). This model demonstrated how motivation can work together to shape leadership behaviour (Reeve, 2018). 

Each component serves as a different purpose, building characterises of the most effective leaders within bureaucratic organisation (Spangler et al., 2014). High nPow, is the force to influence, direct and impact others, this has been well-established by now. Low nAff, is a reduced desire for friendly interpersonal relationships, which prevent the leaders from producing biased decision-making. High AI is based on [[wikipedia:Self-control|self-control]], maturity, and the ability to channel power socially rather an impulsively (McClelland &amp; Boyatzis, 1982).

Research by McClelland and Burnhamd (1982) found that the LMP may only hold value for specific roles in demonstrating leadership effectiveness. When relevant, it demonstrated that managers of this pattern typically generate higher morale in their subordinates; leadership styles such as those of nations that spend relatively more on military forces than private consumption, which McClelland described as a system's capacity to mobilise resources in the interest of the nation (McClelland &amp; Boyatzis, 1982; Spangler et al., 2014). 


{{RoundBoxTop|theme=8}}
== Recap ==
&lt;quiz display=simple&gt;
{&amp;nbsp;
|type=&quot;{}&quot;}
What is the driving force that guides human behaviour?
{ Motivation }

{What is the key difference between personalised power and socialised power?}
- Personalised power focuses on achievement, and socialised power focuses on affiliation
+ Personalised power focuses on personal dominance and control, and socialised power focuses on benefiting others
- Personalised power is consistently associated with an effective leadership style, whereas socialised power is associated with an ineffective leadership style.

{Which combination of motives is associated with McClelland’s Leadership Motive Pattern in effective managers?}
- High need for achievement, high need for affiliation and low activity inhibition
+ High need for power, low need for affiliation and high activity inhibition
- Low need for power, high need for affiliation and high activity inhibition

{Which behaviour best fits an individual with a high need for power?}
- Avoiding situations where they might influence others
+ Seek opportunities to influence, control, or have an impact on others
- Avoid challenging tasks for fear of failure


&lt;/quiz&gt;

{{RoundBoxBottom}}

== Power motivation and leadership style ==
'''Focus question:''' ''How does a leader's orientation towards power influence their specific leadership style?''

An individual’s desire for power does not automatically determine their leadership style. How an individual in a position of authority understands and exercises power over others can shape their interactions, decision-making approaches, and the goals they prioritise. Examining power orientation alongside psychological characteristics provides a deeper understanding of why leaders may use their influence in various ways and how those differences are reflected in their leadership style. 

=== Power orientation and leadership behaviour ===
Power motivation is the drive to influence others, while power orientation is the how; it is the framework for how a leader becomes influential. A negative stereotype surrounds high power motivation, with the speculation that it automatically relates to undesirable behaviour, unlike prosocial power motivation, which is often associated with generosity. However, those with high power motivation can have different power orientations. Carbalho and Conde (2024) distinguish ego-power orientation and social-power orientations, highlighting that individuals can combine said orientations in different ways. Ego-power is associated with pursuing goals to satisfy the self and achieve a sense of self-fulfilment; this doesn't automatically result in harmful leadership, as it partly depends on the individual's position of influence and work. Social-power orientation links directing power to collective outcomes

=== Leadership trait analysis ===
[https://wsps.ut.ac.ir/article_101018.html Leadership Trait Analysis] (LTA), developed by Margaret Hermann (2003) (Mobaseri &amp; Nosrat Kharazmi, Zohreh, 2025), is a framework for analysing political leaders' psychological characteristics using interviews and public speeches. It examines seven traits across three dimensions: responsiveness to constraints, openness to information and motivation. The seven traits include the need for power, the belief that one can control what happens next, self-confidence, trust in others, conceptual complexity, the intensity of in-group bias or nationalism, and the need for affiliation. Together, these traits help researchers examine how leaders process information, respond to constraints and approach decision-making.

Trump illustrates how psychological frameworks such as the LTA apply to political leadership. Mobaseri and Nosrat Kharazmi (2025) examined Trump's leadership characteristics and political beliefs before his presidency and during his first term. The research explored how much his core beliefs influenced his responses to political events and the COVID-19 crisis. The study highlights the value of examining leaders' beliefs and characteristics over time to understand their responses to the political climate.

The analysis found Trump low in need for power, perceived control, self-confidence, in-group bias, and trust in others, but high in conceptual complexity. These traits informed Mobaseri and Nosrat Kharazmi's (2025) account of his leadership: resistance to adaptation, disregard for policymaking, charisma, and sensitivity to context in decisions.

The findings show how leadership reflects the interaction between a leader's psychology and their situation. LTA offers a way to analyse individual differences that shape leadership style.

=== Leadership styles and effectiveness ===
Power orientation can be reflected in different leadership styles, which describe how leaders direct, influence and interact with followers. For example, a leader who prioritises complete personal control may favour a more autocratic approach, while a leader who values engagement may be more inclined towards a democratic leadership. However, while leadership styles reflect theoretical models, they can also be shaped by individual characteristics and techniques (Khajeh et al., 2018; &quot;What Are the Different Leadership Styles?&quot;, 2024). Different styles place varying emphasis on factors seen in Table 2 (Deakin University, 2024; Bwalya, 2023). 

Effective leadership involves more than holding a position of authority; there are five essential characteristics of leadership: self-image, self-control, socialised power, sustained dialogue, and strategic intent, providing a practical framework for a successful leader (Power, 2026). Power, motivation, and leadership matter across contexts, from political leaders to supervisors, who need to build relationships with employees and an environment of trust if they want to do so. The characteristics emphasise the importance of authority, responsibility, communication, and directing efforts towards organisational goals (Power, 2026; Friederichs et al., 2023)

Research suggests that transformational leadership can produce positive outcomes by motivating and inspiring followers and benefiting the group rather than serving personal interests (Peyton et al., 2019). This shows how power can support group goals rather than simply reinforcing leadership status. Nevertheless, no single leadership style guarantees effectiveness; outcomes depend on how the leader behaves and responds to the situation at hand.

{| class=&quot;wikitable&quot;
|+Table 2. Leadership styles  (Bwalya, 2023)
! colspan=&quot;3&quot; |Leadership styles
|-
|Style
|Description
|Example Leaders
|-
|Autocratic 
|Leader holds complete control over decision-making with no input from followers. Consistently exercises control over the decision-making process. Expects strict compliance with policies and procedures, and does not take input from followers. They micromanage and control subordinate work. They make quick decisions because they do not have to consult. There is a lack of creative innovation (Bwalya, 2023). 
|Adolf Hitler and  Kim Jong-un 
|-
|Democratic 
|Leader is involved in team members' decision-making process, continuously encourages communication, and seeks feedback on matters, valuing input and ideas, wanting followers to participate in shaping strategies and goals (Bwalya, 2023).
|Former President of South Africa, Nelson Mandela and Former Prime Minister of New Zealand Jacinda Ardern 
|-
|Laissex-faire
| The leader is distant and has minimal involvement in decisions, unlike autocratic leadership, as laissez-faire lets followers make decisions with little guidance or supervision, trusting their ability to manage responsibilities. They are comfortable with mistakes and take accountability for followers' mistakes. This empowers employees and enables faster decision-making. However, the lack of guidance can cause confusion and lack of coordination (Bwalya, 2023). 
|Former President Herbert Hoover and Mahatma Ghandi
|-
|Servant 
|Leader is prosocial and motivated by power, focusing on the needs and well-being of others. Aiming to support and empower followers, in hopes they reach their full potential (Bwalya, 2023). 
|Pope Francis
|-
|Transformational 
|Based on inspiration and motivation to achieve performance, with high expectations and focus on challenging others to exceed self-interest. Focuses on transforming followers through inspiration, motivation, and effective communication. They rely on the leader's influence; if the leader fails to provide proper guidance, it can impact followers (Bwalya, 2023). 
|Former President of South Africa Nelson Mandela and Former President of the United States Barack Obama 
|-
|Transactional
|Focuses on the exchange relationship between the leader and their followers. The leader maintains stability and achieves goals by providing rewards and punishments based on performance. Very goal-oriented, with clear expectations, and quick decision-making (Bwalya, 2023).  
|Bill Gates and Former Chancellor of Germany Angela Merkel
|}

{{RoundBoxTop|theme=8}}[[Image: Hand Gesture - Holding a Magnifying Glass.gif|right|128px]] 
==Quiz==
&lt;quiz display=simple&gt; 
Which statement best explains the relationship between a leader’s power motivation and their leadership style?

|type=&quot;()&quot;} 

- Leaders with high power motivation are more likely to adopt an autocratic style, regardless of their values or circumstances
+ A leader’s power motivation determines their leadership style, while their psychological characteristics have very little influence
- Power motivation can influence a leader’s behaviour, but their power orientation, psychological characteristics and circumstances also shape how they exercise influence
&lt;/quiz&gt;
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== Implicit and explicit power motivation ==
'''Focus question:''' ''What is implicit motivation, and how does it differ from explicit power motivation in leaders?''

Human motivation can operate through two systems: [[Motivation and emotion/Book/2020/Implicit motives|implicit and explicit motivation]]. Both influencing behaviour, but very different in the extent to which the individuals are consciously aware of their motives behind their behaviour. When looking at leadership, it is helpful to dissect the distinctions to understand why a leader's states goals may not fully reflect their underlying needs which influence their behaviour. 

Implicit motive (nPow) is [[wikipedia:Unconscious_mind|unconscious]] motivation outside an individual’s awareness, mind map below in Figure 3 illustrates it. McClelland identified three implicit motives that shape thoughts, feelings, and actions: achievement, affiliation, and power. Developed through early preverbal experiences, they remain dormant until activated by incentives. Their influence appears in recurring patterns of thought, [[wikipedia:Emotion|emotion]], and behaviour, even when people cannot identify their motives (Reeve, 2018). Unlike explicit motives, implicit motives are difficult to measure directly. Researchers use the Picture-Story Exercise (PSE), asking participants to create stories from images and analysing them for themes related to the three motives. 

[[File:Implicit_Motives_associations.png|thumb| '''Figure 3.''' Mind map of implicit motives]]Explicit motives are conscious, self-attributed motives people can describe through their goals, values, and preferences (Slabbinck &amp; Van Witteloostuijn, 2020). Often assessed with self-report questionnaires, explicit power motives reflect desires for influence, status, and leadership. Their dimensions, dominance, prestige, and leadership, can help explain how power motives relate to dark personality traits. Dominance involves controlling others and is associated with [[Motivation and emotion/Book/2024/Machiavellianism and power motivation|Machiavellianism]] and counterproductive work behaviour. Prestige involves gaining influence by displaying knowledge or status and is linked to [[Motivation and emotion/Book/2010/Narcissism|narcissism]]. Leadership involves guiding groups toward shared goals and may predict organisational citizenship behaviour and align with transformational leadership.

A strong explicit power motive does not automatically lead to destructive leadership. It can support productive leadership, but may also overlap with dark traits such as narcissism, Machiavellianism, and psychopathy.

When implicit and explicit motives align, congruence, individuals are more likely to experience greater well-being and engagement, whereas misalignment can contribute to stress and reduced well-being (Ran et al., 2021; Thrash et al., 2012).

Applying this to leadership styles highlights how a leader's effectiveness and well-being depend on whether their chosen leadership style aligns with their implicit motive. When a leader's leadership style conflicts with their implicit motive, they experience ''motive incongruence,'' which can lead to chronic stress, burnout, and friction, whereas alignment predicts greater flow, high energy, and effortless leadership (Ran et al., 2021; Thrash et al., 2012).

== Power motivation and leadership effectiveness ==
'''Focus question:''' ''How does power motivation influence leadership effectiveness?''

Power motivation influences leadership effectiveness through how it is expressed and regulated. Social incentives arise from others’ rewards, expectations, and norms, whereas activity incentives come from the activity itself. Individuals with high nPower may seek positions of authority and careers offering influence and advancement. Although power motivation can be associated with aggression, social norms, laws, and consequences can constrain its expression (Reeve, 2018).

=== Destructive power dynamics and power abuse ===
There is a ''fickle'' relationship between aggression and the need or desire for power are closely linked. Studies have linked aggressive tendencies to dominance and the need for power (Verona et al., 2023). Verona et al. (2023) define human aggression as behaving with the intent to cause harm to another individual, and the target of the behaviour is driven to avoid it. Aggression can also take direct vs indirect and overt vs covert forms. That said, no concrete evidence links any level of ''feeling'' power to aggression. 

An individual with a high need for power may desire impact, control, or influence over another person or group, or even the world at large; aggression can be a means of satisfying those power needs. However, social norms, laws, and consequences can constrain this expression, causing that aggression to manifest in a more covert form. Individuals, both men and women, report more impulses to act aggressively than others; this behaviour would include yelling, throwing or destroying items and insulting others. Other factors of aggression and its link with high power-seeking individuals include finding a release through drinking, using this as a way to inflate their sense of control. Furthermore, men respond to stress and other setbacks with the behaviour of inflicting abuse on their partners, as well as an increased level of sexual misconduct (Reeve, 2018; Spanler et al., 2014). This indicates that a sense of power comes not only from leadership and reputation but can also be built through strategies of drinking, risk-taking, and posturing (Reeve, 2018).

Those who harbour inclinations that are both benevolent and malevolent towards others strive to improve the world while also influencing everyone else (Reeve, 2018). The ''dark side'' of implicit motive is the combination of opportunity to use power for personal benefit, which is the 'abuse of power.' Unrestrained affiliation can lead to favouritism and corruption in political and bureaucratic organisations. Achievement ignores political/interpersonal issues. High need for achievement: find it difficult working in groups, making decisions, and enforcing authority, ignoring interpersonal relationships (Spanier et al., 2014).[[File:The_Dark_Triad_Traits.jpg|thumb|'''Figure 4.''' The dark triad, and its associated personality traits]]

=== The dark triad traits ===
First proposed by Paulhus and Williams (2002), the [[Motivation and emotion/Book/2021/Dark triad personality and motivation|&quot;Dark Triad&quot;]] traits- narcissism, Machiavellianism, and psychopathy, seen in Figure 4, are three overlapping personality traits that can strongly motivate individuals to seek and wield power. When an individual has these traits, it often means they restrain and fuel their ruthlessness and self-serving behaviour. Research has found that scoring high on these traits increases an individual’s likelihood of committing crimes, causing distress, and creating severe issues for organisations when in authoritative leadership positions (LeBreton et al., 2018).  

Findings on the dark triad suggest that leadership outcomes depend not only on a leader's desire for influence, but also on their personality and how they exercise authority. However, the dark triad should not be associated with high implicit power motivation, as a strong unconscious drive to influence or impact others is not the same as the dark triad traits. An individual can have a strong implicit need for power without dark personality traits. Dark triad traits are associated with excessive admiration-seeking behaviour, manipulation, and callousness; these traits can interfere with relationships and judgement calls. Specific characteristics of the traits are listed in Table 3. (LeBreton et al., 2018).
{| class=&quot;wikitable&quot;
|+Table 3. Dark triad characteristic defined (LeBreton et al., 2018). 
!Dark triad traits
!Characteristics
|-
|Machiavellianism
|Cynical, strategic, and manipulative
|-
|Psychopathy
|Erratic behaviour, interpersonal manipulation, callous affect and criminal tendencies
|-
|Narcissism
|Pride, aggression, envy, grandiosity, constant need for admiration, poor self-esteem
|} 

=== '''Key predictors of effective leadership''' ===
Power motivation can support effective leadership when regulated and directed toward collective rather than personal benefit. McClelland's research suggests effective leaders combine a strong need for power with high self-discipline, or “power under control,” which is linked to charismatic leadership and group morale (Reeve, 2018). However, a desire for influence alone does not ensure effectiveness. 

Self-regulation is especially important for leaders with potentially destructive personality tendencies. Stress, exhaustion, hunger, and cognitive overload can weaken willpower, making defensive reactions harder to control and potentially harming others. Strong motivation and self-awareness help leaders manage counterproductive tendencies and limit their disruptive effects.

Other motives also shape leadership. A strong need for affiliation can promote communication, respect, appreciation, and support, strengthening leader–follower relationships. Achievement motivation can encourage goal pursuit, but excessive striving may undermine effectiveness: highly active, achievement-oriented leaders can become frustrated when results fall short of expectations.

[[Motivation and emotion/Book/2018/Emotional intelligence and leadership effectiveness|Moral identity]] also influences how leaders use power. Those with weaker moral identities may prioritise [[wikipedia:Self-interest|self-interest,]] while a prosocial approach uses influence to benefit others. This approach is associated with less power-related anxiety and greater well-being, suggesting that leaders’ purposes for exercising power affect their effectiveness.

{{RoundBoxTop|theme=3}}[[File:John F. Kennedy speaks at Rice University.jpg|thumb|President John F. Kennedy speaking at Rice University |'''Figure 5.''' John F. Kennedy speaking at Rice University]]

== Case study: John F. Kennedy ==

John F. Kennedy (JFK) is often recognised as an example of charismatic political leadership because of his optimistic public image, ambitious presidency, and compelling communication. Despite his relatively short time in office, Kennedy established a distinctive presidential identity by blending political leadership with popular culture and staying engaged with government and the public, which can be seen in Figure 5 (Reeve, 2018; McCann &amp; Mollan, 2023).
Kennedy's leadership aligns with McClelland's theory of motivational needs, with his profile characterised by a high need for power and a low need for affiliation (McCann &amp; Mollan, 2023). His charismatic communication also reflects transformational leadership, which emphasises inspiring followers to work towards shared goals. McClelland (1970) found that students who listened to Kennedy's inaugural address reported stronger feelings of inspiration and uplift, illustrating how a leader's communication can influence their audience.
Kennedy therefore shows how power motivation can support leadership by enabling individuals to influence, inspire, and mobilise others. However, effective leadership also depends on how that influence is exercised, particularly when responding to challenging political situations.
{{RoundBoxBottom}}

{{RoundBoxTop|theme=6}}
== Quiz yourself ==
&lt;quiz display=simple&gt;
{Which combination of implicit motives is associated with effective leadership according to McClelland's leadership motive pattern?
|type=&quot;()&quot;}
- High power, high affiliation, and low inhibition
+ High power, low affiliation, and high inhibition
- Low power, high affiliation, and high inhibition
- High power, low affiliation, and low inhibition

{Does a high need for power necessarily result in aggressive behaviour?
|type=&quot;()&quot;}
- True
+ False

&lt;/quiz&gt;
{{RoundBoxBottom}}

== Conclusion ==
Psychological theory and research suggest that power motivation shapes how individuals seek, maintain, and regulate influence. McClelland's Three Need Theory explains differences in needs for power, achievement, and affiliation. The Two Faces of Power distinguishes personalised power, focused on personal control and self-interest, from socialised power, which uses influence to benefit others. This distinction explains why power motivation can produce very different leadership outcomes (McClelland, 1970; Carvalho &amp; Conde, 2024). The LMP further suggests that a high need for power, low need for affiliation, and high activity inhibition can support effective leadership by balancing influence with self-control (Reeve, 2018).

Power motivation is neither inherently positive nor negative; its effects depend on how leaders exercise authority, regulate behaviour, and balance personal ambitions with others’ needs. Effective leadership depends not on how much power a person wants, but on how they use it. Leaders who regulate their power motivation and direct influence toward collective goals, development, and positive outcomes are more likely to be well received by the public and subordinates (Peyton et al., 2019; Friederichs et al., 2023). Understanding power motivation helps explain both effective leadership and the risks of abuse, underscoring the importance of self-regulation and ethical influence.

{{RoundBoxTop|theme=11}}[[Image:Nuvola_apps_filetypes.png|right|102px]]
;Reflection activity

Think of a time you influenced a group decision at university, work, or in a team sport. Reflect on:

* What was the situation, and how did you respond?
* How did you influence others or make decisions?
* What motivated your behaviour?
{{RoundBoxBottom}}

==See also==
* [[wikipedia:Donald_Trump|Donald Trump]] (Wikipedia)
* [[Motivation and emotion/Book/2018/Emotional intelligence and leadership effectiveness|Emotional intelligence and leadership effectiveness]] (Book chapter, 2018)
* [[Motivation and emotion/Book/2015/Leadership motivation#Leadership Motive Pattern|Leadership motivation]] (Book chapter, 2015)
* [[Motivation and emotion/Book/2011/Maslow's hierarchy of needs|Maslow's hierarchy of needs]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2019/Two-factor motivation theory|Two-factor motivation theory]] (Book chapter, 2019)
* [[wikipedia:David_McClelland|David Clelland]] (Wikipedia)
* [[wikipedia:Need_for_power|Need for power]] (Wikipedia)
* [[wikipedia:Need_theory|Need theory]] (Wikipedia)

==References==

{{Hanging indent|1=

Bargh, J. A., &amp; Lee-Chai, A. Y. (2002). The use and abuse of power : Multiple perspectives in the causes of corruption. Psychology.

Bwalya, A. (2023). Leadership styles. Article in Journal of Entrepreneurship, Management and Innovation, 11(8), 181–193. https://doi.org/10.6084/m9.figshare.23932113

Carvalho, J. M. S., &amp; Conde, A. (2024). Individual power in human motivation – review and theoretical perspective. Acta Psychologica, 249, 104452–104452. https://doi.org/10.1016/j.actpsy.2024.104452

Deakin University. (2024, December 5). What are the different leadership styles? Deakin.Edu.Au. https://leadership.deakin.edu.au/blog/different-leadership-styles

Friederichs, K. M., Waldenmeier, K., &amp; Baumann, N. (2023). The benefits of prosocial power motivation in leadership: Action orientation fosters a win-win. Plos One, 18(7), e0287394–e0287394. https://doi.org/10.1371/journal.pone.0287394

Gambino, L. (2021, January 9). Trump has lost Twitter, his biggest political megaphone. Now what? The Guardian. https://www.theguardian.com/us-news/2021/jan/08/trump-has-lost-twitter-his-biggest-political-megaphone-now-what

Khajeh, A., Abu, M., &amp; Asaari, H. (2018). Impact of leadership styles on organizational performance. Journal of Human Resources Management Research, 2018(2166–0018), 2166–2184. https://ibimapublishing.com/articles/JHRMR/2018/687849/687849-1.pdf

Kurt, D. S. (2021, May 23). McClelland’s Three Needs Theory: Power, Achievement, and Affiliation. Education Library. https://educationlibrary.org/mcclellands-three-needs-theory-power-achievement-and-affiliation/#1

LeBreton, J. M., Shiverdecker, L. K., &amp; Grimaldi, E. M. (2018). The dark triad and workplace behavior. Annual Review of Organizational Psychology and Organizational Behavior, 5(1), 387–414. https://doi.org/10.1146/annurev-orgpsych-032117-104451

Magee, J. C., &amp; Langner, C. A. (2008). How personalized and socialized power motivation facilitate antisocial and prosocial decision-making. Journal of Research in Personality, 42(6), 1547–1559. https://doi.org/10.1016/j.jrp.2008.07.009

McCann, L., &amp; Mollan, S. (2023, November 20). JFK 60 years on: His leadership style and the reality behind the myths. The Conversation. https://theconversation.com/jfk-60-years-on-his-leadership-style-and-the-reality-behind-the-myths-216477

McClelland, D. C. (1970). The two faces of power. Journal of International Affairs, 24(1), 29–47. JSTOR. https://www.jstor.org/stable/24356663

Mobaseri, Y., &amp; Nosrat Kharazmi, Zohreh. (2025). Cognitive characteristic and crisis behaviour: An analysis of Donald Trump’s leadership style and operational code in the time of crisis. Journal of World Sociopolitical Studies, 9(1), 87–115. https://doi.org/10.22059/wsps.2025.384855.1468

Peyton, T., Zigarmi, D., &amp; Fowler, S. N. (2019). Examining the relationship between leaders’ power use, followers’ motivational outlooks, and followers’ work intentions. Frontiers in Psychology, 9(2620). https://doi.org/10.3389/fpsyg.2018.02620

Power , D. P. G. (2026). The five essentials of leadership {{!}} APS. Psychology.Org.Au. https://psychology.org.au/inpsych/2017/august/power

Ran, Y., Liu, Q., Cheng, Q., &amp; Zhang, Y. (2021). Implicit-explicit power motives congruence and forgiveness in the workplace conflict: The mediating role of empathy. International Journal of Conflict Management, 32(3), 445–468. https://doi.org/10.1108/ijcma-06-2020-0116

Reeve, J. (2018). Understanding motivation and emotion (7th edn, pp. 152–176). John Wiley &amp; Sons, Inc.

Roeloffs, M. W. (2025, January 20). Billionaires worth a combined $1.2 trillion attended Trump’s inauguration: Here’s who was there—From musk to Bezos. Forbes. https://www.forbes.com/sites/maryroeloffs/2025/01/20/billionaires-worth-a-combined-12-trillion-attended-trumps-inauguration-heres-who-was-there-from-musk-to-bezos/

Slabbinck, H., &amp; Van Witteloostuijn, A. (2020). Explicit and implicit basic human motives, and public service motivation. Frontiers in Psychology, 11(1542). https://doi.org/10.3389/fpsyg.2020.01542

Spangler, W. D., Tikhomirov, A., Sotak, K. L., &amp; Palrecha, R. (2014). Leader motive profiles in eight types of organizations. The Leadership Quarterly, 25(6), 1080–1094. https://doi.org/10.1016/j.leaqua.2014.10.001

Spanler, W. D., Tikhomirov, A., Lee Sotak, K., &amp; Palrecha, R. (2014). Leader motive profiles in eight types of organizations. ScienceDirect, 25(6). https://www-sciencedirect-com.ezproxy.canberra.edu.au/science/article/pii/S1048984314001040

Thrash, T. M., Maruskin, L. A., &amp; Martin, C. C. (2012). Implicit–explicit motive congruence. In R. M. Ryan (Ed.), The oxford handbook of human motivation (pp. 141–156). Oxford University Press. https://psycnet.apa.org/record/2012-03687-009

Verona, E., McKinley, S. J., Hoffmann, A., Murphy, B. A., &amp; Watts, A. L. (2023). Psychopathy facets, perceived power, and forms of aggression. Personality Disorders: Theory, Research, and Treatment, 14(3), 259–273. https://doi.org/10.1037/per0000562

}}

==External links==
* [https://www.forbes.com/sites/maryroeloffs/2025/01/20/billionaires-worth-a-combined-12-trillion-attended-trumps-inauguration-heres-who-was-there-from-musk-to-bezos/ Billionaires Worth A Combined $1.35 Trillion Attended Trump’s Inauguration: Here’s Who Was There—From Musk To Bezos] (Roeloffs, 2025)
* [https://www.stand-deliver.com/columns/leadership/1319-donald-trump-s-leadership-style-is-it-all-about-me.html Donald Trump’s Leadership Style: Is it all about “me”?] (Steve Adubato , 2019)
* [https://educationlibrary.org/mcclellands-three-needs-theory-power-achievement-and-affiliation/#1 McClelland’s Three Needs Theory: Power, Achievement, and Affiliation] (Kurt, 2021)
* [https://psychology.org.au/inpsych/2017/august/power The five essentials of leadership] (Power , 2026)
* [https://www.theguardian.com/us-news/2021/jan/08/trump-has-lost-twitter-his-biggest-political-megaphone-now-what Trump has lost Twitter, his biggest political megaphone. Now what?] (Gambino, 2021)
* [https://theconversation.com/jfk-60-years-on-his-leadership-style-and-the-reality-behind-the-myths-216477 JFK 60 years on: his leadership style and the reality behind the myths] (McCann &amp; Mollan, 2023)

==See also==
* [[Motivation and emotion/Book/2024/Power motivation and leadership|Power motivation and leadership]] (Book chapter, 2024)

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__TOC__

==Overview==
{{RoundBoxTop|theme=11}}
[[File:Donald Trump takes the oath of office (2025).jpg|thumb|President-elect Donald Trump takes the oath of office |'''Figure 1'''. Donald Trump's 2025 Inauguration surrounded by some of the world's wealthiest and most powerful individuals]]

Imagine a leader standing at their inauguration, surrounded by a concentration of wealthy and influential individuals. At first glance, this may reflect a preference for resources and influence. However, a closer look raises a psychological question: what motivates a leader to seek and exercise power, and how does this shape the way they lead?

This scenario reflects the leadership of United States President Donald Trump, whose 2025 administration included a notable concentration of wealthy and influential individuals (Roeloffs, 2025). This concentration of political and economic power can be illustrated in Figure 1. This scenario can play as a contemporary example for examining the relationship between power motivation and leadership.{{ic|[[w:Donald Trump|Second inauguration of Donald Trump]]}}Power is reflected not only in who a leader surrounds themselves with, but also in how they exercise their influence. For example, Trump uses social media as a political megaphone, bypassing traditional bureaucratic communication channels (Gambino, 2021). His public leadership style places considerable emphasis on personal image and the need of personal control with the disregard of external influences of power (Adubato, 2019; Mobaseri &amp; Nosrat Kharazmi, Zohreh, 2025).

This raises the question: does the desire for power necessarily make someone an effective leader? Individuals seek leadership for various reasons, and how they use their influence shapes their interactions with followers, decision-making, and pursuit of goals. Psychology helps explain these differences by examining power motivation and how individual motives influence leadership behaviour.
{{RoundBoxBottom}}

This chapter will explore [https://pmc.ncbi.nlm.nih.gov/articles/PMC10355387/ power motivation] (Friederichs et al., 2023), the desire to [[wikipedia:Influence|influence]], [[wikipedia:Control|control]], and have the ability to impact others, affecting [[Motivation and emotion/Book/2015/Leadership motivation|leadership]] styles, behaviour and effectiveness (McClelland, 1970). How power is expressed i.e., socialised or personalised power, determines a leader's behaviour and their effectiveness, (Reeve, 2018; McClelland, 1970; Carvalho &amp; Conde, 2024).

Understanding power motivation provides the groundwork that can explain why leaders exercise authority in certain ways and the how followers respond. Psychological science provides a means to clarify why some power-motivated leaders use influence to control, while others use it to empower (Reeve, 2018).

{{RoundBoxTop|theme=11}}
[[File:P psychology.png|right]]
'''Focus questions:'''

*What psychological theories explain power motivation in leaders?

*How does a leader's orientation towards power influence their specific leadership style?

*What is implicit motivation, and how does it differ from explicit power motivation in leaders?

*How does power motivation influence leadership effectiveness?
{{RoundBoxBottom}}

==Understanding power motivation through psychological theories==
'''Focus question:''' ''What psychological theories explain power motivation in leaders?''

The definition of motivation and power, one describes the push to act while the other if often associated with [[wikipedia:Aggression|aggression]], influence, [[wikipedia:Authority|authority]] and control, together they hold a heavy meaning. In psychology, [[Motivation and emotion/Lectures/Introduction|motivation]] is the driving force that guides human behaviour; it is the use of will-power and self-discipline, channelling efforts to achieve a [[wikipedia:Goal|goal]]. Certain individuals have predominant motive of power, being motivated by the internal urge to dominate, influence, or control (Kurt, 2021). Power motivation is the broad construct that refers to the desire for leadership, authority or status, it is built up of three characteristics: strong action, emotional impact, and concern for status, frame, and reputation. All characteristics are heavily influenced by cultural values and socialised experiences (McClelland,1970).

Power seekers can be effective, well-adjusted, and highly motivated. Power is a source of human control; only the mentally healthy can wield it successfully. Those with the need of power, [[wikipedia:Need_for_power|nPower]], struggle to feel satisfied unless they are in a position that fulfils their power-hungry needs, such as making decisions, influencing an audience, or obtaining information to become influential. Such occupations are teachers, journalists, clergy, psychologists, diplomats, business executives, political leaders and advisors (Reeve, 2018). [[wikipedia:David_McClelland|David McClelland's]] is popular within the psychology community for his thoughts on power motivation, with the most well-known theories, the [[wikipedia:Need_theory|Three Need Theory]] and the [https://www.jstor.org/stable/pdf/24356663.pdf Two Faces of Power] theory.

Other theories of motivation include the [[Motivation and emotion/Book/2011/Maslow's hierarchy of needs|Maslow's hierachy of need,]] and [[Motivation and emotion/Book/2019/Two-factor motivation theory|Herzberg's two-factor theory]]. These theories offer broader perspectives on the factors that drive human behaviour and motivation.

=== Three need theory ===
[[File:DavidMcClelland.jpg|thumb|'''Figure 2.''' David McClelland]]McClelland, a Harvard psychologist who conducted extensive research into human motivation (seen in Figure 2.), proposed the three need Theory. The theory identifies three acquired motivational needs: the need for [[wikipedia:Need_for_achievement|achievement]], the need for [[wikipedia:Need_for_affiliation|affiliation]], and the need for power (McClelland, 1970). Although individuals can experiences all three needs, the strength of each varies between individuals and can influence their behaviour. Table 1 summarises these needs and their defining characteristics being examined from high to low behaviour (Kurt, 2021).

nPower in leadership involves the desire to influence others and have an impact on their behaviour. A strong need for achievement may motivate individuals to pursue challenging goals, a strong need for affliction may encourage them to maintain positive interpersonal relationships, and a strong need for power can motivate individuals to seek positions of authority. However the nPower alone does not determine whether someone will be an effective leader; its expression and the way an individual exercises their influence matters.      

 {| class=&quot;wikitable&quot;
|+Table 1: Three need theory
!Need
!Definition
!High behaviour
!Low behaviour
|-
|Need for Achievement 
|Situations that challenge individuals with explicit standards.
|Individual exhibits a need to win and receive recognition.
|Constant fear of failure, typically avoids responsibilities. 
|-
|Need for Affiliation 
|Situations that afford warm relationship opportunities.
|A desire within for control, typically exaggerates own position.
|A heavily dependent individual, tries to minimise own position and importance.
|-
|Need for Power 
|Situations that enable others to exert influence over others.
|Individual demands and expects loyalty and harmony.
|Individual remains 'aloof' and keeps social distance from influence over others. 
|}

==== Two faces of power ====
McClelland's Two Faces of Power framework distinguishes between two ways the nPower can be expressed, personalised power or socialised power, also referred to as ''pP''ower, and ''s''Power (McClelland, 1970). ''pP''ower centres on personal control, it is seen as an socially unacceptable way of expression, closely linked dominance and status. Those influenced by ''p''Power may tend to seek to strengthen their own position and influence (McClelland, 1970). While McClelland was doing his research of these mannerisms of power, he though that if those who obtained ''pP''ower were in the environment of international relations the consequences would be ''ominous''. While, ''s''Power, is the more socially acceptable form of expression, with leaders being motivated through the benefit of others; it incorporates feelings of personal strength, and the known knowledge of being careful (Bargh &amp; Lee-Chai, 2002; Friederichs et al., 2023; Magee &amp; Langner, 2008; McClellad, 1970). 

These forms of expression are not necessarily mutually exclusive. Leaders may display elements of both; McClelland believes that a true leader can balance personal dominance and socialised leadership (Bargh &amp; Lee-Chai, 2002). ''p''Power can become problematic when leaders become too absorbed by the maintenance of their position and influence, the ability to dominate, manipulate, and disagree. However, the issue isn't high-power motivation; it's how it is expressed (McClelland, 1970). 

=== The leadership motive pattern ===
McClelland and David Burnham (1975) proposed the idea that effective leadership is associated with a certain specific combination of motives known as the [[Motivation and emotion/Book/2015/Leadership motivation#Leadership Motive Pattern|Leadership Motive Pattern]] (LMP) (Spangler et al., 2014). This consists of three primary elements, high need for power (nPow), a low need for affiliation (nAff) and a high activity inhibition (AI). This model demonstrated how motivation can work together to shape leadership behaviour (Reeve, 2018). 

Each component serves as a different purpose, building characterises of the most effective leaders within bureaucratic organisation (Spangler et al., 2014). High nPow, is the force to influence, direct and impact others, this has been well-established by now. Low nAff, is a reduced desire for friendly interpersonal relationships, which prevent the leaders from producing biased decision-making. High AI is based on [[wikipedia:Self-control|self-control]], maturity, and the ability to channel power socially rather an impulsively (McClelland &amp; Boyatzis, 1982).

Research by McClelland and Burnhamd (1982) found that the LMP may only hold value for specific roles in demonstrating leadership effectiveness. When relevant, it demonstrated that managers of this pattern typically generate higher morale in their subordinates; leadership styles such as those of nations that spend relatively more on military forces than private consumption, which McClelland described as a system's capacity to mobilise resources in the interest of the nation (McClelland &amp; Boyatzis, 1982; Spangler et al., 2014). 


{{RoundBoxTop|theme=8}}
== Recap ==
&lt;quiz display=simple&gt;
{&amp;nbsp;
|type=&quot;{}&quot;}
What is the driving force that guides human behaviour?
{ Motivation }

{What is the key difference between personalised power and socialised power?}
- Personalised power focuses on achievement, and socialised power focuses on affiliation
+ Personalised power focuses on personal dominance and control, and socialised power focuses on benefiting others
- Personalised power is consistently associated with an effective leadership style, whereas socialised power is associated with an ineffective leadership style.

{Which combination of motives is associated with McClelland’s Leadership Motive Pattern in effective managers?}
- High need for achievement, high need for affiliation and low activity inhibition
+ High need for power, low need for affiliation and high activity inhibition
- Low need for power, high need for affiliation and high activity inhibition

{Which behaviour best fits an individual with a high need for power?}
- Avoiding situations where they might influence others
+ Seek opportunities to influence, control, or have an impact on others
- Avoid challenging tasks for fear of failure


&lt;/quiz&gt;

{{RoundBoxBottom}}

== Power motivation and leadership style ==
'''Focus question:''' ''How does a leader's orientation towards power influence their specific leadership style?''

An individual’s desire for power does not automatically determine their leadership style. How an individual in a position of authority understands and exercises power over others can shape their interactions, decision-making approaches, and the goals they prioritise. Examining power orientation alongside psychological characteristics provides a deeper understanding of why leaders may use their influence in various ways and how those differences are reflected in their leadership style (Carbalho and Conde, 2024) 

=== Power orientation and leadership behaviour ===
Power motivation is the drive to influence others, while power orientation is the how; it is the framework for how a leader becomes influential. A negative stereotype surrounds high power motivation, with the speculation that it automatically relates to undesirable behaviour, unlike prosocial power motivation, which is often associated with generosity. However, those with high power motivation can have different power orientations. Carbalho and Conde (2024) distinguish ego-power orientation and social-power orientations, highlighting that individuals can combine said orientations in different ways. Ego-power is associated with pursuing goals to satisfy the self and achieve a sense of self-fulfilment; this doesn't automatically result in harmful leadership, as it partly depends on the individual's position of influence and work. Social-power orientation links directing power to collective outcomes (Carbalho and Conde, 2024).

=== Leadership trait analysis ===
[https://wsps.ut.ac.ir/article_101018.html Leadership Trait Analysis] (LTA), developed by Margaret Hermann (2003) (Mobaseri &amp; Nosrat Kharazmi, Zohreh, 2025), is a framework for analysing political leaders' psychological characteristics using interviews and public speeches. It examines seven traits across three dimensions: responsiveness to constraints, openness to information and motivation. The seven traits include the need for power, the belief that one can control what happens next, self-confidence, trust in others, conceptual complexity, the intensity of in-group bias or nationalism, and the need for affiliation. Together, these traits help researchers examine how leaders process information, respond to constraints and approach decision-making.

Trump illustrates how psychological frameworks such as the LTA apply to political leadership. Mobaseri and Nosrat Kharazmi (2025) examined Trump's leadership characteristics and political beliefs before his presidency and during his first term. The research explored how much his core beliefs influenced his responses to political events and the COVID-19 crisis. The study highlights the value of examining leaders' beliefs and characteristics over time to understand their responses to the political climate.

The analysis found Trump low in need for power, perceived control, self-confidence, in-group bias, and trust in others, but high in conceptual complexity. These traits informed Mobaseri and Nosrat Kharazmi's (2025) account of his leadership: resistance to adaptation, disregard for policymaking, charisma, and sensitivity to context in decisions.

The findings show how leadership reflects the interaction between a leader's psychology and their situation. LTA offers a way to analyse individual differences that shape leadership style.

=== Leadership styles and effectiveness ===
Power orientation can be reflected in different leadership styles, which describe how leaders direct, influence and interact with followers. For example, a leader who prioritises complete personal control may favour a more autocratic approach, while a leader who values engagement may be more inclined towards a democratic leadership. However, while leadership styles reflect theoretical models, they can also be shaped by individual characteristics and techniques (Khajeh et al., 2018; &quot;What Are the Different Leadership Styles?&quot;, 2024). Different styles place varying emphasis on factors seen in Table 2 (Deakin University, 2024; Bwalya, 2023). 

Effective leadership involves more than holding a position of authority; there are five essential characteristics of leadership: self-image, self-control, socialised power, sustained dialogue, and strategic intent, providing a practical framework for a successful leader (Power, 2026). Power, motivation, and leadership matter across contexts, from political leaders to supervisors, who need to build relationships with employees and an environment of trust if they want to do so. The characteristics emphasise the importance of authority, responsibility, communication, and directing efforts towards organisational goals (Power, 2026; Friederichs et al., 2023)

Research suggests that transformational leadership can produce positive outcomes by motivating and inspiring followers and benefiting the group rather than serving personal interests (Peyton et al., 2019). This shows how power can support group goals rather than simply reinforcing leadership status. Nevertheless, no single leadership style guarantees effectiveness; outcomes depend on how the leader behaves and responds to the situation at hand.

{| class=&quot;wikitable&quot;
|+Table 2. Leadership styles  (Bwalya, 2023)
! colspan=&quot;3&quot; |Leadership styles
|-
|Style
|Description
|Example Leaders
|-
|Autocratic 
|Leader holds complete control over decision-making with no input from followers. Consistently exercises control over the decision-making process. Expects strict compliance with policies and procedures, and does not take input from followers. They micromanage and control subordinate work. They make quick decisions because they do not have to consult. There is a lack of creative innovation (Bwalya, 2023). 
|Adolf Hitler and  Kim Jong-un 
|-
|Democratic 
|Leader is involved in team members' decision-making process, continuously encourages communication, and seeks feedback on matters, valuing input and ideas, wanting followers to participate in shaping strategies and goals (Bwalya, 2023).
|Former President of South Africa, Nelson Mandela and Former Prime Minister of New Zealand Jacinda Ardern 
|-
|Laissex-faire
| The leader is distant and has minimal involvement in decisions, unlike autocratic leadership, as laissez-faire lets followers make decisions with little guidance or supervision, trusting their ability to manage responsibilities. They are comfortable with mistakes and take accountability for followers' mistakes. This empowers employees and enables faster decision-making. However, the lack of guidance can cause confusion and lack of coordination (Bwalya, 2023). 
|Former President Herbert Hoover and Mahatma Ghandi
|-
|Servant 
|Leader is prosocial and motivated by power, focusing on the needs and well-being of others. Aiming to support and empower followers, in hopes they reach their full potential (Bwalya, 2023). 
|Pope Francis
|-
|Transformational 
|Based on inspiration and motivation to achieve performance, with high expectations and focus on challenging others to exceed self-interest. Focuses on transforming followers through inspiration, motivation, and effective communication. They rely on the leader's influence; if the leader fails to provide proper guidance, it can impact followers (Bwalya, 2023). 
|Former President of South Africa Nelson Mandela and Former President of the United States Barack Obama 
|-
|Transactional
|Focuses on the exchange relationship between the leader and their followers. The leader maintains stability and achieves goals by providing rewards and punishments based on performance. Very goal-oriented, with clear expectations, and quick decision-making (Bwalya, 2023).  
|Bill Gates and Former Chancellor of Germany Angela Merkel
|}

{{RoundBoxTop|theme=8}}[[Image: Hand Gesture - Holding a Magnifying Glass.gif|right|128px]] 
==Quiz==
&lt;quiz display=simple&gt; 
Which statement best explains the relationship between a leader’s power motivation and their leadership style?

|type=&quot;()&quot;} 

- Leaders with high power motivation are more likely to adopt an autocratic style, regardless of their values or circumstances
+ A leader’s power motivation determines their leadership style, while their psychological characteristics have very little influence
- Power motivation can influence a leader’s behaviour, but their power orientation, psychological characteristics and circumstances also shape how they exercise influence
&lt;/quiz&gt;
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== Implicit and explicit power motivation ==
'''Focus question:''' ''What is implicit motivation, and how does it differ from explicit power motivation in leaders?''

Human motivation can operate through two systems: [[Motivation and emotion/Book/2020/Implicit motives|implicit and explicit motivation]]. Both influencing behaviour, but very different in the extent to which the individuals are consciously aware of their motives behind their behaviour. When looking at leadership, it is helpful to dissect the distinctions to understand why a leader's states goals may not fully reflect their underlying needs which influence their behaviour. 

Implicit motive (nPow) is [[wikipedia:Unconscious_mind|unconscious]] motivation outside an individual’s awareness, mind map below in Figure 3 illustrates it. McClelland identified three implicit motives that shape thoughts, feelings, and actions: achievement, affiliation, and power. Developed through early preverbal experiences, they remain dormant until activated by incentives. Their influence appears in recurring patterns of thought, [[wikipedia:Emotion|emotion]], and behaviour, even when people cannot identify their motives (Reeve, 2018). Unlike explicit motives, implicit motives are difficult to measure directly. Researchers use the Picture-Story Exercise (PSE), asking participants to create stories from images and analysing them for themes related to the three motives. 

[[File:Implicit_Motives_associations.png|thumb| '''Figure 3.''' Mind map of implicit motives]]Explicit motives are conscious, self-attributed motives people can describe through their goals, values, and preferences (Slabbinck &amp; Van Witteloostuijn, 2020). Often assessed with self-report questionnaires, explicit power motives reflect desires for influence, status, and leadership. Their dimensions, dominance, prestige, and leadership, can help explain how power motives relate to dark personality traits. Dominance involves controlling others and is associated with [[Motivation and emotion/Book/2024/Machiavellianism and power motivation|Machiavellianism]] and counterproductive work behaviour. Prestige involves gaining influence by displaying knowledge or status and is linked to [[Motivation and emotion/Book/2010/Narcissism|narcissism]]. Leadership involves guiding groups toward shared goals and may predict organisational citizenship behaviour and align with transformational leadership.

A strong explicit power motive does not automatically lead to destructive leadership. It can support productive leadership, but may also overlap with dark traits such as narcissism, Machiavellianism, and psychopathy.

When implicit and explicit motives align, congruence, individuals are more likely to experience greater well-being and engagement, whereas misalignment can contribute to stress and reduced well-being (Ran et al., 2021; Thrash et al., 2012).

Applying this to leadership styles highlights how a leader's effectiveness and well-being depend on whether their chosen leadership style aligns with their implicit motive. When a leader's leadership style conflicts with their implicit motive, they experience ''motive incongruence,'' which can lead to chronic stress, burnout, and friction, whereas alignment predicts greater flow, high energy, and effortless leadership (Ran et al., 2021; Thrash et al., 2012).

== Power motivation and leadership effectiveness ==
'''Focus question:''' ''How does power motivation influence leadership effectiveness?''

Power motivation influences leadership effectiveness through how it is expressed and regulated. Social incentives arise from others’ rewards, expectations, and norms, whereas activity incentives come from the activity itself. Individuals with high nPower may seek positions of authority and careers offering influence and advancement. Although power motivation can be associated with aggression, social norms, laws, and consequences can constrain its expression (Reeve, 2018).

=== Destructive power dynamics and power abuse ===
There is a ''fickle'' relationship between aggression and the need or desire for power are closely linked. Studies have linked aggressive tendencies to dominance and the need for power (Verona et al., 2023). Verona et al. (2023) define human aggression as behaving with the intent to cause harm to another individual, and the target of the behaviour is driven to avoid it. Aggression can also take direct vs indirect and overt vs covert forms. That said, no concrete evidence links any level of ''feeling'' power to aggression. 

An individual with a high need for power may desire impact, control, or influence over another person or group, or even the world at large; aggression can be a means of satisfying those power needs. However, social norms, laws, and consequences can constrain this expression, causing that aggression to manifest in a more covert form. Individuals, both men and women, report more impulses to act aggressively than others; this behaviour would include yelling, throwing or destroying items and insulting others. Other factors of aggression and its link with high power-seeking individuals include finding a release through drinking, using this as a way to inflate their sense of control. Furthermore, men respond to stress and other setbacks with the behaviour of inflicting abuse on their partners, as well as an increased level of sexual misconduct (Reeve, 2018; Spanler et al., 2014). This indicates that a sense of power comes not only from leadership and reputation but can also be built through strategies of drinking, risk-taking, and posturing (Reeve, 2018).

Those who harbour inclinations that are both benevolent and malevolent towards others strive to improve the world while also influencing everyone else (Reeve, 2018). The ''dark side'' of implicit motive is the combination of opportunity to use power for personal benefit, which is the 'abuse of power.' Unrestrained affiliation can lead to favouritism and corruption in political and bureaucratic organisations. Achievement ignores political/interpersonal issues. High need for achievement: find it difficult working in groups, making decisions, and enforcing authority, ignoring interpersonal relationships (Spanier et al., 2014).[[File:The_Dark_Triad_Traits.jpg|thumb|'''Figure 4.''' The dark triad, and its associated personality traits]]

=== The dark triad traits ===
First proposed by Paulhus and Williams (2002), the [[Motivation and emotion/Book/2021/Dark triad personality and motivation|&quot;Dark Triad&quot;]] traits- narcissism, Machiavellianism, and psychopathy, seen in Figure 4, are three overlapping personality traits that can strongly motivate individuals to seek and wield power. When an individual has these traits, it often means they restrain and fuel their ruthlessness and self-serving behaviour. Research has found that scoring high on these traits increases an individual’s likelihood of committing crimes, causing distress, and creating severe issues for organisations when in authoritative leadership positions (LeBreton et al., 2018).  

Findings on the dark triad suggest that leadership outcomes depend not only on a leader's desire for influence, but also on their personality and how they exercise authority. However, the dark triad should not be associated with high implicit power motivation, as a strong unconscious drive to influence or impact others is not the same as the dark triad traits. An individual can have a strong implicit need for power without dark personality traits. Dark triad traits are associated with excessive admiration-seeking behaviour, manipulation, and callousness; these traits can interfere with relationships and judgement calls. Specific characteristics of the traits are listed in Table 3. (LeBreton et al., 2018).
{| class=&quot;wikitable&quot;
|+Table 3. Dark triad characteristic defined (LeBreton et al., 2018). 
!Dark triad traits
!Characteristics
|-
|Machiavellianism
|Cynical, strategic, and manipulative
|-
|Psychopathy
|Erratic behaviour, interpersonal manipulation, callous affect and criminal tendencies
|-
|Narcissism
|Pride, aggression, envy, grandiosity, constant need for admiration, poor self-esteem
|} 

=== '''Key predictors of effective leadership''' ===
Power motivation can support effective leadership when regulated and directed toward collective rather than personal benefit. McClelland's research suggests effective leaders combine a strong need for power with high self-discipline, or “power under control,” which is linked to charismatic leadership and group morale (Reeve, 2018). However, a desire for influence alone does not ensure effectiveness. 

Self-regulation is especially important for leaders with potentially destructive personality tendencies. Stress, exhaustion, hunger, and cognitive overload can weaken willpower, making defensive reactions harder to control and potentially harming others. Strong motivation and self-awareness help leaders manage counterproductive tendencies and limit their disruptive effects.

Other motives also shape leadership. A strong need for affiliation can promote communication, respect, appreciation, and support, strengthening leader–follower relationships. Achievement motivation can encourage goal pursuit, but excessive striving may undermine effectiveness: highly active, achievement-oriented leaders can become frustrated when results fall short of expectations.

[[Motivation and emotion/Book/2018/Emotional intelligence and leadership effectiveness|Moral identity]] also influences how leaders use power. Those with weaker moral identities may prioritise [[wikipedia:Self-interest|self-interest,]] while a prosocial approach uses influence to benefit others. This approach is associated with less power-related anxiety and greater well-being, suggesting that leaders’ purposes for exercising power affect their effectiveness.

{{RoundBoxTop|theme=3}}[[File:John F. Kennedy speaks at Rice University.jpg|thumb|President John F. Kennedy speaking at Rice University |'''Figure 5.''' John F. Kennedy speaking at Rice University]]

== Case study: John F. Kennedy ==

John F. Kennedy (JFK) is often recognised as an example of charismatic political leadership because of his optimistic public image, ambitious presidency, and compelling communication. Despite his relatively short time in office, Kennedy established a distinctive presidential identity by blending political leadership with popular culture and staying engaged with government and the public, which can be seen in Figure 5 (Reeve, 2018; McCann &amp; Mollan, 2023).
Kennedy's leadership aligns with McClelland's theory of motivational needs, with his profile characterised by a high need for power and a low need for affiliation (McCann &amp; Mollan, 2023). His charismatic communication also reflects transformational leadership, which emphasises inspiring followers to work towards shared goals. McClelland (1970) found that students who listened to Kennedy's inaugural address reported stronger feelings of inspiration and uplift, illustrating how a leader's communication can influence their audience.
Kennedy therefore shows how power motivation can support leadership by enabling individuals to influence, inspire, and mobilise others. However, effective leadership also depends on how that influence is exercised, particularly when responding to challenging political situations.
{{RoundBoxBottom}}

{{RoundBoxTop|theme=6}}
== Quiz yourself ==
&lt;quiz display=simple&gt;
{Which combination of implicit motives is associated with effective leadership according to McClelland's leadership motive pattern?
|type=&quot;()&quot;}
- High power, high affiliation, and low inhibition
+ High power, low affiliation, and high inhibition
- Low power, high affiliation, and high inhibition
- High power, low affiliation, and low inhibition

{Does a high need for power necessarily result in aggressive behaviour?
|type=&quot;()&quot;}
- True
+ False

&lt;/quiz&gt;
{{RoundBoxBottom}}

== Conclusion ==
Psychological theory and research suggest that power motivation shapes how individuals seek, maintain, and regulate influence. McClelland's Three Need Theory explains differences in needs for power, achievement, and affiliation. The Two Faces of Power distinguishes personalised power, focused on personal control and self-interest, from socialised power, which uses influence to benefit others. This distinction explains why power motivation can produce very different leadership outcomes (McClelland, 1970; Carvalho &amp; Conde, 2024). The LMP further suggests that a high need for power, low need for affiliation, and high activity inhibition can support effective leadership by balancing influence with self-control (Reeve, 2018).

Power motivation is neither inherently positive nor negative; its effects depend on how leaders exercise authority, regulate behaviour, and balance personal ambitions with others’ needs. Effective leadership depends not on how much power a person wants, but on how they use it. Leaders who regulate their power motivation and direct influence toward collective goals, development, and positive outcomes are more likely to be well received by the public and subordinates (Peyton et al., 2019; Friederichs et al., 2023). Understanding power motivation helps explain both effective leadership and the risks of abuse, underscoring the importance of self-regulation and ethical influence.

{{RoundBoxTop|theme=11}}[[Image:Nuvola_apps_filetypes.png|right|102px]]
;Reflection activity

Think of a time you influenced a group decision at university, work, or in a team sport. Reflect on:

* What was the situation, and how did you respond?
* How did you influence others or make decisions?
* What motivated your behaviour?
{{RoundBoxBottom}}

==See also==
* [[wikipedia:Donald_Trump|Donald Trump]] (Wikipedia)
* [[Motivation and emotion/Book/2018/Emotional intelligence and leadership effectiveness|Emotional intelligence and leadership effectiveness]] (Book chapter, 2018)
* [[Motivation and emotion/Book/2015/Leadership motivation#Leadership Motive Pattern|Leadership motivation]] (Book chapter, 2015)
* [[Motivation and emotion/Book/2011/Maslow's hierarchy of needs|Maslow's hierarchy of needs]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2019/Two-factor motivation theory|Two-factor motivation theory]] (Book chapter, 2019)
* [[wikipedia:David_McClelland|David Clelland]] (Wikipedia)
* [[wikipedia:Need_for_power|Need for power]] (Wikipedia)
* [[wikipedia:Need_theory|Need theory]] (Wikipedia)

==References==

{{Hanging indent|1=

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Friederichs, K. M., Waldenmeier, K., &amp; Baumann, N. (2023). The benefits of prosocial power motivation in leadership: Action orientation fosters a win-win. Plos One, 18(7), e0287394–e0287394. https://doi.org/10.1371/journal.pone.0287394

Gambino, L. (2021, January 9). Trump has lost Twitter, his biggest political megaphone. Now what? The Guardian. https://www.theguardian.com/us-news/2021/jan/08/trump-has-lost-twitter-his-biggest-political-megaphone-now-what

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Kurt, D. S. (2021, May 23). McClelland’s Three Needs Theory: Power, Achievement, and Affiliation. Education Library. https://educationlibrary.org/mcclellands-three-needs-theory-power-achievement-and-affiliation/#1

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McClelland, D. C. (1970). The two faces of power. Journal of International Affairs, 24(1), 29–47. JSTOR. https://www.jstor.org/stable/24356663

Mobaseri, Y., &amp; Nosrat Kharazmi, Zohreh. (2025). Cognitive characteristic and crisis behaviour: An analysis of Donald Trump’s leadership style and operational code in the time of crisis. Journal of World Sociopolitical Studies, 9(1), 87–115. https://doi.org/10.22059/wsps.2025.384855.1468

Peyton, T., Zigarmi, D., &amp; Fowler, S. N. (2019). Examining the relationship between leaders’ power use, followers’ motivational outlooks, and followers’ work intentions. Frontiers in Psychology, 9(2620). https://doi.org/10.3389/fpsyg.2018.02620

Power , D. P. G. (2026). The five essentials of leadership {{!}} APS. Psychology.Org.Au. https://psychology.org.au/inpsych/2017/august/power

Ran, Y., Liu, Q., Cheng, Q., &amp; Zhang, Y. (2021). Implicit-explicit power motives congruence and forgiveness in the workplace conflict: The mediating role of empathy. International Journal of Conflict Management, 32(3), 445–468. https://doi.org/10.1108/ijcma-06-2020-0116

Reeve, J. (2018). Understanding motivation and emotion (7th edn, pp. 152–176). John Wiley &amp; Sons, Inc.

Roeloffs, M. W. (2025, January 20). Billionaires worth a combined $1.2 trillion attended Trump’s inauguration: Here’s who was there—From musk to Bezos. Forbes. https://www.forbes.com/sites/maryroeloffs/2025/01/20/billionaires-worth-a-combined-12-trillion-attended-trumps-inauguration-heres-who-was-there-from-musk-to-bezos/

Slabbinck, H., &amp; Van Witteloostuijn, A. (2020). Explicit and implicit basic human motives, and public service motivation. Frontiers in Psychology, 11(1542). https://doi.org/10.3389/fpsyg.2020.01542

Spangler, W. D., Tikhomirov, A., Sotak, K. L., &amp; Palrecha, R. (2014). Leader motive profiles in eight types of organizations. The Leadership Quarterly, 25(6), 1080–1094. https://doi.org/10.1016/j.leaqua.2014.10.001

Spanler, W. D., Tikhomirov, A., Lee Sotak, K., &amp; Palrecha, R. (2014). Leader motive profiles in eight types of organizations. ScienceDirect, 25(6). https://www-sciencedirect-com.ezproxy.canberra.edu.au/science/article/pii/S1048984314001040

Thrash, T. M., Maruskin, L. A., &amp; Martin, C. C. (2012). Implicit–explicit motive congruence. In R. M. Ryan (Ed.), The oxford handbook of human motivation (pp. 141–156). Oxford University Press. https://psycnet.apa.org/record/2012-03687-009

Verona, E., McKinley, S. J., Hoffmann, A., Murphy, B. A., &amp; Watts, A. L. (2023). Psychopathy facets, perceived power, and forms of aggression. Personality Disorders: Theory, Research, and Treatment, 14(3), 259–273. https://doi.org/10.1037/per0000562

}}

==External links==
* [https://www.forbes.com/sites/maryroeloffs/2025/01/20/billionaires-worth-a-combined-12-trillion-attended-trumps-inauguration-heres-who-was-there-from-musk-to-bezos/ Billionaires Worth A Combined $1.35 Trillion Attended Trump’s Inauguration: Here’s Who Was There—From Musk To Bezos] (Roeloffs, 2025)
* [https://www.stand-deliver.com/columns/leadership/1319-donald-trump-s-leadership-style-is-it-all-about-me.html Donald Trump’s Leadership Style: Is it all about “me”?] (Steve Adubato , 2019)
* [https://educationlibrary.org/mcclellands-three-needs-theory-power-achievement-and-affiliation/#1 McClelland’s Three Needs Theory: Power, Achievement, and Affiliation] (Kurt, 2021)
* [https://psychology.org.au/inpsych/2017/august/power The five essentials of leadership] (Power , 2026)
* [https://www.theguardian.com/us-news/2021/jan/08/trump-has-lost-twitter-his-biggest-political-megaphone-now-what Trump has lost Twitter, his biggest political megaphone. Now what?] (Gambino, 2021)
* [https://theconversation.com/jfk-60-years-on-his-leadership-style-and-the-reality-behind-the-myths-216477 JFK 60 years on: his leadership style and the reality behind the myths] (McCann &amp; Mollan, 2023)

==See also==
* [[Motivation and emotion/Book/2024/Power motivation and leadership|Power motivation and leadership]] (Book chapter, 2024)

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      <text bytes="10303" sha1="c1yy04thzff4hyu3tbwnkfixqfos9z1" xml:space="preserve">{{title|Types of impulsivity:&lt;br&gt;What are the different types of impulsivity and how do they affect motivation?}}

==Overview==
{{RoundBoxTop|theme=2}}

[[File:Ice Hockey sharks ducks.jpg|thumb|306x306px|Figure 1. The exciting sport of ice hockey ]]

'''Scenario'''

&quot;Why do we act before we think?&quot;

Bella is trying to study for a final exam and the pressure is on to get a good grade. Her friend texts her inviting her to a hockey game and she immediately says yes and stops her study session - this is an example of 'response impulsivity' (see Figure 1). She is naturally sensation seeking and spontaneous and while.e this makes her a fun friend to have these 'personality traits' make her behaviour more impulsive. While her study helps her long term goal of graduating, her immediate enjoyment of the hockey takes priority. this is an example of 'choice impulsivity'. All of this reduces her 'motivation' to pursue and prioritise her longer term academic goal. 

{{RoundBoxBottom}}

* Impulsivity is a tendency to act quickly without considering potential consequences, this could be difficulty resisting urges or making split second decisions, acting reactively or simply thrill seeking. Impulsively affects motivation&lt;ref&gt;{{Cite journal|date=2018|title=Motivation|url=https://doi.org/10.5040/9781350982789|journal=Motivation|doi=10.5040/9781350982789}}&lt;/ref&gt; as immediate rewards can become far more appealing than long term successes, this can make it harder to remain focused on the bigger picture. Read more about dysfunctional impulsivity here&lt;ref&gt;{{Cite journal|date=2025-04-22|title=Dysfunctional impulsivity|url=https://en.wikipedia.org/w/index.php?title=Dysfunctional_impulsivity&amp;oldid=1286851256|journal=Wikipedia|language=en}}&lt;/ref&gt;
* It is &lt;u&gt;NOT&lt;/u&gt; purely negative it can also help with creativity, decisiveness and spontaneity (see Figure 2.)
* We can help understand how rewards, self control and emotions affect human behaviour by using psychological concepts

{{RoundBoxTop|theme=2}}
'''Focus questions'''
* What is impulsivity defined and what are the different types?
* What theories explain the effect of impulsivity on motivation, and how can this be applied to everyday life?
* How does acting before thinking affect motivation and longer-term goal achievement?
* How are positive and negative emotions triggering impulsive behaviour?
* What strategies could help people to maintain motivation?
{{RoundBoxBottom}}

== 1. What is impulsivity and how is it conceptualised? ==
[[File:Frozen above Crater Lake.jpg|thumb|370x370px|Figure 2. Spontaneous activity: Cliff Jumping]]

As defined by Moeller et al. (2001) impulsivity is a predisposition toward rapid and unplanned reactions to internal or external stimuli without considering the negative consequences.  

[[w:Impulsivity|Impulsivity]] can be regarded as a multidimensional construct in the sense that it is defined by several distinct characteristics as opposed to one single trait (Birkley and Smith, 2011). 

One widely recognised framework is the '''UPPS-P Model''' which identifies five dimensions of impulsivity: negative urgency, positive urgency, lack of premeditation, lack of perseverance and sensation seeking (Um et al. 2018). Using a multidimensional approach like this one can help to explain why one displays a form of impulsivity e.g. acting out when they are stressed/emotional without displaying other forms. 

''As you continue reading about the forms of impulsivity, think about the fact it includes different tendencies and is dependent on individual circumstances.''

== 2. How do psychological theories explain the effect impulsivity has on emotion? ==

&lt;u&gt;'''Barrett Model'''&lt;/u&gt; (Patton et al. 1995) - This model helps to explain how people think, act and plan accordingly rather than just seeng one simple behaviour.

==== 1. Attentional Impulsiveness - ====

* Difficulty concentrating and/or maintaining attention, and often characterized by quickly changing thoughts. 

==== 2. Motor Impulsiveness - ====

* Individual acts immediately/spur of the moment without thinking it through first 

'''3. Nonplanning Impulsiveness -''' 

* Characterised by focus on the present without carefully considering the future and potential consequences. 

'''&lt;u&gt;Self Regulation Theory&lt;/u&gt;''' (Steel, 2007) -

*suggest explanation of how self regulation manages behaviour in relation to goals. 
*suggest highlighting the relationship between impulsivity, procrastination and goal management within this theory 
*suggest using bellas scenario as an applied case. is she resisting an immediate opportunity or keeping her academic goal central? or both? 

'''&lt;u&gt;Goal Management Perspective&lt;/u&gt;''' (Gustavson et al. 2014) -

*

== 3. Some strategies to manage impulsivity ==

=== Identifying Triggers ===

* Suggest returning to your overview scenario as an example in this section. would be good to apply each of the below in a case study scenario. you could also adjust your questions to reflect your overview scenario as well. 
* consider both emotional and situational triggers e.g. excitement and frustration vs distractions 

=== Mindfulness - (Salmoirago-Blotcher 2019) ===

* define mindfulness 
* suggest proposed reason it may help someon notice an urge prior to acting on it 
* include hypothetical or example from listed study explaining how mindfulness would be applied 

=== Delayed Rewards ===

* suggest explaining why people prefer immediate rewards and why they might work towards a larger or more important future outcome 
* you could go into some neuroscience in this section. e.g. dopaminergic pathways 
* goal setting could be incorporated 

=== CBT / Therapy ===

''Would you consider impulsivity adaptive or maladaptive?''

* suggest discussion that seperates thoughts, behaviours and emotion. this will set out the CBT framework 
* core principles of CBT / therapy. [https://www.apa.org/ptsd-guideline/patients-and-families/cognitive-behavioral starter reference] 
* I would note the limitations of therapy in this section, not every therapy will equally address impulsivity. some are better than others (DBT is also useful) 
&lt;quiz display=&quot;simple&quot;&gt;
{A person who has higher choice impulsivity usually prefers larger/delayed rewards instead of immediate/ smaller rewards:
|type=&quot;()&quot;}
+ False
- True

{Motivation can affect impulsive choices by making immediate rewards more appealing=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;&lt;quiz display=&quot;simple&quot;&gt;
{Impulsivity is a single behaviour that affects everyone the same way:
|type=&quot;()&quot;}
+ False
- True

&lt;/quiz&gt;

==Conclusion==
* Impulsivity affects day to day life such as making decisions, staying motivated and goal achievement - short and long term. understanding this concept and taking appropriate steps to manage it can help to reduce procrastination and help to make better long term decisions

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages? (Even for the topic development, have a go at the likely take-home message)
}}

== See also ==
{{expand}}

* [[wikipedia:Impulsivity|Impulsivity]] (Wikipedia)

==References==

{{Hanging indent|1=

Birkley, E. L, &amp; Smith, G. T. (2011). Recent advances in understanding the personality underpinnings of impulsive behavior and their role in risk for addictive behaviors. Current Drug Abuse Reviews, 4(4), 215–227. https://doi.org/10.2174/1874473711104040215

Um, M., Hershberge, A. R., Whitt, Z. T., &amp; Cyders, M. A. (2018). Recommendations for applying a multi-dimensional model of impulsive personality to diagnosis and treatment. Borderline Personality Disorder and Emotion Dysregulation, 5, Article 6. https://doi.org/10.1186/s40479-018-0084-x

Moeller, F. G., Barratt, E. S., Dougherty, D. M., Schmitz, J. M., &amp; Swann, A. C. (2001). Psychiatric aspects of impulsivity. American Journal of Psychiatry, 158(11), 1783–1793. https://doi.org/10.1176/appi.ajp.158.11.1783

Steel, P. (2007). The nature of procrastination: A meta-analytic and theoretical review of quintessential self-regulatory failure. Psychological Bulletin, 133(1), 65–94. https://doi.org/10.1037/0033-2909.133.1.65

Gustavson, D. E., Miyake, A., Hewitt, J. K., &amp; Friedman, N. P. (2014). Genetic relations among procrastination, impulsivity, and goal-management ability: Implications for the evolutionary origin of procrastination. Psychological Science, 25(6), 1178–1188. https://doi.org/10.1177/0956797614526260

Salmoirago-Blotcher, E., Druker, S., Meleo-Meyer, F., Frisard, C., Crawford, S., &amp; Pbert, L. (2019). Beneficial effects of school-based mindfulness training on impulsivity in healthy adolescents: Results from a pilot randomized controlled trial. Explore, 15(2), 160–164. https://doi.org/10.1016/j.explore.2018.07.003

}}

==External links==
* {{Citation|title=The Science of Self Control: Find Motivation, Increase Your Focus, and Hack Dopamine|url=https://www.youtube.com/watch?v=E4rTyhYfZhE|date=2026-01-22|accessdate=2026-08-28|last=Mel Robbins}}&lt;ref&gt;{{Citation|title=The Science of Self Control: Find Motivation, Increase Your Focus, and Hack Dopamine|url=https://www.youtube.com/watch?v=E4rTyhYfZhE|date=2026-01-22|accessdate=2026-08-28|last=Mel Robbins}}&lt;/ref&gt;
* Wypych,&amp;#x20;Marek&amp;#x3B;&amp;#x20;Matuszewski,&amp;#x20;Jacek&amp;#x3B;&amp;#x20;Dragan,&amp;#x20;Wojciech Ł&amp;#x20;(2018-06-05).&amp;#x20;&quot;Roles of Impulsivity, Motivation, and Emotion Regulation in Procrastination – Path Analysis and Comparison Between Students and Non-students&quot;.&amp;#x20;''Frontiers in Psychology''&amp;#x20;(Frontiers)&amp;#x20;'''9'''.&amp;#x20;&lt;ref&gt;{{Cite journal|last=Wypych|first=Marek|last2=Matuszewski|first2=Jacek|last3=Dragan|first3=Wojciech Ł|date=2018-06-05|title=Roles of Impulsivity, Motivation, and Emotion Regulation in Procrastination – Path Analysis and Comparison Between Students and Non-students|url=https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2018.00891/full|journal=Frontiers in Psychology|language=English|publisher=Frontiers|volume=9|doi=10.3389/fpsyg.2018.00891|issn=1664-1078}}&lt;/ref&gt;

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      <text bytes="47038" sha1="acm1pij26hbo4luthq1hj9gqeprecfz" xml:space="preserve">[[File:Pharoah - James VI and I - Trump.png|thumb|Religious and media leaders from the time of the Pharaohs convinced common folk to give increasing shares of what they produced to elites.]]
:''This book uses dates in [[:w:ISO 8601|ISO 8601]], YYYY-MM-DD, when convenient.'' 

== Invitation to edit this book ==

You, dear reader, are invited to contribute questions, ideas and citations to support or refute claims made in this book possibly adding chapters. Wikiversity like other Wikimedia Foundation Projects invites humans to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] while writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]]. Others are invited to change or revert what you wrote. What stays tends to be written from a neutral point of view citing credible sources. If someone reverts your edit or you have a question, take it to the ''[[Wikiversity:FAQ|''''“Discuss”'''' page]]'' associated with the specific Wikiversity page most related to your concerns. 

Those who teach media literacy are encouraged to invite their students to debate and revise the contents of this book. Doing so would build on a tradition of [[:w:Wikipedia:Student assignments|instructors requiring students to edit wikipedia article(s).]]  Editing [[:w:Wikipedia|Wikipedia]] and other [[:w:Wikimedia Foundation|Wikimedia Foundation]] projects like this book is itself an exercise in media literacy: 

:''Central tenets of media literacy might include writing from a neutral point of view citing credible sources and engaging others, some of whom may disagree, in civil, supportive conversations about what can and cannot be said based on a reasonable evaluation of the available evidence. Wikimedia rules invite contributors to do just that, encouraging them to “be bold but not reckless,” contributing revisions written from a neutral point of view, citing credible sources -- and raising other questions and concerns on the ''''“Discuss”'''' page associated with the specific Wikiversity page most related to your concerns, as mentioned above.''&lt;ref&gt;For more on this, see Graves (2024).&lt;/ref&gt; 
== Text, self-help book and points of discussion ==

This book is intended as a text, self-help book and points of discussion considering four levels of media literacy: 

:1. '''Think before you share''': Follow the money. Every media organization sells changes in audience behaviors to those who control much of their money. Major media everywhere promote ''entrepreneurs of hate''&lt;ref&gt;Mokyr (2017, p. 60).&lt;/ref&gt; to convince the public to give increasing shares of what they produce to elites to &quot;protect them from designated evil others.&quot; To counter this, DiResta (2024, p. 335) recommends, &quot;Think before you share.&quot;
:2. '''Look for information to contradict preconceptions''' (Disconfirmation bias): [[w:Information is a public good: Designing experiments to improve government#Previous research|Virtually everyone]] (a) thinks they know more than they do ([[w:Overconfidence effect|overconfidence effect]]), and (b) prefers information and sources consistent with preconceptions ([[w:Confirmation bias|confirmation bias]]). The major media everywhere exploit this to please those who control most of the money for the media. Humans can counter this by searching for sources to help us understand our designated enemies. ''If we cannot explain circumstances under which we could see ourselves doing what we see our designated enemies doing, we have not looked hard enough.'' 
:3. '''Talk''': Push ourselves to have friendly supportive conversations with others with whom we may vehemently disagree, seeking common ground, agreeing to disagree agreeably where we differ, and building collaboration on areas of common concern.&lt;ref&gt;Graves and Bailey (2025).&lt;/ref&gt;  
:4. '''Teach''': Humans who develop skills in the first three levels can leverage that knowledge in helping others acquire those skills. If each one teaches two&lt;ref&gt;&quot;[[:w:Each one teach one|Each one teach one]]&quot; is an African-American proverb from the time of legalized slavery. However, if each one teaches only one, the growth in literacy will only be linear. Having &quot;each one teaching two&quot;, on average, unleashes the power of doubling and [[:w:exponential growth|exponential growth]], which has the potential of educating the entirety of humanity in a reasonable period of time -- namely after 33 doublings starting from one.&lt;/ref&gt; in a certain period of time, that time period becomes a [[:w:Doubling time|doubling time]]. Ten doublings is a thousand -- actually 1,024 to be precise.&lt;ref&gt;2 time 2 = 4 times 2 = 8 times 2 = 16 times 2 = 32 times 2 = 64 times 2 = 128 times 2 = 256 times 2 = 512 times 2 = 1024: That's 10 doublings, as anyone with a modest understanding of modern digital [[:w:computer|computer]]s will tell you.&lt;/ref&gt; Twenty doublings become a million. Thirty doublings become a billion. Three more doublings become 8 billion, the [[:w:World population|world population]] as of approximately 2022-11-15.&lt;ref&gt;This book uses dates in [[:w:ISO 8601|ISO 8601]], YYYY-MM-DD, when convenient.&lt;/ref&gt; Many organizations, including several United Nations agencies and the [[Yonty Friesem on media education|Media Education Lab]], have been working on [[w:media literacy|media literacy]] for decades and have trained many.&lt;ref&gt;''[[Wikibooks:Antiracist Activism for Teachers and Students]]'' includes a chapter on [[Wikibooks:Antiracist Activism for Teachers and Students/Points to Consider for Teaching Anti-racism/Media Literacy In Schools|Media Literacy In Schools]].&lt;/ref&gt; This book is being written hoping to increase the effectiveness and accelerate the rate of growth in media literacy and thereby accelerate progress against many of the most pressing issues facing humanity today.&lt;ref&gt;[[w:Nolan Higdon|Nolan Higdon]] and Spencer Graves discussed marketing media literacy in a &quot;[[:Category:Media reform to improve democracy|Media &amp; Democracy]]&quot; episode on, &quot;[[Media literacy and why you should care]]&quot;.&lt;/ref&gt;

Much of this book is a [[w:Monograph|research monograph]] summarizing research that seems to have been underreported by the major media to avoid offending people who control most of the money for the media. These research results seem to be central to major political divisions. Each chapter ends in exercises to help the reader practice media literacy skills and have fun doing it. Remember: 

:''I am entitled to my [[Wiktionary:cockamamie|cockamamie]] ideas, and you are entitled to yours.''

Humor is important but must be offered in a way that does not offend others. If others are offended, they may be less interested in dialogue. The term &quot;cockamamie&quot; is used here, hoping that this style of [[w:Self-deprecation|self-deprecation]] might be more inviting for dialogue.

''Never say, &quot;You're wrong.&quot; Instead, ask, &quot;May I offer a contrary perspective?&quot; Or &quot;May I share with you another view that I've heard?&quot;''

Much of the information in this book seems to have been largely overlooked and perhaps suppressed, apparently because it would either offend people who control substantial portions of the money for the media our would increase the cost of producing news; see the brief discussion of conflicts of interest by the major media in the next &quot;Key claims&quot; section.

==Key claims==

* ''Primary drivers of every major conflict include differences between the media or difference in interpretation that the different parties find credible''.
:-- This works, because everything we think we know is coded in systems of connections between neurons in our brains. These systems are more unique than fingerprints and evolve over time. The words we use do not mean the same to two different humans nor even to the same human at different points in time. In many cases these differences are inconsequential. ''Sometimes they are fatal.''&lt;ref&gt;Graves and Bailey (2026).&lt;/ref&gt;
:-- ''[[w:Social constructionism|Show me someone who knows the truth]], and I will show you someone who is dangerous'' -- especially during war or any other situation where humans may be moved to violence encouraged by their belief system.&lt;ref&gt;[[w:Collateral damage|Collateral damage]] that &quot;they&quot; commit proves to &quot;us&quot; that &quot;they&quot; are subhuman or at best criminally misled and must be resisted by any means necessary. By contrast, collateral damage that &quot;we&quot; commit is unfortunate but necessary.&lt;/ref&gt;
* We can reduce political polarization and violence by sharing this observation with others, including with humans with whom we may vehemently disagree, inviting pleasant conversations, seeking common ground and agreeing to disagree agreeably in other areas, building coalitions for positive change. 
* ''The major media everywhere have [[w:Conflict of interest|conflicts of interest ]] in honestly reporting on [[v:Information is a public good per communications prof Pickard|anything that might offend anyone who controls large portions of the money for the media]].''&lt;ref&gt;Pickard and Graves (2025), accessed 2026-02-08; Pickard (2020).&lt;/ref&gt; 
:--The most important things you need to know to be a responsible citizen will rarely if ever appear in the major media. 
:--[[v:Media Reform Coalition challenges anti-democratic media bias in the UK|British journalist and media reform advocate Dan Hind]] said that the content produced by the [[w:BBC|BBC]] was frivolous, soap opera stuff, because leading media personalities know very little about issues of substance and believe &quot;they might get in trouble if&quot; they produced anything serious. Similar analyses seem to apply to the major media everywhere&lt;ref&gt;Hind and Graves (2025), accessed 2026-02-09.&lt;/ref&gt; but may not apply to non-profit and local media, which seem more likely to produce [[w:Investigative journalism|investigative]] / [[v:Dean Starkman and the watchdog that didn't bark|accountability journalism]]:&lt;ref&gt;Usher and Kim-Leffingwell (2022); see also Starkman and Graves (2025), accessed 2026-02-09.&lt;/ref&gt; [[w:Watchdog journalism|Watchdogs]] tend to protect the people who feed them. Argentine journalist [[w:Horacio Verbitsky|Horacio Verbitsky]] said, &quot;Journalism is disseminating information that someone does not want known; the rest is [[w:propaganda|propaganda]].&quot;&lt;ref&gt;p. 16 in Verbitsky (1997); English translation from [[Wikiquote:Horacio Verbitsky]], accessed 2026-02-09.&lt;/ref&gt;
* ''The major media everywhere create the stage upon which politicians read their lines.'' 
:-- Major media promote ''entrepreneurs of hate''&lt;ref&gt;Mokyr (2017, p. 60).&lt;/ref&gt; to make it easier for elites to pick everyone else's pockets. This is particularly effective with for-profit social media, which make money herding their audience into echo chambers, where erroneous preconceptions are reinforced, increasing political polarization and violence. [[Facebook whistleblower Frances Haugen says|Facebook whistleblower Frances Haugen said]], &quot;The shortest path to a click is anger or hate.&quot; A leading expert on for-profit social media is Renée DiResta,&lt;ref&gt;DiResta (2024).&lt;/ref&gt; whose research documents how lies spread on social media threaten public health and prepped a small army of humans throughout the 2020 US presidential election cycle to believe that there were major deficiencies in the integrity of US election procedures. When Trump lost, he was able to recruit [[w:January 6 United States Capitol attack|a crowd to attack the capitol on January 6, 2021]]. Social media influencers made so much money spreading lies that it seemed profitable for them to file frivolous lawsuits ([[w:Strategic lawsuit against public participation|SLAPP]]), hoping that DiResta's legal bills would convince her to stop trying to expose their lies. After Republicans regained control of the US House in 2022, they subpoenaed her, claiming she had taken orders from the &quot;[[w:Deep state|deep state]]&quot; to tell Facebook to censor conservatives. [[Managing the good and the evils of social media|When interviewed for ''Media &amp; Democracy'', she reported legal bills of $7 million]]. 
:-- The social psychology behind this phenomenon exploits especially [[w:confirmation bias|confirmation bias]]. It has contributed to [[Media Literacy and You/Media consolidation, social media, and political polarization|the dramatic increase in political polarization and violence worldwide]], especially since the end of the [[w:Fairness doctrine|Fairness doctrine]] in 1987. 
:-- Democracy may be best protected by local news nonprofits, managed jointly by journalists and boards selected at random from registered voters, according to Pickard (2023), discussed in the section below on &quot;[[Media Literacy and You#Government subsidies for news|Government subsidies for news]]&quot;.
:-- Their selection of acceptable topics for news and entertainment create and maintain the &quot;[[w:Overton window|Overton window]]&quot;, which is the range of acceptable political discourse. For example, in early 1964, US President [[w:Lyndon B. Johnson|Lyndon Johnson]] understood that he could lose the 1964 presidential election that year if he were seen to be soft on communism. His response was to clandestinely provoke an attack on US naval vessels in the Gulf of Tonkin, which he could then denounce as &quot;unprovoked&quot;. During a dark and stormy night 1964-08-04 the [[w:USS Maddox (DD-731)|USS ''Maddox'']] and [[w:USS Turner Joy|''Turner Joy'']] spent a couple of hours &quot;defending themselves&quot; against radar snow, then [[w:Gulf of Tonkin incident|reported that they had sunk two attacking North Vietnamese torpedo boats]]; subsequent investigations found no evidence of the reported attacks. That incident was used to justify the [[w:Gulf of Tonkin Resolution|Gulf of Tonkin Resolution]], with only two dissenting votes in the US Congress: Those two dissenters were defeated in their next reelection campaigns, illustrating the point that 

::''the major media create the environment in which many politicians cannot get elected without betraying the nation.''
 
:-- Nick Hart,&lt;ref name=Hart&gt;&lt;!--Nick Hart--&gt;{{cite Q|Q135663983}}&lt;/ref&gt; President and CEO of the Data Foundation,&lt;ref&gt;&lt;!--Data Foundation--&gt;{{cite Q|Q134705118}}&lt;/ref&gt; noted that President Trump in his first term signed the [[w:Foundations for Evidence-Based Policymaking Act|Foundations for Evidence-Based Policymaking Act]] of 2019, which was bipartisan legislation ostensibly mandating evidence-informed public policy.&lt;ref&gt;Hart mentioned the [[w:Foundations for Evidence-Based Policymaking Act|Foundations for Evidence-Based Policymaking Act]] when he was interviewed for [[Evidence-informed public policy|&quot;Media &amp; Democracy&quot; 2025-07-31]].&lt;/ref&gt; Tragically, the record since 2019 suggests that, 

::''The US Congress is rarely allowed to consider solid research suppressed by the major media.'' 

* ''The development of technology is never neutral in its impact on inequality but is driven to benefit people with power.''&lt;ref&gt;Acemoglu and Johnson (2023)&lt;/ref&gt;. 
:-- [[Media Literacy and You/The impact of the media on political economy since the time of the Pharaohs|Improvements in agricultural technology from pre-history to the time of King James of the King James bible were managed to benefit elites.]] Then pamphlets and newspapers began to appear, the head of state stopped granting as many monopolies, and commoners began getting permission to become entrepreneurs. That transformed economic stagnation into growth in GDP per capita adjusted for inflation, initiating the [[w:Industrial Revolution|Industrial Revolution]], as documented in the chapter below on [[/The impact of the media on political economy since the time of the Pharaohs/]]. It also led to increasing inequality until organized labor got enough political power to demand and get a bigger share of the fruits of their labors. 
:--[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|In the US those benefits peaked during the Great Depression]], when the standard conservative mantra that blames the poor for their poverty did not sell newspapers. US President Franklin Roosevelt taxed the ultra-wealthy like they had never been taxed before or since, and dramatically reduced inequality, which continued to decline until increasing concentration of ownership of the media ushered in a new era of increasing inequality starting with the presidency of Ronald Reagan. 
:-- [[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future#Role of the media|Acemoglu and Johnson insist that technology, including artificial intelligence, can be developed to benefit all. However, but it will not happen without action by the poor and middle class as follows]]: 
:# Alter the narrative, 
:# Build countervailing powers [like organized labor], and 
:# Develop technical, regulatory, and policy solutions to tackle specific aspects of technology’s social bias.&lt;ref&gt;Acemoglu and Johnson (2023, ch. 11).&lt;/ref&gt;
:-- For more on this, see, e.g., the chapter on [[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Fox, the Great Depression, the Great Recession, and our future]]. 

=== The value of noncommercial news outlets ===

Some of the problems with the media and their contributions to increasing political polarization and violence are documented in the research summary on &quot;[[Information is a public good: Designing experiments to improve government]]&quot; and in the podcast series available on Wikiversity under &quot;[[:Category:Media reform to improve democracy]]&quot; with leading experts discussing their recommendations. One of the most compelling of the references discussed in that podcast series is Usher and Kim-Leffingwell (2022), who tallied all the federal prosecutions for political corruption in each of the 94 [[w:United States federal judicial district|US federal court district]]s between 2003 and 2019. During that period, the number of journalists in the US fell by a factor of roughly 3 -- between 60 and 70 percent. They found no statistically significant impact on federal prosecutions for political corruption of that decline in the number of journalists. 

However, each member of the [[w:Institute for Nonprofit News|Institute for Nonprofit News]] (INN) in a federal court district in one year was associated with on average 1.4 additional prosecutions for political corruption the following year. Since federal prosecutions for political corruption averaged roughly 10 per federal court district per year during that period, each member of INN in a federal court district one year was associated with a 14 percent increase in federal prosecutions the following year.

This suggests that the major media outlets that had so dramatically reduced their staffs had not substantively reduced the amount of investigative journalism they did. If we assume that the people prosecuted for political corruption also control substantive advertising budgets, then the major media outlets have conflicts of interest in honestly reporting on such. They may report on it if some other organization like a member of INN does the research and they are threatened with a loss of audience from not reporting on it. 

:'''''Major point''''': You and I benefit, the vast majority of humans on earth benefit, from news reports presumably published by members of INN that contributed to those on average 1.4 additional prosecutions for political corruption estimated by Usher and Kim-Leffingwell (2022). We benefit even if we never heard about the news reports that contributed to those prosecutions. We benefit even if we have never heard of the news outlets that presumably did the investigative journalism behind those additional prosecutions. Why? Because on average those news reports likely deterred other incidents of political corruption, which likely contributed to broadly shared economic growth and the development of new technology that ultimately benefit the vast majority of humanity. Other aspects of this are documented in the research on the impact of [[w:news desert|news desert]]s, which we summarize next.

=== Costs increase in news deserts===

There's a growing body of research describing what happens when local newspapers die. 

Perhaps most important, a 2018 research report by Gao et al. reported that the death of a local newspaper was followed by … increases in local tax revenue, averaging $85 per human per year.&lt;ref name = Gao2018&gt;Gao et al. (2018).&lt;/ref&gt; That $85 was roughly 13 hundredths of a percent of the 2019 US GDP. That's mentioned in the 2025-07-17 interview with [[Democratic delusions: Fix the media to fix democracy|Natalie Fenton about her new book, ''Democratic Delusions, How the Media Hollows out democracy and What We Can Do About It'']].

One of the most spectacular example of the cost of a news desert is the [[w:City of Bell scandal|Scandal of Bell, California]]. Their local newspaper died around 1999. Roughly a decade later the city was nearly bankrupt in spite of having property tax rates among the highest in the nation. An investigation by the ''[[w:Los Angeles Times|Los Angeles Times]]'' documented that the city manager had a compensation package worth $1.5 million a year, well over double that of the President of the United States. Other senior city officials were similarly well-remunerated. Some of the city officials went to jail over that. Did the city manager decide after 1999, &quot;Wow: The watchdog is dead. Let's have a party&quot;? 

Malfeasance also increases in business as pollution and workplace accidents increase as does the cost of capital, because investors know their money is not as secure without a local newspaper. That leads to a reduction in investments in new products, services and processes -- slowing economic growth. See &quot;[[Local newspapers limit malfeasance]]&quot;, esp. Kim et al. (2021). 

And executive compensation in increases in nonprofits, so less of what people donate goes to the charitable purpose for which they donated, according to Felix et al. (2024). Also, voter participation and split-ticket voting decline, per Benton (2019) and other references discussed in &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. And the ultra-right does better, as noted in [[News from Germany 1900-1945 and implications for today]] and the section on &quot;[[Information is a public good: Designing experiments to improve government#Previous research|Previous research]]&quot; in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;.&lt;ref&gt;Flößer (2024).&lt;/ref&gt; 

The 0.13 percent of GDP savings estimated by Gao et al. (2018) is roughly $120 per human per year. With over 300 million humans in the U.S, that is roughly $40 billion nationwide. 

{| class=&quot;wikitable&quot;
|+ Table 1. Costs increase in news deserts
|- 
! Entity !! What !!Source
|-
| rowspan=4 |local government || costs +0.13% of GDP || Gao et al. (2018)
|- 
| costs +0.05 - 0.11% of GDP || Baker and Murphy (2026 ) 
|- 
| pol. corruption charges +6.9% || Greenwood (2026)  
|- 
| pol. corruption charges +15% per member of INN || Usher and Kim-Leffingwell (2022) 
|- 
| local businesses || pollution &amp; workplace accidents incr., innovation &amp; econ growth decr. || Kim et al. (2021)
|- 
| nonprofits || exec. compensation incr. || Felix et al. (2024) 
|- 
| rowspan=2 | elections
| voter participation &amp; split-ticket voting decl. || Benton (2019)
|-
| Ultra-right does better || Flößer (2024)
|}

=== Government subsidies for news === 

John (1995) documented how in the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;This is discussed in the 2025-06-08 [[Media concentration per Columbia History Professor Richard John|interview with him]], available on Wikiversity under [[:Category:Media reform to improve democracy]], accessed 2026-04-30.&lt;/ref&gt; This encouraged literacy and limited political corruption, both of which helped [[The Great American Paradox|the early United States stay together and grow]]  while contemporary [[w:New Spain|New Spain]] / [[w:Mexico|Mexico]], fractured, shrank, and stagnated economically. As documented with Figure 1 in the chapter below on [[/The impact of the media on political economy since the time of the Pharaohs/]], that growth catapulted the young United States into its current position of dominance in the international political economy, a position it has been losing since at least 1990 -- or since the Reagan Revolution began in 1981, according to the analysis in the chapter below on [[/Fox, the Great Depression, the Great Recession, and our future/]]. Other countries now have stronger democracies due in part to government subsidies for media in the range of 0.05 and 0.25 percent of GDP with a firewall that limits political interference in the content, according to Neff and Pickard (2024). Table 1 in &quot;[[Information is a public good: Designing experiments to improve government]] compares media subsidies in various places with &quot;other points of reference&quot;.  

McChesney and Nichols (2010, pp. 310-311, note 88) suggested that the relatively high rate of economic growth of the economy in the early US was due in part to postal subsidies under the US [[w:Postal Service Act|Postal Service Act]] of 1792.&lt;ref&gt;See also the Wikiversity article on &quot;[[The Great American Paradox]]&quot;, accessed 2026-04-30.&lt;/ref&gt; They estimated those subsidies at 0.21 percent of GDP. To improve the current political economy of the US, they recommended subsidies of 0.15 percent of GDP distributed to local news nonprofits on the basis of local elections.&lt;ref&gt;McChesney and Nichols (2021, 2022).&lt;/ref&gt; The Wikipedia article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot; documents how some jurisdictions can devote that much money to local news nonprofits by matching what they spend on accounting, advertising, and public relations.&lt;ref&gt;See the section on &quot;[[Information is a public good: Designing experiments to improve government#Sampling units / experimental polities|Sampling units / experimental polities]]&quot; in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;, accessed 2026-04-30.&lt;/ref&gt;  

Pickard (2023) describes three basic strategies for confronting concentrated commercial media power: (1) break them up, (2) regulate them, and (3) create non-commercial, public alternatives. A fourth possibility might be [[w:externality|a graduated tax on income and wealth]] in proportion to the threat that major corporations pose to democracy. 

One class of noncommercial alternatives that Pickard mentions is local multimedia / Public Media Centers (PMCs) with management split between local journalists and boards, e.g., selected at random from registered voters. A key here is to have the boards selected in a way that cannot be influenced by people with power, whether business or political elites. Picard recommends considering '''six discrete layers''' when discussing PMCs, each of which, he says, must be radically democratised: 
# funding, 
# governance, 
# ascertainment (to determine a community’s ''critical information needs''), 
# infrastructure (including universal broadband service), 
# algorithmic (e.g., not allowing companies like Google and Facebook to suppress indexing information the might challenge their hegemony of those markets, [[w:Deep web|treating them like pedophilia and the Islamic State]]), 
# engagement, involving local communities in making their own news and in communicating their own stories; this is paramount to building trust and the grassroots-level support that this new local journalistic model requires.

All this needs to be managed in ways that provide substantive support to news deserts and underserved communities that have long been subjected to various kinds of informational redlining. This might be done by including the proposed PMCs within local libraries staffed by professional journalists, who provide training in media literacy in local schools for children and supervise students producing school newspapers. PMCs could host regular, e.g., monthly events, where local residents could share their concerns with journalist, who would use that input to help prioritize different issues for news coverage. Journalist could also coach local residents in how to research issues and collaborate with journalists in producing news reports that may be better researched and more relevant to local concerns than could be produced without such collaboration.

Management of such PMCs might be split between journalists on staff and boards of, e.g., six members selected at random from voter registration rolls serving staggered terms of one year with a new member rotated in every 2 months.  

Another alternative that could be done in parallel with local PMCs calls for 200 journalists in each US Congressional district funded at $10 billion annually in 2022 dollars, which is just a little under 4 hundredths of one percent of GDP; if such allocations are expressed as fractions of a percent of GDP, they would grow naturally with the economy. (The nominal GDP for the US was roughly $26.1 trillion in 2022.&lt;ref&gt;Johnston and Williamson (2026).&lt;/ref&gt; For 2026 it is estimated at $32.4 trillion.&lt;ref&gt;[[w:United States|United States]], accessed 2026-04-30.&lt;/ref&gt;) 

A similar model is the [[w:BBC|BBC]]’s Local Democracy Reporting Service (LDRS), in which the BBC funds journalists to cover the work of local councils and other local public bodies, funded at £8 million per year, which is a little under 2 hundredths of a percent of the [[w:United Kingdom|UK]]'s GDP of £7.27 trillion.&lt;ref&gt;[[w:United Kingdom|United Kingdom]], accessed 2026-04-30.&lt;/ref&gt; 

Pickard (2023) ended by saying, &quot;Today we face a crossroads: technocracy and oligarchy from above or radical democracy and structural reform from below. ... [T]his is not just a journalism crisis: it is a
democracy crisis.&quot;

==Table of Contents==
*[[/Introduction/]] including an exercise, asking all to discuss perceptions of the settlement of ''[[w:Dominion Voting Systems v. Fox News Network|Dominion Voting Systems v. Fox News Network]]'' in a friendly supportive manner with humans with whom they may vehemently disagree, because the alternative could be killing humans over misunderstandings. 

===Part I. The media and political economy===
# [[/The impact of the media on political economy since the time of the Pharaohs/]] describes how religious leaders in hierarchical societies prior to [[w:James VI and I|King James of the King James bible]] convinced commoners to live in poverty while giving increasing shares of what they produced so religious and secular elites could live in opulence. During the reign of King James, pamphlets and newspapers began to compete with the church for helping commoners understand their roles in society. This produced the Industrial Revolution and modern democracies. Media consolidation since World War II slowed, then reversed this trend. 
# [[/Fox, the Great Depression, the Great Recession, and our future/]] describes the unprecedented performance of the US political economy during the presidency of Franklin Roosevelt (FDR), insisting that much of what FDR achieved can be replicated, giving a media system that supports honest discussion of the available evidence. 
# [[/Media consolidation, social media, and political polarization/]] (Combine from McChesney and Nichols discussing the [[w:Postal Service Act|US Postal Service Act]] of 1792 with [[Media concentration per Columbia History Professor Richard John]], the section on &quot;[[v:Information is a public good: Designing experiments to improve government#Threats from social media|Threats from social media]]&quot; in &quot;[[Information is a public good: Designing experiments to improve government]], and the comments by [[v:Facebook whistleblower Frances Haugen says|Facebook whistleblower Frances Haugen that, &quot;the shortest path to a click is anger or hate.&quot;]].

===Part II. The media and war===
# [[/Deterrence without threat/]]: The historical record is clear: Nations that have prepared for war often got war, not peace. This happens for at least two reasons: First, some leaders cannot resist the temptation to use force inappropriately, sometimes clandestinely provoking others to do things that are then denounced as &quot;unprovoked&quot;; sometimes the media environment pushes them to do such. Alternatively, potential adversaries may believe -- or claim -- that you are actually preparing a first strike, and they must move preemptively or lose their ability to retaliate adequately. We can avoid these possibilities with three supportive policies: [a] Legislation that ''prohibits'' projecting force beyond our own borders. [b] Civilian-based defense training in nonviolent noncooperation like what helped Denmark survive Nazi occupation with minimal damage. And [c] a media system that penalizes rather than encourages a bellicose foreign policy.  
# [[/Responding to a nuclear attack/]]: The ''worst'' response to a nuclear attack would be a nuclear response: The death toll from the 1945 [[w:Atomic bombings of Hiroshima and Nagasaki|Atomic bombings of Hiroshima and Nagasaki]] was estimated at between 150,000 and a quarter of a million. By contrast, simulations of nuclear wars of different magnitudes estimated that between 4 and 95 percent of humanity around the world would starve to death if they did not die of something else sooner. The range depends on whether the war was &quot;limited&quot;, e.g., between India and Pakistan, and massive between the US and Russia. (Also add material from [[Nuclear weapons and effective defense]]). 
# [[/Threats from excessive government secrecy/]] (draft in [https://sanjosepeace.org/restrict-secrecy-more-than-data-collection/ &quot;Restrict secrecy more than data collection&quot;], adding material from [https://kkfi.org/program-episodes/does-us-government-secrecy-threaten-national-security/ Connelly (2023) ''The Declassification Engine: What History Reveals About America's Top Secrets''], [[Wikipedia:Moynihan Commission on Government Secrecy]] and [[1998 Embassy bombings and September 11]].
# [[/Shouting fire in a crowded theater/|Shouting ''fire'' in a crowded theater]]: Legal concerns about &quot;[[w:Shouting fire in a crowded theater|Shouting ''fire'' in a crowded theater]]&quot; date, at least in large part, from the [[w:Supreme Court of the United States|US Supreme Court]] decisions in ''[[w:Schenck v. United States|Schenck v. United States]]'' (1919) and ''[[w: Brandenburg v. Ohio| Brandenburg v. Ohio]]'' (1969). In ''Schenck'' the Court ruled that the government had a right to imprison Schenck and others, because their distribution of fliers encouraging draft resistance presented a [[w:clear and present danger|clear and present danger]] to the efficacy of ongoing military activities during [[w:World War I|World War I]], then in progress. The Court in ''Brandenburg'' held that the government cannot punish inflammatory speech ''unless that speech is &quot;directed to inciting or producing imminent lawless action and is likely to incite or produce such action&quot;.'' Some could argue that many uses of military force by the US and Israel since 1948 have violated international law, encouraged by biases in the major US media &quot;directed to inciting or producing imminent lawless action&quot;, though it may not be feasible to convince a court of that. Still, it might be useful to simulate such a case in a mock trial like the 1966 [[w:Russell Tribunal|Russell Tribunal]].&lt;ref&gt;Andersen (2006) provides such documentation for several such uses of force. Andersen (2026) and Johnson (2026) organize evidence supporting such claims for the current [[w:Gaza war|Gaza war]], which began with [[w:October 7 attacks|Palestinian attacks 2023-10-07]]. Might, e.g., Palestinians -- or at least Palestinian Americans -- be able to sue the [[w:Anti-Defamation League|Anti-Defamation League]] (ADL), the [[w:AIPAC|American Israel Public Affairs Committee]] (AIPAC), and all the major media outlets in the US for inciting genocide in the current [[w:Gaza war|Gaza war]]? That history includes routine suppression of coverage by the major media especially in the US of routine denial of equal protection of Israeli laws to non-Jews in Israel and under Israeli occupation, including suppression of Israeli violence against nonviolent protestors peaceably assembling and petitioning for a redress of grievances combined with over reporting of Palestinian violence and unquestioning coverage of fraudulent claims of Palestinian violence by Israel and supporters. The suppressions included underreporting of Palestinian nonviolence such as the [[w:2018–2019 Gaza border protests|(2018-2019) Great March of Return]], and suppression of the grievances inspiring such nonviolence such as indefinite detention without charges of thousands of Palestinians, including children, routine destruction of Palestinian property by settlers, confiscation of Palestinian property at gunpoint, closing [[w:Gaza Strip|Gaza]] to international trade, and maintaining Gaza on starvation rations. These routine biases in reporting have been encouraged by charges that more honest reporting would be &quot;[[w:Antisemitism|antisemetic]],  according to the ADL and AIPAC. This denial of coverage thereby encouraged Israel to increase the rate of such violations until the [[w:October 7 attacks|2023-10-07 attacks on Israel from Gaza]] unleashed Israeli &quot;retaliations&quot; way out of proportion to the alleged provocation. Sucharov (2022) reported that 69% of American Jews opposed privileging Jews over non-Jews in Israel. Their support of Israel in the current Gaza war is consistent with the media biases documented by Johnson (2026) and others including Andersen (2006, 2026). Regarding whether Israel could achieve anything positive from this war, Samuelson (2025) is skeptical. He summarized quantitative analyses of 60 previous insurgencies. The results including the observation that it is exceedingly difficult to defeat an insurgency without responding to the grievances that support it without force ratios far beyond Israel's resources.&lt;/ref&gt;

===Part III. Climate, immigrants, education, public health, and criminal justice===
# [[/Global warming/]] [Summarize research especially on conflicts of interest of major media in honestly reporting on this issue and the research on global warming itself and activities of groups concerned about this issue. Decompose into global population times CO2 equivalents per human.] 
# [[/Immigrants/]] [Summarize research documenting that [[w:Sanctuary city|sanctuary cities tend to have higher median incomes and no more crime than non-sanctuary jurisdictions]], and some studies report less crime. Moreover economists have documented that immigrants tend to be more entrepreneurial, overrepresented in patent applications, and generally increasing the rate of economic growth. See, e.g., Aghion et al. (2022) ''The power of creative destruction''; Aghion shared the 2025 Nobel Memorial Prize in Economics with two others.] 
# [[/Education/]] (draft in [[Invest in children]].) 
# [[/Public health/]] [Draft in [[UN public health data]] to be revised to be consistent with Bezruchka (2023, 2025).]
# [[/Substance abuse and addictive behavior/]] (Research cited in &quot;[[Wikipedia:War on drugs]]&quot; insists that the US and the world would have fewer problems with substance abuse and addiction problems with 100 percent public funding for treatment programs and complete decriminalization of possession and use of retail quantities of addictive substances. We would also likely have fewer problems with immigrants, as that would make it harder for the US to intervene in the internal affairs of foreign countries funded off the books, as exposed in the [[w:Iran–Contra affair|Iran–Contra affair]]. See [[w:Alfred W. McCoy|Alfred W. McCoy]] (1972; 3rd ed. 2003) ''The politics of heroin''. Journalist [[w:Gary Webb|Gary Webb]] published similar claims that the US intervention in Nicaragua in the Iran-Contra Affair was funded in part by drug money. The story was officially retracted by the ''San José Mercury News'', and Webb allegedly killed himself with 2 bullets to the head.
# [[/Criminal justice/]] (The section on &quot;[[w:United States incarceration rate#Editorial policies of major media|Editorial policies of major media]]&quot; in &quot;[[Wikipedia:United States incarceration rate]]&quot; cites research claiming that within the range range of experience in the US political economy since 1925, the incarceration rate is uncorrelated with crime: It's a function of the public's perception of crime, and that's a function of the media. That suggest that the US would be safer and more prosperous if incarceration policies were driving more by research than by editorial policies of the media. For example, there is also research that says that incarcerees who receive visits are less likely to recidivate, but that evidence is overlooked when convicts are incarcerated substantial distance from their family and friends and when the cost of phone services is substantially higher for incarcerees than among the general pubic. Also, it's known that better educated incarcerees are less likely to recidivate, but it's difficult and maybe impossible for many incarcerees to obtain education in prison.) 
# [[/Empower women and girls/]] [Cite research claiming that a primary restraint on population growth is empowering women and girls. Empowering women and girls is not just a matter of equity: It is also a means to reduce the threats of global warming, of increasing exposure to animal diseases and other problems that come with unrestrained population growth.]

=== Continuation ===

* [[/The evolving media literacy movement/]] to invite others to keep this book current with the evolving understanding of media literacy, how to encourage and promote it and the benefits of doing so.

==See also==

* [[Wikibooks:Antiracist Activism for Teachers and Students/Points to Consider for Teaching Anti-racism/Media Literacy In Schools]]

==Notes==
{{reflist}}
	
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* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* [[d:Q131398359|Victor Pickard (2020) ''Democracy without journalism? : confronting the misinformation society'' (Oxford U. Pr.)]].
* &lt;!-- Victor Pickard (2023-05-12) &quot;Another Media System is Possible: Ripping Open the Overton Window, from Platforms to Public Broadcasting&quot;--&gt;{{cite Q|Q131398460}}
* &lt;!--Doug Samuelson (2025)  Assessing Israel’s Approach in Gaza--&gt;{{cite Q|Q138843324}} 
* [[d:Q138037937|Dean Starkman and Spencer Graves (2025) &quot;Dean Starkman and the watchdog that didn't bark anglais&quot; on Wikiversity]].
* &lt;!--Mira Sucharov (2022)  Do American Jews Really Know What 'Zionist' Means?--&gt;{{cite Q|Q125903777}}
* [[d:Q134715465|Nikki Usher and Sanghoon Kim-Leffingwell (2022) &quot;How Loud Does the Watchdog Bark? A Reconsideration of Local Journalism, News Non-profits, and Political Corruption&quot;, ''SSRN Electronic Journal'']].
* [[d:Q61013892|Horacio Verbitsky (1997) ''Un mundo sin periodistas'' (in Spanish: A world without journalists; Editorial Sudamericana)]].

[[Category:Communication]]
[[Category:Political science]]
[[Category:Law]]
[[Category:Psychology]]
[[Category:Sociology]]
[[Category:Education]]
[[Category:Economics]]
[[Category:Media Literacy and You]]
[[Category:Freedom and abundance]]
&lt;!--
https://en.wikiversity.org/wiki/Category_Review
--&gt;</text>
      <sha1>acm1pij26hbo4luthq1hj9gqeprecfz</sha1>
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  </page>
  <page>
    <title>BIM-126-02-Data-Science-Linked-Open-Exhibition</title>
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      <text bytes="38508" sha1="lv9oq4ns7flf9lq7r29erflue9140pn" xml:space="preserve">==== Linked Open Exhibition ====

DE - See language switch - top right

''Materials and Tasks for the module &quot;BIM-126-02, SoSe 2026, Worthington/Blümel&quot; for students at Hochschule Hannover. The materials are prepared with several colleagues from the [https://www.tib.eu/de/forschung-entwicklung/forschungsgruppen-und-labs/open-science Open Science Lab at TIB] Hannover.''

* Project GitHub repo: https://github.com/NFDI4Culture/linked-open-exhibition
* Single exhibition entry example: https://github.com/NFDI4Culture/prototype-linkedOE
* Exercise: [[Linked-Open-Exhibition-Exercise]]

==== Summary ====
The eight session course covers an introduction to Linked Open Data (LOD) in the context of :

# Open Galleries Libraries Archives and Museums (GLAM), and; 
# The use of Wikimedia Foundation platforms.

The Wikimedia Foundation platforms that will be used are: Wikidata; Wikibase, MediaWiki, and  Wikimedia Commons.

AI LLM will be used in the workflows: Code assistant ''copilot'', and a variety of AI LLM chat services for file generation and configurations to create SPARQL queries, Jinja 2.0 templates, etc. 

„KI-Servicezentrum für Sensible und Kritische Infrastrukturen“ (KISSKI) can be used for unmetered ChatGPT5 https://kisski.gwdg.de/leistungen/2-02-llm-service/ | https://chat-ai.academiccloud.de/chat  

The Methodologies employed are: Open-source software, Open Science, and rapid prototyping.

==== Linked Open Exhibition ====
The question being explored for the class is how can LOD be uséd to benefit museum exhibitions as Linked Open Exhibitions – a record of the exhibition, a catalogues of items in an exhibition, and other important data? As examples '''to gain exhibitions increased visitors numbers and create greater depth of engagement'''.

With a focus of the question on how to make LOD records of '''items in an exhibition'''.

==== Learning points – In order of priority ====

# '''Wikidata/Wikibase LOD concepts:''' Items, Properties, Values, Qualifiers, Wikibase schemas, Classes, Lexemes, Knowledge Base, and Knowledge Graphs.
# '''Linked Open Data (LOD):''' Semantic web, 5 star, RDF/Triples, Ontologies, Taxonomies, and controlled vocabularies.
# '''Using LOD source:''' Identifiers, PIDs, information sources, media sources, and import and export tooling.
# '''Data modelling:''' Methodologies, schema use, visualisation, and testing.
# '''Data workflow tools:''' Git, IDE, AI code assistant (copilot), AI Chat, using Wikimedia Foundation tooling, data import and export tools, generating PIDs and making deposits in a scholarly repository.
# '''Data presentation and data use:''' Wikidata Query Service results, MediaWiki infoboxes, AI Chat SPARQL query processing.
# '''Open Science practice:''' Open-source software, Open Notebook Science, Open Licencing, PIDs, FAIR Data Principles, and ethical and good practice AI use.

==== Sessions ====
The sessions would be about cataloguing Sprengel Museum exhibitions using LOD and how to make visualisations and presentations.

'''Learning to use LOD is the goal of the learning.''' The method will be to build out from a kernel of an ‘exhibition’ and add ‘item in an exhibition’. From the start the students will be the ones who make the LOD. This will start with minimal entries my by the students, then layering these up with – Identifiers, LOD Media sources, schemas, etc. And finally moving onto how to present the data in a way that satisfies the ‘use case’: '''to gain exhibitions increased visitors numbers and create greater depth of engagement'''. Here presentation technologies are used: MediaWiki infoboxes, Wikidata Query Service results, AI Chat SPARQL queries and other features, etc.

==== Session 1: Exhibition timeline creation - build out, add exhibitions ====

[[File:Timeline 2026 06 02.jpg|alt=Timeline|left|thumb]]
[[File:Network 2026 06 02.jpg|alt=Graph|left|thumb]]

# Record minimal information for an exhibition in Wikidata as Linked Open Data: Title, museum, date, etc. e.g., https://www.wikidata.org/wiki/Q138547468 –  See: Table 1: ''Minimal data entries for an exhibition''
# View the exhibition record in Wikidata Query Service results link 
## timeline https://w.wiki/J8NJ
## graph https://w.wiki/J8aS 
# Review exhibition entries.
# Cover topics raised by making a LOD entry: Wikidata basics, Wikidata good practice, consulting schemas, importance of review and using GitHub Issues, comparing available data – before and after.
The exercise: Create a Linked Open Data record for an exhibition using Wikidata (minimal entry).

===== A. Creating the exhibition entry in Wikidata. =====
# Login to Wikidata: https://www.wikidata.org/
# Have a source at hand to make a data entry, e.g.,
#* https://www.sprengel-museum.de/ausstellungen/archiv
#* https://www.sprengel-museum.de/besuch?view=article&amp;id=65:publikationen&amp;catid=2:uncategorised
#* https://portal.dnb.de/opac/showFullRecord?currentResultId=sprengel+and+museum+and+ausstellung%26any&amp;currentPosition=1
# Check there is no existing entry for the exhibition is on Wikidata. Use the search function. 
# Create an item or edit an existing item.
#* Note: Check which language you are using. We will be adding Deutsch and English entries (starting with Deutsch).
# Create the following data entries in Wikidata, see: Table 1: ''Minimal data entries for an exhibition.''
# Review exhibition Wikidata entries. Review is carried out by using three questions. Add comments if needed, corrections can be made. Results and notes can be added to the Discussion Page of the entry, e.g., 
#* All entries present [   ]
#* All entries correct [   ]
#* Entries are in Deutsch and English – within reason [   ]

===== ''Table'' ''1: Minimal data entries for an exhibition'' =====
{| class=&quot;wikitable&quot;
| colspan=&quot;7&quot; |'''Fields used to make an exhibition entry. See example: https://www.wikidata.org/wiki/Q138547468'''
|-
|A
|Label
| colspan=&quot;5&quot; |Note: Keep short. Use title from exhibition
|-
|B
|Description
| colspan=&quot;5&quot; |Note: Use to differentiate from other entries. Follow this example: Gabriela Jolowicz Holzschnitte Ausstellung im Sprengel Museum, Hannover, 2026
|-
|
|'''Property (P) and Item (Q)'''
|'''URI'''
|'''DE'''
|'''EN'''
|'''Add'''
|'''Note'''
|-
|1
|P31
|https://www.wikidata.org/wiki/Property:P31
|ist ein(e)
|instance of
|Q464980
|Add item
|-
|2
|Q464980
|https://www.wikidata.org/wiki/Q464980
|Ausstellung
|Exhibition
|
|(Used above)
|-
|3
|P1476
|https://www.wikidata.org/wiki/Property:P1476
|Titel
|Title
|Title
|Plain text
|-
|4
|P276
|https://www.wikidata.org/wiki/Property:P276
|Ort
|Location
|Sprengel Museum Hannover Q510144
|Add item
|-
|5
|P580
|https://www.wikidata.org/wiki/Property:P580
|Startzeitpunkt
|Start time
|Date
|YYYY-MM-DD
|-
|6
|P582
|https://www.wikidata.org/wiki/Property:P582
|Endzeitpunkt
|End time
|Date
|YYYY-MM-DD
|-
|7
|P1640
|https://www.wikidata.org/wiki/Property:P1640
|Kurator
|Curator
|Person
|Add item (if don't exists will need to create/can omit at present)
|-
|8
|P710
|https://www.wikidata.org/wiki/Property:P710
|Teilnehmer
|Participant
|Person (the artist)
|Add item (if don't exists will need to create/can omit at present)
|-
|9
|P856
|https://www.wikidata.org/wiki/Property:P856
|offizielle Website
|Official website
|URL
|URL
|}

===== Homework exercises: Session #1 =====
# Complete your allocated exhibition. Make sure all fields are complete from Table 1. If something cannot be added, either: A. Make a note in the exhibition allocation spreadsheet, or B. Send and email to [mailto:Simon.worththington@tib.eu simon.worththington@tib.eu] and I will help resolve your issue.  '''Note: If you did not create an exhibition entry during the class make sure one is complete before the next class.'''
# Create a GitHub account and add your GitHub handle next to your name, column ‘GitHub handle’,  in the exhibition allocation spreadsheet.
# Review your classmates exhibition entries. You have all been allocated a entry to review, see the Exhibition Allocation spreadsheet. Your name will be in column G. This first review has three questions – tick the boxes to show if each item has been complete and either add comments or correct the Wikidata exhibition entry.  '''Note: If your allocated Exhibition entry hasn’t been made by you classmate then please contact them and ask them to complete the entry.'''  Questions are:
## Are all the required fields present?
## Are all the fields correct?
## Is there an Deutsch and English entry?


END of SESSION 1

---

==== Session 2: Exhibition cataloguing - build up, add items, artists, catalogues ====
The session has five exercies:

# Exhibition update
# Artist
# Exhibition catalogue
# AI LLM SPARQL experiments
# &lt;s&gt;Artwork&lt;/s&gt;

The exercises include the following concepts:

==== Exercises ====

==== 1. Exhibition updates ====

* Homework review: Complete all fields for an exhibition. Review your assigned review exhibition answering the three questions:

&lt;blockquote&gt;[ ] Sind alle erforderlichen Felder vorhanden?

[ ] Sind alle Felder korrekt ausgefüllt?

[ ] Gibt es einen Eintrag in Deutsch und Englisch&lt;/blockquote&gt;

* For the label. Convert words in all caps to sentence case. Use: https://convertcase.net/title-case-converter/ | Change from, e.g., ADRIAN SAUER: TRUTH TABLESPECTRUM INTERNATIONALER PREIS FÜR FOTOGRAFIE DER STIFTUNG NIEDERSACHSEN to  Adrian Sauer: Truth Tablespectrum Internationaler Preis Für Fotografie Der Stiftung Niedersachsen.

* Add the English language versions. Use DeepL to translate: https://www.deepl.com/en/translator
** Title: Add English title

* Add the following. Change P710 Teilnehmer (Participant) to P921 zentrales Thema '''artists name.''' 
** Qualifier on central theme to indicate the person is contributing artwork.

* Use: Qualifier P170 creator and add artist Q483501 (type artists and it will automcomplete)

* Reference: Gemeinsame Normdatei (GND) ID for a person, e.g., Gabriela Jolowicz https://d-nb.info/gnd/134184963 | Search your persons name and copy in the last part of number 134184963
* Talk page: Add in the review questions for your Wikidata entry:

&lt;blockquote&gt;[ ] Sind alle erforderlichen Felder vorhanden?

[ ] Sind alle Felder korrekt ausgefüllt?

[ ] Gibt es einen Eintrag in Deutsch und Englisch?&lt;/blockquote&gt;Notice the useful links that tell you more about connected Linked Open Data!

Note: SPARQL query showing data model. Properties and and values. Results: https://w.wiki/JMLX Made with Gemini AI: https://gemini.google.com/share/c43f34a67f67

==== Concepts ====

* Wikidata parts – see about and diagram:
** https://www.wikidata.org/wiki/Wikidata:Introduction/de
** https://www.wikidata.org/wiki/Wikidata:Introduction#/media/File:Datamodel_in_Wikidata.svg
* Applying a review process using Talk pages
* Adding References
* Using a type of LOD source – '''An authority record''' Gemeinsame Normdatei (GND) ID https://portal.dnb.de/opac.htm  
* SPARQL query

---

==== 2. Artists ====
The objective here is to ensure all artists have been included in exhibition listing and to then review the existing artists entry.

Later a SPARQL query will be made to compare statements about all the artists in our dataset.

* Before reviewing artists items make sure all artists have been listed in the exhibition item, with qualifier of being an artist and a reference to their GND record.

===== Important statements =====
{| class=&quot;wikitable&quot;
|Concept
|CIDOC CRM (Full)
|Linked Art (Selection)
|Wikidata Equivalent
|Note
|-
|Entity
|E21 Person
|Person
|Q5 (human)
|The base instance.
|-
|Label/Name
|P1 is identified by → E33_E41
|identified_by (Name)
|
|Linked Art flattens this into a simple list of names.
|-
|
|
|
|P735 Given name
|
|-
|
|
|
|P734 Family name
|
|-
|Profession
|P2 has type → E55 Type
|classified_as
|P106 (occupation)
|Map to AAT 300025103 (artist).
|-
|Birth
|P98i was born → E67 Birth
|born (Birth)
|P569 (date of birth)
|CRM treats birth as an event; Wikidata as a property.
|-
|Death
|P100i died in → E69 Death
|died (Death)
|P570 (date of death)
|If the artist is still living, this is omitted.
|-
|Nationality
|P107i member of → E74 Group
|classified_as (Type)
|P27 (citizenship)
|Linked Art often models nationality as a Type.
|-
|Reference
|P1 identifies ← E42 Identifier
|identified_by (Identifier)
|QID (The URI itself)
|Used to link to external authorities (ULAN, VIAF).
|-
|Commons category
|?
|?
|P373 search name
|&lt;nowiki&gt;https://commons.wikimedia.org/&lt;/nowiki&gt;
|}


From Google Gemini: https://gemini.google.com/share/578cc1b886d0

---

===== Schemas and communities need consulting. =====
From Wikimedia:

* WikiProject Visual Arts: https://en.wikipedia.org/wiki/Wikipedia:WikiProject_Visual_arts
* Wikiproject Exhibitions: https://www.wikidata.org/wiki/Wikidata:WikiProject_Exhibitions

Semi-formal

Generic Wikibase Model for Cultural Data: https://kgi4nfdi.github.io/Guidelines/guide/wikibase/data_modelling_import/

Formal:

CIDOC Conceptual Reference Model (CRM) - https://cidoc-crm.org/

Linked Art (based on CIDOC) https://linked.art/model/actor/

Iconclass https://www.inconclass.org/

AAT &lt;nowiki&gt;https://www.getty.edu/research/tools/vocabularies/aat/&lt;/nowiki&gt; 

==== Concepts ====

* Data modeling
* Schemas
* Use case
* Bottom up design
* Identifiers

---

==== 3. Exhibition Catalogue ====
Search in both of these two places to find information about the catalogue for your assigned exhibition.

* Sprengel Museum publication catalogue - https://www.sprengel-museum.de/besuch?view=article&amp;id=65:publikationen&amp;catid=2:uncategorised
* DND (example) you can search for the exhibition name or Sprengel Museum '''-'''  https://portal.dnb.de/opac/simpleSearch?query=sprengel+and+museum+and+ausstellung&amp;cqlMode=true 

''Note: Make a note of any links you find in the exhibition listings spreadsheet.''

===== Make a Wikidata entry for the catalogue =====
Note: first search for publication before making Wikidata entry. Use title, use ISBN, use GND.

An example publication from DNB and Sprengel Shop.

* https://portal.dnb.de/opac/showFullRecord?currentResultId=Gabriela+and+Jolowicz%26any&amp;currentPosition=0
* https://www.sprengel-museum.de/besuch?view=article&amp;id=65:publikationen&amp;catid=2:uncategorised

===== Enter these statements =====
Note: Remember Label and Description
{| class=&quot;wikitable&quot;
|Property
|Label
|Description/Example
|-
|P31
|instance of
|catalogue (Q2352616)
|-
|P1476
|title
|The official title of the catalogue (e.g., Vermeer and the Masters of Genre Painting)
|-
|P50
|author
|The main curator or art historian (item link)
|-
|P123
|publisher
|The museum or publishing house (e.g., Louvre Museum)
|-
|P577
|publication date
|Year of release (e.g., 2024)
|-
|P212
|ISBN-13
|The 13-digit standard book identifier
|-
|
|GND
|ID
|-
|P973
|described at URL
|A link to the catalogue's page on the museum’s website
|}
Google Gemini  https://gemini.google.com/share/9a21f5522192

Example input: https://www.wikidata.org/wiki/Q138646145

===== Link the record back to the exhibition =====
P972	Title

==== Concepts ====

* Data modeling
* Identifier
* Data as CC Zero / Copyright of data
---

==== 4. AI LLM SPARQL experiments ====
The Wikidata has a SPARQL interface where the LOD in Wikidata can be searched (queried) and outputted in a number of ways, formats, and a visualisations. As well as being saved on the web.

We will us AI LLM chat to generate SPARQL queries.

Later we will learn the fundamentals of writing a SPARQL query. But for the moment we want to see how they have be generated, the options, and creative applications.

Using chat services or code assistants can be a valuable way to learn about new technologies.
{| class=&quot;wikitable&quot;
|Service
|Best For
|Standout Feature
|Key Model(s)
|-
|'''ChatGPT'''
|General Use &amp; Tasks
|Deep Research &amp; Agent Mode
|GPT-5.4, GPT-5
|-
|'''Claude'''
|Coding &amp; Writing
|Artifacts (interactive workspace)
|Claude 4.5, 4.6
|-
|'''Google Gemini'''
|Google Ecosystem
|Nano Banana (native image/video)
|Gemini 3.1 Pro
|-
|Perplexity
|Real-time Research
|Native Citations &amp; Search Labs
|Sonar, GPT-5, Claude
|-
|MS Copilot
|Office Productivity
|Copilot Vision &amp; 365 Integration
|GPT-5.2, Prometheus
|-
|DeepSeek
|Logical Reasoning
|High-tier performance at low cost
|DeepSeek-V3, R1
|-
|Grok
|Real-time Social Info
|Unfiltered X (Twitter) integration
|Grok 4.1
|-
|'''Meta AI'''
|Social Media
|Seamless integration in WhatsApp/IG
|Llama 4 (Scout)
|-
|Poe
|Model Testing
|Access multiple LLMs in one app
|Multi-model aggregator
|-
|Mistral (Le Chat)
|Privacy &amp; Developers
|European-hosted, GDPR-focused
|Mistral Large 3
|}
Some of these can also be used via KISSKI

„KI-Servicezentrum für Sensible und Kritische Infrastrukturen“ (KISSKI) can be used for unmetered ChatGPT5 https://kisski.gwdg.de/leistungen/2-02-llm-service/ | https://chat-ai.academiccloud.de/chat  

=== The exercise ===
The group will be split into a number of Zoom breakout groups and then the group spends 20 minutes experimenting generating SPARQL queries and other creative applications.

Paste in results here: https://tib.cloud/apps/files/files/8251374?dir=/NFDI4Culture/HsH/BIM26/bim26-shared&amp;editing=false&amp;openfile=true 

Each room is assigned a Chat engine.

Maximum there will be four groups.

·      Group #1: '''ChatGPT'''

·      Group #2: '''Claude'''

·      Group #3: '''Google Gemini'''

·       Group #4: '''Meta AI'''

=== Example exercise ===
Chat bots can read  a SPARQL query or a Wikidata address.

e.g.,

Item https://www.wikidata.org/wiki/Q138547468

query graph https://w.wiki/JPNc

query timeline https://w.wiki/JPPN

Item Sprengel Museum https://www.wikidata.org/wiki/Q510144 

Then the chatbot can be instructed to do things based on the information provided.

You should ask the chat bot to generate Wikidata SPARQL queries and then paste the queries into the SPARQL querie interface. https://query.wikidata.org/

Use these examples and invent your own:

# Create dashboard (count of things)
# Create inventory (table)
# Create graph data model

Some output SPARQL queries

·       Map of artists place of birth - https://w.wiki/JPT3 

·       List of exhibitions - https://w.wiki/JPR3 

·       As plot of exhibitions - https://w.wiki/J8aS

==== Homework: Session 2 ====
Create a bottom up  data model of an artwork in an exhibition. Include only the minimum information needed. The result should be a table like the ones presented for exhibition, artist, and catalogue. The table should include properties and attributes. You should consult the schemas mentioned above. You can use AI but attribute the AI and link to your question. If you use AI review the results and make notes about what you changed.

Note: Think about how parts are related and what you need to add and what already exists in Wikidata.

Submit your results as a spreadsheet or table.  

===== Session 3: Museum visit - Sprengel Museum =====
19 March 2026

===== Session #4: Schemas and Prototyping (the end of class project) =====

===== Recap and outline =====
Done

* Creating exhibition entries in Wikidata
* Filling our data models for Artist and Catalogue
* Exploring the museum and its activities to help steer the prototype

To do

* Decide on the ideas for the prototype
* Data model for items in an exhibition (Artwork and Exhibition)
* Complete a data model for the end of the project that can be used by museums and complies to the sector standards – CIDOC and Wikidata.

===== What have we learned about the ‘Museum’s Story’ =====
TBC

===== Schemas =====
An opportunity to become familiar with how Linked Open Data is structured using common agreements on  working practices.

Over the period of the course a data model will be developed and finalised to describe ‘items in an exhibition’. The data model will be published  for community consultation and testing.

===== Schemas and key concepts =====
Table: https://tib.cloud/s/ZKNAAo3B8ATXsAP 

* Schema
* Terminology Service
* Controlled Vocabulary
* Taxonomy
* Ontology
* Knowledge Graph

Table X: link: https://tib.cloud/s/ZKNAAo3B8ATXsAP Terminology used in Linked Open Data (LOD) 
{| class=&quot;wikitable&quot; 
|-
! **Concept**
! **Wikidata link (Concept)**
! **Primary Focus**
! **Analogy**
! **Example resource**
! **URL**
! **Example use**
! **URL**
|-
| Schema
| Q1397073
| Data Structure
| The Template. Conceptual schema / data model
| Schema.org
| https://schema.org/
| VisualArtwork
| https://schema.org/VisualArtwork
|-
|
|
|
|
|
|
| Smithsonian American Art Museum (SAAM) &quot;Among the Sierra Nevada, California&quot;
| https://www.wikidata.org/wiki/Q20475372
|-
| Terminology Service
| Q22692845
| Distribution
| A Library of Vocabularies, Schemas, Ontologies, etc
| TIB Terminology Service
| https://terminology.tib.eu/ts/
| NFDI4CULTURE
| https://terminology.tib.eu/ts/ontologies?and=false&amp;page=1&amp;sortedBy=title&amp;size=10&amp;collection=NFDI4CULTURE
|-
| Controlled Vocabulary
| Q1469824
| Consistency
| The Dictionary
| Integrated Authority File / die Gemeinsame Normdatei (GND)
| https://portal.dnb.de/opac/showShortList
| Persons: Dürer, Albrecht
| https://d-nb.info/gnd/117751669
|-
| Taxonomy
| Q8269924
| Hierarchy
| Sorting things by type (general classification)
| Getty Art &amp; Architecture Thesaurus (AAT)
| https://www.getty.edu/research/tools/vocabularies/aat/
| German Surrealist Max Ernst (painting techniques used)
| https://www.guggenheim-venice.it/en/art/conservation-department-new/technical-studies-and-conservation-campaigns/portrait-of-an-artist-at-work-max-ernsts-surrealist-techniques/#:~:text=Frottage%20and%20Grattage,in%20his%20drawings%20in%201925.
|-
|
|
|
|
| Iconclass
| https://iconclass.org/
| Max Ernst’s &quot;The Virgin Spanking the Christ Child&quot; (Parady)
| https://www.wikiart.org/en/max-ernst/the-virgin-spanking-the-christ-child-before-three-witnesses-andre-breton-paul-eluard-and-the-1926
|-
| Ontology
| Q324254
| Semantics: Meaning &amp; logic (information science)
| The Rulebook or Writing Style Guide
| CIDOC (Comité International pour la DOCumentation / International Committee for Documentation)
| https://cidoc-crm.org/
| Sloane Lab Knowledge Base - unifying 3 collections
| https://knowledgebase.sloanelab.org/resource/Start
|-
| Knowledge Graph
| Q33002955
| Network of things and relations
| A Navigational Map
| Census of Antique Works of Art and Architecture Known in the Renaissance
| https://www.census.de/
| Artemis search
| https://database.census.de/#/detail/10013099
|-
|
|
|
|
| Research Space
| https://researchspace.org/
| Hokusai: The Great Picture Book of Everything
| https://hokusai-great-picture-book-everything.researchspace.org/resource/rsp:Start
|}

===== Schemas exercise =====
Spreadsheet to work on: https://tib.cloud/s/PicTdwCEqCQ6pBp

(password: bim2026)

We will be looking at: Exhibition, Artist, and Catalogue.

'''''Enter the URLs found. Add new rows, columns, comments if needed. Keep manual searches as well as AI searches for comparison.'''''

===== Exercise #1: Enter links into the spreadsheet of matching items from the following: =====

* Wikidata:WikiProject Exhibitions/Properties
* Generic Wikibase Model for Cultural Data - Wikibase4Research NFDI4Culture
* CIDOC CRM (Full)
* Terminology Service (NFDII4Culture)
* Wikidata

===== Exercise #2: Use AI LLM to find matching items =====

* https://gemini.google.com/ 

==== Prototyping ====
Either in this session or in the next session the group will be divided into teams.

===== Schema =====

# Data model development: ‘items in an exhibition’

===== Quarto publication parts =====

# A catalogue of a Sprengel Museum exhibition
# A catalogue of all exhibitions and exhibition catalogues
# Catalogue of exhibition entries
---

==== Learning to use Quarto and inserting an exhibition entry ====
Tools: Quarto, GitHub, VS Code, Jupyter Notebooks, Codespace if needed, copilot: Agentic Coding)

'''Requirements'''

# A laptop or computer where you can install VScode
# You will need 2FA on your mobile (optional)
# Create a GitHub account
# Install VScode
# Connect Github account to VScode
# Create GitHub reposoitory

'''Fork the following repository:''' https://github.com/mrchristian/prototype 

'''Model: Auto'''

'''How the repo was setup. Agent promts:'''&lt;blockquote&gt;''I want to run a Quarto website project, please setup the basics. The project will be published on GitHub Pages. Set the output directory to docs.'' &lt;/blockquote&gt;Create a page for the quarto project that retrieves the data used for thie Wikidata item and renders it as  professional webpage ''&lt;Insert your exhibition here – or use this one&gt;''  https://www.wikidata.org/wiki/Q138547468 The approach should create a SPARQL query for the data and then render this as HTML using a Jupyter Notebook.

All entries: https://tib.cloud/s/fncf8W6pXs8qgiq (needs password)

===== Tasks =====

* Change exhibition - manual
* Run Jupyter Notebook 
* Run and preview Quarto 
* Publish to your GitHub Pages 

===== Step-by-step =====

====== Part one: Working environment ======
'''''NOTE: If you are having problems running locally then use the Codespace online option.'''''

# Create GitHub account - https://github.com/
# Have 2FA available - usually on mobile (Google authenticator) (optional)
# Install VSCode - https://code.visualstudio.com/download
# Install GitHub Desktop - https://desktop.github.com/download/
# Add Github account when prompted, use 2FA

====== Step two: The prototype ======
# Fork the repository:  https://github.com/mrchristian/prototype
# If working locally continue - if using Codespace - launch Codespace (see below and then continue)
# Test Quarto in the Terminal: 
## &lt;code&gt;quarto check&lt;/code&gt; 
## &lt;code&gt;quarto render&lt;/code&gt;
## &lt;code&gt;quarto preview&lt;/code&gt; (control C - to stop)
# If not working run Quarto from Agent
# Change Wikidata exhibition in Notebook
# Run notebook
# Run &lt;code&gt;quarto render&lt;/code&gt; &lt;code&gt;quarto preview&lt;/code&gt;
# Save all (or use auto save)
# Git: Message, Commit and Push
# On GitHub.com your repository
## Turn on Pages: GitHub Actions
## Code: About cog - Click use my GitHub Pages
## Actions tab: Publish Quarto Project
# ENDE - Rinse repeat  :-)

===== Codespace option: =====
Videolink: https://tib.cloud/s/LDtkN6QsdFkGGR6 (10 Minuten Zeit)

Codespace is an online Virtual Machine which can be launched from GitHub.

The repository includes a Dev Container configuration so you can work entirely in the browser without installing anything locally.

# On the repository page on GitHub, click Code → Codespaces → Create codespace on main.
# Wait for the container to build — Python packages from &lt;code&gt;requirements.txt&lt;/code&gt; are installed automatically - about 5 minutes.
# Once everything is installed the Codespace can be used anytime. It automatically shutsdown when left alone and can be restarted any time.
# Work done in Codespace must be pushed back to the repository.
# If Codespace is not used for 28 days the Codespace is deleted.

---

===== Homework - session #4 =====

* Get all books from HsH library that are Sprengel Museum exhibition catalogues. Bring to the next class
* Make an exhibition entry if not done
* Work with VSCode and the Agent and experiment
* Add entries from existing ontologies: https://tib.cloud/s/PicTdwCEqCQ6pBp?dir=/&amp;editing=false&amp;openfile=true

==== Sitzung 5: Prototyping: Running Quarto Prototype, Federation, Prototype Teams ====

* Running Quarto Prototype - https://github.com/mrchristian/prototype 
* DNB data download https://github.com/NFDI4Culture/linked-open-exhibition
* Data Federation - WB4R

===== Links =====
https://wikibase.wbworkshop.tibwiki.io/wiki/Main_Page

Glossar - https://nfdi4culture.github.io/linked-open-exhibition/Documentation/glossary

===== DNB Search =====
https://portal.dnb.de/opac/moveDown?currentResultId=Sprengel+and+Museum%26any&amp;categoryId=books

Sprengel Museum, 602 Artikel

'''About the DNB'''
https://www.dnb.de/librarylab
https://deutsche-nationalbibliothek.github.io/jupyterlite/lab/

'''Also'''

https://wiki.dnb.de/spaces/LINKEDDATASERVICE/pages/449878933/DNB+SPARQL+Service+BETA

===== Prototype Teams =====

* DNB Data
* Katalog scan
* Exhibition entries
* Datenmodell (alle)
===== --- =====

== Session 6: Class Project – Prototyping: ''Linked Open Exhibitions'' ==
Prototype URL (currently 2026-04-29 a shell framework): https://nfdi4culture.github.io/linked-open-exhibition/  

==== Program: ====
11:30 – 11:50 (20 min)  '''Outline: Class Project – Prototyping: Linked Open Exhibitions.''' What is it and what needs to be delivered. Allocation to sub-project and tasks outline. 

'''Activity #1: Bottom-up data modeling: Data mapping'''

11:50 – 12:20 (30 min) Data finding and exploration (break out rooms)

12:20 – 12:40 (20 min) Review data findings (class discussion)

12:40 – 12:55 (15 min) Pause Break

'''Activity #2: Top-down data modeling: Schema mapping'''

12:55 – 13:35 (40 min) Map data against schemas (break out rooms)

13:35 – 13:55 (20 min) Review findings (class discussion)

'''13:55 – 14:15 (20 min) Work time: Open time-slot to review running ‘Tech Stack’ or address any other questions'''

---

==== Important links ====

* '''Main Prototype repository:''' https://nfdi4culture.github.io/linked-open-exhibition/
* Quarto setup: ‘''BIM Prototype 02 Quarto Website’:'' https://mrchristian.github.io/prototype/
* Instructions for ‘Tech Stack’: ''Einführung in Quarto und Einfügen eines Ausstellungsbeitrags'' [[BIM-126-02-Data-Science-Linked-Open-Exhibition#Einführung in Quarto und Einfügen eines Ausstellungsbeitrags|https://en.wikiversity.org/wiki/BIM-126-02-Data-Science-Linked-Open-Exhibition#Einf%C3%BChrung_in_Quarto_und_Einf%C3%BCgen_eines_Ausstellungsbeitrags]]
* Earlier Prototype (2025): https://nfdi4culture.github.io/open-museum/ 

==== ''Outline: Class Project – Prototyping: Linked Open Exhibitions'' ====
Prototype: https://nfdi4culture.github.io/linked-open-exhibition/ 

Repo: https://nfdi4culture.github.io/linked-open-exhibition/

Why?

* Rapid Prototyping in this context is used to learn about ‘Data Modeling using Linked Open Data’.   '''''NB: The data modeling skills and experience learned here is a core competence that gives a foundation to be able to create data models in a wide set of professional contexts.'''''
** How to do data modeling
** To use method: Bottom-up; KISS (Keep it Short and Simple); Top-down
** Evaluation and validation
** Operationalize a data model
** User testing
** Good practice, including Open Scholarship (Open Science) practice. e.g. FAIR Data Principles
** Experiment with AI LLMs and agentic coding in the workflow
* Rapid Prototyping is a Design Research methodology – meaning to create or discover knowledge by doing.

What?

Create a website prototype a the whole class: https://nfdi4culture.github.io/linked-open-exhibition/

The website is made of three data driven sub-projects:

# Manual Wikidata entries for Sprengel Museum website – class entries already made
# Bulk exhibition entries derived from 600+ DNB records for ‘Sprengel Museum’ - imported
# HsH Library information records for a search on the Sprengel Museum and one scan of a Sprengel Museum catalogue for Text and Data Mining (TDM) – to do

How?

Simon Worthington will act as Publication Manager. This involves running or guiding complex software parts.

Copilot agentic coding will be used (experimented with) for some parts.

Class is divided into three teams of the sub-projects:  

# Sprengel Museum exhibitions website; 
# DNB records ‘Sprengel Museum’
# Text and Data Mining: Library catalogue Sprengel Museum

Each team carries out the same tasks for their parts to complete a round of data modeling:

# Collect data – bottom-up method
# Validate the data – top-down method
# Presentation of data – Quarto website ‘[https://nfdi4culture.github.io/linked-open-exhibition/ Linked Open Exhibitions]’

Goal: Definition-of-done (DoD) ''NB: Developer speak''

* A documented data model (Table) with diagram (Mermaid, GraphVis, or Draw.io)
* Mapping of data model to schemas (Table)
* Idea for presentation of data for each sub-section in the prototype and implementation with Publication Manager assistance, e.g., for DNB a chronological list of exhibitions with images.
* Documentation of AI LLM use as an assistant, attribution, and comments on good practice
* Data provenance and good practice checklist completion
* The final result ‘Class Project – Prototyping: Linked Open Exhibitions’ will be made as an institutional deposit with [https://zenodo.org/ Zenodo]. 


---

==== Activity #1: Collecting data and bottom up data modeling ====
Confirm, create, or expand existing data models by looking at the source. Each project has a source:

* Team #1: Sprengel Museum website, exhibition listings: 
** https://www.sprengel-museum.de/ and 
** spreadsheet of entered exhibitions CSV GitHub | Spreadsheet TIB Cloud (passworded)
** In prototype: https://nfdi4culture.github.io/linked-open-exhibition/exhibitions.html 
* Team #2: DNB records of search for ‘Sprengel Museum’:
** https://portal.dnb.de/opac/moveDown?currentResultId=Sprengel+and+Museum%26any&amp;categoryId=books | https://wikibase.wbworkshop.tibwiki.io/ 
** CSV https://github.com/NFDI4Culture/linked-open-exhibition/blob/main/catalogues/sprengel_exhibitions.csv
** Images of book covers https://github.com/NFDI4Culture/linked-open-exhibition/tree/main/catalogues/images 
* Team #3: HsH Library information on catalogues for ‘Sprengel Museum’:
** https://katalog.bib.hs-hannover.de/vufind/Search/Results?lookfor=Sprengel%2BMuseum
** Team 3 have to start from scratch as as yet we don’t have a library record or item in an exhibition data model. Tip: look back at the other models to start building up your data models.

'''&gt;&gt;&gt; Add to data model here:''' https://tib.cloud/s/PicTdwCEqCQ6pBp (passworded)

==== OBJECTIVE ====
To ensure that the data model can represent the source. Are there enough entries to describe the things that make up the source.

The process is iterative, meaning it keeps on being repeated with improvements and changes being made.

==== TASKS ====

* Edit the purple grey area, thje green are will be edited in the next activity
* Review and correct existing information
* Add new concepts if the source needs it
* Orange areas need filling in. The cells might need editing or added to.
* Data types can be found on Property Pages only Items (QIDs) don’t have data types, in &lt;nowiki&gt;https://www.wikidata.org/wiki/Property:P1476&lt;/nowiki&gt; under the Label - ''Data type''
* URI is equivelent to URL
Tips
* Look at other examples on Wikidata: Artists, exhibitions, catalogues, bibliographic, or items in an exhibition.
* Use an AI to lookup schema explanations or options. Register with KISSKI to get better AI privacy use.

==== Activity #2: Top down data modeling validation ====
* Team #1: Sprengel Museum website
* Team #2: DNB records of search for ‘Sprengel Museum’   
* Team #3: HsH Library information on catalogues for ‘Sprengel Museum’

===== OBJECTIVE =====
Map all concepts

==== TASKS ====
Look up the concept in the different resources and add mapping links,

Work time: Open time-slot to review running ‘Tech Stack’ or address any other questions

---

===== Homework =====
* Complete the Bottom-up and Top-down modelling
* Team #3: Visit the library and make a digital scan on a copier machine, store as PDF. The scan will be used for text and data mining and the file deleted and destroyed after. We will only be extracting metadata from the scan.
* Come along to the next class with ideas and suggestions for what you would like to have displayed from your data and data models in the prototype.
---

== Delivery and contribution to the Class Project: Prototyping: Linked Open Exhibitions. ==
Linked Open Exhibitions (Prototype): https://nfdi4culture.github.io/linked-open-exhibition/  

Tasks to be to be completed by students and that will be evaluated and contribute to the assessment:

# Complete the Wikidata entry for a Sprengel Museum exhibition
# Completion of the GitHub task of forking repository and publishing Wikidata entry https://github.com/mrchristian/prototype 
# Adding Data Model mapping to standards to forked repository (still to be taught in class)
# Adding SPARQL Query network diagram to forked repository (still to be taught in class)
# Adding ORCID ID to forked repository (still to be taught in class)
# AI LLMs: 
## Agentic coding: VSCode Copilot exercise - plan, execute (still to be taught in class)
## Document AI LLM use with list of use, pro and cons, and attribution - guidelines to be provided
# Completion of a Team Task for Class Project: Prototyping: Linked Open Exhibitions (still to be taught in class, will be assigned using GitHub Issue).
## The three teams are:
### Exhibition manual Wikidata entries
### DNB entries sorting
### Exhibition catalogue from HsH Library - Text and Data Mining

== Session #8: Class Project ==
Links

*Project GitHub repo - Class Project - Publication: https://github.com/NFDI4Culture/linked-open-exhibition
* Single exhibition entry example: https://github.com/mrchristian/prototype
* Exercise: [[Linked-Open-Exhibition-Exercise]] (7 tasks to be covered for class project)
* List of Wikidata entries made (passworded); Team allocation: https://tib.cloud/s/fncf8W6pXs8qgiq

Schedule

Linked Open Exhibition: art gallery, foundation and museum in Toulouse - https://www.wikidata.org/wiki/Q16303680

* Bemberg Foundation
* Bemberg Collection

--

11:30-13:30 - Introduction; Guest Chloë Farr - Open Science Lab guest from Canada - scanning and data extraction expert; Prototype work Final Project - teams A. DNB, B. Wikidata, C. Catalogue scan; Tasks for Final Project.

13:30-13:45 - Pause

13:45-14:15 - Final Project Climic. Prototype teams task allocation; Tasks recap.

Final Project&lt;blockquote&gt;Demonstrate examples of how a curator could make a ''Linked Open Exhibition - Catalogue'': Bibliographic records, Wikidata entries, scanning print catalogues.&lt;/blockquote&gt;Deadline 31st July

Publication: https://github.com/NFDI4Culture/linked-open-exhibition (make a contribution)

Personal exhibition entries: Fork of https://github.com/mrchristian/prototype (complete entry)

Carry out 7 tasks: [[Linked-Open-Exhibition-Exercise]] 

Prototype Team task completion: https://github.com/NFDI4Culture/linked-open-exhibition/issues
[[Category:Wikidata]]</text>
      <sha1>lv9oq4ns7flf9lq7r29erflue9140pn</sha1>
    </revision>
    <revision>
      <id>2841306</id>
      <parentid>2841304</parentid>
      <timestamp>2026-10-18T16:14:35Z</timestamp>
      <contributor>
        <username>Mrchristian</username>
        <id>281704</id>
      </contributor>
      <origin>2841306</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="38491" sha1="dt9fjw1r0ixlu6fr5ibgwr7o4qcngft" xml:space="preserve">==== Linked Open Exhibition ====

DE - See language switch - top right

''Materials and Tasks for the module &quot;BIM-126-02, SoSe 2026, Worthington/Blümel&quot; for students at Hochschule Hannover. The materials are prepared with several colleagues from the [https://www.tib.eu/de/forschung-entwicklung/forschungsgruppen-und-labs/open-science Open Science Lab at TIB] Hannover.''

* Project GitHub repo: https://github.com/NFDI4Culture/linked-open-exhibition
* Single exhibition entry example: https://github.com/NFDI4Culture/prototype-linkedOE
* Exercise: [[Linked-Open-Exhibition-Exercise]]

==== Summary ====
The eight session course covers an introduction to Linked Open Data (LOD) in the context of :

# Open Galleries Libraries Archives and Museums (GLAM), and; 
# The use of Wikimedia Foundation platforms.

The Wikimedia Foundation platforms that will be used are: Wikidata; Wikibase, MediaWiki, and  Wikimedia Commons.

AI LLM will be used in the workflows: Code assistant ''copilot'', and a variety of AI LLM chat services for file generation and configurations to create SPARQL queries, Jinja 2.0 templates, etc. 

„KI-Servicezentrum für Sensible und Kritische Infrastrukturen“ (KISSKI) can be used for unmetered ChatGPT5 https://kisski.gwdg.de/leistungen/2-02-llm-service/ | https://chat-ai.academiccloud.de/chat  

The Methodologies employed are: Open-source software, Open Science, and rapid prototyping.

==== Linked Open Exhibition ====
The question being explored for the class is how can LOD be uséd to benefit museum exhibitions as Linked Open Exhibitions – a record of the exhibition, a catalogues of items in an exhibition, and other important data? As examples '''to gain exhibitions increased visitors numbers and create greater depth of engagement'''.

With a focus of the question on how to make LOD records of '''items in an exhibition'''.

==== Learning points – In order of priority ====

# '''Wikidata/Wikibase LOD concepts:''' Items, Properties, Values, Qualifiers, Wikibase schemas, Classes, Lexemes, Knowledge Base, and Knowledge Graphs.
# '''Linked Open Data (LOD):''' Semantic web, 5 star, RDF/Triples, Ontologies, Taxonomies, and controlled vocabularies.
# '''Using LOD source:''' Identifiers, PIDs, information sources, media sources, and import and export tooling.
# '''Data modelling:''' Methodologies, schema use, visualisation, and testing.
# '''Data workflow tools:''' Git, IDE, AI code assistant (copilot), AI Chat, using Wikimedia Foundation tooling, data import and export tools, generating PIDs and making deposits in a scholarly repository.
# '''Data presentation and data use:''' Wikidata Query Service results, MediaWiki infoboxes, AI Chat SPARQL query processing.
# '''Open Science practice:''' Open-source software, Open Notebook Science, Open Licencing, PIDs, FAIR Data Principles, and ethical and good practice AI use.

==== Sessions ====
The sessions would be about cataloguing Sprengel Museum exhibitions using LOD and how to make visualisations and presentations.

'''Learning to use LOD is the goal of the learning.''' The method will be to build out from a kernel of an ‘exhibition’ and add ‘item in an exhibition’. From the start the students will be the ones who make the LOD. This will start with minimal entries my by the students, then layering these up with – Identifiers, LOD Media sources, schemas, etc. And finally moving onto how to present the data in a way that satisfies the ‘use case’: '''to gain exhibitions increased visitors numbers and create greater depth of engagement'''. Here presentation technologies are used: MediaWiki infoboxes, Wikidata Query Service results, AI Chat SPARQL queries and other features, etc.

==== Session 1: Exhibition timeline creation - build out, add exhibitions ====

[[File:Timeline 2026 06 02.jpg|alt=Timeline|left|thumb]]
[[File:Network 2026 06 02.jpg|alt=Graph|left|thumb]]

# Record minimal information for an exhibition in Wikidata as Linked Open Data: Title, museum, date, etc. e.g., https://www.wikidata.org/wiki/Q138547468 –  See: Table 1: ''Minimal data entries for an exhibition''
# View the exhibition record in Wikidata Query Service results link 
## timeline https://w.wiki/J8NJ
## graph https://w.wiki/J8aS 
# Review exhibition entries.
# Cover topics raised by making a LOD entry: Wikidata basics, Wikidata good practice, consulting schemas, importance of review and using GitHub Issues, comparing available data – before and after.
The exercise: Create a Linked Open Data record for an exhibition using Wikidata (minimal entry).

===== A. Creating the exhibition entry in Wikidata. =====
# Login to Wikidata: https://www.wikidata.org/
# Have a source at hand to make a data entry, e.g.,
#* https://www.sprengel-museum.de/ausstellungen/archiv
#* https://www.sprengel-museum.de/besuch?view=article&amp;id=65:publikationen&amp;catid=2:uncategorised
#* https://portal.dnb.de/opac/showFullRecord?currentResultId=sprengel+and+museum+and+ausstellung%26any&amp;currentPosition=1
# Check there is no existing entry for the exhibition is on Wikidata. Use the search function. 
# Create an item or edit an existing item.
#* Note: Check which language you are using. We will be adding Deutsch and English entries (starting with Deutsch).
# Create the following data entries in Wikidata, see: Table 1: ''Minimal data entries for an exhibition.''
# Review exhibition Wikidata entries. Review is carried out by using three questions. Add comments if needed, corrections can be made. Results and notes can be added to the Discussion Page of the entry, e.g., 
#* All entries present [   ]
#* All entries correct [   ]
#* Entries are in Deutsch and English – within reason [   ]

===== ''Table'' ''1: Minimal data entries for an exhibition'' =====
{| class=&quot;wikitable&quot;
| colspan=&quot;7&quot; |'''Fields used to make an exhibition entry. See example: https://www.wikidata.org/wiki/Q138547468'''
|-
|A
|Label
| colspan=&quot;5&quot; |Note: Keep short. Use title from exhibition
|-
|B
|Description
| colspan=&quot;5&quot; |Note: Use to differentiate from other entries. Follow this example: Gabriela Jolowicz Holzschnitte Ausstellung im Sprengel Museum, Hannover, 2026
|-
|
|'''Property (P) and Item (Q)'''
|'''URI'''
|'''DE'''
|'''EN'''
|'''Add'''
|'''Note'''
|-
|1
|P31
|https://www.wikidata.org/wiki/Property:P31
|ist ein(e)
|instance of
|Q464980
|Add item
|-
|2
|Q464980
|https://www.wikidata.org/wiki/Q464980
|Ausstellung
|Exhibition
|
|(Used above)
|-
|3
|P1476
|https://www.wikidata.org/wiki/Property:P1476
|Titel
|Title
|Title
|Plain text
|-
|4
|P276
|https://www.wikidata.org/wiki/Property:P276
|Ort
|Location
|Sprengel Museum Hannover Q510144
|Add item
|-
|5
|P580
|https://www.wikidata.org/wiki/Property:P580
|Startzeitpunkt
|Start time
|Date
|YYYY-MM-DD
|-
|6
|P582
|https://www.wikidata.org/wiki/Property:P582
|Endzeitpunkt
|End time
|Date
|YYYY-MM-DD
|-
|7
|P1640
|https://www.wikidata.org/wiki/Property:P1640
|Kurator
|Curator
|Person
|Add item (if don't exists will need to create/can omit at present)
|-
|8
|P710
|https://www.wikidata.org/wiki/Property:P710
|Teilnehmer
|Participant
|Person (the artist)
|Add item (if don't exists will need to create/can omit at present)
|-
|9
|P856
|https://www.wikidata.org/wiki/Property:P856
|offizielle Website
|Official website
|URL
|URL
|}

===== Homework exercises: Session #1 =====
# Complete your allocated exhibition. Make sure all fields are complete from Table 1. If something cannot be added, either: A. Make a note in the exhibition allocation spreadsheet, or B. Send and email to [mailto:Simon.worththington@tib.eu simon.worththington@tib.eu] and I will help resolve your issue.  '''Note: If you did not create an exhibition entry during the class make sure one is complete before the next class.'''
# Create a GitHub account and add your GitHub handle next to your name, column ‘GitHub handle’,  in the exhibition allocation spreadsheet.
# Review your classmates exhibition entries. You have all been allocated a entry to review, see the Exhibition Allocation spreadsheet. Your name will be in column G. This first review has three questions – tick the boxes to show if each item has been complete and either add comments or correct the Wikidata exhibition entry.  '''Note: If your allocated Exhibition entry hasn’t been made by you classmate then please contact them and ask them to complete the entry.'''  Questions are:
## Are all the required fields present?
## Are all the fields correct?
## Is there an Deutsch and English entry?


END of SESSION 1

---

==== Session 2: Exhibition cataloguing - build up, add items, artists, catalogues ====
The session has five exercies:

# Exhibition update
# Artist
# Exhibition catalogue
# AI LLM SPARQL experiments
# &lt;s&gt;Artwork&lt;/s&gt;

The exercises include the following concepts:

==== Exercises ====

==== 1. Exhibition updates ====

* Homework review: Complete all fields for an exhibition. Review your assigned review exhibition answering the three questions:

&lt;blockquote&gt;[ ] Sind alle erforderlichen Felder vorhanden?

[ ] Sind alle Felder korrekt ausgefüllt?

[ ] Gibt es einen Eintrag in Deutsch und Englisch&lt;/blockquote&gt;

* For the label. Convert words in all caps to sentence case. Use: https://convertcase.net/title-case-converter/ | Change from, e.g., ADRIAN SAUER: TRUTH TABLESPECTRUM INTERNATIONALER PREIS FÜR FOTOGRAFIE DER STIFTUNG NIEDERSACHSEN to  Adrian Sauer: Truth Tablespectrum Internationaler Preis Für Fotografie Der Stiftung Niedersachsen.

* Add the English language versions. Use DeepL to translate: https://www.deepl.com/en/translator
** Title: Add English title

* Add the following. Change P710 Teilnehmer (Participant) to P921 zentrales Thema '''artists name.''' 
** Qualifier on central theme to indicate the person is contributing artwork.

* Use: Qualifier P170 creator and add artist Q483501 (type artists and it will automcomplete)

* Reference: Gemeinsame Normdatei (GND) ID for a person, e.g., Gabriela Jolowicz https://d-nb.info/gnd/134184963 | Search your persons name and copy in the last part of number 134184963
* Talk page: Add in the review questions for your Wikidata entry:

&lt;blockquote&gt;[ ] Sind alle erforderlichen Felder vorhanden?

[ ] Sind alle Felder korrekt ausgefüllt?

[ ] Gibt es einen Eintrag in Deutsch und Englisch?&lt;/blockquote&gt;Notice the useful links that tell you more about connected Linked Open Data!

Note: SPARQL query showing data model. Properties and and values. Results: https://w.wiki/JMLX Made with Gemini AI: https://gemini.google.com/share/c43f34a67f67

==== Concepts ====

* Wikidata parts – see about and diagram:
** https://www.wikidata.org/wiki/Wikidata:Introduction/de
** https://www.wikidata.org/wiki/Wikidata:Introduction#/media/File:Datamodel_in_Wikidata.svg
* Applying a review process using Talk pages
* Adding References
* Using a type of LOD source – '''An authority record''' Gemeinsame Normdatei (GND) ID https://portal.dnb.de/opac.htm  
* SPARQL query

---

==== 2. Artists ====
The objective here is to ensure all artists have been included in exhibition listing and to then review the existing artists entry.

Later a SPARQL query will be made to compare statements about all the artists in our dataset.

* Before reviewing artists items make sure all artists have been listed in the exhibition item, with qualifier of being an artist and a reference to their GND record.

===== Important statements =====
{| class=&quot;wikitable&quot;
|Concept
|CIDOC CRM (Full)
|Linked Art (Selection)
|Wikidata Equivalent
|Note
|-
|Entity
|E21 Person
|Person
|Q5 (human)
|The base instance.
|-
|Label/Name
|P1 is identified by → E33_E41
|identified_by (Name)
|
|Linked Art flattens this into a simple list of names.
|-
|
|
|
|P735 Given name
|
|-
|
|
|
|P734 Family name
|
|-
|Profession
|P2 has type → E55 Type
|classified_as
|P106 (occupation)
|Map to AAT 300025103 (artist).
|-
|Birth
|P98i was born → E67 Birth
|born (Birth)
|P569 (date of birth)
|CRM treats birth as an event; Wikidata as a property.
|-
|Death
|P100i died in → E69 Death
|died (Death)
|P570 (date of death)
|If the artist is still living, this is omitted.
|-
|Nationality
|P107i member of → E74 Group
|classified_as (Type)
|P27 (citizenship)
|Linked Art often models nationality as a Type.
|-
|Reference
|P1 identifies ← E42 Identifier
|identified_by (Identifier)
|QID (The URI itself)
|Used to link to external authorities (ULAN, VIAF).
|-
|Commons category
|?
|?
|P373 search name
|&lt;nowiki&gt;https://commons.wikimedia.org/&lt;/nowiki&gt;
|}


From Google Gemini: https://gemini.google.com/share/578cc1b886d0

---

===== Schemas and communities need consulting. =====
From Wikimedia:

* WikiProject Visual Arts: https://en.wikipedia.org/wiki/Wikipedia:WikiProject_Visual_arts
* Wikiproject Exhibitions: https://www.wikidata.org/wiki/Wikidata:WikiProject_Exhibitions

Semi-formal

Generic Wikibase Model for Cultural Data: https://kgi4nfdi.github.io/Guidelines/guide/wikibase/data_modelling_import/

Formal:

CIDOC Conceptual Reference Model (CRM) - https://cidoc-crm.org/

Linked Art (based on CIDOC) https://linked.art/model/actor/

Iconclass https://www.inconclass.org/

AAT https://www.getty.edu/research/tools/vocabularies/aat/ 

==== Concepts ====

* Data modeling
* Schemas
* Use case
* Bottom up design
* Identifiers

---

==== 3. Exhibition Catalogue ====
Search in both of these two places to find information about the catalogue for your assigned exhibition.

* Sprengel Museum publication catalogue - https://www.sprengel-museum.de/besuch?view=article&amp;id=65:publikationen&amp;catid=2:uncategorised
* DND (example) you can search for the exhibition name or Sprengel Museum '''-'''  https://portal.dnb.de/opac/simpleSearch?query=sprengel+and+museum+and+ausstellung&amp;cqlMode=true 

''Note: Make a note of any links you find in the exhibition listings spreadsheet.''

===== Make a Wikidata entry for the catalogue =====
Note: first search for publication before making Wikidata entry. Use title, use ISBN, use GND.

An example publication from DNB and Sprengel Shop.

* https://portal.dnb.de/opac/showFullRecord?currentResultId=Gabriela+and+Jolowicz%26any&amp;currentPosition=0
* https://www.sprengel-museum.de/besuch?view=article&amp;id=65:publikationen&amp;catid=2:uncategorised

===== Enter these statements =====
Note: Remember Label and Description
{| class=&quot;wikitable&quot;
|Property
|Label
|Description/Example
|-
|P31
|instance of
|catalogue (Q2352616)
|-
|P1476
|title
|The official title of the catalogue (e.g., Vermeer and the Masters of Genre Painting)
|-
|P50
|author
|The main curator or art historian (item link)
|-
|P123
|publisher
|The museum or publishing house (e.g., Louvre Museum)
|-
|P577
|publication date
|Year of release (e.g., 2024)
|-
|P212
|ISBN-13
|The 13-digit standard book identifier
|-
|
|GND
|ID
|-
|P973
|described at URL
|A link to the catalogue's page on the museum’s website
|}
Google Gemini  https://gemini.google.com/share/9a21f5522192

Example input: https://www.wikidata.org/wiki/Q138646145

===== Link the record back to the exhibition =====
P972	Title

==== Concepts ====

* Data modeling
* Identifier
* Data as CC Zero / Copyright of data
---

==== 4. AI LLM SPARQL experiments ====
The Wikidata has a SPARQL interface where the LOD in Wikidata can be searched (queried) and outputted in a number of ways, formats, and a visualisations. As well as being saved on the web.

We will us AI LLM chat to generate SPARQL queries.

Later we will learn the fundamentals of writing a SPARQL query. But for the moment we want to see how they have be generated, the options, and creative applications.

Using chat services or code assistants can be a valuable way to learn about new technologies.
{| class=&quot;wikitable&quot;
|Service
|Best For
|Standout Feature
|Key Model(s)
|-
|'''ChatGPT'''
|General Use &amp; Tasks
|Deep Research &amp; Agent Mode
|GPT-5.4, GPT-5
|-
|'''Claude'''
|Coding &amp; Writing
|Artifacts (interactive workspace)
|Claude 4.5, 4.6
|-
|'''Google Gemini'''
|Google Ecosystem
|Nano Banana (native image/video)
|Gemini 3.1 Pro
|-
|Perplexity
|Real-time Research
|Native Citations &amp; Search Labs
|Sonar, GPT-5, Claude
|-
|MS Copilot
|Office Productivity
|Copilot Vision &amp; 365 Integration
|GPT-5.2, Prometheus
|-
|DeepSeek
|Logical Reasoning
|High-tier performance at low cost
|DeepSeek-V3, R1
|-
|Grok
|Real-time Social Info
|Unfiltered X (Twitter) integration
|Grok 4.1
|-
|'''Meta AI'''
|Social Media
|Seamless integration in WhatsApp/IG
|Llama 4 (Scout)
|-
|Poe
|Model Testing
|Access multiple LLMs in one app
|Multi-model aggregator
|-
|Mistral (Le Chat)
|Privacy &amp; Developers
|European-hosted, GDPR-focused
|Mistral Large 3
|}
Some of these can also be used via KISSKI

„KI-Servicezentrum für Sensible und Kritische Infrastrukturen“ (KISSKI) can be used for unmetered ChatGPT5 https://kisski.gwdg.de/leistungen/2-02-llm-service/ | https://chat-ai.academiccloud.de/chat  

=== The exercise ===
The group will be split into a number of Zoom breakout groups and then the group spends 20 minutes experimenting generating SPARQL queries and other creative applications.

Paste in results here: https://tib.cloud/apps/files/files/8251374?dir=/NFDI4Culture/HsH/BIM26/bim26-shared&amp;editing=false&amp;openfile=true 

Each room is assigned a Chat engine.

Maximum there will be four groups.

·      Group #1: '''ChatGPT'''

·      Group #2: '''Claude'''

·      Group #3: '''Google Gemini'''

·       Group #4: '''Meta AI'''

=== Example exercise ===
Chat bots can read  a SPARQL query or a Wikidata address.

e.g.,

Item https://www.wikidata.org/wiki/Q138547468

query graph https://w.wiki/JPNc

query timeline https://w.wiki/JPPN

Item Sprengel Museum https://www.wikidata.org/wiki/Q510144 

Then the chatbot can be instructed to do things based on the information provided.

You should ask the chat bot to generate Wikidata SPARQL queries and then paste the queries into the SPARQL querie interface. https://query.wikidata.org/

Use these examples and invent your own:

# Create dashboard (count of things)
# Create inventory (table)
# Create graph data model

Some output SPARQL queries

·       Map of artists place of birth - https://w.wiki/JPT3 

·       List of exhibitions - https://w.wiki/JPR3 

·       As plot of exhibitions - https://w.wiki/J8aS

==== Homework: Session 2 ====
Create a bottom up  data model of an artwork in an exhibition. Include only the minimum information needed. The result should be a table like the ones presented for exhibition, artist, and catalogue. The table should include properties and attributes. You should consult the schemas mentioned above. You can use AI but attribute the AI and link to your question. If you use AI review the results and make notes about what you changed.

Note: Think about how parts are related and what you need to add and what already exists in Wikidata.

Submit your results as a spreadsheet or table.  

===== Session 3: Museum visit - Sprengel Museum =====
19 March 2026

===== Session #4: Schemas and Prototyping (the end of class project) =====

===== Recap and outline =====
Done

* Creating exhibition entries in Wikidata
* Filling our data models for Artist and Catalogue
* Exploring the museum and its activities to help steer the prototype

To do

* Decide on the ideas for the prototype
* Data model for items in an exhibition (Artwork and Exhibition)
* Complete a data model for the end of the project that can be used by museums and complies to the sector standards – CIDOC and Wikidata.

===== What have we learned about the ‘Museum’s Story’ =====
TBC

===== Schemas =====
An opportunity to become familiar with how Linked Open Data is structured using common agreements on  working practices.

Over the period of the course a data model will be developed and finalised to describe ‘items in an exhibition’. The data model will be published  for community consultation and testing.

===== Schemas and key concepts =====
Table: https://tib.cloud/s/ZKNAAo3B8ATXsAP 

* Schema
* Terminology Service
* Controlled Vocabulary
* Taxonomy
* Ontology
* Knowledge Graph

Table X: link: https://tib.cloud/s/ZKNAAo3B8ATXsAP Terminology used in Linked Open Data (LOD) 
{| class=&quot;wikitable&quot; 
|-
! **Concept**
! **Wikidata link (Concept)**
! **Primary Focus**
! **Analogy**
! **Example resource**
! **URL**
! **Example use**
! **URL**
|-
| Schema
| Q1397073
| Data Structure
| The Template. Conceptual schema / data model
| Schema.org
| https://schema.org/
| VisualArtwork
| https://schema.org/VisualArtwork
|-
|
|
|
|
|
|
| Smithsonian American Art Museum (SAAM) &quot;Among the Sierra Nevada, California&quot;
| https://www.wikidata.org/wiki/Q20475372
|-
| Terminology Service
| Q22692845
| Distribution
| A Library of Vocabularies, Schemas, Ontologies, etc
| TIB Terminology Service
| https://terminology.tib.eu/ts/
| NFDI4CULTURE
| https://terminology.tib.eu/ts/ontologies?and=false&amp;page=1&amp;sortedBy=title&amp;size=10&amp;collection=NFDI4CULTURE
|-
| Controlled Vocabulary
| Q1469824
| Consistency
| The Dictionary
| Integrated Authority File / die Gemeinsame Normdatei (GND)
| https://portal.dnb.de/opac/showShortList
| Persons: Dürer, Albrecht
| https://d-nb.info/gnd/117751669
|-
| Taxonomy
| Q8269924
| Hierarchy
| Sorting things by type (general classification)
| Getty Art &amp; Architecture Thesaurus (AAT)
| https://www.getty.edu/research/tools/vocabularies/aat/
| German Surrealist Max Ernst (painting techniques used)
| https://www.guggenheim-venice.it/en/art/conservation-department-new/technical-studies-and-conservation-campaigns/portrait-of-an-artist-at-work-max-ernsts-surrealist-techniques/#:~:text=Frottage%20and%20Grattage,in%20his%20drawings%20in%201925.
|-
|
|
|
|
| Iconclass
| https://iconclass.org/
| Max Ernst’s &quot;The Virgin Spanking the Christ Child&quot; (Parady)
| https://www.wikiart.org/en/max-ernst/the-virgin-spanking-the-christ-child-before-three-witnesses-andre-breton-paul-eluard-and-the-1926
|-
| Ontology
| Q324254
| Semantics: Meaning &amp; logic (information science)
| The Rulebook or Writing Style Guide
| CIDOC (Comité International pour la DOCumentation / International Committee for Documentation)
| https://cidoc-crm.org/
| Sloane Lab Knowledge Base - unifying 3 collections
| https://knowledgebase.sloanelab.org/resource/Start
|-
| Knowledge Graph
| Q33002955
| Network of things and relations
| A Navigational Map
| Census of Antique Works of Art and Architecture Known in the Renaissance
| https://www.census.de/
| Artemis search
| https://database.census.de/#/detail/10013099
|-
|
|
|
|
| Research Space
| https://researchspace.org/
| Hokusai: The Great Picture Book of Everything
| https://hokusai-great-picture-book-everything.researchspace.org/resource/rsp:Start
|}

===== Schemas exercise =====
Spreadsheet to work on: https://tib.cloud/s/PicTdwCEqCQ6pBp

(password: bim2026)

We will be looking at: Exhibition, Artist, and Catalogue.

'''''Enter the URLs found. Add new rows, columns, comments if needed. Keep manual searches as well as AI searches for comparison.'''''

===== Exercise #1: Enter links into the spreadsheet of matching items from the following: =====

* Wikidata:WikiProject Exhibitions/Properties
* Generic Wikibase Model for Cultural Data - Wikibase4Research NFDI4Culture
* CIDOC CRM (Full)
* Terminology Service (NFDII4Culture)
* Wikidata

===== Exercise #2: Use AI LLM to find matching items =====

* https://gemini.google.com/ 

==== Prototyping ====
Either in this session or in the next session the group will be divided into teams.

===== Schema =====

# Data model development: ‘items in an exhibition’

===== Quarto publication parts =====

# A catalogue of a Sprengel Museum exhibition
# A catalogue of all exhibitions and exhibition catalogues
# Catalogue of exhibition entries
---

==== Learning to use Quarto and inserting an exhibition entry ====
Tools: Quarto, GitHub, VS Code, Jupyter Notebooks, Codespace if needed, copilot: Agentic Coding)

'''Requirements'''

# A laptop or computer where you can install VScode
# You will need 2FA on your mobile (optional)
# Create a GitHub account
# Install VScode
# Connect Github account to VScode
# Create GitHub reposoitory

'''Fork the following repository:''' https://github.com/mrchristian/prototype 

'''Model: Auto'''

'''How the repo was setup. Agent promts:'''&lt;blockquote&gt;''I want to run a Quarto website project, please setup the basics. The project will be published on GitHub Pages. Set the output directory to docs.'' &lt;/blockquote&gt;Create a page for the quarto project that retrieves the data used for thie Wikidata item and renders it as  professional webpage ''&lt;Insert your exhibition here – or use this one&gt;''  https://www.wikidata.org/wiki/Q138547468 The approach should create a SPARQL query for the data and then render this as HTML using a Jupyter Notebook.

All entries: https://tib.cloud/s/fncf8W6pXs8qgiq (needs password)

===== Tasks =====

* Change exhibition - manual
* Run Jupyter Notebook 
* Run and preview Quarto 
* Publish to your GitHub Pages 

===== Step-by-step =====

====== Part one: Working environment ======
'''''NOTE: If you are having problems running locally then use the Codespace online option.'''''

# Create GitHub account - https://github.com/
# Have 2FA available - usually on mobile (Google authenticator) (optional)
# Install VSCode - https://code.visualstudio.com/download
# Install GitHub Desktop - https://desktop.github.com/download/
# Add Github account when prompted, use 2FA

====== Step two: The prototype ======
# Fork the repository:  https://github.com/mrchristian/prototype
# If working locally continue - if using Codespace - launch Codespace (see below and then continue)
# Test Quarto in the Terminal: 
## &lt;code&gt;quarto check&lt;/code&gt; 
## &lt;code&gt;quarto render&lt;/code&gt;
## &lt;code&gt;quarto preview&lt;/code&gt; (control C - to stop)
# If not working run Quarto from Agent
# Change Wikidata exhibition in Notebook
# Run notebook
# Run &lt;code&gt;quarto render&lt;/code&gt; &lt;code&gt;quarto preview&lt;/code&gt;
# Save all (or use auto save)
# Git: Message, Commit and Push
# On GitHub.com your repository
## Turn on Pages: GitHub Actions
## Code: About cog - Click use my GitHub Pages
## Actions tab: Publish Quarto Project
# ENDE - Rinse repeat  :-)

===== Codespace option: =====
Videolink: https://tib.cloud/s/LDtkN6QsdFkGGR6 (10 Minuten Zeit)

Codespace is an online Virtual Machine which can be launched from GitHub.

The repository includes a Dev Container configuration so you can work entirely in the browser without installing anything locally.

# On the repository page on GitHub, click Code → Codespaces → Create codespace on main.
# Wait for the container to build — Python packages from &lt;code&gt;requirements.txt&lt;/code&gt; are installed automatically - about 5 minutes.
# Once everything is installed the Codespace can be used anytime. It automatically shutsdown when left alone and can be restarted any time.
# Work done in Codespace must be pushed back to the repository.
# If Codespace is not used for 28 days the Codespace is deleted.

---

===== Homework - session #4 =====

* Get all books from HsH library that are Sprengel Museum exhibition catalogues. Bring to the next class
* Make an exhibition entry if not done
* Work with VSCode and the Agent and experiment
* Add entries from existing ontologies: https://tib.cloud/s/PicTdwCEqCQ6pBp?dir=/&amp;editing=false&amp;openfile=true

==== Sitzung 5: Prototyping: Running Quarto Prototype, Federation, Prototype Teams ====

* Running Quarto Prototype - https://github.com/mrchristian/prototype 
* DNB data download https://github.com/NFDI4Culture/linked-open-exhibition
* Data Federation - WB4R

===== Links =====
https://wikibase.wbworkshop.tibwiki.io/wiki/Main_Page

Glossar - https://nfdi4culture.github.io/linked-open-exhibition/Documentation/glossary

===== DNB Search =====
https://portal.dnb.de/opac/moveDown?currentResultId=Sprengel+and+Museum%26any&amp;categoryId=books

Sprengel Museum, 602 Artikel

'''About the DNB'''
https://www.dnb.de/librarylab
https://deutsche-nationalbibliothek.github.io/jupyterlite/lab/

'''Also'''

https://wiki.dnb.de/spaces/LINKEDDATASERVICE/pages/449878933/DNB+SPARQL+Service+BETA

===== Prototype Teams =====

* DNB Data
* Katalog scan
* Exhibition entries
* Datenmodell (alle)
===== --- =====

== Session 6: Class Project – Prototyping: ''Linked Open Exhibitions'' ==
Prototype URL (currently 2026-04-29 a shell framework): https://nfdi4culture.github.io/linked-open-exhibition/  

==== Program: ====
11:30 – 11:50 (20 min)  '''Outline: Class Project – Prototyping: Linked Open Exhibitions.''' What is it and what needs to be delivered. Allocation to sub-project and tasks outline. 

'''Activity #1: Bottom-up data modeling: Data mapping'''

11:50 – 12:20 (30 min) Data finding and exploration (break out rooms)

12:20 – 12:40 (20 min) Review data findings (class discussion)

12:40 – 12:55 (15 min) Pause Break

'''Activity #2: Top-down data modeling: Schema mapping'''

12:55 – 13:35 (40 min) Map data against schemas (break out rooms)

13:35 – 13:55 (20 min) Review findings (class discussion)

'''13:55 – 14:15 (20 min) Work time: Open time-slot to review running ‘Tech Stack’ or address any other questions'''

---

==== Important links ====

* '''Main Prototype repository:''' https://nfdi4culture.github.io/linked-open-exhibition/
* Quarto setup: ‘''BIM Prototype 02 Quarto Website’:'' https://mrchristian.github.io/prototype/
* Instructions for ‘Tech Stack’: ''Einführung in Quarto und Einfügen eines Ausstellungsbeitrags'' [[BIM-126-02-Data-Science-Linked-Open-Exhibition#Einführung in Quarto und Einfügen eines Ausstellungsbeitrags|https://en.wikiversity.org/wiki/BIM-126-02-Data-Science-Linked-Open-Exhibition#Einf%C3%BChrung_in_Quarto_und_Einf%C3%BCgen_eines_Ausstellungsbeitrags]]
* Earlier Prototype (2025): https://nfdi4culture.github.io/open-museum/ 

==== ''Outline: Class Project – Prototyping: Linked Open Exhibitions'' ====
Prototype: https://nfdi4culture.github.io/linked-open-exhibition/ 

Repo: https://nfdi4culture.github.io/linked-open-exhibition/

Why?

* Rapid Prototyping in this context is used to learn about ‘Data Modeling using Linked Open Data’.   '''''NB: The data modeling skills and experience learned here is a core competence that gives a foundation to be able to create data models in a wide set of professional contexts.'''''
** How to do data modeling
** To use method: Bottom-up; KISS (Keep it Short and Simple); Top-down
** Evaluation and validation
** Operationalize a data model
** User testing
** Good practice, including Open Scholarship (Open Science) practice. e.g. FAIR Data Principles
** Experiment with AI LLMs and agentic coding in the workflow
* Rapid Prototyping is a Design Research methodology – meaning to create or discover knowledge by doing.

What?

Create a website prototype a the whole class: https://nfdi4culture.github.io/linked-open-exhibition/

The website is made of three data driven sub-projects:

# Manual Wikidata entries for Sprengel Museum website – class entries already made
# Bulk exhibition entries derived from 600+ DNB records for ‘Sprengel Museum’ - imported
# HsH Library information records for a search on the Sprengel Museum and one scan of a Sprengel Museum catalogue for Text and Data Mining (TDM) – to do

How?

Simon Worthington will act as Publication Manager. This involves running or guiding complex software parts.

Copilot agentic coding will be used (experimented with) for some parts.

Class is divided into three teams of the sub-projects:  

# Sprengel Museum exhibitions website; 
# DNB records ‘Sprengel Museum’
# Text and Data Mining: Library catalogue Sprengel Museum

Each team carries out the same tasks for their parts to complete a round of data modeling:

# Collect data – bottom-up method
# Validate the data – top-down method
# Presentation of data – Quarto website ‘[https://nfdi4culture.github.io/linked-open-exhibition/ Linked Open Exhibitions]’

Goal: Definition-of-done (DoD) ''NB: Developer speak''

* A documented data model (Table) with diagram (Mermaid, GraphVis, or Draw.io)
* Mapping of data model to schemas (Table)
* Idea for presentation of data for each sub-section in the prototype and implementation with Publication Manager assistance, e.g., for DNB a chronological list of exhibitions with images.
* Documentation of AI LLM use as an assistant, attribution, and comments on good practice
* Data provenance and good practice checklist completion
* The final result ‘Class Project – Prototyping: Linked Open Exhibitions’ will be made as an institutional deposit with [https://zenodo.org/ Zenodo]. 


---

==== Activity #1: Collecting data and bottom up data modeling ====
Confirm, create, or expand existing data models by looking at the source. Each project has a source:

* Team #1: Sprengel Museum website, exhibition listings: 
** https://www.sprengel-museum.de/ and 
** spreadsheet of entered exhibitions CSV GitHub | Spreadsheet TIB Cloud (passworded)
** In prototype: https://nfdi4culture.github.io/linked-open-exhibition/exhibitions.html 
* Team #2: DNB records of search for ‘Sprengel Museum’:
** https://portal.dnb.de/opac/moveDown?currentResultId=Sprengel+and+Museum%26any&amp;categoryId=books | https://wikibase.wbworkshop.tibwiki.io/ 
** CSV https://github.com/NFDI4Culture/linked-open-exhibition/blob/main/catalogues/sprengel_exhibitions.csv
** Images of book covers https://github.com/NFDI4Culture/linked-open-exhibition/tree/main/catalogues/images 
* Team #3: HsH Library information on catalogues for ‘Sprengel Museum’:
** https://katalog.bib.hs-hannover.de/vufind/Search/Results?lookfor=Sprengel%2BMuseum
** Team 3 have to start from scratch as as yet we don’t have a library record or item in an exhibition data model. Tip: look back at the other models to start building up your data models.

'''&gt;&gt;&gt; Add to data model here:''' https://tib.cloud/s/PicTdwCEqCQ6pBp (passworded)

==== OBJECTIVE ====
To ensure that the data model can represent the source. Are there enough entries to describe the things that make up the source.

The process is iterative, meaning it keeps on being repeated with improvements and changes being made.

==== TASKS ====

* Edit the purple grey area, thje green are will be edited in the next activity
* Review and correct existing information
* Add new concepts if the source needs it
* Orange areas need filling in. The cells might need editing or added to.
* Data types can be found on Property Pages only Items (QIDs) don’t have data types, in &lt;nowiki&gt;https://www.wikidata.org/wiki/Property:P1476&lt;/nowiki&gt; under the Label - ''Data type''
* URI is equivelent to URL
Tips
* Look at other examples on Wikidata: Artists, exhibitions, catalogues, bibliographic, or items in an exhibition.
* Use an AI to lookup schema explanations or options. Register with KISSKI to get better AI privacy use.

==== Activity #2: Top down data modeling validation ====
* Team #1: Sprengel Museum website
* Team #2: DNB records of search for ‘Sprengel Museum’   
* Team #3: HsH Library information on catalogues for ‘Sprengel Museum’

===== OBJECTIVE =====
Map all concepts

==== TASKS ====
Look up the concept in the different resources and add mapping links,

Work time: Open time-slot to review running ‘Tech Stack’ or address any other questions

---

===== Homework =====
* Complete the Bottom-up and Top-down modelling
* Team #3: Visit the library and make a digital scan on a copier machine, store as PDF. The scan will be used for text and data mining and the file deleted and destroyed after. We will only be extracting metadata from the scan.
* Come along to the next class with ideas and suggestions for what you would like to have displayed from your data and data models in the prototype.
---

== Delivery and contribution to the Class Project: Prototyping: Linked Open Exhibitions. ==
Linked Open Exhibitions (Prototype): https://nfdi4culture.github.io/linked-open-exhibition/  

Tasks to be to be completed by students and that will be evaluated and contribute to the assessment:

# Complete the Wikidata entry for a Sprengel Museum exhibition
# Completion of the GitHub task of forking repository and publishing Wikidata entry https://github.com/mrchristian/prototype 
# Adding Data Model mapping to standards to forked repository (still to be taught in class)
# Adding SPARQL Query network diagram to forked repository (still to be taught in class)
# Adding ORCID ID to forked repository (still to be taught in class)
# AI LLMs: 
## Agentic coding: VSCode Copilot exercise - plan, execute (still to be taught in class)
## Document AI LLM use with list of use, pro and cons, and attribution - guidelines to be provided
# Completion of a Team Task for Class Project: Prototyping: Linked Open Exhibitions (still to be taught in class, will be assigned using GitHub Issue).
## The three teams are:
### Exhibition manual Wikidata entries
### DNB entries sorting
### Exhibition catalogue from HsH Library - Text and Data Mining

== Session #8: Class Project ==
Links

*Project GitHub repo - Class Project - Publication: https://github.com/NFDI4Culture/linked-open-exhibition
* Single exhibition entry example: https://github.com/mrchristian/prototype
* Exercise: [[Linked-Open-Exhibition-Exercise]] (7 tasks to be covered for class project)
* List of Wikidata entries made (passworded); Team allocation: https://tib.cloud/s/fncf8W6pXs8qgiq

Schedule

Linked Open Exhibition: art gallery, foundation and museum in Toulouse - https://www.wikidata.org/wiki/Q16303680

* Bemberg Foundation
* Bemberg Collection

--

11:30-13:30 - Introduction; Guest Chloë Farr - Open Science Lab guest from Canada - scanning and data extraction expert; Prototype work Final Project - teams A. DNB, B. Wikidata, C. Catalogue scan; Tasks for Final Project.

13:30-13:45 - Pause

13:45-14:15 - Final Project Climic. Prototype teams task allocation; Tasks recap.

Final Project&lt;blockquote&gt;Demonstrate examples of how a curator could make a ''Linked Open Exhibition - Catalogue'': Bibliographic records, Wikidata entries, scanning print catalogues.&lt;/blockquote&gt;Deadline 31st July

Publication: https://github.com/NFDI4Culture/linked-open-exhibition (make a contribution)

Personal exhibition entries: Fork of https://github.com/mrchristian/prototype (complete entry)

Carry out 7 tasks: [[Linked-Open-Exhibition-Exercise]] 

Prototype Team task completion: https://github.com/NFDI4Culture/linked-open-exhibition/issues
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      <text bytes="29883" sha1="qvrhyyjejrnjyszzy1tc1o66v2mr6vv" xml:space="preserve">{{title|Dreams and emotional problem-solving:&lt;br&gt;How do REM dreams contribute to emotional processing and adaptive coping?}}
__TOC__

==Overview==
{{RoundBoxTop|theme=11}}
'''Case study: Natalie part 1 ''' [[File:Dreaming.jpg|Dreaming|right|thumb|250px|'''Figure 1'''. Natalie's recurring dream after her breakup leaves her feeling sad when she wakes]]
Since her breakup, Natalie keeps having the same dream. She's been left behind somewhere, calling out to someone who never turns around (see Figure 1). When she wakes the details fade, but the feeling stays. Then one night, after her first good day in weeks, the dream changes: she stops calling out, notices a lit doorway, and walks through it. She wakes feeling better, and that afternoon she finally packs away his things. Did the dream help her move on, show that she was already moving on, or give her something to work with once awake? 
{{RoundBoxBottom}}

[[w:Dream|Dreams]] are commonly reported after awakenings from [[w:Rapid eye movement sleep|rapid eye movement (REM) sleep]] (Solms, 2000), and REM sleep has been described as a form of &quot;overnight therapy&quot; (Walker &amp; van der Helm, 2009, p. 731). Whether dreams contribute to this emotional work, or merely reflect processing that occurs elsewhere, remains unresolved. The answer has practical implications: if dreams help people heal, emotional dreams may be part of recovery; if they only mirror emotional states, they may signal when support is needed while awake.

Three concepts need to be kept apart. ''Emotional processing'' refers to overnight changes in the retention or intensity of emotional memories. [[w:Emotional self-regulation|''Emotion regulation'']] is any process, deliberate or automatic, that alters the course of an emotional response (Gross, 2015). [[Motivation and emotion/Book/2020/Coping and emotion|''Coping'']] refers to the thoughts and behaviours people use to manage stress, and it is adaptive only when it suits the situation and improves outcomes (Folkman &amp; Moskowitz, 2004). A dream may therefore reflect emotional processing without regulating emotion, or ease distress without changing how a person copes. 

{{RoundBoxTop|theme=15}}
'''Focus questions'''

* How do REM sleep and dreaming each contribute to overnight emotional processing? 
* What do competing theories propose dreams do with emotion? 
* How is dream emotion related to the way people cope while awake? 
* How can people work with emotional dreams to support coping?  

{{RoundBoxBottom}}

== How do REM sleep and dreaming each contribute to overnight emotional processing? ==
REM sleep is a brain state characterised by rapid eye movements, heightened brain activity, and muscle paralysis, whereas dreaming is a conscious experience. Because the two usually coincide, findings about one are often attributed to the other. 

===REM sleep and emotional memories ===
According to the ''sleep to forget, sleep to remember'' model, the brain replays recent emotional memories during REM sleep, when [[wikipedia:Norepinephrine|noradrenaline]], a neurotransmitter involved in arousal, is low (Walker &amp; van der Helm, 2009). Replay in this calm state is thought to preserve a memory's content while weakening its emotional charge, so that a past argument can be recalled clearly without making the heart race. The model makes two predictions: emotional memories should be retained better after sleep, and emotional reactivity to them should decline. If the charge survives the night, replay should recur, which may explain recurring dreams like Natalie's.  

Early neuroimaging appeared to support the second prediction. When 34 adults viewed emotional images twice, 12 hours apart, responses in the [[w:Amygdala|amygdala]], a region involved in threat detection, decreased in those who slept between sessions and increased in those who stayed awake (van der Helm et al, 2011). Noradrenaline was inferred from brainwave patterns rather than measured, however, so the study could not show that low-noradrenaline REM sleep was responsible.     

Larger reviews support neither prediction. For memory, a [[w:Meta-analysis|meta-analysis]] of 31 studies found that sleep did not strengthen emotional memories more than neutral ones (Lipinska et al., 2019). For emotional reactivity, a review of 24 studies found that sleep did not consistently change physiological responses to negative images, although only five studies measured them; participants also rated the images as more arousing after sleep (Lipinska et al., 2022). Because both reviews compared sleep with wakefulness, neither could isolate REM sleep. That requires selective REM deprivation, which involves stressful repeated awakenings that disturb other sleep stages, and the few human studies suggest that reducing REM sleep may strengthen emotional memories (Pesonen et al., 2024). The overnight-therapy account therefore remains plausible but unconfirmed.

===What does dreaming add? ===

Dreaming is more than a by-product of REM sleep: it can stop after brain damage while REM sleep continues, and some dreams occur outside REM sleep (Solms, 2000). Only one study has  measured both in the same people. Lara-Carrasco et al. (2009) partly deprived about half of 35 adults of REM sleep, collected their dreams, and had everyone rate negative images that evening and the next morning. Contrary to the REM model, the deprived group showed a larger overnight decrease in arousal. Separately, participants whose final dream was less negative rated the images as less unpleasant by morning. 

The authors had predicted the reverse, expecting the participants who adapted best to report more negative dreams. The result instead fits emotion carrying over into the morning ratings although the hour between waking and rating may have shaped this link. REM sleep and dream emotion thus tracked different aspects of the emotional response, so dreaming may contribute something of its own. Being correlational, however, the findings cannot show whether dreams produce overnight change or merely reflect it, which is exactly where the [[#What do competing theories propose dreams do with emotion?|theories]] disagree.    
{{Robelbox|theme={{{theme|11}}}|title=Quiz}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
&lt;quiz display=simple&gt;
{Which statement best summarises the evidence on REM sleep and upsetting memories? 
|type=&quot;()&quot;}
- REM sleep reliably reduces the emotional intensity of upsetting memories  
+ The idea that REM sleep reduces the intensity of upsetting memories is plausible but unconfirmed 
&lt;/quiz&gt;
&lt;/div&gt;
{{Robelbox/close}}

== What do competing theories propose dreams do with emotion? ==
The three leading theories agree that waking emotion shapes dream emotion but disagree about what dream emotion does next, and over what timescale (see Table 1). Timescale determines how each can be tested: relief by morning can be checked against the next day's mood, whereas change over weeks is much harder to observe. 
{| class=&quot;wikitable&quot; style=&quot;width:100%;&quot;
|+ style=&quot;text-align:left;&quot; | '''Table 1'''&lt;br /&gt;''Three Theories of What Dreams Do With Emotion''
|-
! scope=&quot;col&quot; |
! scope=&quot;col&quot; |Continuity hypothesis 
! scope=&quot;col&quot; |Fear extinction theory 
! scope=&quot;col&quot; |Mood regulation theory 
|-
! scope=&quot;row&quot; |Core claim 
|Dreams simulate current concerns 
|Dreams place fear memories in safe new contexts
|Dreams work through low mood across the night 
|-
! scope=&quot;row&quot; |Natalie's recurring dream means 
|She is still preoccupied with the loss 
|Extinction under heavy emotional load 
|Regulation not yet complete 
|-
! scope=&quot;row&quot; |Main prediction 
|Dream emotion carries into the next morning 
|Fear gradually decreases 
|Mood is better by morning, if it was low
|-
! scope=&quot;row&quot; |Timescale 
|Immediate 
|Weeks or longer
|One night 
|}
''Note.'' Based on Cartwright et al. (1998), Domhoff (2019), and Nielsen and Levin (2007). 
=== Continuity hypothesis ===
The continuity hypothesis holds that dreams dramatise the dreamer's current concerns. In Domhoff's (2019) neurocognitive version, dreaming is an &quot;embodied simulation&quot; (p. 265) generated by the [[w:Default mode network|default mode network]], which also supports daydreaming. On this view, Natalie's dream portrays her loss without resolving it, much as daydreaming about an ex-partner would. Domhoff concludes that an emotion-regulating function &quot;remains highly unlikely, and at best inconclusive, after decades of research studies&quot; (p. 287), noting that at least a quarter of REM dream reports contain no emotion. The hypothesis is parsimonious, but because mirroring can accommodate almost any association between dreams and waking life, it can be distinguished from functional theories only when dream emotion predicts outcomes that waking mood alone does not. 

===Fear extinction theory ===
[[w:Extinction (psychology)|Extinction]] occurs when repeated encounters with a feared cue pass without harm, so that a new safety memory forms and competes with the original fear memory instead of erasing it. Nielsen and Levin (2007) propose that dreams support this process offline by recombining elements of fear memories with safe or neutral material. In their illustration, a dream set in a dark alley changes when &quot;suddenly I found myself in a brightly lit street&quot; (p. 302), and the fear subsides, as it did for Natalie at the lit doorway. 

Two factors influence whether this process succeeds. ''Affect load'' is a state: the current burden that recent stress places on a person's capacity to regulate emotion. ''Affect distress'' is a trait: a stable tendency to respond to emotional events with heightened distress (Nielsen &amp; Levin, 2007, p. 301-302). Bad dreams and nightmares lie on a continuum, with nightmares indicating that extinction is struggling under heavy affect load. From this perspective, Natalie's recurring dream reflects the strain of the breakup rather than a breakdown in extinction. 

It follows that a frightening dream need not bring relief the next day, whereas people whose dreams repeatedly engage with fear should regulate better over time. The theory's weakness is its flexibility. Relief after a frightening dream can be seen as successful extinction and distress as extinction overloaded, so unless a successful dream is defined in advance, almost any outcome fits. 

===Mood regulation theory ===
Mood regulation theory proposes that successive REM dreams across one night work through low mood, shifting from negative towards positive emotion. Cartwright et al. (1998) tested this in 60 students without depression. Depressed mood fell overnight, and lower mood before sleep predicted a more negative first dream, but only the 10 students with the lowest pre-sleep mood showed the predicted sequence of negative dreams early and more positive dreams later. The authors therefore proposed a threshold: dreams moderate mood only when unhappiness is &quot;at least modest&quot; (p. 7). 

This threshold both protects the theory and limits it. It explains why studies of contented people find little, but it leaves the core pattern resting on 10 participants and never formally tested, Kramer's group, who first proposed the theory, had once failed to replicate their own effect (Nielsen &amp; Levin, 2007). Mood improved even on a night when every REM period was interrupted, so overnight relief did not depend on undisturbed dreaming. The authors suggested that describing dreams on waking may itself have helped (Cartwright et al., 1998).
{{Robelbox|theme={{{theme|11}}}|title=Quiz}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
&lt;quiz display=simple&gt;
{According to fear extinction theory, when should the benefits of a frightening dream appear?  
|type=&quot;()&quot;}
- By the next morning.
+ Gradually, over weeks or longer.
&lt;/quiz&gt;
&lt;/div&gt;
{{Robelbox/close}}

== How is dream emotion related to the way people cope while awake? ==
Gross (2015) defines emotion regulation by &quot;the activation of a goal to influence the emotion trajectory&quot; (p. 5), a goal that can operate implicitly. Because a dream has no obvious goal, any regulation it achieves must be implicit, and the question for coping is whether its effects carry into waking life. ''Within-person'' comparisons test continuity and mood regulation by asking whether nights with more negative dreams are followed by more negative days. ''Between-person'' comparisons 
test fear extinction by asking whether people who generally dream one way also regulate emotion differently. 

===Next-morning mood ===
Night-to-night evidence generally supports continuity. Over five days, 40 adults rated their dream emotions and morning mood, then viewed negative images, sometimes while trying to [[Motivation and emotion/Book/2025/Cognitive strategies and emotion regulation|reappraise]] them (Sikka et al., 2022). More negative dream emotion was associated with more negative morning mood but not with how strongly participants reacted to the images or how well they regulated, and [[w:Bayes factor|Bayesian analyses]] favoured the absence of both links, which counts as evidence against them. A larger study of 4,715 mornings from 536 adults found the same carry-over, with frightening dreams followed by about 7% more negative mood. Dreams that combined fear with joy, however, were more often followed by mornings free of negative mood (Baber et al., 2026). 

These results contradict mood regulation's overnight prediction, at least in largely healthy samples, but their support for continuity is weaker than it first appears. Dream emotion is reported after waking, so a lingering morning mood could affect both ratings. Most dreams were also recalled at home from unidentified sleep stages, and were not necessarily REM dreams. Nor can these results refute fear extinction, which never predicted overnight relief. 
===Between-person comparisons ===
Between people, the pattern reverses. People whose dreams were more fearful on average reported greater use of adaptive regulation strategies, such as positive reappraisal and acceptance, even after controlling for [[w:Neuroticism|neuroticism]], which itself wasassociated with fearful dreaming (Baber et al., 2026). In a separate study of 89 adults who kept a week-long dream diary, those who reported dream fear more often responded more calmly to frightening images while awake, with smaller pupil responses, weaker amygdala activity, and stronger activity in the medial [[w:Prefrontal cortex|prefrontal cortex]], which helps dampen fear (Sterpenich et al., 2020). Because self-report and neural measures converge, the association is credible and fits the gradual effect that fear extinction predicts. 

The direction of influence is unclear, however, since people who suppress fear during the day may simply experience more of it at night (Sterpenich et al., 2020). Baber et al. (2026) found a counterintuitive result: participants who reported more adaptive regulation felt worse after frightening dreams than those who reported less. The authors suggested that such people may be more aware of their emotions, may reappraise the dream on waking as only a dream, or may need a brief rise in distress to desensitise, as in [[w:Exposure therapy|exposure therapy]]. The last two possibilities place regulation after waking, with the dream supplying the material.  

Coping itself has rarely been measured. Among 35 female students preparing for examinations, those who dreamed about the exam reported less active problem-solving while awake, whereas greater waking use of positive reappraisal was associated with more problem-solving within dreams (Delorme et al., 2002). Coping style may shape dream content as much as dreams shape coping. 

===Dreaming through a real loss ===
Real loss provides the strongest test, because adaptation to it unfolds over months. 
Cartwright et al. (2006) woke 30 adults going through divorce, 20 of them depressed, from every REM period on three nights over five months. Depressed participants who later recovered had more fully developed dreams, and their dreams about the former spouse contained mostly negative emotion and were linked to other memories. Among those who stayed depressed, spouse dreams were emotionally flat and isolated. Recovery was thus associated with dreams that engaged with the loss, even painfully. This fits fear extinction's idea of recombination better than overnight mood repair, although Cartwright et al. interpreted it as mood regulation through links to earlier memories. 

The spouse-dream comparison rested on only six people who recovered and four who did not. A more serious problem is that severe depression blunts dream emotion, so flat dreams may indicate deeper depression rather than cause slower recovery (Cartwright et al., 2006). The same problem of direction applies throughout this section. 
{{Robelbox|theme={{{theme|11}}}|title=Quiz}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
&lt;quiz display=simple&gt;
{In the same person, what usually follows a night with a frightening dream?
|type=&quot;()&quot;}
- Better emotion regulation the next day.   
+ A somewhat worse morning mood. 
&lt;/quiz&gt;
&lt;/div&gt;
{{Robelbox/close}}

== How can people work with emotional dreams to support coping?  ==
Correlational studies cannot establish whether dreams influence coping, but experiments that change dreams can. The only such experiments with emotional outcomes come from nightmare treatment (see [[Motivation and emotion/Book/2020/Nightmares and emotion|Nightmares and emotion]]), so they serve  here as a test case. 
{{RoundBoxTop|theme=11}}
[[File:Woman writing on a notebook with a pen.jpg|Woman writing on a notebook with a pen|right|thumb|200px|'''Figure 2'''. Rewriting a recurring dream's ending while awake is the core of imagery rehearsal therapy.]]
'''Case study: Natalie part 2'''

During a stressful fortnight, the old dream returns and Natalie starts staying up late to avoid it. Her psychologist suggests writing the dream down and giving it a new ending in which she stops calling out and walks the other way. She rehearses the new ending every evening  (see Figure 2). Within weeks, the dream comes less often and bothers her less. Oddly, she cannot recall ever dreaming the new ending. So what helped? 
{{RoundBoxBottom}}
===Does the new ending need to be dreamed? ===
Imagery rehearsal therapy (IRT), in which a nightmare is rewritten and the new version rehearsed while awake, is recommended for [[w:Nightmare disorder|nightmare disorder]] (Morgenthaler et al., 2018). In one trial, 36 patients rehearsed new endings and heard a sound during REM sleep, that, for half of them, had been paired with the new ending. This cued group had fewer nightmares and more positive dreams, although their dreams rarely resembled the rehearsed scripts. Yet distress, sleep quality, and depression improved no more than in the comparison group (Schwartz et al., 2022), so the cue altered dream content without adding emotional benefit. 

A later analysis of the same patients examined cathartic dreams, in which threat gives way to resolution, as with Natalie's lit doorway (Perogamvros et al., 2025). These dreams became more common with cueing, and their increase correlated with reduced depression. Because depression decreased no further in the cued group, cathartic dreams appear to accompany recovery rather than causing it, although with 18 participants per group a modest effect could have been missed. Similarly, re-imagining a nightmare without changing it reduced nightmares and distress about as much as rewriting it, relative to a wait-list (Kunze et al., 2017), and adding IRT to [[w:Insomia|insomnia]] therapy gave 108 veterans with severe [[w:Post-traumatic stress disorder|post-traumatic stress disorder]] no additional benefit (Harb et al., 2019).  

===From less distress to better coping ===
What these interventions share is engagement with the dream while awake. Natalie's late nights are a form of [[w:Avoidance coping|avoidance coping]], which may maintain distressing dreams, whereas writing and rehearsing the dream is closer to [[w:Emotional approach coping|emotional approach coping]], in which emotions are processed instead of avoided (Folkman &amp; Moskowitz, 2004; Rousseau &amp; Belleville, 2018). Other mechanisms proposed for IRT, such as a growing sense of control and changed beliefs about nightmares, also operate while awake, although few have been tested directly (Rousseau &amp; Belleville, 2018). 

In practical terms, low mood after a distressing dream is a typical carry-over effect and need not signal a problem. A recurring dream indicates an unresolved concern but says little about whether recovery is under way. Working with the dream while awake is the best-supported approach, and frequent, distressing nightmares warrant professional help. Even so, less distress about a dream is not yet adaptive coping, which requires better management of the stressor itself (Folkman &amp; Moskowitz, 2004). No study has measured that outcome, so whether Natalie copes better with her breakup remains unknown.

==Conclusion==
Natalie's story raised three possibilities: dreams might help people recover, show recovery already under way, or provide material to work with while awake. The evidence favours the second and third. That REM sleep reduces the emotional intensity of memories overnight remains unconfirmed. From night to morning, dream emotion carries over into mood, as the continuity hypothesis predicts (see Table 1). Over longer periods, fear extinction theory fits better: people with more fearful dreams report more adaptive emotion regulation, and those recovering from loss tend to dream about it with strong emotion. These associations are correlational, however, and experiments that change dream content have not shown that improvement depends on the changed dream. 

The most defensible answer to the chapter's question is that REM dreams contribute to emotional processing and adaptive coping mainly by reflecting current emotional states and supplying material that people regulate while awake rather than by acting as overnight therapy. In Natalie's case, the lit doorway was likely a sign of change already under way, and what helped was what she did with it after waking. Whether dreaming itself causes adaptive coping remains open, and answering that will require studies that track dream emotion and coping in the same people over weeks or months. 

{{RoundBoxTop|theme=15}}
'''Take-home messages'''

* A single night of sleep does not reliably take the sting out of an upsetting memory. 
* Emotional dreams mirror what a person is carrying; they do not appear to heal it. 
* Dreams that engage emotionally with a loss tend to accompany recovery, even when that emotion is painful. 
* For a recurring, distressing dream, working with it while awake, by facing or rewriting it, is the best-supported approach.
{{RoundBoxBottom}}

==See also==

* [[Motivation and emotion/Book/2020/Coping and emotion|Coping and emotion]] (Book chapter, 2020)
* [[Motivation and emotion/Book/2025/Dreams and emotional problem-solving|Dreams and emotional problem-solving]] (Book chapter, 2025)
* [[w:Emotional self-regulation|Emotional self-regulation]] (Wikipedia)
* [[w:Nightmare disorder|Nightmare disorder]] (Wikipedia)
* [[Motivation and emotion/Book/2020/Nightmares and emotion|Nightmares and emotion]] (Book chapter, 2020)

==References==
{{Hanging indent|1=
Baber, G. R., Hamilton, N. A., Girard, J. M., Sikka, P., Watts, A., Jun, D., Gratton, M. K. P., Cohen, J. M., Quesada, A. K., Nichols, E. C., &amp; Cunningham, T. J. (2026). Testing affect regulation theories of dreaming. ''Sleep, 49''(5), Article zsag046. https://doi.org/10.1093/sleep/zsag046

Cartwright, R., Agargun, M. Y., Kirkby, J., &amp; Friedman, J. K. (2006). Relation of dreams to waking concerns. ''Psychiatry Research, 141''(3), 261–270. https://doi.org/10.1016/j.psychres.2005.05.013

Cartwright, R., Luten, A., Young, M., Mercer, P., &amp; Bears, M. (1998). Role of REM sleep and dream affect in overnight mood regulation: A study of normal volunteers. ''Psychiatry Research, 81''(1), 1–8. https://doi.org/10.1016/S0165-1781(98)00089-4

Delorme, M.-A., Lortie-Lussier, M., &amp; De Koninck, J. (2002). Stress and coping in the waking and dreaming states during an examination period. ''Dreaming, 12''(4), 171–183. https://doi.org/10.1023/A:1021128326940

Domhoff, G. W. (2019). The neurocognitive theory of dreams at age 20: An assessment and a comparison with four other theories of dreaming. ''Dreaming, 29''(4), 265–302. https://doi.org/10.1037/drm0000119

Folkman, S., &amp; Moskowitz, J. T. (2004). Coping: Pitfalls and promise. ''Annual Review of Psychology, 55'', 745–774. https://doi.org/10.1146/annurev.psych.55.090902.141456

Gross, J. J. (2015). Emotion regulation: Current status and future prospects. ''Psychological Inquiry, 26''(1), 1–26. https://doi.org/10.1080/1047840X.2014.940781

Harb, G. C., Cook, J. M., Phelps, A. J., Gehrman, P. R., Forbes, D., Localio, R., Harpaz-Rotem, I., Gur, R. C., &amp; Ross, R. J. (2019). Randomized controlled trial of imagery rehearsal for posttraumatic nightmares in combat veterans. ''Journal of Clinical Sleep Medicine, 15''(5), 757–767. https://doi.org/10.5664/jcsm.7770

Kunze, A. E., Arntz, A., Morina, N., Kindt, M., &amp; Lancee, J. (2017). Efficacy of imagery rescripting and imaginal exposure for nightmares: A randomized wait-list controlled trial. ''Behaviour Research and Therapy, 97'', 14–25. https://doi.org/10.1016/j.brat.2017.06.005

Lara-Carrasco, J., Nielsen, T. A., Solomonova, E., Levrier, K., &amp; Popova, A. (2009). Overnight emotional adaptation to negative stimuli is altered by REM sleep deprivation and is correlated with intervening dream emotions. ''Journal of Sleep Research, 18''(2), 178–187. https://doi.org/10.1111/j.1365-2869.2008.00709.x

Lipinska, G., Austin, H., Moonsamy, J. R., Henry, M., Lewis, R., Baldwin, D. S., Thomas, K. G. F., &amp; Stuart, B. (2022). Preferential consolidation of emotional reactivity during sleep: A systematic review and meta-analysis. ''Frontiers in Behavioral Neuroscience, 16'', Article 976047. https://doi.org/10.3389/fnbeh.2022.976047

Lipinska, G., Stuart, B., Thomas, K. G. F., Baldwin, D. S., &amp; Bolinger, E. (2019). Preferential consolidation of emotional memory during sleep: A meta-analysis. ''Frontiers in Psychology, 10'', Article 1014. https://doi.org/10.3389/fpsyg.2019.01014

Morgenthaler, T. I., Auerbach, S., Casey, K. R., Kristo, D., Maganti, R., Ramar, K., Zak, R., &amp; Kartje, R. (2018). Position paper for the treatment of nightmare disorder in adults: An American Academy of Sleep Medicine position paper. ''Journal of Clinical Sleep Medicine, 14''(6), 1041–1055. https://doi.org/10.5664/jcsm.7178

Nielsen, T., &amp; Levin, R. (2007). Nightmares: A new neurocognitive model. ''Sleep Medicine Reviews, 11''(4), 295–310. https://doi.org/10.1016/j.smrv.2007.03.004

Perogamvros, L., Rochas, V., Beau, J.-B., Sterpenich, V., &amp; Bayer, L. (2025). The cathartic dream: Using a large language model to study a new type of functional dream in healthy and clinical populations. ''Journal of Sleep Research, 34''(6), Article e70001. https://doi.org/10.1111/jsr.70001

Pesonen, A.-K., Koskinen, M.-K., Vuorenhela, N., Halonen, R., Mäkituuri, S., Selin, M., Luokkala, S., Suutari, A., &amp; Hovatta, I. (2024). The effect of REM-sleep disruption on affective processing: A systematic review of human and animal experimental studies. ''Neuroscience and Biobehavioral Reviews, 162'', Article 105714. https://doi.org/10.1016/j.neubiorev.2024.105714

Rousseau, A., &amp; Belleville, G. (2018). The mechanisms of action underlying the efficacy of psychological nightmare treatments: A systematic review and thematic analysis of discussed hypotheses. ''Sleep Medicine Reviews, 39'', 122–133. https://doi.org/10.1016/j.smrv.2017.08.004

Schwartz, S., Clerget, A., &amp; Perogamvros, L. (2022). Enhancing imagery rehearsal therapy for nightmares with targeted memory reactivation. ''Current Biology, 32''(22), 4808–4816. https://doi.org/10.1016/j.cub.2022.09.032

Sikka, P., Engelbrektsson, H., Zhang, J., &amp; Gross, J. J. (2022). Negative dream affect is associated with next-day affect level, but not with affect reactivity or affect regulation. ''Frontiers in Behavioral Neuroscience, 16'', Article 981289. https://doi.org/10.3389/fnbeh.2022.981289

Solms, M. (2000). Dreaming and REM sleep are controlled by different brain mechanisms. ''Behavioral and Brain Sciences, 23''(6), 843–850. https://doi.org/10.1017/S0140525X00003988

Sterpenich, V., Perogamvros, L., Tononi, G., &amp; Schwartz, S. (2020). Fear in dreams and in wakefulness: Evidence for day/night affective homeostasis. ''Human Brain Mapping, 41''(3), 840–850. https://doi.org/10.1002/hbm.24843

van der Helm, E., Yao, J., Dutt, S., Rao, V., Saletin, J. M., &amp; Walker, M. P. (2011). REM sleep depotentiates amygdala activity to previous emotional experiences. ''Current Biology, 21''(23), 2029–2032. https://doi.org/10.1016/j.cub.2011.10.052

Walker, M. P., &amp; van der Helm, E. (2009). Overnight therapy? The role of sleep in emotional brain processing. ''Psychological Bulletin, 135''(5), 731–748. https://doi.org/10.1037/a0016570
}}

==External links==
* [https://shows.acast.com/sleep-science-pod/episodes/ep12-sleep-dreams-and-mental-health Sleep, dreams and mental health] (The Sleep Science Pod)
* [https://theconversation.com/the-science-of-dreams-and-nightmares-what-is-going-on-in-our-brains-while-were-sleeping-210901 The science of dreams and nightmares – what is going on in our brains while we're sleeping?] (The Conversation)
* [https://www.scientificamerican.com/podcast/episode/dreams-help-soothe-your-bad-memorie-11-11-28/ Dreams help sooth your bad memories] (Scientific American)

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      <text bytes="29884" sha1="kkwgk7wblm8ma9tqf4orr6lxc9rc31b" xml:space="preserve">{{title|Dreams and emotional problem-solving:&lt;br&gt;How do REM dreams contribute to emotional processing and adaptive coping?}}
__TOC__

==Overview==
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'''Case study: Natalie part 1 ''' [[File:Dreaming.jpg|Dreaming|right|thumb|250px|'''Figure 1'''. Natalie's recurring dream after her breakup leaves her feeling sad when she wakes]]
Since her breakup, Natalie keeps having the same dream. She's been left behind somewhere, calling out to someone who never turns around (see Figure 1). When she wakes the details fade, but the feeling stays. Then one night, after her first good day in weeks, the dream changes: she stops calling out, notices a lit doorway, and walks through it. She wakes feeling better, and that afternoon she finally packs away his things. Did the dream help her move on, show that she was already moving on, or give her something to work with once awake? 
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[[w:Dream|Dreams]] are commonly reported after awakenings from [[w:Rapid eye movement sleep|rapid eye movement (REM) sleep]] (Solms, 2000), and REM sleep has been described as a form of &quot;overnight therapy&quot; (Walker &amp; van der Helm, 2009, p. 731). Whether dreams contribute to this emotional work, or merely reflect processing that occurs elsewhere, remains unresolved. The answer has practical implications: if dreams help people heal, emotional dreams may be part of recovery; if they only mirror emotional states, they may signal when support is needed while awake.

Three concepts need to be kept apart. ''Emotional processing'' refers to overnight changes in the retention or intensity of emotional memories. [[w:Emotional self-regulation|''Emotion regulation'']] is any process, deliberate or automatic, that alters the course of an emotional response (Gross, 2015). [[Motivation and emotion/Book/2020/Coping and emotion|''Coping'']] refers to the thoughts and behaviours people use to manage stress, and it is adaptive only when it suits the situation and improves outcomes (Folkman &amp; Moskowitz, 2004). A dream may therefore reflect emotional processing without regulating emotion, or ease distress without changing how a person copes. 

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'''Focus questions'''

* How do REM sleep and dreaming each contribute to overnight emotional processing? 
* What do competing theories propose dreams do with emotion? 
* How is dream emotion related to the way people cope while awake? 
* How can people work with emotional dreams to support coping?  

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== How do REM sleep and dreaming each contribute to overnight emotional processing? ==
REM sleep is a brain state characterised by rapid eye movements, heightened brain activity, and muscle paralysis, whereas dreaming is a conscious experience. Because the two usually coincide, findings about one are often attributed to the other. 

===REM sleep and emotional memories ===
According to the ''sleep to forget, sleep to remember'' model, the brain replays recent emotional memories during REM sleep, when [[wikipedia:Norepinephrine|noradrenaline]], a neurotransmitter involved in arousal, is low (Walker &amp; van der Helm, 2009). Replay in this calm state is thought to preserve a memory's content while weakening its emotional charge, so that a past argument can be recalled clearly without making the heart race. The model makes two predictions: emotional memories should be retained better after sleep, and emotional reactivity to them should decline. If the charge survives the night, replay should recur, which may explain recurring dreams like Natalie's.  

Early neuroimaging appeared to support the second prediction. When 34 adults viewed emotional images twice, 12 hours apart, responses in the [[w:Amygdala|amygdala]], a region involved in threat detection, decreased in those who slept between sessions and increased in those who stayed awake (van der Helm et al, 2011). Noradrenaline was inferred from brainwave patterns rather than measured, however, so the study could not show that low-noradrenaline REM sleep was responsible.     

Larger reviews support neither prediction. For memory, a [[w:Meta-analysis|meta-analysis]] of 31 studies found that sleep did not strengthen emotional memories more than neutral ones (Lipinska et al., 2019). For emotional reactivity, a review of 24 studies found that sleep did not consistently change physiological responses to negative images, although only five studies measured them; participants also rated the images as more arousing after sleep (Lipinska et al., 2022). Because both reviews compared sleep with wakefulness, neither could isolate REM sleep. That requires selective REM deprivation, which involves stressful repeated awakenings that disturb other sleep stages, and the few human studies suggest that reducing REM sleep may strengthen emotional memories (Pesonen et al., 2024). The overnight-therapy account therefore remains plausible but unconfirmed.

===What does dreaming add? ===

Dreaming is more than a by-product of REM sleep: it can stop after brain damage while REM sleep continues, and some dreams occur outside REM sleep (Solms, 2000). Only one study has  measured both in the same people. Lara-Carrasco et al. (2009) partly deprived about half of 35 adults of REM sleep, collected their dreams, and had everyone rate negative images that evening and the next morning. Contrary to the REM model, the deprived group showed a larger overnight decrease in arousal. Separately, participants whose final dream was less negative rated the images as less unpleasant by morning. 

The authors had predicted the reverse, expecting the participants who adapted best to report more negative dreams. The result instead fits emotion carrying over into the morning ratings although the hour between waking and rating may have shaped this link. REM sleep and dream emotion thus tracked different aspects of the emotional response, so dreaming may contribute something of its own. Being correlational, however, the findings cannot show whether dreams produce overnight change or merely reflect it, which is exactly where the [[#What do competing theories propose dreams do with emotion?|theories]] disagree.    
{{Robelbox|theme={{{theme|11}}}|title=Quiz}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
&lt;quiz display=simple&gt;
{Which statement best summarises the evidence on REM sleep and upsetting memories? 
|type=&quot;()&quot;}
- REM sleep reliably reduces the emotional intensity of upsetting memories  
+ The idea that REM sleep reduces the intensity of upsetting memories is plausible but unconfirmed 
&lt;/quiz&gt;
&lt;/div&gt;
{{Robelbox/close}}

== What do competing theories propose dreams do with emotion? ==
The three leading theories agree that waking emotion shapes dream emotion but disagree about what dream emotion does next, and over what timescale (see Table 1). Timescale determines how each can be tested: relief by morning can be checked against the next day's mood, whereas change over weeks is much harder to observe. 
{| class=&quot;wikitable&quot; style=&quot;width:100%;&quot;
|+ style=&quot;text-align:left;&quot; | '''Table 1'''&lt;br /&gt;''Three Theories of What Dreams Do With Emotion''
|-
! scope=&quot;col&quot; |
! scope=&quot;col&quot; |Continuity hypothesis 
! scope=&quot;col&quot; |Fear extinction theory 
! scope=&quot;col&quot; |Mood regulation theory 
|-
! scope=&quot;row&quot; |Core claim 
|Dreams simulate current concerns 
|Dreams place fear memories in safe new contexts
|Dreams work through low mood across the night 
|-
! scope=&quot;row&quot; |Natalie's recurring dream means 
|She is still preoccupied with the loss 
|Extinction under heavy emotional load 
|Regulation not yet complete 
|-
! scope=&quot;row&quot; |Main prediction 
|Dream emotion carries into the next morning 
|Fear gradually decreases 
|Mood is better by morning, if it was low
|-
! scope=&quot;row&quot; |Timescale 
|Immediate 
|Weeks or longer
|One night 
|}
''Note.'' Based on Cartwright et al. (1998), Domhoff (2019), and Nielsen and Levin (2007). 
=== Continuity hypothesis ===
The continuity hypothesis holds that dreams dramatise the dreamer's current concerns. In Domhoff's (2019) neurocognitive version, dreaming is an &quot;embodied simulation&quot; (p. 265) generated by the [[w:Default mode network|default mode network]], which also supports daydreaming. On this view, Natalie's dream portrays her loss without resolving it, much as daydreaming about an ex-partner would. Domhoff concludes that an emotion-regulating function &quot;remains highly unlikely, and at best inconclusive, after decades of research studies&quot; (p. 287), noting that at least a quarter of REM dream reports contain no emotion. The hypothesis is parsimonious, but because mirroring can accommodate almost any association between dreams and waking life, it can be distinguished from functional theories only when dream emotion predicts outcomes that waking mood alone does not. 

===Fear extinction theory ===
[[w:Extinction (psychology)|Extinction]] occurs when repeated encounters with a feared cue pass without harm, so that a new safety memory forms and competes with the original fear memory instead of erasing it. Nielsen and Levin (2007) propose that dreams support this process offline by recombining elements of fear memories with safe or neutral material. In their illustration, a dream set in a dark alley changes when &quot;suddenly I found myself in a brightly lit street&quot; (p. 302), and the fear subsides, as it did for Natalie at the lit doorway. 

Two factors influence whether this process succeeds. ''Affect load'' is a state: the current burden that recent stress places on a person's capacity to regulate emotion. ''Affect distress'' is a trait: a stable tendency to respond to emotional events with heightened distress (Nielsen &amp; Levin, 2007, p. 301-302). Bad dreams and nightmares lie on a continuum, with nightmares indicating that extinction is struggling under heavy affect load. From this perspective, Natalie's recurring dream reflects the strain of the breakup rather than a breakdown in extinction. 

It follows that a frightening dream need not bring relief the next day, whereas people whose dreams repeatedly engage with fear should regulate better over time. The theory's weakness is its flexibility. Relief after a frightening dream can be seen as successful extinction and distress as extinction overloaded, so unless a successful dream is defined in advance, almost any outcome fits. 

===Mood regulation theory ===
Mood regulation theory proposes that successive REM dreams across one night work through low mood, shifting from negative towards positive emotion. Cartwright et al. (1998) tested this in 60 students without depression. Depressed mood fell overnight, and lower mood before sleep predicted a more negative first dream, but only the 10 students with the lowest pre-sleep mood showed the predicted sequence of negative dreams early and more positive dreams later. The authors therefore proposed a threshold: dreams moderate mood only when unhappiness is &quot;at least modest&quot; (p. 7). 

This threshold both protects the theory and limits it. It explains why studies of contented people find little, but it leaves the core pattern resting on 10 participants and never formally tested, Kramer's group, who first proposed the theory, had once failed to replicate their own effect (Nielsen &amp; Levin, 2007). Mood improved even on a night when every REM period was interrupted, so overnight relief did not depend on undisturbed dreaming. The authors suggested that describing dreams on waking may itself have helped (Cartwright et al., 1998).
{{Robelbox|theme={{{theme|11}}}|title=Quiz}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
&lt;quiz display=simple&gt;
{According to fear extinction theory, when should the benefits of a frightening dream appear?  
|type=&quot;()&quot;}
- By the next morning.
+ Gradually, over weeks or longer.
&lt;/quiz&gt;
&lt;/div&gt;
{{Robelbox/close}}

== How is dream emotion related to the way people cope while awake? ==
Gross (2015) defines emotion regulation by &quot;the activation of a goal to influence the emotion trajectory&quot; (p. 5), a goal that can operate implicitly. Because a dream has no obvious goal, any regulation it achieves must be implicit, and the question for coping is whether its effects carry into waking life. ''Within-person'' comparisons test continuity and mood regulation by asking whether nights with more negative dreams are followed by more negative days. ''Between-person'' comparisons 
test fear extinction by asking whether people who generally dream one way also regulate emotion differently. 

===Next-morning mood ===
Night-to-night evidence generally supports continuity. Over five days, 40 adults rated their dream emotions and morning mood, then viewed negative images, sometimes while trying to [[Motivation and emotion/Book/2025/Cognitive strategies and emotion regulation|reappraise]] them (Sikka et al., 2022). More negative dream emotion was associated with more negative morning mood but not with how strongly participants reacted to the images or how well they regulated, and [[w:Bayes factor|Bayesian analyses]] favoured the absence of both links, which counts as evidence against them. A larger study of 4,715 mornings from 536 adults found the same carry-over, with frightening dreams followed by about 7% more negative mood. Dreams that combined fear with joy, however, were more often followed by mornings free of negative mood (Baber et al., 2026). 

These results contradict mood regulation's overnight prediction, at least in largely healthy samples, but their support for continuity is weaker than it first appears. Dream emotion is reported after waking, so a lingering morning mood could affect both ratings. Most dreams were also recalled at home from unidentified sleep stages, and were not necessarily REM dreams. Nor can these results refute fear extinction, which never predicted overnight relief. 
===Between-person comparisons ===
Between people, the pattern reverses. People whose dreams were more fearful on average reported greater use of adaptive regulation strategies, such as positive reappraisal and acceptance, even after controlling for [[w:Neuroticism|neuroticism]], which itself wasassociated with fearful dreaming (Baber et al., 2026). In a separate study of 89 adults who kept a week-long dream diary, those who reported dream fear more often responded more calmly to frightening images while awake, with smaller pupil responses, weaker amygdala activity, and stronger activity in the medial [[w:Prefrontal cortex|prefrontal cortex]], which helps dampen fear (Sterpenich et al., 2020). Because self-report and neural measures converge, the association is credible and fits the gradual effect that fear extinction predicts. 

The direction of influence is unclear, however, since people who suppress fear during the day may simply experience more of it at night (Sterpenich et al., 2020). Baber et al. (2026) found a counterintuitive result: participants who reported more adaptive regulation felt worse after frightening dreams than those who reported less. The authors suggested that such people may be more aware of their emotions, may reappraise the dream on waking as only a dream, or may need a brief rise in distress to desensitise, as in [[w:Exposure therapy|exposure therapy]]. The last two possibilities place regulation after waking, with the dream supplying the material.  

Coping itself has rarely been measured. Among 35 female students preparing for examinations, those who dreamed about the exam reported less active problem-solving while awake, whereas greater waking use of positive reappraisal was associated with more problem-solving within dreams (Delorme et al., 2002). Coping style may shape dream content as much as dreams shape coping. 

===Dreaming through a real loss ===
Real loss provides the strongest test, because adaptation to it unfolds over months. 
Cartwright et al. (2006) woke 30 adults going through divorce, 20 of them depressed, from every REM period on three nights over five months. Depressed participants who later recovered had more fully developed dreams, and their dreams about the former spouse contained mostly negative emotion and were linked to other memories. Among those who stayed depressed, spouse dreams were emotionally flat and isolated. Recovery was thus associated with dreams that engaged with the loss, even painfully. This fits fear extinction's idea of recombination better than overnight mood repair, although Cartwright et al. interpreted it as mood regulation through links to earlier memories. 

The spouse-dream comparison rested on only six people who recovered and four who did not. A more serious problem is that severe depression blunts dream emotion, so flat dreams may indicate deeper depression rather than cause slower recovery (Cartwright et al., 2006). The same problem of direction applies throughout this section. 
{{Robelbox|theme={{{theme|11}}}|title=Quiz}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
&lt;quiz display=simple&gt;
{In the same person, what usually follows a night with a frightening dream?
|type=&quot;()&quot;}
- Better emotion regulation the next day.   
+ A somewhat worse morning mood. 
&lt;/quiz&gt;
&lt;/div&gt;
{{Robelbox/close}}

== How can people work with emotional dreams to support coping?  ==
Correlational studies cannot establish whether dreams influence coping, but experiments that change dreams can. The only such experiments with emotional outcomes come from nightmare treatment (see [[Motivation and emotion/Book/2020/Nightmares and emotion|Nightmares and emotion]]), so they serve  here as a test case. 
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[[File:Woman writing on a notebook with a pen.jpg|Woman writing on a notebook with a pen|right|thumb|200px|'''Figure 2'''. Rewriting a recurring dream's ending while awake is the core of imagery rehearsal therapy.]]
'''Case study: Natalie part 2'''

During a stressful fortnight, the old dream returns and Natalie starts staying up late to avoid it. Her psychologist suggests writing the dream down and giving it a new ending in which she stops calling out and walks the other way. She rehearses the new ending every evening  (see Figure 2). Within weeks, the dream comes less often and bothers her less. Oddly, she cannot recall ever dreaming the new ending. So what helped? 
{{RoundBoxBottom}}
===Does the new ending need to be dreamed? ===
Imagery rehearsal therapy (IRT), in which a nightmare is rewritten and the new version rehearsed while awake, is recommended for [[w:Nightmare disorder|nightmare disorder]] (Morgenthaler et al., 2018). In one trial, 36 patients rehearsed new endings and heard a sound during REM sleep, that, for half of them, had been paired with the new ending. This cued group had fewer nightmares and more positive dreams, although their dreams rarely resembled the rehearsed scripts. Yet distress, sleep quality, and depression improved no more than in the comparison group (Schwartz et al., 2022), so the cue altered dream content without adding emotional benefit. 

A later analysis of the same patients examined cathartic dreams, in which threat gives way to resolution, as with Natalie's lit doorway (Perogamvros et al., 2025). These dreams became more common with cueing, and their increase correlated with reduced depression. Because depression decreased no further in the cued group, cathartic dreams appear to accompany recovery rather than causing it, although with 18 participants per group a modest effect could have been missed. Similarly, re-imagining a nightmare without changing it reduced nightmares and distress about as much as rewriting it, relative to a wait-list (Kunze et al., 2017), and adding IRT to [[w:Insomia|insomnia]] therapy gave 108 veterans with severe [[w:Post-traumatic stress disorder|post-traumatic stress disorder]] no additional benefit (Harb et al., 2019).  

===From less distress to better coping ===
What these interventions share is engagement with the dream while awake. Natalie's late nights are a form of [[w:Avoidance coping|avoidance coping]], which may maintain distressing dreams, whereas writing and rehearsing the dream is closer to [[w:Emotional approach coping|emotional approach coping]], in which emotions are processed instead of avoided (Folkman &amp; Moskowitz, 2004; Rousseau &amp; Belleville, 2018). Other mechanisms proposed for IRT, such as a growing sense of control and changed beliefs about nightmares, also operate while awake, although few have been tested directly (Rousseau &amp; Belleville, 2018). 

In practical terms, low mood after a distressing dream is a typical carry-over effect and need not signal a problem. A recurring dream indicates an unresolved concern but says little about whether recovery is under way. Working with the dream while awake is the best-supported approach, and frequent, distressing nightmares warrant professional help. Even so, less distress about a dream is not yet adaptive coping, which requires better management of the stressor itself (Folkman &amp; Moskowitz, 2004). No study has measured that outcome, so whether Natalie copes better with her breakup remains unknown.

==Conclusion==
Natalie's story raised three possibilities: dreams might help people recover, show recovery already under way, or provide material to work with while awake. The evidence favours the second and third. That REM sleep reduces the emotional intensity of memories overnight remains unconfirmed. From night to morning, dream emotion carries over into mood, as the continuity hypothesis predicts (see Table 1). Over longer periods, fear extinction theory fits better: people with more fearful dreams report more adaptive emotion regulation, and those recovering from loss tend to dream about it with strong emotion. These associations are correlational, however, and experiments that change dream content have not shown that improvement depends on the changed dream. 

The most defensible answer to the chapter's question is that REM dreams contribute to emotional processing and adaptive coping mainly by reflecting current emotional states and supplying material that people regulate while awake rather than by acting as overnight therapy. In Natalie's case, the lit doorway was likely a sign of change already under way, and what helped was what she did with it after waking. Whether dreaming itself causes adaptive coping remains open, and answering that will require studies that track dream emotion and coping in the same people over weeks or months. 

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'''Take-home messages'''

* A single night of sleep does not reliably take the sting out of an upsetting memory. 
* Emotional dreams mirror what a person is carrying; they do not appear to heal it. 
* Dreams that engage emotionally with a loss tend to accompany recovery, even when that emotion is painful. 
* For a recurring, distressing dream, working with it while awake, by facing or rewriting it, is the best-supported approach.
{{RoundBoxBottom}}

==See also==

* [[Motivation and emotion/Book/2020/Coping and emotion|Coping and emotion]] (Book chapter, 2020)
* [[Motivation and emotion/Book/2025/Dreams and emotional problem-solving|Dreams and emotional problem-solving]] (Book chapter, 2025)
* [[w:Emotional self-regulation|Emotional self-regulation]] (Wikipedia)
* [[w:Nightmare disorder|Nightmare disorder]] (Wikipedia)
* [[Motivation and emotion/Book/2020/Nightmares and emotion|Nightmares and emotion]] (Book chapter, 2020)

==References==
{{Hanging indent|1=
Baber, G. R., Hamilton, N. A., Girard, J. M., Sikka, P., Watts, A., Jun, D., Gratton, M. K. P., Cohen, J. M., Quesada, A. K., Nichols, E. C., &amp; Cunningham, T. J. (2026). Testing affect regulation theories of dreaming. ''Sleep, 49''(5), Article zsag046. https://doi.org/10.1093/sleep/zsag046

Cartwright, R., Agargun, M. Y., Kirkby, J., &amp; Friedman, J. K. (2006). Relation of dreams to waking concerns. ''Psychiatry Research, 141''(3), 261–270. https://doi.org/10.1016/j.psychres.2005.05.013

Cartwright, R., Luten, A., Young, M., Mercer, P., &amp; Bears, M. (1998). Role of REM sleep and dream affect in overnight mood regulation: A study of normal volunteers. ''Psychiatry Research, 81''(1), 1–8. https://doi.org/10.1016/S0165-1781(98)00089-4

Delorme, M.-A., Lortie-Lussier, M., &amp; De Koninck, J. (2002). Stress and coping in the waking and dreaming states during an examination period. ''Dreaming, 12''(4), 171–183. https://doi.org/10.1023/A:1021128326940

Domhoff, G. W. (2019). The neurocognitive theory of dreams at age 20: An assessment and a comparison with four other theories of dreaming. ''Dreaming, 29''(4), 265–302. https://doi.org/10.1037/drm0000119

Folkman, S., &amp; Moskowitz, J. T. (2004). Coping: Pitfalls and promise. ''Annual Review of Psychology, 55'', 745–774. https://doi.org/10.1146/annurev.psych.55.090902.141456

Gross, J. J. (2015). Emotion regulation: Current status and future prospects. ''Psychological Inquiry, 26''(1), 1–26. https://doi.org/10.1080/1047840X.2014.940781

Harb, G. C., Cook, J. M., Phelps, A. J., Gehrman, P. R., Forbes, D., Localio, R., Harpaz-Rotem, I., Gur, R. C., &amp; Ross, R. J. (2019). Randomized controlled trial of imagery rehearsal for posttraumatic nightmares in combat veterans. ''Journal of Clinical Sleep Medicine, 15''(5), 757–767. https://doi.org/10.5664/jcsm.7770

Kunze, A. E., Arntz, A., Morina, N., Kindt, M., &amp; Lancee, J. (2017). Efficacy of imagery rescripting and imaginal exposure for nightmares: A randomized wait-list controlled trial. ''Behaviour Research and Therapy, 97'', 14–25. https://doi.org/10.1016/j.brat.2017.06.005

Lara-Carrasco, J., Nielsen, T. A., Solomonova, E., Levrier, K., &amp; Popova, A. (2009). Overnight emotional adaptation to negative stimuli is altered by REM sleep deprivation and is correlated with intervening dream emotions. ''Journal of Sleep Research, 18''(2), 178–187. https://doi.org/10.1111/j.1365-2869.2008.00709.x

Lipinska, G., Austin, H., Moonsamy, J. R., Henry, M., Lewis, R., Baldwin, D. S., Thomas, K. G. F., &amp; Stuart, B. (2022). Preferential consolidation of emotional reactivity during sleep: A systematic review and meta-analysis. ''Frontiers in Behavioral Neuroscience, 16'', Article 976047. https://doi.org/10.3389/fnbeh.2022.976047

Lipinska, G., Stuart, B., Thomas, K. G. F., Baldwin, D. S., &amp; Bolinger, E. (2019). Preferential consolidation of emotional memory during sleep: A meta-analysis. ''Frontiers in Psychology, 10'', Article 1014. https://doi.org/10.3389/fpsyg.2019.01014

Morgenthaler, T. I., Auerbach, S., Casey, K. R., Kristo, D., Maganti, R., Ramar, K., Zak, R., &amp; Kartje, R. (2018). Position paper for the treatment of nightmare disorder in adults: An American Academy of Sleep Medicine position paper. ''Journal of Clinical Sleep Medicine, 14''(6), 1041–1055. https://doi.org/10.5664/jcsm.7178

Nielsen, T., &amp; Levin, R. (2007). Nightmares: A new neurocognitive model. ''Sleep Medicine Reviews, 11''(4), 295–310. https://doi.org/10.1016/j.smrv.2007.03.004

Perogamvros, L., Rochas, V., Beau, J.-B., Sterpenich, V., &amp; Bayer, L. (2025). The cathartic dream: Using a large language model to study a new type of functional dream in healthy and clinical populations. ''Journal of Sleep Research, 34''(6), Article e70001. https://doi.org/10.1111/jsr.70001

Pesonen, A.-K., Koskinen, M.-K., Vuorenhela, N., Halonen, R., Mäkituuri, S., Selin, M., Luokkala, S., Suutari, A., &amp; Hovatta, I. (2024). The effect of REM-sleep disruption on affective processing: A systematic review of human and animal experimental studies. ''Neuroscience and Biobehavioral Reviews, 162'', Article 105714. https://doi.org/10.1016/j.neubiorev.2024.105714

Rousseau, A., &amp; Belleville, G. (2018). The mechanisms of action underlying the efficacy of psychological nightmare treatments: A systematic review and thematic analysis of discussed hypotheses. ''Sleep Medicine Reviews, 39'', 122–133. https://doi.org/10.1016/j.smrv.2017.08.004

Schwartz, S., Clerget, A., &amp; Perogamvros, L. (2022). Enhancing imagery rehearsal therapy for nightmares with targeted memory reactivation. ''Current Biology, 32''(22), 4808–4816. https://doi.org/10.1016/j.cub.2022.09.032

Sikka, P., Engelbrektsson, H., Zhang, J., &amp; Gross, J. J. (2022). Negative dream affect is associated with next-day affect level, but not with affect reactivity or affect regulation. ''Frontiers in Behavioral Neuroscience, 16'', Article 981289. https://doi.org/10.3389/fnbeh.2022.981289

Solms, M. (2000). Dreaming and REM sleep are controlled by different brain mechanisms. ''Behavioral and Brain Sciences, 23''(6), 843–850. https://doi.org/10.1017/S0140525X00003988

Sterpenich, V., Perogamvros, L., Tononi, G., &amp; Schwartz, S. (2020). Fear in dreams and in wakefulness: Evidence for day/night affective homeostasis. ''Human Brain Mapping, 41''(3), 840–850. https://doi.org/10.1002/hbm.24843

van der Helm, E., Yao, J., Dutt, S., Rao, V., Saletin, J. M., &amp; Walker, M. P. (2011). REM sleep depotentiates amygdala activity to previous emotional experiences. ''Current Biology, 21''(23), 2029–2032. https://doi.org/10.1016/j.cub.2011.10.052

Walker, M. P., &amp; van der Helm, E. (2009). Overnight therapy? The role of sleep in emotional brain processing. ''Psychological Bulletin, 135''(5), 731–748. https://doi.org/10.1037/a0016570
}}

==External links==
* [https://shows.acast.com/sleep-science-pod/episodes/ep12-sleep-dreams-and-mental-health Sleep, dreams and mental health] (The Sleep Science Pod)
* [https://theconversation.com/the-science-of-dreams-and-nightmares-what-is-going-on-in-our-brains-while-were-sleeping-210901 The science of dreams and nightmares – what is going on in our brains while we're sleeping?] (The Conversation)
* [https://www.scientificamerican.com/podcast/episode/dreams-help-soothe-your-bad-memorie-11-11-28/ Dreams help soothe your bad memories] (Scientific American)

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==Overview==
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'''Case study: Natalie part 1 ''' [[File:Dreaming.jpg|Dreaming|right|thumb|250px|'''Figure 1'''. Natalie's recurring dream after her breakup leaves her feeling sad when she wakes]]
Since her breakup, Natalie keeps having the same dream. She's been left behind somewhere, calling out to someone who never turns around (see Figure 1). When she wakes the details fade, but the feeling stays. Then one night, after her first good day in weeks, the dream changes: she stops calling out, notices a lit doorway, and walks through it. She wakes feeling better, and that afternoon she finally packs away his things. Did the dream help her move on, show that she was already moving on, or give her something to work with once awake? 
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[[w:Dream|Dreams]] are commonly reported after awakenings from [[w:Rapid eye movement sleep|rapid eye movement (REM) sleep]] (Solms, 2000), and REM sleep has been described as a form of &quot;overnight therapy&quot; (Walker &amp; van der Helm, 2009, p. 731). Whether dreams contribute to this emotional work, or merely reflect processing that occurs elsewhere, remains unresolved. The answer has practical implications: if dreams help people heal, emotional dreams may be part of recovery; if they only mirror emotional states, they may signal when support is needed while awake.

Three concepts need to be kept apart. ''Emotional processing'' refers to overnight changes in the retention or intensity of emotional memories. [[w:Emotional self-regulation|''Emotion regulation'']] is any process, deliberate or automatic, that alters the course of an emotional response (Gross, 2015). [[Motivation and emotion/Book/2020/Coping and emotion|''Coping'']] refers to the thoughts and behaviours people use to manage stress, and it is adaptive only when it suits the situation and improves outcomes (Folkman &amp; Moskowitz, 2004). A dream may therefore reflect emotional processing without regulating emotion, or ease distress without changing how a person copes. 

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'''Focus questions'''

* How do REM sleep and dreaming each contribute to overnight emotional processing? 
* What do competing theories propose dreams do with emotion? 
* How is dream emotion related to the way people cope while awake? 
* How can people work with emotional dreams to support coping?  

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== How do REM sleep and dreaming each contribute to overnight emotional processing? ==
REM sleep is a brain state characterised by rapid eye movements, heightened brain activity, and muscle paralysis, whereas dreaming is a conscious experience. Because the two usually coincide, findings about one are often attributed to the other. 

===REM sleep and emotional memories ===
According to the ''sleep to forget, sleep to remember'' model, the brain replays recent emotional memories during REM sleep, when [[wikipedia:Norepinephrine|noradrenaline]], a neurotransmitter involved in arousal, is low (Walker &amp; van der Helm, 2009). Replay in this calm state is thought to preserve a memory's content while weakening its emotional charge, so that a past argument can be recalled clearly without making the heart race. The model makes two predictions: emotional memories should be retained better after sleep, and emotional reactivity to them should decline. If the charge survives the night, replay should recur, which may explain recurring dreams like Natalie's.  

Early neuroimaging appeared to support the second prediction. When 34 adults viewed emotional images twice, 12 hours apart, responses in the [[w:Amygdala|amygdala]], a region involved in threat detection, decreased in those who slept between sessions and increased in those who stayed awake (van der Helm et al, 2011). Noradrenaline was inferred from brainwave patterns rather than measured, however, so the study could not show that low-noradrenaline REM sleep was responsible.     

Larger reviews support neither prediction. For memory, a [[w:Meta-analysis|meta-analysis]] of 31 studies found that sleep did not strengthen emotional memories more than neutral ones (Lipinska et al., 2019). For emotional reactivity, a review of 24 studies found that sleep did not consistently change physiological responses to negative images, although only five studies measured them; participants also rated the images as more arousing after sleep (Lipinska et al., 2022). Because both reviews compared sleep with wakefulness, neither could isolate REM sleep. That requires selective REM deprivation, which involves stressful repeated awakenings that disturb other sleep stages, and the few human studies suggest that reducing REM sleep may strengthen emotional memories (Pesonen et al., 2024). The overnight-therapy account therefore remains plausible but unconfirmed.

===What does dreaming add? ===

Dreaming is more than a by-product of REM sleep: it can stop after brain damage while REM sleep continues, and some dreams occur outside REM sleep (Solms, 2000). Only one study has  measured both in the same people. Lara-Carrasco et al. (2009) partly deprived about half of 35 adults of REM sleep, collected their dreams, and had everyone rate negative images that evening and the next morning. Contrary to the REM model, the deprived group showed a larger overnight decrease in arousal. Separately, participants whose final dream was less negative rated the images as less unpleasant by morning. 

The authors had predicted the reverse, expecting the participants who adapted best to report more negative dreams. The result instead fits emotion carrying over into the morning ratings although the hour between waking and rating may have shaped this link. REM sleep and dream emotion thus tracked different aspects of the emotional response, so dreaming may contribute something of its own. Being correlational, however, the findings cannot show whether dreams produce overnight change or merely reflect it, which is exactly where the [[#What do competing theories propose dreams do with emotion?|theories]] disagree.    
{{Robelbox|theme={{{theme|11}}}|title=Quiz}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
&lt;quiz display=simple&gt;
{Which statement best summarises the evidence on REM sleep and upsetting memories? 
|type=&quot;()&quot;}
- REM sleep reliably reduces the emotional intensity of upsetting memories  
+ The idea that REM sleep reduces the intensity of upsetting memories is plausible but unconfirmed 
&lt;/quiz&gt;
&lt;/div&gt;
{{Robelbox/close}}

== What do competing theories propose dreams do with emotion? ==
The three leading theories agree that waking emotion shapes dream emotion but disagree about what dream emotion does next, and over what timescale (see Table 1). Timescale determines how each can be tested: relief by morning can be checked against the next day's mood, whereas change over weeks is much harder to observe. 
{| class=&quot;wikitable&quot; style=&quot;width:100%;&quot;
|+ style=&quot;text-align:left;&quot; | '''Table 1'''&lt;br /&gt;''Three Theories of What Dreams Do With Emotion''
|-
! scope=&quot;col&quot; |
! scope=&quot;col&quot; |Continuity hypothesis 
! scope=&quot;col&quot; |Fear extinction theory 
! scope=&quot;col&quot; |Mood regulation theory 
|-
! scope=&quot;row&quot; |Core claim 
|Dreams simulate current concerns 
|Dreams place fear memories in safe new contexts
|Dreams work through low mood across the night 
|-
! scope=&quot;row&quot; |Natalie's recurring dream means 
|She is still preoccupied with the loss 
|Extinction under heavy emotional load 
|Regulation not yet complete 
|-
! scope=&quot;row&quot; |Main prediction 
|Dream emotion carries into the next morning 
|Fear gradually decreases 
|Mood is better by morning, if it was low
|-
! scope=&quot;row&quot; |Timescale 
|Immediate 
|Weeks or longer
|One night 
|}
''Note.'' Based on Cartwright et al. (1998), Domhoff (2019), and Nielsen and Levin (2007). 
=== Continuity hypothesis ===
The continuity hypothesis holds that dreams dramatise the dreamer's current concerns. In Domhoff's (2019) neurocognitive version, dreaming is an &quot;embodied simulation&quot; (p. 265) generated by the [[w:Default mode network|default mode network]], which also supports daydreaming. On this view, Natalie's dream portrays her loss without resolving it, much as daydreaming about an ex-partner would. Domhoff concludes that an emotion-regulating function &quot;remains highly unlikely, and at best inconclusive, after decades of research studies&quot; (p. 287), noting that at least a quarter of REM dream reports contain no emotion. The hypothesis is parsimonious, but because mirroring can accommodate almost any association between dreams and waking life, it can be distinguished from functional theories only when dream emotion predicts outcomes that waking mood alone does not. 

===Fear extinction theory ===
[[w:Extinction (psychology)|Extinction]] occurs when repeated encounters with a feared cue pass without harm, so that a new safety memory forms and competes with the original fear memory instead of erasing it. Nielsen and Levin (2007) propose that dreams support this process offline by recombining elements of fear memories with safe or neutral material. In their illustration, a dream set in a dark alley changes when &quot;suddenly I found myself in a brightly lit street&quot; (p. 302), and the fear subsides, as it did for Natalie at the lit doorway. 

Two factors influence whether this process succeeds. ''Affect load'' is a state: the current burden that recent stress places on a person's capacity to regulate emotion. ''Affect distress'' is a trait: a stable tendency to respond to emotional events with heightened distress (Nielsen &amp; Levin, 2007, p. 301-302). Bad dreams and nightmares lie on a continuum, with nightmares indicating that extinction is struggling under heavy affect load. From this perspective, Natalie's recurring dream reflects the strain of the breakup rather than a breakdown in extinction. 

It follows that a frightening dream need not bring relief the next day, whereas people whose dreams repeatedly engage with fear should regulate better over time. The theory's weakness is its flexibility. Relief after a frightening dream can be seen as successful extinction and distress as extinction overloaded, so unless a successful dream is defined in advance, almost any outcome fits. 

===Mood regulation theory ===
Mood regulation theory proposes that successive REM dreams across one night work through low mood, shifting from negative towards positive emotion. Cartwright et al. (1998) tested this in 60 students without depression. Depressed mood fell overnight, and lower mood before sleep predicted a more negative first dream, but only the 10 students with the lowest pre-sleep mood showed the predicted sequence of negative dreams early and more positive dreams later. The authors therefore proposed a threshold: dreams moderate mood only when unhappiness is &quot;at least modest&quot; (p. 7). 

This threshold both protects the theory and limits it. It explains why studies of contented people find little, but it leaves the core pattern resting on 10 participants and never formally tested, Kramer's group, who first proposed the theory, had once failed to replicate their own effect (Nielsen &amp; Levin, 2007). Mood improved even on a night when every REM period was interrupted, so overnight relief did not depend on undisturbed dreaming. The authors suggested that describing dreams on waking may itself have helped (Cartwright et al., 1998).
{{Robelbox|theme={{{theme|11}}}|title=Quiz}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
&lt;quiz display=simple&gt;
{According to fear extinction theory, when should the benefits of a frightening dream appear?  
|type=&quot;()&quot;}
- By the next morning.
+ Gradually, over weeks or longer.
&lt;/quiz&gt;
&lt;/div&gt;
{{Robelbox/close}}

== How is dream emotion related to the way people cope while awake? ==
Gross (2015) defines emotion regulation by &quot;the activation of a goal to influence the emotion trajectory&quot; (p. 5), a goal that can operate implicitly. Because a dream has no obvious goal, any regulation it achieves must be implicit, and the question for coping is whether its effects carry into waking life. ''Within-person'' comparisons test continuity and mood regulation by asking whether nights with more negative dreams are followed by more negative days. ''Between-person'' comparisons 
test fear extinction by asking whether people who generally dream one way also regulate emotion differently. 

===Next-morning mood ===
Night-to-night evidence generally supports continuity. Over five days, 40 adults rated their dream emotions and morning mood, then viewed negative images, sometimes while trying to [[Motivation and emotion/Book/2025/Cognitive strategies and emotion regulation|reappraise]] them (Sikka et al., 2022). More negative dream emotion was associated with more negative morning mood but not with how strongly participants reacted to the images or how well they regulated, and [[w:Bayes factor|Bayesian analyses]] favoured the absence of both links, which counts as evidence against them. A larger study of 4,715 mornings from 536 adults found the same carry-over, with frightening dreams followed by about 7% more negative mood. Dreams that combined fear with joy, however, were more often followed by mornings free of negative mood (Baber et al., 2026). 

These results contradict mood regulation's overnight prediction, at least in largely healthy samples, but their support for continuity is weaker than it first appears. Dream emotion is reported after waking, so a lingering morning mood could affect both ratings. Most dreams were also recalled at home from unidentified sleep stages, and were not necessarily REM dreams. Nor can these results refute fear extinction, which never predicted overnight relief. 
===Between-person comparisons ===
Between people, the pattern reverses. People whose dreams were more fearful on average reported greater use of adaptive regulation strategies, such as positive reappraisal and acceptance, even after controlling for [[w:Neuroticism|neuroticism]], which itself wasassociated with fearful dreaming (Baber et al., 2026). In a separate study of 89 adults who kept a week-long dream diary, those who reported dream fear more often responded more calmly to frightening images while awake, with smaller pupil responses, weaker amygdala activity, and stronger activity in the medial [[w:Prefrontal cortex|prefrontal cortex]], which helps dampen fear (Sterpenich et al., 2020). Because self-report and neural measures converge, the association is credible and fits the gradual effect that fear extinction predicts. 

The direction of influence is unclear, however, since people who suppress fear during the day may simply experience more of it at night (Sterpenich et al., 2020). Baber et al. (2026) found a counterintuitive result: participants who reported more adaptive regulation felt worse after frightening dreams than those who reported less. The authors suggested that such people may be more aware of their emotions, may reappraise the dream on waking as only a dream, or may need a brief rise in distress to desensitise, as in [[w:Exposure therapy|exposure therapy]]. The last two possibilities place regulation after waking, with the dream supplying the material.  

Coping itself has rarely been measured. Among 35 female students preparing for examinations, those who dreamed about the exam reported less active problem-solving while awake, whereas greater waking use of positive reappraisal was associated with more problem-solving within dreams (Delorme et al., 2002). Coping style may shape dream content as much as dreams shape coping. 

===Dreaming through a real loss ===
Real loss provides the strongest test, because adaptation to it unfolds over months. 
Cartwright et al. (2006) woke 30 adults going through divorce, 20 of them depressed, from every REM period on three nights over five months. Depressed participants who later recovered had more fully developed dreams, and their dreams about the former spouse contained mostly negative emotion and were linked to other memories. Among those who stayed depressed, spouse dreams were emotionally flat and isolated. Recovery was thus associated with dreams that engaged with the loss, even painfully. This fits fear extinction's idea of recombination better than overnight mood repair, although Cartwright et al. interpreted it as mood regulation through links to earlier memories. 

The spouse-dream comparison rested on only six people who recovered and four who did not. A more serious problem is that severe depression blunts dream emotion, so flat dreams may indicate deeper depression rather than cause slower recovery (Cartwright et al., 2006). The same problem of direction applies throughout this section. 
{{Robelbox|theme={{{theme|11}}}|title=Quiz}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
&lt;quiz display=simple&gt;
{In the same person, what usually follows a night with a frightening dream?
|type=&quot;()&quot;}
- Better emotion regulation the next day.   
+ A somewhat worse morning mood. 
&lt;/quiz&gt;
&lt;/div&gt;
{{Robelbox/close}}

== How can people work with emotional dreams to support coping?  ==
Correlational studies cannot establish whether dreams influence coping, but experiments that change dreams can. The only such experiments with emotional outcomes come from nightmare treatment (see [[Motivation and emotion/Book/2020/Nightmares and emotion|Nightmares and emotion]]), so they serve  here as a test case. 
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[[File:Woman writing on a notebook with a pen.jpg|Woman writing on a notebook with a pen|right|thumb|200px|'''Figure 2'''. Rewriting a recurring dream's ending while awake is the core of imagery rehearsal therapy.]]
'''Case study: Natalie part 2'''

During a stressful fortnight, the old dream returns and Natalie starts staying up late to avoid it. Her psychologist suggests writing the dream down and giving it a new ending in which she stops calling out and walks the other way. She rehearses the new ending every evening  (see Figure 2). Within weeks, the dream comes less often and bothers her less. Oddly, she cannot recall ever dreaming the new ending. So what helped? 
{{RoundBoxBottom}}
===Does the new ending need to be dreamed? ===
Imagery rehearsal therapy (IRT), in which a nightmare is rewritten and the new version rehearsed while awake, is recommended for [[w:Nightmare disorder|nightmare disorder]] (Morgenthaler et al., 2018). In one trial, 36 patients rehearsed new endings and heard a sound during REM sleep, that, for half of them, had been paired with the new ending. This cued group had fewer nightmares and more positive dreams, although their dreams rarely resembled the rehearsed scripts. Yet distress, sleep quality, and depression improved no more than in the comparison group (Schwartz et al., 2022), so the cue altered dream content without adding emotional benefit. 

A later analysis of the same patients examined cathartic dreams, in which threat gives way to resolution, as with Natalie's lit doorway (Perogamvros et al., 2025). These dreams became more common with cueing, and their increase correlated with reduced depression. Because depression decreased no further in the cued group, cathartic dreams appear to accompany recovery rather than causing it, although with 18 participants per group a modest effect could have been missed. Similarly, re-imagining a nightmare without changing it reduced nightmares and distress about as much as rewriting it, relative to a wait-list (Kunze et al., 2017), and adding IRT to [[w:Insomnia|insomnia]] therapy gave 108 veterans with severe [[w:Post-traumatic stress disorder|post-traumatic stress disorder]] no additional benefit (Harb et al., 2019).

===From less distress to better coping ===
What these interventions share is engagement with the dream while awake. Natalie's late nights are a form of [[w:Avoidance coping|avoidance coping]], which may maintain distressing dreams, whereas writing and rehearsing the dream is closer to [[w:Emotional approach coping|emotional approach coping]], in which emotions are processed instead of avoided (Folkman &amp; Moskowitz, 2004; Rousseau &amp; Belleville, 2018). Other mechanisms proposed for IRT, such as a growing sense of control and changed beliefs about nightmares, also operate while awake, although few have been tested directly (Rousseau &amp; Belleville, 2018). 

In practical terms, low mood after a distressing dream is a typical carry-over effect and need not signal a problem. A recurring dream indicates an unresolved concern but says little about whether recovery is under way. Working with the dream while awake is the best-supported approach, and frequent, distressing nightmares warrant professional help. Even so, less distress about a dream is not yet adaptive coping, which requires better management of the stressor itself (Folkman &amp; Moskowitz, 2004). No study has measured that outcome, so whether Natalie copes better with her breakup remains unknown.

==Conclusion==
Natalie's story raised three possibilities: dreams might help people recover, show recovery already under way, or provide material to work with while awake. The evidence favours the second and third. That REM sleep reduces the emotional intensity of memories overnight remains unconfirmed. From night to morning, dream emotion carries over into mood, as the continuity hypothesis predicts (see Table 1). Over longer periods, fear extinction theory fits better: people with more fearful dreams report more adaptive emotion regulation, and those recovering from loss tend to dream about it with strong emotion. These associations are correlational, however, and experiments that change dream content have not shown that improvement depends on the changed dream. 

The most defensible answer to the chapter's question is that REM dreams contribute to emotional processing and adaptive coping mainly by reflecting current emotional states and supplying material that people regulate while awake rather than by acting as overnight therapy. In Natalie's case, the lit doorway was likely a sign of change already under way, and what helped was what she did with it after waking. Whether dreaming itself causes adaptive coping remains open, and answering that will require studies that track dream emotion and coping in the same people over weeks or months. 

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'''Take-home messages'''

* A single night of sleep does not reliably take the sting out of an upsetting memory. 
* Emotional dreams mirror what a person is carrying; they do not appear to heal it. 
* Dreams that engage emotionally with a loss tend to accompany recovery, even when that emotion is painful. 
* For a recurring, distressing dream, working with it while awake, by facing or rewriting it, is the best-supported approach.
{{RoundBoxBottom}}

==See also==

* [[Motivation and emotion/Book/2020/Coping and emotion|Coping and emotion]] (Book chapter, 2020)
* [[Motivation and emotion/Book/2025/Dreams and emotional problem-solving|Dreams and emotional problem-solving]] (Book chapter, 2025)
* [[w:Emotional self-regulation|Emotional self-regulation]] (Wikipedia)
* [[w:Nightmare disorder|Nightmare disorder]] (Wikipedia)
* [[Motivation and emotion/Book/2020/Nightmares and emotion|Nightmares and emotion]] (Book chapter, 2020)

==References==
{{Hanging indent|1=
Baber, G. R., Hamilton, N. A., Girard, J. M., Sikka, P., Watts, A., Jun, D., Gratton, M. K. P., Cohen, J. M., Quesada, A. K., Nichols, E. C., &amp; Cunningham, T. J. (2026). Testing affect regulation theories of dreaming. ''Sleep, 49''(5), Article zsag046. https://doi.org/10.1093/sleep/zsag046

Cartwright, R., Agargun, M. Y., Kirkby, J., &amp; Friedman, J. K. (2006). Relation of dreams to waking concerns. ''Psychiatry Research, 141''(3), 261–270. https://doi.org/10.1016/j.psychres.2005.05.013

Cartwright, R., Luten, A., Young, M., Mercer, P., &amp; Bears, M. (1998). Role of REM sleep and dream affect in overnight mood regulation: A study of normal volunteers. ''Psychiatry Research, 81''(1), 1–8. https://doi.org/10.1016/S0165-1781(98)00089-4

Delorme, M.-A., Lortie-Lussier, M., &amp; De Koninck, J. (2002). Stress and coping in the waking and dreaming states during an examination period. ''Dreaming, 12''(4), 171–183. https://doi.org/10.1023/A:1021128326940

Domhoff, G. W. (2019). The neurocognitive theory of dreams at age 20: An assessment and a comparison with four other theories of dreaming. ''Dreaming, 29''(4), 265–302. https://doi.org/10.1037/drm0000119

Folkman, S., &amp; Moskowitz, J. T. (2004). Coping: Pitfalls and promise. ''Annual Review of Psychology, 55'', 745–774. https://doi.org/10.1146/annurev.psych.55.090902.141456

Gross, J. J. (2015). Emotion regulation: Current status and future prospects. ''Psychological Inquiry, 26''(1), 1–26. https://doi.org/10.1080/1047840X.2014.940781

Harb, G. C., Cook, J. M., Phelps, A. J., Gehrman, P. R., Forbes, D., Localio, R., Harpaz-Rotem, I., Gur, R. C., &amp; Ross, R. J. (2019). Randomized controlled trial of imagery rehearsal for posttraumatic nightmares in combat veterans. ''Journal of Clinical Sleep Medicine, 15''(5), 757–767. https://doi.org/10.5664/jcsm.7770

Kunze, A. E., Arntz, A., Morina, N., Kindt, M., &amp; Lancee, J. (2017). Efficacy of imagery rescripting and imaginal exposure for nightmares: A randomized wait-list controlled trial. ''Behaviour Research and Therapy, 97'', 14–25. https://doi.org/10.1016/j.brat.2017.06.005

Lara-Carrasco, J., Nielsen, T. A., Solomonova, E., Levrier, K., &amp; Popova, A. (2009). Overnight emotional adaptation to negative stimuli is altered by REM sleep deprivation and is correlated with intervening dream emotions. ''Journal of Sleep Research, 18''(2), 178–187. https://doi.org/10.1111/j.1365-2869.2008.00709.x

Lipinska, G., Austin, H., Moonsamy, J. R., Henry, M., Lewis, R., Baldwin, D. S., Thomas, K. G. F., &amp; Stuart, B. (2022). Preferential consolidation of emotional reactivity during sleep: A systematic review and meta-analysis. ''Frontiers in Behavioral Neuroscience, 16'', Article 976047. https://doi.org/10.3389/fnbeh.2022.976047

Lipinska, G., Stuart, B., Thomas, K. G. F., Baldwin, D. S., &amp; Bolinger, E. (2019). Preferential consolidation of emotional memory during sleep: A meta-analysis. ''Frontiers in Psychology, 10'', Article 1014. https://doi.org/10.3389/fpsyg.2019.01014

Morgenthaler, T. I., Auerbach, S., Casey, K. R., Kristo, D., Maganti, R., Ramar, K., Zak, R., &amp; Kartje, R. (2018). Position paper for the treatment of nightmare disorder in adults: An American Academy of Sleep Medicine position paper. ''Journal of Clinical Sleep Medicine, 14''(6), 1041–1055. https://doi.org/10.5664/jcsm.7178

Nielsen, T., &amp; Levin, R. (2007). Nightmares: A new neurocognitive model. ''Sleep Medicine Reviews, 11''(4), 295–310. https://doi.org/10.1016/j.smrv.2007.03.004

Perogamvros, L., Rochas, V., Beau, J.-B., Sterpenich, V., &amp; Bayer, L. (2025). The cathartic dream: Using a large language model to study a new type of functional dream in healthy and clinical populations. ''Journal of Sleep Research, 34''(6), Article e70001. https://doi.org/10.1111/jsr.70001

Pesonen, A.-K., Koskinen, M.-K., Vuorenhela, N., Halonen, R., Mäkituuri, S., Selin, M., Luokkala, S., Suutari, A., &amp; Hovatta, I. (2024). The effect of REM-sleep disruption on affective processing: A systematic review of human and animal experimental studies. ''Neuroscience and Biobehavioral Reviews, 162'', Article 105714. https://doi.org/10.1016/j.neubiorev.2024.105714

Rousseau, A., &amp; Belleville, G. (2018). The mechanisms of action underlying the efficacy of psychological nightmare treatments: A systematic review and thematic analysis of discussed hypotheses. ''Sleep Medicine Reviews, 39'', 122–133. https://doi.org/10.1016/j.smrv.2017.08.004

Schwartz, S., Clerget, A., &amp; Perogamvros, L. (2022). Enhancing imagery rehearsal therapy for nightmares with targeted memory reactivation. ''Current Biology, 32''(22), 4808–4816. https://doi.org/10.1016/j.cub.2022.09.032

Sikka, P., Engelbrektsson, H., Zhang, J., &amp; Gross, J. J. (2022). Negative dream affect is associated with next-day affect level, but not with affect reactivity or affect regulation. ''Frontiers in Behavioral Neuroscience, 16'', Article 981289. https://doi.org/10.3389/fnbeh.2022.981289

Solms, M. (2000). Dreaming and REM sleep are controlled by different brain mechanisms. ''Behavioral and Brain Sciences, 23''(6), 843–850. https://doi.org/10.1017/S0140525X00003988

Sterpenich, V., Perogamvros, L., Tononi, G., &amp; Schwartz, S. (2020). Fear in dreams and in wakefulness: Evidence for day/night affective homeostasis. ''Human Brain Mapping, 41''(3), 840–850. https://doi.org/10.1002/hbm.24843

van der Helm, E., Yao, J., Dutt, S., Rao, V., Saletin, J. M., &amp; Walker, M. P. (2011). REM sleep depotentiates amygdala activity to previous emotional experiences. ''Current Biology, 21''(23), 2029–2032. https://doi.org/10.1016/j.cub.2011.10.052

Walker, M. P., &amp; van der Helm, E. (2009). Overnight therapy? The role of sleep in emotional brain processing. ''Psychological Bulletin, 135''(5), 731–748. https://doi.org/10.1037/a0016570
}}

==External links==
* [https://shows.acast.com/sleep-science-pod/episodes/ep12-sleep-dreams-and-mental-health Sleep, dreams and mental health] (The Sleep Science Pod)
* [https://theconversation.com/the-science-of-dreams-and-nightmares-what-is-going-on-in-our-brains-while-were-sleeping-210901 The science of dreams and nightmares – what is going on in our brains while we're sleeping?] (The Conversation)
* [https://www.scientificamerican.com/podcast/episode/dreams-help-soothe-your-bad-memorie-11-11-28/ Dreams help soothe your bad memories] (Scientific American)

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==Overview==
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'''Case study: Natalie part 1 ''' [[File:Dreaming.jpg|Dreaming|right|thumb|250px|'''Figure 1'''. Natalie's recurring dream after her breakup leaves her feeling sad when she wakes]]
Since her breakup, Natalie keeps having the same dream. She's been left behind somewhere, calling out to someone who never turns around (see Figure 1). When she wakes the details fade, but the feeling stays. Then one night, after her first good day in weeks, the dream changes: she stops calling out, notices a lit doorway, and walks through it. She wakes feeling better, and that afternoon she finally packs away his things. Did the dream help her move on, show that she was already moving on, or give her something to work with once awake? 
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[[w:Dream|Dreams]] are commonly reported after awakenings from [[w:Rapid eye movement sleep|rapid eye movement (REM) sleep]] (Solms, 2000), and REM sleep has been described as a form of &quot;overnight therapy&quot; (Walker &amp; van der Helm, 2009, p. 731). Whether dreams contribute to this emotional work, or merely reflect processing that occurs elsewhere, remains unresolved. The answer has practical implications: if dreams help people heal, emotional dreams may be part of recovery; if they only mirror emotional states, they may signal when support is needed while awake.

Three concepts need to be kept apart. ''Emotional processing'' refers to overnight changes in the retention or intensity of emotional memories. [[w:Emotional self-regulation|''Emotion regulation'']] is any process, deliberate or automatic, that alters the course of an emotional response (Gross, 2015). [[Motivation and emotion/Book/2020/Coping and emotion|''Coping'']] refers to the thoughts and behaviours people use to manage stress, and it is adaptive only when it suits the situation and improves outcomes (Folkman &amp; Moskowitz, 2004). A dream may therefore reflect emotional processing without regulating emotion, or ease distress without changing how a person copes. 

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'''Focus questions'''

* How do REM sleep and dreaming each contribute to overnight emotional processing? 
* What do competing theories propose dreams do with emotion? 
* How is dream emotion related to the way people cope while awake? 
* How can people work with emotional dreams to support coping?  

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== How do REM sleep and dreaming each contribute to overnight emotional processing? ==
REM sleep is a brain state characterised by rapid eye movements, heightened brain activity, and muscle paralysis, whereas dreaming is a conscious experience. Because the two usually coincide, findings about one are often attributed to the other. 

===REM sleep and emotional memories ===
According to the ''sleep to forget, sleep to remember'' model, the brain replays recent emotional memories during REM sleep, when [[wikipedia:Norepinephrine|noradrenaline]], a neurotransmitter involved in arousal, is low (Walker &amp; van der Helm, 2009). Replay in this calm state is thought to preserve a memory's content while weakening its emotional charge, so that a past argument can be recalled clearly without making the heart race. The model makes two predictions: emotional memories should be retained better after sleep, and emotional reactivity to them should decline. If the charge survives the night, replay should recur, which may explain recurring dreams like Natalie's.  

Early neuroimaging appeared to support the second prediction. When 34 adults viewed emotional images twice, 12 hours apart, responses in the [[w:Amygdala|amygdala]], a region involved in threat detection, decreased in those who slept between sessions and increased in those who stayed awake (van der Helm et al., 2011). Noradrenaline was inferred from brainwave patterns rather than measured, however, so the study could not show that low-noradrenaline REM sleep was responsible.     

Larger reviews support neither prediction. For memory, a [[w:Meta-analysis|meta-analysis]] of 31 studies found that sleep did not strengthen emotional memories more than neutral ones (Lipinska et al., 2019). For emotional reactivity, a review of 24 studies found that sleep did not consistently change physiological responses to negative images, although only five studies measured them; participants also rated the images as more arousing after sleep (Lipinska et al., 2022). Because both reviews compared sleep with wakefulness, neither could isolate REM sleep. That requires selective REM deprivation, which involves stressful repeated awakenings that disturb other sleep stages, and the few human studies suggest that reducing REM sleep may strengthen emotional memories (Pesonen et al., 2024). The overnight-therapy account therefore remains plausible but unconfirmed.

===What does dreaming add? ===

Dreaming is more than a by-product of REM sleep: it can stop after brain damage while REM sleep continues, and some dreams occur outside REM sleep (Solms, 2000). Only one study has  measured both in the same people. Lara-Carrasco et al. (2009) partly deprived about half of 35 adults of REM sleep, collected their dreams, and had everyone rate negative images that evening and the next morning. Contrary to the REM model, the deprived group showed a larger overnight decrease in arousal. Separately, participants whose final dream was less negative rated the images as less unpleasant by morning. 

The authors had predicted the reverse, expecting the participants who adapted best to report more negative dreams. The result instead fits emotion carrying over into the morning ratings although the hour between waking and rating may have shaped this link. REM sleep and dream emotion thus tracked different aspects of the emotional response, so dreaming may contribute something of its own. Being correlational, however, the findings cannot show whether dreams produce overnight change or merely reflect it, which is exactly where the [[#What do competing theories propose dreams do with emotion?|theories]] disagree.    
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{Which statement best summarises the evidence on REM sleep and upsetting memories? 
|type=&quot;()&quot;}
- REM sleep reliably reduces the emotional intensity of upsetting memories  
+ The idea that REM sleep reduces the intensity of upsetting memories is plausible but unconfirmed 
&lt;/quiz&gt;
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== What do competing theories propose dreams do with emotion? ==
The three leading theories agree that waking emotion shapes dream emotion but disagree about what dream emotion does next, and over what timescale (see Table 1). Timescale determines how each can be tested: relief by morning can be checked against the next day's mood, whereas change over weeks is much harder to observe. 
{| class=&quot;wikitable&quot; style=&quot;width:100%;&quot;
|+ style=&quot;text-align:left;&quot; | '''Table 1'''&lt;br /&gt;''Three Theories of What Dreams Do With Emotion''
|-
! scope=&quot;col&quot; |
! scope=&quot;col&quot; |Continuity hypothesis 
! scope=&quot;col&quot; |Fear extinction theory 
! scope=&quot;col&quot; |Mood regulation theory 
|-
! scope=&quot;row&quot; |Core claim 
|Dreams simulate current concerns 
|Dreams place fear memories in safe new contexts
|Dreams work through low mood across the night 
|-
! scope=&quot;row&quot; |Natalie's recurring dream means 
|She is still preoccupied with the loss 
|Extinction under heavy emotional load 
|Regulation not yet complete 
|-
! scope=&quot;row&quot; |Main prediction 
|Dream emotion carries into the next morning 
|Fear gradually decreases 
|Mood is better by morning, if it was low
|-
! scope=&quot;row&quot; |Timescale 
|Immediate 
|Weeks or longer
|One night 
|}
''Note.'' Based on Cartwright et al. (1998), Domhoff (2019), and Nielsen and Levin (2007). 
=== Continuity hypothesis ===
The continuity hypothesis holds that dreams dramatise the dreamer's current concerns. In Domhoff's (2019) neurocognitive version, dreaming is an &quot;embodied simulation&quot; (p. 265) generated by the [[w:Default mode network|default mode network]], which also supports daydreaming. On this view, Natalie's dream portrays her loss without resolving it, much as daydreaming about an ex-partner would. Domhoff concludes that an emotion-regulating function &quot;remains highly unlikely, and at best inconclusive, after decades of research studies&quot; (p. 287), noting that at least a quarter of REM dream reports contain no emotion. The hypothesis is parsimonious, but because mirroring can accommodate almost any association between dreams and waking life, it can be distinguished from functional theories only when dream emotion predicts outcomes that waking mood alone does not. 

===Fear extinction theory ===
[[w:Extinction (psychology)|Extinction]] occurs when repeated encounters with a feared cue pass without harm, so that a new safety memory forms and competes with the original fear memory instead of erasing it. Nielsen and Levin (2007) propose that dreams support this process offline by recombining elements of fear memories with safe or neutral material. In their illustration, a dream set in a dark alley changes when &quot;suddenly I found myself in a brightly lit street&quot; (p. 302), and the fear subsides, as it did for Natalie at the lit doorway. 

Two factors influence whether this process succeeds. ''Affect load'' is a state: the current burden that recent stress places on a person's capacity to regulate emotion. ''Affect distress'' is a trait: a stable tendency to respond to emotional events with heightened distress (Nielsen &amp; Levin, 2007, p. 301-302). Bad dreams and nightmares lie on a continuum, with nightmares indicating that extinction is struggling under heavy affect load. From this perspective, Natalie's recurring dream reflects the strain of the breakup rather than a breakdown in extinction. 

It follows that a frightening dream need not bring relief the next day, whereas people whose dreams repeatedly engage with fear should regulate better over time. The theory's weakness is its flexibility. Relief after a frightening dream can be seen as successful extinction and distress as extinction overloaded, so unless a successful dream is defined in advance, almost any outcome fits. 

===Mood regulation theory ===
Mood regulation theory proposes that successive REM dreams across one night work through low mood, shifting from negative towards positive emotion. Cartwright et al. (1998) tested this in 60 students without depression. Depressed mood fell overnight, and lower mood before sleep predicted a more negative first dream, but only the 10 students with the lowest pre-sleep mood showed the predicted sequence of negative dreams early and more positive dreams later. The authors therefore proposed a threshold: dreams moderate mood only when unhappiness is &quot;at least modest&quot; (p. 7). 

This threshold both protects the theory and limits it. It explains why studies of contented people find little, but it leaves the core pattern resting on 10 participants and never formally tested, Kramer's group, who first proposed the theory, had once failed to replicate their own effect (Nielsen &amp; Levin, 2007). Mood improved even on a night when every REM period was interrupted, so overnight relief did not depend on undisturbed dreaming. The authors suggested that describing dreams on waking may itself have helped (Cartwright et al., 1998).
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{According to fear extinction theory, when should the benefits of a frightening dream appear?  
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- By the next morning.
+ Gradually, over weeks or longer.
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== How is dream emotion related to the way people cope while awake? ==
Gross (2015) defines emotion regulation by &quot;the activation of a goal to influence the emotion trajectory&quot; (p. 5), a goal that can operate implicitly. Because a dream has no obvious goal, any regulation it achieves must be implicit, and the question for coping is whether its effects carry into waking life. ''Within-person'' comparisons test continuity and mood regulation by asking whether nights with more negative dreams are followed by more negative days. ''Between-person'' comparisons 
test fear extinction by asking whether people who generally dream one way also regulate emotion differently. 

===Next-morning mood ===
Night-to-night evidence generally supports continuity. Over five days, 40 adults rated their dream emotions and morning mood, then viewed negative images, sometimes while trying to [[Motivation and emotion/Book/2025/Cognitive strategies and emotion regulation|reappraise]] them (Sikka et al., 2022). More negative dream emotion was associated with more negative morning mood but not with how strongly participants reacted to the images or how well they regulated, and [[w:Bayes factor|Bayesian analyses]] favoured the absence of both links, which counts as evidence against them. A larger study of 4,715 mornings from 536 adults found the same carry-over, with frightening dreams followed by about 7% more negative mood. Dreams that combined fear with joy, however, were more often followed by mornings free of negative mood (Baber et al., 2026). 

These results contradict mood regulation's overnight prediction, at least in largely healthy samples, but their support for continuity is weaker than it first appears. Dream emotion is reported after waking, so a lingering morning mood could affect both ratings. Most dreams were also recalled at home from unidentified sleep stages, and were not necessarily REM dreams. Nor can these results refute fear extinction, which never predicted overnight relief. 
===Between-person comparisons ===
Between people, the pattern reverses. People whose dreams were more fearful on average reported greater use of adaptive regulation strategies, such as positive reappraisal and acceptance, even after controlling for [[w:Neuroticism|neuroticism]], which itself wasassociated with fearful dreaming (Baber et al., 2026). In a separate study of 89 adults who kept a week-long dream diary, those who reported dream fear more often responded more calmly to frightening images while awake, with smaller pupil responses, weaker amygdala activity, and stronger activity in the medial [[w:Prefrontal cortex|prefrontal cortex]], which helps dampen fear (Sterpenich et al., 2020). Because self-report and neural measures converge, the association is credible and fits the gradual effect that fear extinction predicts. 

The direction of influence is unclear, however, since people who suppress fear during the day may simply experience more of it at night (Sterpenich et al., 2020). Baber et al. (2026) found a counterintuitive result: participants who reported more adaptive regulation felt worse after frightening dreams than those who reported less. The authors suggested that such people may be more aware of their emotions, may reappraise the dream on waking as only a dream, or may need a brief rise in distress to desensitise, as in [[w:Exposure therapy|exposure therapy]]. The last two possibilities place regulation after waking, with the dream supplying the material.  

Coping itself has rarely been measured. Among 35 female students preparing for examinations, those who dreamed about the exam reported less active problem-solving while awake, whereas greater waking use of positive reappraisal was associated with more problem-solving within dreams (Delorme et al., 2002). Coping style may shape dream content as much as dreams shape coping. 

===Dreaming through a real loss ===
Real loss provides the strongest test, because adaptation to it unfolds over months. 
Cartwright et al. (2006) woke 30 adults going through divorce, 20 of them depressed, from every REM period on three nights over five months. Depressed participants who later recovered had more fully developed dreams, and their dreams about the former spouse contained mostly negative emotion and were linked to other memories. Among those who stayed depressed, spouse dreams were emotionally flat and isolated. Recovery was thus associated with dreams that engaged with the loss, even painfully. This fits fear extinction's idea of recombination better than overnight mood repair, although Cartwright et al. interpreted it as mood regulation through links to earlier memories. 

The spouse-dream comparison rested on only six people who recovered and four who did not. A more serious problem is that severe depression blunts dream emotion, so flat dreams may indicate deeper depression rather than cause slower recovery (Cartwright et al., 2006). The same problem of direction applies throughout this section. 
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{In the same person, what usually follows a night with a frightening dream?
|type=&quot;()&quot;}
- Better emotion regulation the next day.   
+ A somewhat worse morning mood. 
&lt;/quiz&gt;
&lt;/div&gt;
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== How can people work with emotional dreams to support coping?  ==
Correlational studies cannot establish whether dreams influence coping, but experiments that change dreams can. The only such experiments with emotional outcomes come from nightmare treatment (see [[Motivation and emotion/Book/2020/Nightmares and emotion|Nightmares and emotion]]), so they serve  here as a test case. 
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[[File:Woman writing on a notebook with a pen.jpg|Woman writing on a notebook with a pen|right|thumb|200px|'''Figure 2'''. Rewriting a recurring dream's ending while awake is the core of imagery rehearsal therapy.]]
'''Case study: Natalie part 2'''

During a stressful fortnight, the old dream returns and Natalie starts staying up late to avoid it. Her psychologist suggests writing the dream down and giving it a new ending in which she stops calling out and walks the other way. She rehearses the new ending every evening  (see Figure 2). Within weeks, the dream comes less often and bothers her less. Oddly, she cannot recall ever dreaming the new ending. So what helped? 
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===Does the new ending need to be dreamed? ===
Imagery rehearsal therapy (IRT), in which a nightmare is rewritten and the new version rehearsed while awake, is recommended for [[w:Nightmare disorder|nightmare disorder]] (Morgenthaler et al., 2018). In one trial, 36 patients rehearsed new endings and heard a sound during REM sleep, that, for half of them, had been paired with the new ending. This cued group had fewer nightmares and more positive dreams, although their dreams rarely resembled the rehearsed scripts. Yet distress, sleep quality, and depression improved no more than in the comparison group (Schwartz et al., 2022), so the cue altered dream content without adding emotional benefit. 

A later analysis of the same patients examined cathartic dreams, in which threat gives way to resolution, as with Natalie's lit doorway (Perogamvros et al., 2025). These dreams became more common with cueing, and their increase correlated with reduced depression. Because depression decreased no further in the cued group, cathartic dreams appear to accompany recovery rather than causing it, although with 18 participants per group a modest effect could have been missed. Similarly, re-imagining a nightmare without changing it reduced nightmares and distress about as much as rewriting it, relative to a wait-list (Kunze et al., 2017), and adding IRT to [[w:Insomnia|insomnia]] therapy gave 108 veterans with severe [[w:Post-traumatic stress disorder|post-traumatic stress disorder]] no additional benefit (Harb et al., 2019).

===From less distress to better coping ===
What these interventions share is engagement with the dream while awake. Natalie's late nights are a form of [[w:Avoidance coping|avoidance coping]], which may maintain distressing dreams, whereas writing and rehearsing the dream is closer to [[w:Emotional approach coping|emotional approach coping]], in which emotions are processed instead of avoided (Folkman &amp; Moskowitz, 2004; Rousseau &amp; Belleville, 2018). Other mechanisms proposed for IRT, such as a growing sense of control and changed beliefs about nightmares, also operate while awake, although few have been tested directly (Rousseau &amp; Belleville, 2018). 

In practical terms, low mood after a distressing dream is a typical carry-over effect and need not signal a problem. A recurring dream indicates an unresolved concern but says little about whether recovery is under way. Working with the dream while awake is the best-supported approach, and frequent, distressing nightmares warrant professional help. Even so, less distress about a dream is not yet adaptive coping, which requires better management of the stressor itself (Folkman &amp; Moskowitz, 2004). No study has measured that outcome, so whether Natalie copes better with her breakup remains unknown.

==Conclusion==
Natalie's story raised three possibilities: dreams might help people recover, show recovery already under way, or provide material to work with while awake. The evidence favours the second and third. That REM sleep reduces the emotional intensity of memories overnight remains unconfirmed. From night to morning, dream emotion carries over into mood, as the continuity hypothesis predicts (see Table 1). Over longer periods, fear extinction theory fits better: people with more fearful dreams report more adaptive emotion regulation, and those recovering from loss tend to dream about it with strong emotion. These associations are correlational, however, and experiments that change dream content have not shown that improvement depends on the changed dream. 

The most defensible answer to the chapter's question is that REM dreams contribute to emotional processing and adaptive coping mainly by reflecting current emotional states and supplying material that people regulate while awake rather than by acting as overnight therapy. In Natalie's case, the lit doorway was likely a sign of change already under way, and what helped was what she did with it after waking. Whether dreaming itself causes adaptive coping remains open, and answering that will require studies that track dream emotion and coping in the same people over weeks or months. 

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'''Take-home messages'''

* A single night of sleep does not reliably take the sting out of an upsetting memory. 
* Emotional dreams mirror what a person is carrying; they do not appear to heal it. 
* Dreams that engage emotionally with a loss tend to accompany recovery, even when that emotion is painful. 
* For a recurring, distressing dream, working with it while awake, by facing or rewriting it, is the best-supported approach.
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==See also==

* [[Motivation and emotion/Book/2020/Coping and emotion|Coping and emotion]] (Book chapter, 2020)
* [[Motivation and emotion/Book/2025/Dreams and emotional problem-solving|Dreams and emotional problem-solving]] (Book chapter, 2025)
* [[w:Emotional self-regulation|Emotional self-regulation]] (Wikipedia)
* [[w:Nightmare disorder|Nightmare disorder]] (Wikipedia)
* [[Motivation and emotion/Book/2020/Nightmares and emotion|Nightmares and emotion]] (Book chapter, 2020)

==References==
{{Hanging indent|1=
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Cartwright, R., Agargun, M. Y., Kirkby, J., &amp; Friedman, J. K. (2006). Relation of dreams to waking concerns. ''Psychiatry Research, 141''(3), 261–270. https://doi.org/10.1016/j.psychres.2005.05.013

Cartwright, R., Luten, A., Young, M., Mercer, P., &amp; Bears, M. (1998). Role of REM sleep and dream affect in overnight mood regulation: A study of normal volunteers. ''Psychiatry Research, 81''(1), 1–8. https://doi.org/10.1016/S0165-1781(98)00089-4

Delorme, M.-A., Lortie-Lussier, M., &amp; De Koninck, J. (2002). Stress and coping in the waking and dreaming states during an examination period. ''Dreaming, 12''(4), 171–183. https://doi.org/10.1023/A:1021128326940

Domhoff, G. W. (2019). The neurocognitive theory of dreams at age 20: An assessment and a comparison with four other theories of dreaming. ''Dreaming, 29''(4), 265–302. https://doi.org/10.1037/drm0000119

Folkman, S., &amp; Moskowitz, J. T. (2004). Coping: Pitfalls and promise. ''Annual Review of Psychology, 55'', 745–774. https://doi.org/10.1146/annurev.psych.55.090902.141456

Gross, J. J. (2015). Emotion regulation: Current status and future prospects. ''Psychological Inquiry, 26''(1), 1–26. https://doi.org/10.1080/1047840X.2014.940781

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Kunze, A. E., Arntz, A., Morina, N., Kindt, M., &amp; Lancee, J. (2017). Efficacy of imagery rescripting and imaginal exposure for nightmares: A randomized wait-list controlled trial. ''Behaviour Research and Therapy, 97'', 14–25. https://doi.org/10.1016/j.brat.2017.06.005

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Lipinska, G., Stuart, B., Thomas, K. G. F., Baldwin, D. S., &amp; Bolinger, E. (2019). Preferential consolidation of emotional memory during sleep: A meta-analysis. ''Frontiers in Psychology, 10'', Article 1014. https://doi.org/10.3389/fpsyg.2019.01014

Morgenthaler, T. I., Auerbach, S., Casey, K. R., Kristo, D., Maganti, R., Ramar, K., Zak, R., &amp; Kartje, R. (2018). Position paper for the treatment of nightmare disorder in adults: An American Academy of Sleep Medicine position paper. ''Journal of Clinical Sleep Medicine, 14''(6), 1041–1055. https://doi.org/10.5664/jcsm.7178

Nielsen, T., &amp; Levin, R. (2007). Nightmares: A new neurocognitive model. ''Sleep Medicine Reviews, 11''(4), 295–310. https://doi.org/10.1016/j.smrv.2007.03.004

Perogamvros, L., Rochas, V., Beau, J.-B., Sterpenich, V., &amp; Bayer, L. (2025). The cathartic dream: Using a large language model to study a new type of functional dream in healthy and clinical populations. ''Journal of Sleep Research, 34''(6), Article e70001. https://doi.org/10.1111/jsr.70001

Pesonen, A.-K., Koskinen, M.-K., Vuorenhela, N., Halonen, R., Mäkituuri, S., Selin, M., Luokkala, S., Suutari, A., &amp; Hovatta, I. (2024). The effect of REM-sleep disruption on affective processing: A systematic review of human and animal experimental studies. ''Neuroscience and Biobehavioral Reviews, 162'', Article 105714. https://doi.org/10.1016/j.neubiorev.2024.105714

Rousseau, A., &amp; Belleville, G. (2018). The mechanisms of action underlying the efficacy of psychological nightmare treatments: A systematic review and thematic analysis of discussed hypotheses. ''Sleep Medicine Reviews, 39'', 122–133. https://doi.org/10.1016/j.smrv.2017.08.004

Schwartz, S., Clerget, A., &amp; Perogamvros, L. (2022). Enhancing imagery rehearsal therapy for nightmares with targeted memory reactivation. ''Current Biology, 32''(22), 4808–4816. https://doi.org/10.1016/j.cub.2022.09.032

Sikka, P., Engelbrektsson, H., Zhang, J., &amp; Gross, J. J. (2022). Negative dream affect is associated with next-day affect level, but not with affect reactivity or affect regulation. ''Frontiers in Behavioral Neuroscience, 16'', Article 981289. https://doi.org/10.3389/fnbeh.2022.981289

Solms, M. (2000). Dreaming and REM sleep are controlled by different brain mechanisms. ''Behavioral and Brain Sciences, 23''(6), 843–850. https://doi.org/10.1017/S0140525X00003988

Sterpenich, V., Perogamvros, L., Tononi, G., &amp; Schwartz, S. (2020). Fear in dreams and in wakefulness: Evidence for day/night affective homeostasis. ''Human Brain Mapping, 41''(3), 840–850. https://doi.org/10.1002/hbm.24843

van der Helm, E., Yao, J., Dutt, S., Rao, V., Saletin, J. M., &amp; Walker, M. P. (2011). REM sleep depotentiates amygdala activity to previous emotional experiences. ''Current Biology, 21''(23), 2029–2032. https://doi.org/10.1016/j.cub.2011.10.052

Walker, M. P., &amp; van der Helm, E. (2009). Overnight therapy? The role of sleep in emotional brain processing. ''Psychological Bulletin, 135''(5), 731–748. https://doi.org/10.1037/a0016570
}}

==External links==
* [https://shows.acast.com/sleep-science-pod/episodes/ep12-sleep-dreams-and-mental-health Sleep, dreams and mental health] (The Sleep Science Pod)
* [https://theconversation.com/the-science-of-dreams-and-nightmares-what-is-going-on-in-our-brains-while-were-sleeping-210901 The science of dreams and nightmares – what is going on in our brains while we're sleeping?] (The Conversation)
* [https://www.scientificamerican.com/podcast/episode/dreams-help-soothe-your-bad-memorie-11-11-28/ Dreams help soothe your bad memories] (Scientific American)

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      <text bytes="65587" sha1="je4n3y3178ygpr5zt0i9ex8a2i68vwv" xml:space="preserve">&lt;noinclude&gt;Feedback [[wikiversity:FAQ/Template|template]] for the [[Motivation and emotion/Assessment/Chapter|book chapter]] exercise for the [[motivation and emotion]] unit.

Designed to be [[Help:Transclusion|transcluded]] on a chapter [[Help:Talk page|talk page]].
__NOTOC__&lt;/noinclude&gt;&lt;includeonly&gt;
==[[Motivation and emotion/Assessment/Chapter|Book chapter]] review and feedback==
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This chapter has been reviewed according to the [[Motivation and emotion/Assessment/Chapter/Marking criteria|marking criteria]]. Written feedback is provided below, plus there is a [[Motivation and emotion/Assessment/Chapter/Feedback|general feedback]] page. Please also check the chapter's [[Help:Page history|page history]] to check for editing changes made whilst reviewing through the chapter. Chapter marks will be available via {{Motivation and emotion/Canvas}} along with [[Motivation and emotion/Assessment/Social contribution|social contribution]] marks and feedback. Keep an eye on Announcements.
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===Overall===
{{{1|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Overview (5%)|Overview]]===
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===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Theory (20%)|Theory]]===
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===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Research (25%)|Research]]===
{{{4|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Integration (10%)|Integration]]===
{{{5|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Conclusion (5%)|Conclusion]]===
{{{6|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Style (20%)|Style]]===
{{{7|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Learning features (5%)|Learning features]]===
{{{8|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Social contribution (10%)|Social contribution]]===
{{{9|No comment}}}

{{RoundBoxBottom}}&lt;/includeonly&gt;&lt;noinclude&gt;{{collapse top|Simple example}}
==Simple example==
See also [[#Detailed example|detailed example]]
&lt;pre&gt;
&lt;!-- Official feedback --&gt;
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~~~~
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gives
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-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:47, 10 October 2025 (UTC)
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==Detailed example==
Example use of the template, with some common feedback comments:
&lt;small&gt;&lt;small&gt;&lt;small&gt;&lt;pre&gt;
&lt;!-- Official book chapter feedback --&gt;
{{MEBF/2026
|1=
&lt;!-- Overall comments... --&gt;
# This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem
# This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem
# This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem
# This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a basic chapter
# This is an insufficient chapter
# The main area(s) for potential improvement:
#* use the best psychological theory about the topic
#* more detailed review of the best psychological research about the topic 
#* quality of written expression
#* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]]
#* integrate more strongly with other chapters by using embedded links to related topics
#* overuse of genAI—express more in your own words; watch out for [[w:AI slop|AI slop]]
#* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter
&lt;!-- Overall - Edit summaries --&gt;
#* [[w:Help:Edit summary|Edit summaries]] are used to clearly communicated the changes made in most or all edits
#* Use more specific [[w:Help:Edit summary|edit summaries]] to clearly communicate the changes made in each edit
#* Use [[w:Help:Edit summary|edit summaries]] to briefly describe the changes made in each edit
&lt;!-- Overall - GenAI --&gt;
#* [[Motivation and emotion/Assessment/Using generative AI|genAI use]] is appropriately acknowledged
#* In some places, there is overreliance on genAI
#* In some places, there is overreliance on genAI, with insufficient acknowledged in edit summaries when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles
#* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in edit summaries with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]].
&lt;!-- Overall – Citations --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims
# Only cite sources that you consult
# All citations need to be in the References
&lt;!-- Overall – Word count --&gt;
# Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand
# Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes.
&lt;!-- Overall – Copyedits --&gt;
# For additional feedback, see the following comments and [ these copyedits]
|2=
&lt;!-- Overview – Comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped
&lt;!-- Overview – Scenario --&gt;
&lt;!-- Overview – Scenario - Description --&gt;
# Engaging scenario or case study
# Reasonably engaging scenario or case study
# Basic scenario or case study
# Use a more practical, real-life scenario; move review of research into a subsequent section
# Consider using an example that more people can relate to (less than 5% of the world population are university students)
# Add an engaging case study or scenario
&lt;!-- Overview – Scenario - Figure --&gt;
# Figure 1 is relevant to the scenario
# Figure 1 could be more relevant to the scenario
# Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section
# Include a relevant image
&lt;!-- Overview – Scenario - Feature box --&gt;
# The scenario uses an appropriate feature box
# Put the scenario in a feature box
&lt;!-- Overview – Explains problem --&gt;
# Clearly explains the psychological problem or phenomenon
# Explains the psychological problem or phenomenon reasonably well/in a basic way
# Briefly explains the psychological problem or phenomenon; provide more detail
# Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections.
# Clarity of written expression can be improved
&lt;!-- Overview – Focus questions --&gt;
# The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient
# The focus questions could be improved by:
## being more specific to the topic (i.e., the sub-title)
## matching the top-level headings more closely
## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]]
## splitting double-barrelled questions into separate questions
## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## being presented in a feature box to help guide the reader (fixed)
# Add focus questions in a feature box
# See copyedits for examples of possible improvements
|3=
&lt;!-- Theory comments... --&gt;
&lt;!-- Theory – Breadth --&gt;
# Excellent—key theories are very well explained and applied
# Very good—key theories are well explained and applied; minor areas for improvements
# Reasonably good—relevant theories are selected, described, and explained, with some room for improvement
# Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement
# A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic
# Insufficient use of relevant psychological theory about this topic
# Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question).
&lt;!-- Theory – Builds on --&gt;
# Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
&lt;!-- Theory – Depth --&gt;
# Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies)
&lt;!-- Theory – Tables/Figures/Lists --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information
&lt;!-- Theory – Citations --&gt;
# Key citations are well used
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
# If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source]
# If you didn't consult an original source, don't cite it
&lt;!-- Theory – Examples --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts
# Consider using more examples to illustrate theoretical concepts
# Use more examples to illustrate theoretical concepts
# Insufficient use of examples to illustrate theoretical concepts
|4=
&lt;!-- Research comments... --&gt;
&lt;!-- Research – Key findings --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research
# Excellent emphasis on systematic reviews and/or meta-analyses
# Greater emphasis on systematic reviews and/or meta-analyses would be ideal
# More detail about key studies would be ideal
# Claims are well referenced
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
&lt;!-- Research – Critical thinking --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident
# [[w:Critical thinking|Critical thinking]] about research could be further evidenced by:
## describing the methodology (e.g., sample, measures) in important studies
## considering the strength of relationships
## acknowledging limitations
## pointing out critiques/counterarguments
## suggesting ''specific'' directions for future research
|5=
&lt;!-- Integration comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research
# The chapter places more emphasis on theory than on research; strive for an integrated balance
# The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links
# Insufficient integration with related [[Motivation and emotion/Book|chapters]]
|6=
&lt;!-- Conclusion comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic summary and conclusion
# Insufficient as a cohesive summary of the best psychological theory and research about the topic
# Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words
# Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the edit summary.
# Highlights the importance of the problem or phenomenon of interest
# Highlight the importance of the problem or phenomenon of interest
&lt;!-- Conclusion – Key points --&gt;
# Key points are well summarised
# Key points are summarised in a basic way
# Summarise key points
&lt;!-- Conclusion – Focus questions --&gt;
# The focus questions are addressed
# The take-away messages for each focus question could be spelt out more clearly
# Address the focus questions
&lt;!-- Conclusion – Take-home messages --&gt;
# Clear take-home message(s)
# Add practical, take-home message(s)
&lt;!-- Conclusion – Word count --&gt;
# Not counted for marking purposes due to being over the maximum word count
|7=
&lt;!-- Written expression – Style comments... --&gt;
&lt;!-- Written expression – Written expression --&gt;
# Written expression
## The quality of written expression is excellent/very good/good/reasonably good/basic
## The quality of written expression is OK but there are several aspects which are below professional standard
## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills.
## Use active (e.g., &quot;this chapter explores&quot; or &quot;this chapter explored&quot;) rather than passive voice (e.g., &quot;this chapter will explore&quot; or &quot;this chapter has explored&quot;) [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/]
## The target audience is international, not domestic. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia].
## Reduce excessive use of bold font
&lt;!-- Written expression – Sentences --&gt;
## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression
## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+.
## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence.
&lt;!-- Written expression – Paragraphs --&gt;
## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences.
## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences.
## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs.
&lt;!-- Written expression – Language --&gt;
## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., &quot;it&quot;) instead of 1st (e.g., &quot;we&quot;) or 2nd person (e.g., &quot;you&quot;) in the main text. 1st or 2nd person can work well for case studies or feature boxes.
## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]].
## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]]
## &quot;Individuals&quot; is overused. &quot;People&quot; is usually a clearer term than &quot;individuals&quot;. Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally.
## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning
## Use permanent, rather than relative, time references. For example, instead of &quot;20 years ago&quot;, refer to something like &quot;at the beginning of the 21st century&quot;. In this way, the text will survive better into the future, without needing to be rewritten.
## Avoid overly emotive language (e.g,. *) in science-based communication
&lt;!-- Written expression – Layout --&gt;
# Layout
## The chapter is well structured, with major sections using sub-sections
## The headings could be more clearly aligned with the focus questions
## The structure is overly complicated; simplify and integrate
## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion
## The chapter structure is underdeveloped; expand by using subheadings
## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings
## Use the default heading style (e.g., remove additional numbers, italics, bold, and/or change in font size)
## See earlier comment about [[#Heading casing|heading casing]]
## Provide more descriptive headings
## Move links from headings into their first mention in text
## Remove abbreviations/citations from headings
## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags)
## Integrate learning features rather than having it as a stand-alone section
## The Overview and Conclusion should not have subheadings (fixed)
## Remove colons (:) from the ends of headings
&lt;!-- Written expression – Grammar --&gt;
# Grammar and spelling are excellent
# Grammar
## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback
## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas].
## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element
## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats')
## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who]
## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect]
## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)]
## Use past tense when describing research studies, although implications of findings could be in the present tense
&lt;!-- Written expression – Abbreviations --&gt;
## Abbreviations
### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out
### Check and correct formatting of abbreviations (such as e.g., i.e., etc.)
### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms.
### Spell out abbreviations on their first use, to explain them to the reader
### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards
### Only introduce abbreviations which are subsequently used
&lt;!-- Written expression – Spelling --&gt;
# Spelling
## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour)
## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages.
&lt;!-- Written expression – Proofreading --&gt;
# Proofreading
## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard
## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info]
&lt;!-- Written expression – APA style --&gt;
# APA style
## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY]
## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing for disorders, therapies, theories, etc.]
## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)]
&lt;!-- Written expression – APA style - Quotes --&gt;
## Use double (not single) quotation marks &quot;to introduce a word or phrase used ... as slang, or as an invented or coined expression&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## &quot;Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## Direct quotes need page numbers—even better, communicate about concepts in your own words
## Direct quotes are overused—it is better to communicate about concepts in your own words
&lt;!-- Written expression – Figures --&gt;
## Figures
### Very well/Well/Reasonably well captioned
### Brief captions; provide more detail to help connect the figure to the text
### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]].
### Add captions
&lt;!-- Written expression – Figures - Citations --&gt;
### Each Figure is referred to at least once within the main text using APA style
### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., &quot;(see Figure 1)&quot;; do not use bold, italics, check and correct capitalisation).
### Refer to each Figure at least once within the main text (e.g., &quot;(see Figure 1)&quot;)
&lt;!-- Written expression – Figures - Other --&gt;
### Some image uploads were removed because of a lack of sufficient/appropriate copyright information
### Numbering needs correcting
### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size)
&lt;!-- Written expression – Tables --&gt;
## Tables
### Very well/Well/Reasonably well captioned
### Brief caption(s); provide more explanatory detail about the table
### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]])
&lt;!-- Written expression – Tables - Citations --&gt;
### Each Table is referred to at least once within the main text using APA style
### Each Table is referred to at least once within the main text
### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation)
### Refer to each Table at least once within the main text (e.g., see Table 1)
&lt;!-- Written expression – Citations --&gt;
# Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags)
## If there are three or more authors, cite the first author followed by et al., then year. For example, either:
### in-text, Smith et al. (2020), or
### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020)
## Do not include author first name or initials
## Use ampersand (&amp;) inside [[w:Bracket#Parentheses|parentheses]] and &quot;and&quot; outside parentheses
## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra &amp; Aardvark, 2020)
## A full stop is needed after &quot;et al&quot; (i.e., &quot;et al.&quot;) because it is an abbreviation of [[wikt:et alii|et alii]]
## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]]
## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point)
## Check and correct placement of full-stops
## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois
## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources
# For citations, use APA style or wiki style, but not both
# Secondary citations are overused; strive to consult primary sources
&lt;!-- Written expression – References --&gt;
## References use excellent/very good/good/reasonably good/basic/poor APA style:
### Check and correct use of italicisation
### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization]
### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-)
### Include dois where available
### Hyperlink dois for 1-click access
### Provide the full titles of journals
### Remove &quot;Retrieved from &quot;
### Use alphabetical order
### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section
### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section
### Remove bullet-points; add hanging indent
&lt;!-- Feedback responsiveness ---&gt;
## No evidence of responsiveness to feedback on talk page
|8=
&lt;!-- Learning features comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features
&lt;!-- Learning features – Wikipedia embedded links --&gt;
# Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles
# Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
# Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
&lt;!-- Learning features – Wikiversity embedded links --&gt;
# Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]
# Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
# Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section
# Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
&lt;!-- Learning features – Figures, tables, feature boxes, scenarios --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s)
# Excellent/Very good/Good/Reasonably good/Basic/No use of table(s)
# Excellent/Very good/Good/Reasonably good/Basic use of feature box(es)
# No use of feature boxes other than the opening scenario
# Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples
# No use of scenarios, case studies, or examples, other than opening scenario
&lt;!-- Learning features – Quizzes --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s)
# The quiz questions could be improved by being more focused on the key points and/or take-home messages
# The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end
# The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]])
# No use of quiz(zes) and/or reflection question(s)
&lt;!-- Learning features – See also --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Also include links to related book chapters
## Also include links to related Wikipedia articles
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite
## Move external links into the [[{{PAGENAME}}#References|External links]] section
## Add more links
# [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count
&lt;!-- Learning features – External links --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section
## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite
## Target an international audience
## Add more links
## Link to the top 3-6 external resources about this topic
# [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count
|9=
&lt;!-- Social contribution comments... --&gt;
# ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]]
# ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence.
# Thanks for the Wiki Commons uploads
# Thanks very much for your extensive contributions
# Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# No logged contributions
}}
~~~~
&lt;/pre&gt;&lt;/small&gt;&lt;/small&gt;&lt;/small&gt;
gives
&lt;!-- Official book chapter feedback --&gt;
{{MEBF/2026
|1=
&lt;!-- Overall comments... --&gt;
# This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem
# This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem
# This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem
# This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a basic chapter
# This is an insufficient chapter
# The main area(s) for potential improvement:
#* use the best psychological theory about the topic
#* more detailed review of the best psychological research about the topic 
#* quality of written expression
#* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]]
#* integrate more strongly with other chapters by using embedded links to related topics
#* overuse of genAI—express more in your own words; watch out for [[w:AI slop|AI slop]]
#* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter
&lt;!-- Overall - Edit summaries --&gt;
#* [[w:Help:Edit summary|Edit summaries]] are used to clearly communicated the changes made in most or all edits
#* Use more specific [[w:Help:Edit summary|edit summaries]] to clearly communicate the changes made in each edit
#* Use [[w:Help:Edit summary|edit summaries]] to briefly describe the changes made in each edit
&lt;!-- Overall - GenAI --&gt;
#* [[Motivation and emotion/Assessment/Using generative AI|genAI use]] is appropriately acknowledged
#* In some places, there is overreliance on genAI
#* In some places, there is overreliance on genAI, with insufficient acknowledged in edit summaries when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles
#* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in edit summaries with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]].
&lt;!-- Overall – Citations --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims
# Only cite sources that you consult
# All citations need to be in the References
&lt;!-- Overall – Word count --&gt;
# Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand
# Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes.
&lt;!-- Overall – Copyedits --&gt;
# For additional feedback, see the following comments and [ these copyedits]
|2=
&lt;!-- Overview – Comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped
&lt;!-- Overview – Scenario --&gt;
&lt;!-- Overview – Scenario - Description --&gt;
# Engaging scenario or case study
# Reasonably engaging scenario or case study
# Basic scenario or case study
# Use a more practical, real-life scenario; move review of research into a subsequent section
# Consider using an example that more people can relate to (less than 5% of the world population are university students)
# Add an engaging case study or scenario
&lt;!-- Overview – Scenario - Figure --&gt;
# Figure 1 is relevant to the scenario
# Figure 1 could be more relevant to the scenario
# Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section
# Include a relevant image
&lt;!-- Overview – Scenario - Feature box --&gt;
# The scenario uses an appropriate feature box
# Put the scenario in a feature box
&lt;!-- Overview – Explains problem --&gt;
# Clearly explains the psychological problem or phenomenon
# Explains the psychological problem or phenomenon reasonably well/in a basic way
# Briefly explains the psychological problem or phenomenon; provide more detail
# Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections.
# Clarity of written expression can be improved
&lt;!-- Overview – Focus questions --&gt;
# The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient
# The focus questions could be improved by:
## being more specific to the topic (i.e., the sub-title)
## matching the top-level headings more closely
## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]]
## splitting double-barrelled questions into separate questions
## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## being presented in a feature box to help guide the reader (fixed)
# Add focus questions in a feature box
# See copyedits for examples of possible improvements
|3=
&lt;!-- Theory comments... --&gt;
&lt;!-- Theory – Breadth --&gt;
# Excellent—key theories are very well explained and applied
# Very good—key theories are well explained and applied; minor areas for improvements
# Reasonably good—relevant theories are selected, described, and explained, with some room for improvement
# Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement
# A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic
# Insufficient use of relevant psychological theory about this topic
# Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question).
&lt;!-- Theory – Builds on --&gt;
# Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
&lt;!-- Theory – Depth --&gt;
# Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies)
&lt;!-- Theory – Tables/Figures/Lists --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information
&lt;!-- Theory – Citations --&gt;
# Key citations are well used
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
# If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source]
# If you didn't consult an original source, don't cite it
&lt;!-- Theory – Examples --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts
# Consider using more examples to illustrate theoretical concepts
# Use more examples to illustrate theoretical concepts
# Insufficient use of examples to illustrate theoretical concepts
|4=
&lt;!-- Research comments... --&gt;
&lt;!-- Research – Key findings --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research
# Excellent emphasis on systematic reviews and/or meta-analyses
# Greater emphasis on systematic reviews and/or meta-analyses would be ideal
# More detail about key studies would be ideal
# Claims are well referenced
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
&lt;!-- Research – Critical thinking --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident
# [[w:Critical thinking|Critical thinking]] about research could be further evidenced by:
## describing the methodology (e.g., sample, measures) in important studies
## considering the strength of relationships
## acknowledging limitations
## pointing out critiques/counterarguments
## suggesting ''specific'' directions for future research
|5=
&lt;!-- Integration comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research
# The chapter places more emphasis on theory than on research; strive for an integrated balance
# The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links
# Insufficient integration with related [[Motivation and emotion/Book|chapters]]
|6=
&lt;!-- Conclusion comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic summary and conclusion
# Insufficient as a cohesive summary of the best psychological theory and research about the topic
# Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words
# Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the edit summary.
# Highlights the importance of the problem or phenomenon of interest
# Highlight the importance of the problem or phenomenon of interest
&lt;!-- Conclusion – Key points --&gt;
# Key points are well summarised
# Key points are summarised in a basic way
# Summarise key points
&lt;!-- Conclusion – Focus questions --&gt;
# The focus questions are addressed
# The take-away messages for each focus question could be spelt out more clearly
# Address the focus questions
&lt;!-- Conclusion – Take-home messages --&gt;
# Clear take-home message(s)
# Add practical, take-home message(s)
&lt;!-- Conclusion – Word count --&gt;
# Not counted for marking purposes due to being over the maximum word count
|7=
&lt;!-- Written expression – Style comments... --&gt;
&lt;!-- Written expression – Written expression --&gt;
# Written expression
## The quality of written expression is excellent/very good/good/reasonably good/basic
## The quality of written expression is OK but there are several aspects which are below professional standard
## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills.
## Use active (e.g., &quot;this chapter explores&quot; or &quot;this chapter explored&quot;) rather than passive voice (e.g., &quot;this chapter will explore&quot; or &quot;this chapter has explored&quot;) [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/]
## The target audience is international, not domestic. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia].
## Reduce excessive use of bold font
&lt;!-- Written expression – Sentences --&gt;
## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression
## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+.
## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence.
&lt;!-- Written expression – Paragraphs --&gt;
## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences.
## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences.
## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs.
&lt;!-- Written expression – Language --&gt;
## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., &quot;it&quot;) instead of 1st (e.g., &quot;we&quot;) or 2nd person (e.g., &quot;you&quot;) in the main text. 1st of 2nd person can work well for case studies or feature boxes.
## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]].## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]]
## &quot;Individuals&quot; is overused. &quot;People&quot; is usually a clearer term than &quot;individuals&quot;. Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally.
## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning
## Use permanent, rather than relative, time references. For example, instead of &quot;20 years ago&quot;, refer to something like &quot;at the beginning of the 21st century&quot;. In this way, the text will survive better into the future, without needing to be rewritten.
## Avoid overly emotive language (e.g,. *) in science-based communication
&lt;!-- Written expression – Layout --&gt;
# Layout
## The chapter is well structured, with major sections using sub-sections
## The headings could be more clearly aligned with the focus questions
## The structure is overly complicated; simplify and integrate
## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion
## The chapter structure is underdeveloped; expand by using subheadings
## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings
## Use the default heading style (e.g.,  remove additional numbers, italics, bo]ld, and/or change in font size)
## See earlier comment about [[#Heading casing|heading casing]]
## Provide more descriptive headings
## Move links from headings into their first mention in text
## Remove abbreviations/citations from headings
## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags)
## Integrate learning features rather than having it as a stand-alone section
## The Overview and Conclusion should not have subheadings (fixed)
## Remove colons (:) from the ends of headings
&lt;!-- Written expression – Grammar --&gt;
# Grammar and spelling are excellent
# Grammar
## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback
## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas].
## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element
## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats')
## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who]
## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect]
## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)]
## Use past tense when describing research studies, although implications of findings could be in the present tense
&lt;!-- Written expression – Abbreviations --&gt;
## Abbreviations
### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out
### Check and correct formatting of abbreviations (such as e.g., i.e., etc.)
### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms.
### Spell out abbreviations on their first use, to explain them to the reader
### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards
### Only introduce abbreviations which are subsequently used
&lt;!-- Written expression – Spelling --&gt;
# Spelling
## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour)
## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages.
&lt;!-- Written expression – Proofreading --&gt;
# Proofreading
## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard
## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info]
&lt;!-- Written expression – APA style --&gt;
# APA style
## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY]
## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing for disorders, therapies, theories, etc.]
## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)]
&lt;!-- Written expression – APA style - Quotes --&gt;
## Use double (not single) quotation marks &quot;to introduce a word or phrase used ... as slang, or as an invented or coined expression&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## &quot;Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## Direct quotes need page numbers—even better, communicate about concepts in your own words
## Direct quotes are overused—it is better to communicate about concepts in your own words
&lt;!-- Written expression – Figures --&gt;
## Figures
### Very well/Well/Reasonably well captioned
### Brief captions; provide more detail to help connect the figure to the text
### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]].
### Add captions
&lt;!-- Written expression – Figures - Citations --&gt;
### Each Figure is referred to at least once within the main text using APA style
### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., &quot;(see Figure 1)&quot;; do not use bold, italics, check and correct capitalisation).
### Refer to each Figure at least once within the main text (e.g., &quot;(see Figure 1)&quot;)
&lt;!-- Written expression – Figures - Other --&gt;
### Some image uploads were removed because of a lack of sufficient/appropriate copyright information
### Numbering needs correcting
### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size)
&lt;!-- Written expression – Tables --&gt;
## Tables
### Very well/Well/Reasonably well captioned
### Brief caption(s); provide more explanatory detail about the table
### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]])
&lt;!-- Written expression – Tables - Citations --&gt;
### Each Table is referred to at least once within the main text using APA style
### Each Table is referred to at least once within the main text
### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation)
### Refer to each Table at least once within the main text (e.g., see Table 1)
&lt;!-- Written expression – Citations --&gt;
# Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags)
## If there are three or more authors, cite the first author followed by et al., then year. For example, either:
### in-text, Smith et al. (2020), or
### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020)
## Do not include author first name or initials
## Use ampersand (&amp;) inside [[w:Bracket#Parentheses|parentheses]] and &quot;and&quot; outside parentheses
## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra &amp; Aardvark, 2020)
## A full stop is needed after &quot;et al&quot; (i.e., &quot;et al.&quot;) because it is an abbreviation of [[wikt:et alii|et alii]]
## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]]
## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point)
## Check and correct placement of full-stops
## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois
## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources
# For citations, use APA style or wiki style, but not both
# Secondary citations are overused; strive to consult primary sources
&lt;!-- Written expression – References --&gt;
## References use excellent/very good/good/reasonably good/basic/poor APA style:
### Check and correct use of italicisation
### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization]
### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-)
### Include dois where available
### Hyperlink dois for 1-click access
### Provide the full titles of journals
### Remove &quot;Retrieved from &quot;
### Use alphabetical order
### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section
### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section
### Remove bullet-points; add hanging indent
&lt;!-- Feedback responsiveness ---&gt;
## No evidence of responsiveness to feedback on talk page
|8=
&lt;!-- Learning features comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features
&lt;!-- Learning features – Wikipedia embedded links --&gt;
# Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles
# Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
# Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
&lt;!-- Learning features – Wikiversity embedded links --&gt;
# Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]
# Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
# Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section
# Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
&lt;!-- Learning features – Figures, tables, feature boxes, scenarios --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s)
# Excellent/Very good/Good/Reasonably good/Basic/No use of table(s)
# Excellent/Very good/Good/Reasonably good/Basic use of feature box(es)
# No use of feature boxes other than the opening scenario
# Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples
# No use of scenarios, case studies, or examples, other than opening scenario
&lt;!-- Learning features – Quizzes --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s)
# The quiz questions could be improved by being more focused on the key points and/or take-home messages
# The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end
# The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]])
# No use of quiz(zes) and/or reflection question(s)
&lt;!-- Learning features – See also --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Also include links to related book chapters
## Also include links to related Wikipedia articles
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite
## Move external links into the [[{{PAGENAME}}#References|External links]] section
## Add more links
# [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count
&lt;!-- Learning features – External links --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section
## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite
## Target an international audience
## Add more links
## Link to the top 3-6 external resources about this topic
# [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count
|9=
&lt;!-- Social contribution comments... --&gt;
# ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]]
# ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence.
# Thanks for the Wiki Commons uploads
# Thanks very much for your extensive contributions
# Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# No logged contributions
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:47, 10 October 2025 (UTC)

==See also==
* [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]]
* [[Template:METF]]
* [[Template:MEMF]]

[[Category:Motivation and emotion/Admin/2026]]
[[Category:Motivation and emotion/Assessment/Chapter]]
&lt;/noinclude&gt;</text>
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      <format>text/x-wiki</format>
      <text bytes="65587" sha1="crs7ij6emuzkiugawzwbkg4qnf1hqn3" xml:space="preserve">&lt;noinclude&gt;Feedback [[wikiversity:FAQ/Template|template]] for the [[Motivation and emotion/Assessment/Chapter|book chapter]] exercise for the [[motivation and emotion]] unit.

Designed to be [[Help:Transclusion|transcluded]] on a chapter [[Help:Talk page|talk page]].
__NOTOC__&lt;/noinclude&gt;&lt;includeonly&gt;
==[[Motivation and emotion/Assessment/Chapter|Book chapter]] review and feedback==
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This chapter has been reviewed according to the [[Motivation and emotion/Assessment/Chapter/Marking criteria|marking criteria]]. Written feedback is provided below, plus there is a [[Motivation and emotion/Assessment/Chapter/Feedback|general feedback]] page. Please also check the chapter's [[Help:Page history|page history]] to check for editing changes made whilst reviewing through the chapter. Chapter marks will be available via {{Motivation and emotion/Canvas}} along with [[Motivation and emotion/Assessment/Social contribution|social contribution]] marks and feedback. Keep an eye on Announcements.
{{RoundBoxBottom}}
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===Overall===
{{{1|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Overview (5%)|Overview]]===
{{{2|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Theory (20%)|Theory]]===
{{{3|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Research (25%)|Research]]===
{{{4|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Integration (10%)|Integration]]===
{{{5|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Conclusion (5%)|Conclusion]]===
{{{6|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Style (20%)|Style]]===
{{{7|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Learning features (5%)|Learning features]]===
{{{8|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Social contribution (10%)|Social contribution]]===
{{{9|No comment}}}

{{RoundBoxBottom}}&lt;/includeonly&gt;&lt;noinclude&gt;{{collapse top|Simple example}}
==Simple example==
See also [[#Detailed example|detailed example]]
&lt;pre&gt;
&lt;!-- Official feedback --&gt;
{{MEBF/2026
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#
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#
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~~~~
&lt;/pre&gt;
gives
&lt;!-- Official book chapter feedback --&gt;
{{MEBF/2026
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#
|2=
&lt;!-- Overview comments... --&gt;
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|3=
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|6=
&lt;!-- Conclusion comments... --&gt;
# 
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|8=
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#
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&lt;!-- Social contribution comments... --&gt;
#
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:47, 10 October 2026 (UTC)
{{Collapse bottom}}
==Detailed example==
Example use of the template, with some common feedback comments:
&lt;small&gt;&lt;small&gt;&lt;small&gt;&lt;pre&gt;
&lt;!-- Official book chapter feedback --&gt;
{{MEBF/2026
|1=
&lt;!-- Overall comments... --&gt;
# This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem
# This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem
# This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem
# This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a basic chapter
# This is an insufficient chapter
# The main area(s) for potential improvement:
#* use the best psychological theory about the topic
#* more detailed review of the best psychological research about the topic 
#* quality of written expression
#* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]]
#* integrate more strongly with other chapters by using embedded links to related topics
#* overuse of genAI—express more in your own words; watch out for [[w:AI slop|AI slop]]
#* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter
&lt;!-- Overall - Edit summaries --&gt;
#* [[w:Help:Edit summary|Edit summaries]] are used to clearly communicated the changes made in most or all edits
#* Use more specific [[w:Help:Edit summary|edit summaries]] to clearly communicate the changes made in each edit
#* Use [[w:Help:Edit summary|edit summaries]] to briefly describe the changes made in each edit
&lt;!-- Overall - GenAI --&gt;
#* [[Motivation and emotion/Assessment/Using generative AI|genAI use]] is appropriately acknowledged
#* In some places, there is overreliance on genAI
#* In some places, there is overreliance on genAI, with insufficient acknowledged in edit summaries when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles
#* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in edit summaries with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]].
&lt;!-- Overall – Citations --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims
# Only cite sources that you consult
# All citations need to be in the References
&lt;!-- Overall – Word count --&gt;
# Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand
# Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes.
&lt;!-- Overall – Copyedits --&gt;
# For additional feedback, see the following comments and [ these copyedits]
|2=
&lt;!-- Overview – Comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped
&lt;!-- Overview – Scenario --&gt;
&lt;!-- Overview – Scenario - Description --&gt;
# Engaging scenario or case study
# Reasonably engaging scenario or case study
# Basic scenario or case study
# Use a more practical, real-life scenario; move review of research into a subsequent section
# Consider using an example that more people can relate to (less than 5% of the world population are university students)
# Add an engaging case study or scenario
&lt;!-- Overview – Scenario - Figure --&gt;
# Figure 1 is relevant to the scenario
# Figure 1 could be more relevant to the scenario
# Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section
# Include a relevant image
&lt;!-- Overview – Scenario - Feature box --&gt;
# The scenario uses an appropriate feature box
# Put the scenario in a feature box
&lt;!-- Overview – Explains problem --&gt;
# Clearly explains the psychological problem or phenomenon
# Explains the psychological problem or phenomenon reasonably well/in a basic way
# Briefly explains the psychological problem or phenomenon; provide more detail
# Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections.
# Clarity of written expression can be improved
&lt;!-- Overview – Focus questions --&gt;
# The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient
# The focus questions could be improved by:
## being more specific to the topic (i.e., the sub-title)
## matching the top-level headings more closely
## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]]
## splitting double-barrelled questions into separate questions
## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## being presented in a feature box to help guide the reader (fixed)
# Add focus questions in a feature box
# See copyedits for examples of possible improvements
|3=
&lt;!-- Theory comments... --&gt;
&lt;!-- Theory – Breadth --&gt;
# Excellent—key theories are very well explained and applied
# Very good—key theories are well explained and applied; minor areas for improvements
# Reasonably good—relevant theories are selected, described, and explained, with some room for improvement
# Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement
# A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic
# Insufficient use of relevant psychological theory about this topic
# Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question).
&lt;!-- Theory – Builds on --&gt;
# Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
&lt;!-- Theory – Depth --&gt;
# Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies)
&lt;!-- Theory – Tables/Figures/Lists --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information
&lt;!-- Theory – Citations --&gt;
# Key citations are well used
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
# If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source]
# If you didn't consult an original source, don't cite it
&lt;!-- Theory – Examples --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts
# Consider using more examples to illustrate theoretical concepts
# Use more examples to illustrate theoretical concepts
# Insufficient use of examples to illustrate theoretical concepts
|4=
&lt;!-- Research comments... --&gt;
&lt;!-- Research – Key findings --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research
# Excellent emphasis on systematic reviews and/or meta-analyses
# Greater emphasis on systematic reviews and/or meta-analyses would be ideal
# More detail about key studies would be ideal
# Claims are well referenced
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
&lt;!-- Research – Critical thinking --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident
# [[w:Critical thinking|Critical thinking]] about research could be further evidenced by:
## describing the methodology (e.g., sample, measures) in important studies
## considering the strength of relationships
## acknowledging limitations
## pointing out critiques/counterarguments
## suggesting ''specific'' directions for future research
|5=
&lt;!-- Integration comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research
# The chapter places more emphasis on theory than on research; strive for an integrated balance
# The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links
# Insufficient integration with related [[Motivation and emotion/Book|chapters]]
|6=
&lt;!-- Conclusion comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic summary and conclusion
# Insufficient as a cohesive summary of the best psychological theory and research about the topic
# Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words
# Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the edit summary.
# Highlights the importance of the problem or phenomenon of interest
# Highlight the importance of the problem or phenomenon of interest
&lt;!-- Conclusion – Key points --&gt;
# Key points are well summarised
# Key points are summarised in a basic way
# Summarise key points
&lt;!-- Conclusion – Focus questions --&gt;
# The focus questions are addressed
# The take-away messages for each focus question could be spelt out more clearly
# Address the focus questions
&lt;!-- Conclusion – Take-home messages --&gt;
# Clear take-home message(s)
# Add practical, take-home message(s)
&lt;!-- Conclusion – Word count --&gt;
# Not counted for marking purposes due to being over the maximum word count
|7=
&lt;!-- Written expression – Style comments... --&gt;
&lt;!-- Written expression – Written expression --&gt;
# Written expression
## The quality of written expression is excellent/very good/good/reasonably good/basic
## The quality of written expression is OK but there are several aspects which are below professional standard
## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills.
## Use active (e.g., &quot;this chapter explores&quot; or &quot;this chapter explored&quot;) rather than passive voice (e.g., &quot;this chapter will explore&quot; or &quot;this chapter has explored&quot;) [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/]
## The target audience is international, not domestic. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia].
## Reduce excessive use of bold font
&lt;!-- Written expression – Sentences --&gt;
## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression
## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+.
## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence.
&lt;!-- Written expression – Paragraphs --&gt;
## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences.
## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences.
## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs.
&lt;!-- Written expression – Language --&gt;
## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., &quot;it&quot;) instead of 1st (e.g., &quot;we&quot;) or 2nd person (e.g., &quot;you&quot;) in the main text. 1st or 2nd person can work well for case studies or feature boxes.
## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]].
## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]]
## &quot;Individuals&quot; is overused. &quot;People&quot; is usually a clearer term than &quot;individuals&quot;. Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally.
## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning
## Use permanent, rather than relative, time references. For example, instead of &quot;20 years ago&quot;, refer to something like &quot;at the beginning of the 21st century&quot;. In this way, the text will survive better into the future, without needing to be rewritten.
## Avoid overly emotive language (e.g,. *) in science-based communication
&lt;!-- Written expression – Layout --&gt;
# Layout
## The chapter is well structured, with major sections using sub-sections
## The headings could be more clearly aligned with the focus questions
## The structure is overly complicated; simplify and integrate
## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion
## The chapter structure is underdeveloped; expand by using subheadings
## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings
## Use the default heading style (e.g., remove additional numbers, italics, bold, and/or change in font size)
## See earlier comment about [[#Heading casing|heading casing]]
## Provide more descriptive headings
## Move links from headings into their first mention in text
## Remove abbreviations/citations from headings
## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags)
## Integrate learning features rather than having it as a stand-alone section
## The Overview and Conclusion should not have subheadings (fixed)
## Remove colons (:) from the ends of headings
&lt;!-- Written expression – Grammar --&gt;
# Grammar and spelling are excellent
# Grammar
## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback
## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas].
## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element
## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats')
## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who]
## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect]
## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)]
## Use past tense when describing research studies, although implications of findings could be in the present tense
&lt;!-- Written expression – Abbreviations --&gt;
## Abbreviations
### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out
### Check and correct formatting of abbreviations (such as e.g., i.e., etc.)
### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms.
### Spell out abbreviations on their first use, to explain them to the reader
### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards
### Only introduce abbreviations which are subsequently used
&lt;!-- Written expression – Spelling --&gt;
# Spelling
## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour)
## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages.
&lt;!-- Written expression – Proofreading --&gt;
# Proofreading
## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard
## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info]
&lt;!-- Written expression – APA style --&gt;
# APA style
## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY]
## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing for disorders, therapies, theories, etc.]
## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)]
&lt;!-- Written expression – APA style - Quotes --&gt;
## Use double (not single) quotation marks &quot;to introduce a word or phrase used ... as slang, or as an invented or coined expression&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## &quot;Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## Direct quotes need page numbers—even better, communicate about concepts in your own words
## Direct quotes are overused—it is better to communicate about concepts in your own words
&lt;!-- Written expression – Figures --&gt;
## Figures
### Very well/Well/Reasonably well captioned
### Brief captions; provide more detail to help connect the figure to the text
### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]].
### Add captions
&lt;!-- Written expression – Figures - Citations --&gt;
### Each Figure is referred to at least once within the main text using APA style
### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., &quot;(see Figure 1)&quot;; do not use bold, italics, check and correct capitalisation).
### Refer to each Figure at least once within the main text (e.g., &quot;(see Figure 1)&quot;)
&lt;!-- Written expression – Figures - Other --&gt;
### Some image uploads were removed because of a lack of sufficient/appropriate copyright information
### Numbering needs correcting
### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size)
&lt;!-- Written expression – Tables --&gt;
## Tables
### Very well/Well/Reasonably well captioned
### Brief caption(s); provide more explanatory detail about the table
### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]])
&lt;!-- Written expression – Tables - Citations --&gt;
### Each Table is referred to at least once within the main text using APA style
### Each Table is referred to at least once within the main text
### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation)
### Refer to each Table at least once within the main text (e.g., see Table 1)
&lt;!-- Written expression – Citations --&gt;
# Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags)
## If there are three or more authors, cite the first author followed by et al., then year. For example, either:
### in-text, Smith et al. (2020), or
### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020)
## Do not include author first name or initials
## Use ampersand (&amp;) inside [[w:Bracket#Parentheses|parentheses]] and &quot;and&quot; outside parentheses
## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra &amp; Aardvark, 2020)
## A full stop is needed after &quot;et al&quot; (i.e., &quot;et al.&quot;) because it is an abbreviation of [[wikt:et alii|et alii]]
## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]]
## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point)
## Check and correct placement of full-stops
## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois
## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources
# For citations, use APA style or wiki style, but not both
# Secondary citations are overused; strive to consult primary sources
&lt;!-- Written expression – References --&gt;
## References use excellent/very good/good/reasonably good/basic/poor APA style:
### Check and correct use of italicisation
### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization]
### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-)
### Include dois where available
### Hyperlink dois for 1-click access
### Provide the full titles of journals
### Remove &quot;Retrieved from &quot;
### Use alphabetical order
### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section
### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section
### Remove bullet-points; add hanging indent
&lt;!-- Feedback responsiveness ---&gt;
## No evidence of responsiveness to feedback on talk page
|8=
&lt;!-- Learning features comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features
&lt;!-- Learning features – Wikipedia embedded links --&gt;
# Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles
# Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
# Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
&lt;!-- Learning features – Wikiversity embedded links --&gt;
# Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]
# Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
# Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section
# Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
&lt;!-- Learning features – Figures, tables, feature boxes, scenarios --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s)
# Excellent/Very good/Good/Reasonably good/Basic/No use of table(s)
# Excellent/Very good/Good/Reasonably good/Basic use of feature box(es)
# No use of feature boxes other than the opening scenario
# Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples
# No use of scenarios, case studies, or examples, other than opening scenario
&lt;!-- Learning features – Quizzes --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s)
# The quiz questions could be improved by being more focused on the key points and/or take-home messages
# The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end
# The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]])
# No use of quiz(zes) and/or reflection question(s)
&lt;!-- Learning features – See also --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Also include links to related book chapters
## Also include links to related Wikipedia articles
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite
## Move external links into the [[{{PAGENAME}}#References|External links]] section
## Add more links
# [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count
&lt;!-- Learning features – External links --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section
## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite
## Target an international audience
## Add more links
## Link to the top 3-6 external resources about this topic
# [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count
|9=
&lt;!-- Social contribution comments... --&gt;
# ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]]
# ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence.
# Thanks for the Wiki Commons uploads
# Thanks very much for your extensive contributions
# Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# No logged contributions
}}
~~~~
&lt;/pre&gt;&lt;/small&gt;&lt;/small&gt;&lt;/small&gt;
gives
&lt;!-- Official book chapter feedback --&gt;
{{MEBF/2026
|1=
&lt;!-- Overall comments... --&gt;
# This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem
# This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem
# This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem
# This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a basic chapter
# This is an insufficient chapter
# The main area(s) for potential improvement:
#* use the best psychological theory about the topic
#* more detailed review of the best psychological research about the topic 
#* quality of written expression
#* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]]
#* integrate more strongly with other chapters by using embedded links to related topics
#* overuse of genAI—express more in your own words; watch out for [[w:AI slop|AI slop]]
#* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter
&lt;!-- Overall - Edit summaries --&gt;
#* [[w:Help:Edit summary|Edit summaries]] are used to clearly communicated the changes made in most or all edits
#* Use more specific [[w:Help:Edit summary|edit summaries]] to clearly communicate the changes made in each edit
#* Use [[w:Help:Edit summary|edit summaries]] to briefly describe the changes made in each edit
&lt;!-- Overall - GenAI --&gt;
#* [[Motivation and emotion/Assessment/Using generative AI|genAI use]] is appropriately acknowledged
#* In some places, there is overreliance on genAI
#* In some places, there is overreliance on genAI, with insufficient acknowledged in edit summaries when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles
#* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in edit summaries with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]].
&lt;!-- Overall – Citations --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims
# Only cite sources that you consult
# All citations need to be in the References
&lt;!-- Overall – Word count --&gt;
# Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand
# Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes.
&lt;!-- Overall – Copyedits --&gt;
# For additional feedback, see the following comments and [ these copyedits]
|2=
&lt;!-- Overview – Comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped
&lt;!-- Overview – Scenario --&gt;
&lt;!-- Overview – Scenario - Description --&gt;
# Engaging scenario or case study
# Reasonably engaging scenario or case study
# Basic scenario or case study
# Use a more practical, real-life scenario; move review of research into a subsequent section
# Consider using an example that more people can relate to (less than 5% of the world population are university students)
# Add an engaging case study or scenario
&lt;!-- Overview – Scenario - Figure --&gt;
# Figure 1 is relevant to the scenario
# Figure 1 could be more relevant to the scenario
# Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section
# Include a relevant image
&lt;!-- Overview – Scenario - Feature box --&gt;
# The scenario uses an appropriate feature box
# Put the scenario in a feature box
&lt;!-- Overview – Explains problem --&gt;
# Clearly explains the psychological problem or phenomenon
# Explains the psychological problem or phenomenon reasonably well/in a basic way
# Briefly explains the psychological problem or phenomenon; provide more detail
# Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections.
# Clarity of written expression can be improved
&lt;!-- Overview – Focus questions --&gt;
# The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient
# The focus questions could be improved by:
## being more specific to the topic (i.e., the sub-title)
## matching the top-level headings more closely
## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]]
## splitting double-barrelled questions into separate questions
## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## being presented in a feature box to help guide the reader (fixed)
# Add focus questions in a feature box
# See copyedits for examples of possible improvements
|3=
&lt;!-- Theory comments... --&gt;
&lt;!-- Theory – Breadth --&gt;
# Excellent—key theories are very well explained and applied
# Very good—key theories are well explained and applied; minor areas for improvements
# Reasonably good—relevant theories are selected, described, and explained, with some room for improvement
# Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement
# A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic
# Insufficient use of relevant psychological theory about this topic
# Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question).
&lt;!-- Theory – Builds on --&gt;
# Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
&lt;!-- Theory – Depth --&gt;
# Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies)
&lt;!-- Theory – Tables/Figures/Lists --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information
&lt;!-- Theory – Citations --&gt;
# Key citations are well used
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
# If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source]
# If you didn't consult an original source, don't cite it
&lt;!-- Theory – Examples --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts
# Consider using more examples to illustrate theoretical concepts
# Use more examples to illustrate theoretical concepts
# Insufficient use of examples to illustrate theoretical concepts
|4=
&lt;!-- Research comments... --&gt;
&lt;!-- Research – Key findings --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research
# Excellent emphasis on systematic reviews and/or meta-analyses
# Greater emphasis on systematic reviews and/or meta-analyses would be ideal
# More detail about key studies would be ideal
# Claims are well referenced
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
&lt;!-- Research – Critical thinking --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident
# [[w:Critical thinking|Critical thinking]] about research could be further evidenced by:
## describing the methodology (e.g., sample, measures) in important studies
## considering the strength of relationships
## acknowledging limitations
## pointing out critiques/counterarguments
## suggesting ''specific'' directions for future research
|5=
&lt;!-- Integration comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research
# The chapter places more emphasis on theory than on research; strive for an integrated balance
# The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links
# Insufficient integration with related [[Motivation and emotion/Book|chapters]]
|6=
&lt;!-- Conclusion comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic summary and conclusion
# Insufficient as a cohesive summary of the best psychological theory and research about the topic
# Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words
# Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the edit summary.
# Highlights the importance of the problem or phenomenon of interest
# Highlight the importance of the problem or phenomenon of interest
&lt;!-- Conclusion – Key points --&gt;
# Key points are well summarised
# Key points are summarised in a basic way
# Summarise key points
&lt;!-- Conclusion – Focus questions --&gt;
# The focus questions are addressed
# The take-away messages for each focus question could be spelt out more clearly
# Address the focus questions
&lt;!-- Conclusion – Take-home messages --&gt;
# Clear take-home message(s)
# Add practical, take-home message(s)
&lt;!-- Conclusion – Word count --&gt;
# Not counted for marking purposes due to being over the maximum word count
|7=
&lt;!-- Written expression – Style comments... --&gt;
&lt;!-- Written expression – Written expression --&gt;
# Written expression
## The quality of written expression is excellent/very good/good/reasonably good/basic
## The quality of written expression is OK but there are several aspects which are below professional standard
## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills.
## Use active (e.g., &quot;this chapter explores&quot; or &quot;this chapter explored&quot;) rather than passive voice (e.g., &quot;this chapter will explore&quot; or &quot;this chapter has explored&quot;) [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/]
## The target audience is international, not domestic. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia].
## Reduce excessive use of bold font
&lt;!-- Written expression – Sentences --&gt;
## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression
## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+.
## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence.
&lt;!-- Written expression – Paragraphs --&gt;
## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences.
## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences.
## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs.
&lt;!-- Written expression – Language --&gt;
## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., &quot;it&quot;) instead of 1st (e.g., &quot;we&quot;) or 2nd person (e.g., &quot;you&quot;) in the main text. 1st of 2nd person can work well for case studies or feature boxes.
## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]].## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]]
## &quot;Individuals&quot; is overused. &quot;People&quot; is usually a clearer term than &quot;individuals&quot;. Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally.
## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning
## Use permanent, rather than relative, time references. For example, instead of &quot;20 years ago&quot;, refer to something like &quot;at the beginning of the 21st century&quot;. In this way, the text will survive better into the future, without needing to be rewritten.
## Avoid overly emotive language (e.g,. *) in science-based communication
&lt;!-- Written expression – Layout --&gt;
# Layout
## The chapter is well structured, with major sections using sub-sections
## The headings could be more clearly aligned with the focus questions
## The structure is overly complicated; simplify and integrate
## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion
## The chapter structure is underdeveloped; expand by using subheadings
## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings
## Use the default heading style (e.g.,  remove additional numbers, italics, bo]ld, and/or change in font size)
## See earlier comment about [[#Heading casing|heading casing]]
## Provide more descriptive headings
## Move links from headings into their first mention in text
## Remove abbreviations/citations from headings
## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags)
## Integrate learning features rather than having it as a stand-alone section
## The Overview and Conclusion should not have subheadings (fixed)
## Remove colons (:) from the ends of headings
&lt;!-- Written expression – Grammar --&gt;
# Grammar and spelling are excellent
# Grammar
## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback
## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas].
## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element
## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats')
## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who]
## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect]
## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)]
## Use past tense when describing research studies, although implications of findings could be in the present tense
&lt;!-- Written expression – Abbreviations --&gt;
## Abbreviations
### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out
### Check and correct formatting of abbreviations (such as e.g., i.e., etc.)
### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms.
### Spell out abbreviations on their first use, to explain them to the reader
### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards
### Only introduce abbreviations which are subsequently used
&lt;!-- Written expression – Spelling --&gt;
# Spelling
## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour)
## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages.
&lt;!-- Written expression – Proofreading --&gt;
# Proofreading
## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard
## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info]
&lt;!-- Written expression – APA style --&gt;
# APA style
## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY]
## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing for disorders, therapies, theories, etc.]
## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)]
&lt;!-- Written expression – APA style - Quotes --&gt;
## Use double (not single) quotation marks &quot;to introduce a word or phrase used ... as slang, or as an invented or coined expression&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## &quot;Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## Direct quotes need page numbers—even better, communicate about concepts in your own words
## Direct quotes are overused—it is better to communicate about concepts in your own words
&lt;!-- Written expression – Figures --&gt;
## Figures
### Very well/Well/Reasonably well captioned
### Brief captions; provide more detail to help connect the figure to the text
### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]].
### Add captions
&lt;!-- Written expression – Figures - Citations --&gt;
### Each Figure is referred to at least once within the main text using APA style
### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., &quot;(see Figure 1)&quot;; do not use bold, italics, check and correct capitalisation).
### Refer to each Figure at least once within the main text (e.g., &quot;(see Figure 1)&quot;)
&lt;!-- Written expression – Figures - Other --&gt;
### Some image uploads were removed because of a lack of sufficient/appropriate copyright information
### Numbering needs correcting
### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size)
&lt;!-- Written expression – Tables --&gt;
## Tables
### Very well/Well/Reasonably well captioned
### Brief caption(s); provide more explanatory detail about the table
### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]])
&lt;!-- Written expression – Tables - Citations --&gt;
### Each Table is referred to at least once within the main text using APA style
### Each Table is referred to at least once within the main text
### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation)
### Refer to each Table at least once within the main text (e.g., see Table 1)
&lt;!-- Written expression – Citations --&gt;
# Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags)
## If there are three or more authors, cite the first author followed by et al., then year. For example, either:
### in-text, Smith et al. (2020), or
### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020)
## Do not include author first name or initials
## Use ampersand (&amp;) inside [[w:Bracket#Parentheses|parentheses]] and &quot;and&quot; outside parentheses
## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra &amp; Aardvark, 2020)
## A full stop is needed after &quot;et al&quot; (i.e., &quot;et al.&quot;) because it is an abbreviation of [[wikt:et alii|et alii]]
## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]]
## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point)
## Check and correct placement of full-stops
## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois
## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources
# For citations, use APA style or wiki style, but not both
# Secondary citations are overused; strive to consult primary sources
&lt;!-- Written expression – References --&gt;
## References use excellent/very good/good/reasonably good/basic/poor APA style:
### Check and correct use of italicisation
### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization]
### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-)
### Include dois where available
### Hyperlink dois for 1-click access
### Provide the full titles of journals
### Remove &quot;Retrieved from &quot;
### Use alphabetical order
### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section
### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section
### Remove bullet-points; add hanging indent
&lt;!-- Feedback responsiveness ---&gt;
## No evidence of responsiveness to feedback on talk page
|8=
&lt;!-- Learning features comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features
&lt;!-- Learning features – Wikipedia embedded links --&gt;
# Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles
# Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
# Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
&lt;!-- Learning features – Wikiversity embedded links --&gt;
# Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]
# Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
# Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section
# Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
&lt;!-- Learning features – Figures, tables, feature boxes, scenarios --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s)
# Excellent/Very good/Good/Reasonably good/Basic/No use of table(s)
# Excellent/Very good/Good/Reasonably good/Basic use of feature box(es)
# No use of feature boxes other than the opening scenario
# Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples
# No use of scenarios, case studies, or examples, other than opening scenario
&lt;!-- Learning features – Quizzes --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s)
# The quiz questions could be improved by being more focused on the key points and/or take-home messages
# The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end
# The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]])
# No use of quiz(zes) and/or reflection question(s)
&lt;!-- Learning features – See also --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Also include links to related book chapters
## Also include links to related Wikipedia articles
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite
## Move external links into the [[{{PAGENAME}}#References|External links]] section
## Add more links
# [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count
&lt;!-- Learning features – External links --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section
## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite
## Target an international audience
## Add more links
## Link to the top 3-6 external resources about this topic
# [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count
|9=
&lt;!-- Social contribution comments... --&gt;
# ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]]
# ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence.
# Thanks for the Wiki Commons uploads
# Thanks very much for your extensive contributions
# Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# No logged contributions
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:47, 10 October 2026 (UTC)

==See also==
* [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]]
* [[Template:METF]]
* [[Template:MEMF]]

[[Category:Motivation and emotion/Admin/2026]]
[[Category:Motivation and emotion/Assessment/Chapter]]
&lt;/noinclude&gt;</text>
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      <text bytes="65585" sha1="r7lvpd3cziwtjw7rbzk7qn101ne37c6" xml:space="preserve">&lt;noinclude&gt;Feedback [[wikiversity:FAQ/Template|template]] for the [[Motivation and emotion/Assessment/Chapter|book chapter]] exercise for the [[motivation and emotion]] unit.

Designed to be [[Help:Transclusion|transcluded]] on a chapter [[Help:Talk page|talk page]].
__NOTOC__&lt;/noinclude&gt;&lt;includeonly&gt;
==[[Motivation and emotion/Assessment/Chapter|Book chapter]] review and feedback==
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This chapter has been reviewed according to the [[Motivation and emotion/Assessment/Chapter/Marking criteria|marking criteria]]. Written feedback is provided below, plus there is a [[Motivation and emotion/Assessment/Chapter/Feedback|general feedback]] page. Please also check the chapter's [[Help:Page history|page history]] to check for editing changes made whilst reviewing through the chapter. Chapter marks will be available via {{Motivation and emotion/Canvas}} along with [[Motivation and emotion/Assessment/Social contribution|social contribution]] marks and feedback. Keep an eye on Announcements.
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{{RoundBoxTop|theme=}}[[File:Wikiuutiset logo typewriter.png|right|85px]]
===Overall===
{{{1|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Overview (5%)|Overview]]===
{{{2|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Theory (20%)|Theory]]===
{{{3|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Research (25%)|Research]]===
{{{4|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Integration (10%)|Integration]]===
{{{5|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Conclusion (5%)|Conclusion]]===
{{{6|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Style (20%)|Style]]===
{{{7|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Learning features (5%)|Learning features]]===
{{{8|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Social contribution (10%)|Social contribution]]===
{{{9|No comment}}}

{{RoundBoxBottom}}&lt;/includeonly&gt;&lt;noinclude&gt;{{collapse top|Simple example}}
==Simple example==
See also [[#Detailed example|detailed example]]
&lt;pre&gt;
&lt;!-- Official feedback --&gt;
{{MEBF/2026
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#
|9=
&lt;!-- Social contribution comments... --&gt;
#
}}
~~~~
&lt;/pre&gt;
gives
&lt;!-- Official book chapter feedback --&gt;
{{MEBF/2026
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&lt;!-- Overall comments... --&gt;
#
|2=
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# 
|3=
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|6=
&lt;!-- Conclusion comments... --&gt;
# 
|7=
&lt;!-- Style comments... --&gt;
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#
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&lt;!-- Social contribution comments... --&gt;
#
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:47, 10 October 2026 (UTC)
{{Collapse bottom}}
==Detailed example==
Example use of the template, with some common feedback comments:
&lt;small&gt;&lt;small&gt;&lt;small&gt;&lt;pre&gt;
&lt;!-- Official book chapter feedback --&gt;
{{MEBF/2026
|1=
&lt;!-- Overall comments... --&gt;
# This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem
# This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem
# This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem
# This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a basic chapter
# This is an insufficient chapter
# The main area(s) for potential improvement:
#* use the best psychological theory about the topic
#* more detailed review of the best psychological research about the topic
#* quality of written expression
#* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]]
#* integrate more strongly with other chapters by using embedded links to related topics
#* overuse of genAI—express more in your own words; watch out for [[w:AI slop|AI slop]]
#* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter
&lt;!-- Overall - Edit summaries --&gt;
#* [[w:Help:Edit summary|Edit summaries]] are used to clearly communicated the changes made in most or all edits
#* Use more specific [[w:Help:Edit summary|edit summaries]] to clearly communicate the changes made in each edit
#* Use [[w:Help:Edit summary|edit summaries]] to briefly describe the changes made in each edit
&lt;!-- Overall - GenAI --&gt;
#* [[Motivation and emotion/Assessment/Using generative AI|genAI use]] is appropriately acknowledged
#* In some places, there is overreliance on genAI
#* In some places, there is overreliance on genAI, with insufficient acknowledged in edit summaries when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles
#* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in edit summaries with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]].
&lt;!-- Overall – Citations --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims
# Only cite sources that you consult
# All citations need to be in the References
&lt;!-- Overall – Word count --&gt;
# Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand
# Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes.
&lt;!-- Overall – Copyedits --&gt;
# For additional feedback, see the following comments and [ these copyedits]
|2=
&lt;!-- Overview – Comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped
&lt;!-- Overview – Scenario --&gt;
&lt;!-- Overview – Scenario - Description --&gt;
# Engaging scenario or case study
# Reasonably engaging scenario or case study
# Basic scenario or case study
# Use a more practical, real-life scenario; move review of research into a subsequent section
# Consider using an example that more people can relate to (less than 5% of the world population are university students)
# Add an engaging case study or scenario
&lt;!-- Overview – Scenario - Figure --&gt;
# Figure 1 is relevant to the scenario
# Figure 1 could be more relevant to the scenario
# Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section
# Include a relevant image
&lt;!-- Overview – Scenario - Feature box --&gt;
# The scenario uses an appropriate feature box
# Put the scenario in a feature box
&lt;!-- Overview – Explains problem --&gt;
# Clearly explains the psychological problem or phenomenon
# Explains the psychological problem or phenomenon reasonably well/in a basic way
# Briefly explains the psychological problem or phenomenon; provide more detail
# Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections.
# Clarity of written expression can be improved
&lt;!-- Overview – Focus questions --&gt;
# The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient
# The focus questions could be improved by:
## being more specific to the topic (i.e., the sub-title)
## matching the top-level headings more closely
## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]]
## splitting double-barrelled questions into separate questions
## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## being presented in a feature box to help guide the reader (fixed)
# Add focus questions in a feature box
# See copyedits for examples of possible improvements
|3=
&lt;!-- Theory comments... --&gt;
&lt;!-- Theory – Breadth --&gt;
# Excellent—key theories are very well explained and applied
# Very good—key theories are well explained and applied; minor areas for improvements
# Reasonably good—relevant theories are selected, described, and explained, with some room for improvement
# Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement
# A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic
# Insufficient use of relevant psychological theory about this topic
# Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question).
&lt;!-- Theory – Builds on --&gt;
# Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
&lt;!-- Theory – Depth --&gt;
# Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies)
&lt;!-- Theory – Tables/Figures/Lists --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information
&lt;!-- Theory – Citations --&gt;
# Key citations are well used
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
# If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source]
# If you didn't consult an original source, don't cite it
&lt;!-- Theory – Examples --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts
# Consider using more examples to illustrate theoretical concepts
# Use more examples to illustrate theoretical concepts
# Insufficient use of examples to illustrate theoretical concepts
|4=
&lt;!-- Research comments... --&gt;
&lt;!-- Research – Key findings --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research
# Excellent emphasis on systematic reviews and/or meta-analyses
# Greater emphasis on systematic reviews and/or meta-analyses would be ideal
# More detail about key studies would be ideal
# Claims are well referenced
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
&lt;!-- Research – Critical thinking --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident
# [[w:Critical thinking|Critical thinking]] about research could be further evidenced by:
## describing the methodology (e.g., sample, measures) in important studies
## considering the strength of relationships
## acknowledging limitations
## pointing out critiques/counterarguments
## suggesting ''specific'' directions for future research
|5=
&lt;!-- Integration comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research
# The chapter places more emphasis on theory than on research; strive for an integrated balance
# The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links
# Insufficient integration with related [[Motivation and emotion/Book|chapters]]
|6=
&lt;!-- Conclusion comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic summary and conclusion
# Insufficient as a cohesive summary of the best psychological theory and research about the topic
# Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words
# Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the edit summary.
# Highlights the importance of the problem or phenomenon of interest
# Highlight the importance of the problem or phenomenon of interest
&lt;!-- Conclusion – Key points --&gt;
# Key points are well summarised
# Key points are summarised in a basic way
# Summarise key points
&lt;!-- Conclusion – Focus questions --&gt;
# The focus questions are addressed
# The take-away messages for each focus question could be spelt out more clearly
# Address the focus questions
&lt;!-- Conclusion – Take-home messages --&gt;
# Clear take-home message(s)
# Add practical, take-home message(s)
&lt;!-- Conclusion – Word count --&gt;
# Not counted for marking purposes due to being over the maximum word count
|7=
&lt;!-- Written expression – Style comments... --&gt;
&lt;!-- Written expression – Written expression --&gt;
# Written expression
## The quality of written expression is excellent/very good/good/reasonably good/basic
## The quality of written expression is OK but there are several aspects which are below professional standard
## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills.
## Use active (e.g., &quot;this chapter explores&quot; or &quot;this chapter explored&quot;) rather than passive voice (e.g., &quot;this chapter will explore&quot; or &quot;this chapter has explored&quot;) [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/]
## The target audience is international, not domestic. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia].
## Reduce excessive use of bold font
&lt;!-- Written expression – Sentences --&gt;
## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression
## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+.
## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence.
&lt;!-- Written expression – Paragraphs --&gt;
## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences.
## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences.
## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs.
&lt;!-- Written expression – Language --&gt;
## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., &quot;it&quot;) instead of 1st (e.g., &quot;we&quot;) or 2nd person (e.g., &quot;you&quot;) in the main text. 1st or 2nd person can work well for case studies or feature boxes.
## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]].
## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]]
## &quot;Individuals&quot; is overused. &quot;People&quot; is usually a clearer term than &quot;individuals&quot;. Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally.
## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning
## Use permanent, rather than relative, time references. For example, instead of &quot;20 years ago&quot;, refer to something like &quot;at the beginning of the 21st century&quot;. In this way, the text will survive better into the future, without needing to be rewritten.
## Avoid overly emotive language (e.g,. *) in science-based communication
&lt;!-- Written expression – Layout --&gt;
# Layout
## The chapter is well structured, with major sections using sub-sections
## The headings could be more clearly aligned with the focus questions
## The structure is overly complicated; simplify and integrate
## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion
## The chapter structure is underdeveloped; expand by using subheadings
## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings
## Use the default heading style (e.g., remove additional numbers, italics, bold, and/or change in font size)
## See earlier comment about [[#Heading casing|heading casing]]
## Provide more descriptive headings
## Move links from headings into their first mention in text
## Remove abbreviations/citations from headings
## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags)
## Integrate learning features rather than having it as a stand-alone section
## The Overview and Conclusion should not have subheadings (fixed)
## Remove colons (:) from the ends of headings
&lt;!-- Written expression – Grammar --&gt;
# Grammar and spelling are excellent
# Grammar
## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback
## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas].
## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element
## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats')
## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who]
## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect]
## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)]
## Use past tense when describing research studies, although implications of findings could be in the present tense
&lt;!-- Written expression – Abbreviations --&gt;
## Abbreviations
### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out
### Check and correct formatting of abbreviations (such as e.g., i.e., etc.)
### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms.
### Spell out abbreviations on their first use, to explain them to the reader
### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards
### Only introduce abbreviations which are subsequently used
&lt;!-- Written expression – Spelling --&gt;
# Spelling
## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour)
## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages.
&lt;!-- Written expression – Proofreading --&gt;
# Proofreading
## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard
## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info]
&lt;!-- Written expression – APA style --&gt;
# APA style
## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY]
## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing for disorders, therapies, theories, etc.]
## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)]
&lt;!-- Written expression – APA style - Quotes --&gt;
## Use double (not single) quotation marks &quot;to introduce a word or phrase used ... as slang, or as an invented or coined expression&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## &quot;Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## Direct quotes need page numbers—even better, communicate about concepts in your own words
## Direct quotes are overused—it is better to communicate about concepts in your own words
&lt;!-- Written expression – Figures --&gt;
## Figures
### Very well/Well/Reasonably well captioned
### Brief captions; provide more detail to help connect the figure to the text
### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]].
### Add captions
&lt;!-- Written expression – Figures - Citations --&gt;
### Each Figure is referred to at least once within the main text using APA style
### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., &quot;(see Figure 1)&quot;; do not use bold, italics, check and correct capitalisation).
### Refer to each Figure at least once within the main text (e.g., &quot;(see Figure 1)&quot;)
&lt;!-- Written expression – Figures - Other --&gt;
### Some image uploads were removed because of a lack of sufficient/appropriate copyright information
### Numbering needs correcting
### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size)
&lt;!-- Written expression – Tables --&gt;
## Tables
### Very well/Well/Reasonably well captioned
### Brief caption(s); provide more explanatory detail about the table
### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]])
&lt;!-- Written expression – Tables - Citations --&gt;
### Each Table is referred to at least once within the main text using APA style
### Each Table is referred to at least once within the main text
### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation)
### Refer to each Table at least once within the main text (e.g., see Table 1)
&lt;!-- Written expression – Citations --&gt;
# Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags)
## If there are three or more authors, cite the first author followed by et al., then year. For example, either:
### in-text, Smith et al. (2020), or
### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020)
## Do not include author first name or initials
## Use ampersand (&amp;) inside [[w:Bracket#Parentheses|parentheses]] and &quot;and&quot; outside parentheses
## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra &amp; Aardvark, 2020)
## A full stop is needed after &quot;et al&quot; (i.e., &quot;et al.&quot;) because it is an abbreviation of [[wikt:et alii|et alii]]
## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]]
## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point)
## Check and correct placement of full-stops
## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois
## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources
# For citations, use APA style or wiki style, but not both
# Secondary citations are overused; strive to consult primary sources
&lt;!-- Written expression – References --&gt;
## References use excellent/very good/good/reasonably good/basic/poor APA style:
### Check and correct use of italicisation
### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization]
### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-)
### Include dois where available
### Hyperlink dois for 1-click access
### Provide the full titles of journals
### Remove &quot;Retrieved from &quot;
### Use alphabetical order
### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section
### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section
### Remove bullet-points; add hanging indent
&lt;!-- Feedback responsiveness ---&gt;
## No evidence of responsiveness to feedback on talk page
|8=
&lt;!-- Learning features comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features
&lt;!-- Learning features – Wikipedia embedded links --&gt;
# Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles
# Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
# Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
&lt;!-- Learning features – Wikiversity embedded links --&gt;
# Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]
# Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
# Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section
# Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
&lt;!-- Learning features – Figures, tables, feature boxes, scenarios --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s)
# Excellent/Very good/Good/Reasonably good/Basic/No use of table(s)
# Excellent/Very good/Good/Reasonably good/Basic use of feature box(es)
# No use of feature boxes other than the opening scenario
# Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples
# No use of scenarios, case studies, or examples, other than opening scenario
&lt;!-- Learning features – Quizzes --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s)
# The quiz questions could be improved by being more focused on the key points and/or take-home messages
# The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end
# The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]])
# No use of quiz(zes) and/or reflection question(s)
&lt;!-- Learning features – See also --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Also include links to related book chapters
## Also include links to related Wikipedia articles
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite
## Move external links into the [[{{PAGENAME}}#References|External links]] section
## Add more links
# [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count
&lt;!-- Learning features – External links --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section
## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite
## Target an international audience
## Add more links
## Link to the top 3-6 external resources about this topic
# [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count
|9=
&lt;!-- Social contribution comments... --&gt;
# ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]]
# ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence.
# Thanks for the Wiki Commons uploads
# Thanks very much for your extensive contributions
# Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# No logged contributions
}}
~~~~
&lt;/pre&gt;&lt;/small&gt;&lt;/small&gt;&lt;/small&gt;
gives
&lt;!-- Official book chapter feedback --&gt;
{{MEBF/2026
|1=
&lt;!-- Overall comments... --&gt;
# This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem
# This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem
# This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem
# This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a basic chapter
# This is an insufficient chapter
# The main area(s) for potential improvement:
#* use the best psychological theory about the topic
#* more detailed review of the best psychological research about the topic
#* quality of written expression
#* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]]
#* integrate more strongly with other chapters by using embedded links to related topics
#* overuse of genAI—express more in your own words; watch out for [[w:AI slop|AI slop]]
#* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter
&lt;!-- Overall - Edit summaries --&gt;
#* [[w:Help:Edit summary|Edit summaries]] are used to clearly communicated the changes made in most or all edits
#* Use more specific [[w:Help:Edit summary|edit summaries]] to clearly communicate the changes made in each edit
#* Use [[w:Help:Edit summary|edit summaries]] to briefly describe the changes made in each edit
&lt;!-- Overall - GenAI --&gt;
#* [[Motivation and emotion/Assessment/Using generative AI|genAI use]] is appropriately acknowledged
#* In some places, there is overreliance on genAI
#* In some places, there is overreliance on genAI, with insufficient acknowledged in edit summaries when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles
#* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in edit summaries with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]].
&lt;!-- Overall – Citations --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims
# Only cite sources that you consult
# All citations need to be in the References
&lt;!-- Overall – Word count --&gt;
# Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand
# Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes.
&lt;!-- Overall – Copyedits --&gt;
# For additional feedback, see the following comments and [ these copyedits]
|2=
&lt;!-- Overview – Comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped
&lt;!-- Overview – Scenario --&gt;
&lt;!-- Overview – Scenario - Description --&gt;
# Engaging scenario or case study
# Reasonably engaging scenario or case study
# Basic scenario or case study
# Use a more practical, real-life scenario; move review of research into a subsequent section
# Consider using an example that more people can relate to (less than 5% of the world population are university students)
# Add an engaging case study or scenario
&lt;!-- Overview – Scenario - Figure --&gt;
# Figure 1 is relevant to the scenario
# Figure 1 could be more relevant to the scenario
# Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section
# Include a relevant image
&lt;!-- Overview – Scenario - Feature box --&gt;
# The scenario uses an appropriate feature box
# Put the scenario in a feature box
&lt;!-- Overview – Explains problem --&gt;
# Clearly explains the psychological problem or phenomenon
# Explains the psychological problem or phenomenon reasonably well/in a basic way
# Briefly explains the psychological problem or phenomenon; provide more detail
# Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections.
# Clarity of written expression can be improved
&lt;!-- Overview – Focus questions --&gt;
# The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient
# The focus questions could be improved by:
## being more specific to the topic (i.e., the sub-title)
## matching the top-level headings more closely
## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]]
## splitting double-barrelled questions into separate questions
## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## being presented in a feature box to help guide the reader (fixed)
# Add focus questions in a feature box
# See copyedits for examples of possible improvements
|3=
&lt;!-- Theory comments... --&gt;
&lt;!-- Theory – Breadth --&gt;
# Excellent—key theories are very well explained and applied
# Very good—key theories are well explained and applied; minor areas for improvements
# Reasonably good—relevant theories are selected, described, and explained, with some room for improvement
# Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement
# A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic
# Insufficient use of relevant psychological theory about this topic
# Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question).
&lt;!-- Theory – Builds on --&gt;
# Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
&lt;!-- Theory – Depth --&gt;
# Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies)
&lt;!-- Theory – Tables/Figures/Lists --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information
&lt;!-- Theory – Citations --&gt;
# Key citations are well used
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
# If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source]
# If you didn't consult an original source, don't cite it
&lt;!-- Theory – Examples --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts
# Consider using more examples to illustrate theoretical concepts
# Use more examples to illustrate theoretical concepts
# Insufficient use of examples to illustrate theoretical concepts
|4=
&lt;!-- Research comments... --&gt;
&lt;!-- Research – Key findings --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research
# Excellent emphasis on systematic reviews and/or meta-analyses
# Greater emphasis on systematic reviews and/or meta-analyses would be ideal
# More detail about key studies would be ideal
# Claims are well referenced
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
&lt;!-- Research – Critical thinking --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident
# [[w:Critical thinking|Critical thinking]] about research could be further evidenced by:
## describing the methodology (e.g., sample, measures) in important studies
## considering the strength of relationships
## acknowledging limitations
## pointing out critiques/counterarguments
## suggesting ''specific'' directions for future research
|5=
&lt;!-- Integration comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research
# The chapter places more emphasis on theory than on research; strive for an integrated balance
# The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links
# Insufficient integration with related [[Motivation and emotion/Book|chapters]]
|6=
&lt;!-- Conclusion comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic summary and conclusion
# Insufficient as a cohesive summary of the best psychological theory and research about the topic
# Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words
# Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the edit summary.
# Highlights the importance of the problem or phenomenon of interest
# Highlight the importance of the problem or phenomenon of interest
&lt;!-- Conclusion – Key points --&gt;
# Key points are well summarised
# Key points are summarised in a basic way
# Summarise key points
&lt;!-- Conclusion – Focus questions --&gt;
# The focus questions are addressed
# The take-away messages for each focus question could be spelt out more clearly
# Address the focus questions
&lt;!-- Conclusion – Take-home messages --&gt;
# Clear take-home message(s)
# Add practical, take-home message(s)
&lt;!-- Conclusion – Word count --&gt;
# Not counted for marking purposes due to being over the maximum word count
|7=
&lt;!-- Written expression – Style comments... --&gt;
&lt;!-- Written expression – Written expression --&gt;
# Written expression
## The quality of written expression is excellent/very good/good/reasonably good/basic
## The quality of written expression is OK but there are several aspects which are below professional standard
## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills.
## Use active (e.g., &quot;this chapter explores&quot; or &quot;this chapter explored&quot;) rather than passive voice (e.g., &quot;this chapter will explore&quot; or &quot;this chapter has explored&quot;) [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/]
## The target audience is international, not domestic. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia].
## Reduce excessive use of bold font
&lt;!-- Written expression – Sentences --&gt;
## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression
## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+.
## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence.
&lt;!-- Written expression – Paragraphs --&gt;
## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences.
## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences.
## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs.
&lt;!-- Written expression – Language --&gt;
## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., &quot;it&quot;) instead of 1st (e.g., &quot;we&quot;) or 2nd person (e.g., &quot;you&quot;) in the main text. 1st of 2nd person can work well for case studies or feature boxes.
## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]].## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]]
## &quot;Individuals&quot; is overused. &quot;People&quot; is usually a clearer term than &quot;individuals&quot;. Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally.
## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning
## Use permanent, rather than relative, time references. For example, instead of &quot;20 years ago&quot;, refer to something like &quot;at the beginning of the 21st century&quot;. In this way, the text will survive better into the future, without needing to be rewritten.
## Avoid overly emotive language (e.g,. *) in science-based communication
&lt;!-- Written expression – Layout --&gt;
# Layout
## The chapter is well structured, with major sections using sub-sections
## The headings could be more clearly aligned with the focus questions
## The structure is overly complicated; simplify and integrate
## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion
## The chapter structure is underdeveloped; expand by using subheadings
## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings
## Use the default heading style (e.g.,  remove additional numbers, italics, bo]ld, and/or change in font size)
## See earlier comment about [[#Heading casing|heading casing]]
## Provide more descriptive headings
## Move links from headings into their first mention in text
## Remove abbreviations/citations from headings
## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags)
## Integrate learning features rather than having it as a stand-alone section
## The Overview and Conclusion should not have subheadings (fixed)
## Remove colons (:) from the ends of headings
&lt;!-- Written expression – Grammar --&gt;
# Grammar and spelling are excellent
# Grammar
## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback
## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas].
## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element
## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats')
## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who]
## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect]
## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)]
## Use past tense when describing research studies, although implications of findings could be in the present tense
&lt;!-- Written expression – Abbreviations --&gt;
## Abbreviations
### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out
### Check and correct formatting of abbreviations (such as e.g., i.e., etc.)
### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms.
### Spell out abbreviations on their first use, to explain them to the reader
### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards
### Only introduce abbreviations which are subsequently used
&lt;!-- Written expression – Spelling --&gt;
# Spelling
## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour)
## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages.
&lt;!-- Written expression – Proofreading --&gt;
# Proofreading
## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard
## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info]
&lt;!-- Written expression – APA style --&gt;
# APA style
## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY]
## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing for disorders, therapies, theories, etc.]
## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)]
&lt;!-- Written expression – APA style - Quotes --&gt;
## Use double (not single) quotation marks &quot;to introduce a word or phrase used ... as slang, or as an invented or coined expression&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## &quot;Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## Direct quotes need page numbers—even better, communicate about concepts in your own words
## Direct quotes are overused—it is better to communicate about concepts in your own words
&lt;!-- Written expression – Figures --&gt;
## Figures
### Very well/Well/Reasonably well captioned
### Brief captions; provide more detail to help connect the figure to the text
### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]].
### Add captions
&lt;!-- Written expression – Figures - Citations --&gt;
### Each Figure is referred to at least once within the main text using APA style
### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., &quot;(see Figure 1)&quot;; do not use bold, italics, check and correct capitalisation).
### Refer to each Figure at least once within the main text (e.g., &quot;(see Figure 1)&quot;)
&lt;!-- Written expression – Figures - Other --&gt;
### Some image uploads were removed because of a lack of sufficient/appropriate copyright information
### Numbering needs correcting
### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size)
&lt;!-- Written expression – Tables --&gt;
## Tables
### Very well/Well/Reasonably well captioned
### Brief caption(s); provide more explanatory detail about the table
### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]])
&lt;!-- Written expression – Tables - Citations --&gt;
### Each Table is referred to at least once within the main text using APA style
### Each Table is referred to at least once within the main text
### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation)
### Refer to each Table at least once within the main text (e.g., see Table 1)
&lt;!-- Written expression – Citations --&gt;
# Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags)
## If there are three or more authors, cite the first author followed by et al., then year. For example, either:
### in-text, Smith et al. (2020), or
### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020)
## Do not include author first name or initials
## Use ampersand (&amp;) inside [[w:Bracket#Parentheses|parentheses]] and &quot;and&quot; outside parentheses
## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra &amp; Aardvark, 2020)
## A full stop is needed after &quot;et al&quot; (i.e., &quot;et al.&quot;) because it is an abbreviation of [[wikt:et alii|et alii]]
## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]]
## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point)
## Check and correct placement of full-stops
## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois
## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources
# For citations, use APA style or wiki style, but not both
# Secondary citations are overused; strive to consult primary sources
&lt;!-- Written expression – References --&gt;
## References use excellent/very good/good/reasonably good/basic/poor APA style:
### Check and correct use of italicisation
### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization]
### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-)
### Include dois where available
### Hyperlink dois for 1-click access
### Provide the full titles of journals
### Remove &quot;Retrieved from &quot;
### Use alphabetical order
### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section
### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section
### Remove bullet-points; add hanging indent
&lt;!-- Feedback responsiveness ---&gt;
## No evidence of responsiveness to feedback on talk page
|8=
&lt;!-- Learning features comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features
&lt;!-- Learning features – Wikipedia embedded links --&gt;
# Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles
# Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
# Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
&lt;!-- Learning features – Wikiversity embedded links --&gt;
# Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]
# Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
# Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section
# Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
&lt;!-- Learning features – Figures, tables, feature boxes, scenarios --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s)
# Excellent/Very good/Good/Reasonably good/Basic/No use of table(s)
# Excellent/Very good/Good/Reasonably good/Basic use of feature box(es)
# No use of feature boxes other than the opening scenario
# Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples
# No use of scenarios, case studies, or examples, other than opening scenario
&lt;!-- Learning features – Quizzes --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s)
# The quiz questions could be improved by being more focused on the key points and/or take-home messages
# The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end
# The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]])
# No use of quiz(zes) and/or reflection question(s)
&lt;!-- Learning features – See also --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Also include links to related book chapters
## Also include links to related Wikipedia articles
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite
## Move external links into the [[{{PAGENAME}}#References|External links]] section
## Add more links
# [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count
&lt;!-- Learning features – External links --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section
## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite
## Target an international audience
## Add more links
## Link to the top 3-6 external resources about this topic
# [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count
|9=
&lt;!-- Social contribution comments... --&gt;
# ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]]
# ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence.
# Thanks for the Wiki Commons uploads
# Thanks very much for your extensive contributions
# Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# No logged contributions
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:47, 10 October 2026 (UTC)

==See also==
* [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]]
* [[Template:METF]]
* [[Template:MEMF]]

[[Category:Motivation and emotion/Admin/2026]]
[[Category:Motivation and emotion/Assessment/Chapter]]
&lt;/noinclude&gt;</text>
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      <text bytes="65721" sha1="sqeuhuavna3iv1ofa7mtja2dwe1hhj1" xml:space="preserve">&lt;noinclude&gt;Feedback [[wikiversity:FAQ/Template|template]] for the [[Motivation and emotion/Assessment/Chapter|book chapter]] exercise for the [[motivation and emotion]] unit.

Designed to be [[Help:Transclusion|transcluded]] on a chapter [[Help:Talk page|talk page]].
__NOTOC__&lt;/noinclude&gt;&lt;includeonly&gt;
==[[Motivation and emotion/Assessment/Chapter|Book chapter]] review and feedback==
{{RoundBoxTop|theme=8}}
This chapter has been reviewed according to the [[Motivation and emotion/Assessment/Chapter/Marking criteria|marking criteria]]. Written feedback is provided below, plus there is a [[Motivation and emotion/Assessment/Chapter/Feedback|general feedback]] page. Please also check the chapter's [[Help:Page history|page history]] to check for editing changes made whilst reviewing through the chapter. Chapter marks will be available via {{Motivation and emotion/Canvas}} along with [[Motivation and emotion/Assessment/Social contribution|social contribution]] marks and feedback. Keep an eye on Announcements.
{{RoundBoxBottom}}
{{RoundBoxTop|theme=}}[[File:Wikiuutiset logo typewriter.png|right|85px]]
===Overall===
{{{1|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Overview (5%)|Overview]]===
{{{2|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Theory (20%)|Theory]]===
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===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Research (25%)|Research]]===
{{{4|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Integration (10%)|Integration]]===
{{{5|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Conclusion (5%)|Conclusion]]===
{{{6|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Style (20%)|Style]]===
{{{7|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Learning features (5%)|Learning features]]===
{{{8|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Social contribution (10%)|Social contribution]]===
{{{9|No comment}}}

{{RoundBoxBottom}}&lt;/includeonly&gt;&lt;noinclude&gt;{{collapse top|Simple example}}
==Simple example==
See also [[#Detailed example|detailed example]]
&lt;pre&gt;
&lt;!-- Official feedback --&gt;
{{MEBF/2026
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#
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#
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~~~~
&lt;/pre&gt;
gives
&lt;!-- Official book chapter feedback --&gt;
{{MEBF/2026
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#
|2=
&lt;!-- Overview comments... --&gt;
# 
|3=
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|6=
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#
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-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:47, 10 October 2026 (UTC)
{{Collapse bottom}}
==Detailed example==
Example use of the template, with some common feedback comments:
&lt;small&gt;&lt;small&gt;&lt;small&gt;&lt;pre&gt;
&lt;!-- Official book chapter feedback --&gt;
{{MEBF/2026
|1=
&lt;!-- Overall comments... --&gt;
# This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem
# This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem
# This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem
# This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a basic chapter
# This is an insufficient chapter
# The main area(s) for potential improvement:
#* use the best psychological theory about the topic
#* more detailed review of the best psychological research about the topic
#* quality of written expression
#* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]]
#* integrate more strongly with other chapters by using embedded links to related topics
#* overuse of unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] (watch out for [[w:AI slop|AI slop]])—express more in your own words
#* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter
&lt;!-- Overall - Edit summaries --&gt;
#* [[w:Help:Edit summary|Edit summaries]] are used to clearly communicated the changes made in most or all edits
#* Use more specific [[w:Help:Edit summary|edit summaries]] to clearly communicate the changes made in each edit
#* Use [[w:Help:Edit summary|edit summaries]] to briefly describe the changes made in each edit
&lt;!-- Overall - GenAI --&gt;
#* [[Motivation and emotion/Assessment/Using generative AI|genAI use]] is appropriately acknowledged
#* In some places, there is overreliance on genAI
#* In some places, there is overreliance on genAI, with insufficient acknowledged in edit summaries when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles
#* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in edit summaries with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]].
&lt;!-- Overall – Citations --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims
# Only cite sources that you consult
# All citations need to be in the References
&lt;!-- Overall – Word count --&gt;
# Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand
# Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes.
&lt;!-- Overall – Copyedits --&gt;
# For additional feedback, see the following comments and [ these copyedits]
|2=
&lt;!-- Overview – Comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped
&lt;!-- Overview – Scenario --&gt;
&lt;!-- Overview – Scenario - Description --&gt;
# Engaging scenario or case study
# Reasonably engaging scenario or case study
# Basic scenario or case study
# Use a more practical, real-life scenario; move review of research into a subsequent section
# Consider using an example that more people can relate to (less than 5% of the world population are university students)
# Add an engaging case study or scenario
&lt;!-- Overview – Scenario - Figure --&gt;
# Figure 1 is relevant to the scenario
# Figure 1 could be more relevant to the scenario
# Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section
# Include a relevant image
&lt;!-- Overview – Scenario - Feature box --&gt;
# The scenario uses an appropriate feature box
# Put the scenario in a feature box
&lt;!-- Overview – Explains problem --&gt;
# Clearly explains the psychological problem or phenomenon
# Explains the psychological problem or phenomenon reasonably well/in a basic way
# Briefly explains the psychological problem or phenomenon; provide more detail
# Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections.
# Clarity of written expression can be improved
&lt;!-- Overview – Focus questions --&gt;
# The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient
# The focus questions could be improved by:
## being more specific to the topic (i.e., the sub-title)
## matching the top-level headings more closely
## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]]
## splitting double-barrelled questions into separate questions
## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## being presented in a feature box to help guide the reader (fixed)
# Add focus questions in a feature box
# See copyedits for examples of possible improvements
|3=
&lt;!-- Theory comments... --&gt;
&lt;!-- Theory – Breadth --&gt;
# Excellent—key theories are very well explained and applied
# Very good—key theories are well explained and applied; minor areas for improvements
# Reasonably good—relevant theories are selected, described, and explained, with some room for improvement
# Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement
# A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic
# Insufficient use of relevant psychological theory about this topic
# Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question).
&lt;!-- Theory – Builds on --&gt;
# Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
&lt;!-- Theory – Depth --&gt;
# Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies)
&lt;!-- Theory – Tables/Figures/Lists --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information
&lt;!-- Theory – Citations --&gt;
# Key citations are well used
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
# If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source]
# If you didn't consult an original source, don't cite it
&lt;!-- Theory – Examples --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts
# Consider using more examples to illustrate theoretical concepts
# Use more examples to illustrate theoretical concepts
# Insufficient use of examples to illustrate theoretical concepts
|4=
&lt;!-- Research comments... --&gt;
&lt;!-- Research – Key findings --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research
# Excellent emphasis on systematic reviews and/or meta-analyses
# Greater emphasis on systematic reviews and/or meta-analyses would be ideal
# More detail about key studies would be ideal
# Claims are well referenced
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
&lt;!-- Research – Critical thinking --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident
# [[w:Critical thinking|Critical thinking]] about research could be further evidenced by:
## describing the methodology (e.g., sample, measures) in important studies
## considering the strength of relationships
## acknowledging limitations
## pointing out critiques/counterarguments
## suggesting ''specific'' directions for future research
|5=
&lt;!-- Integration comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research
# The chapter places more emphasis on theory than on research; strive for an integrated balance
# The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links
# Insufficient integration with related [[Motivation and emotion/Book|chapters]]
|6=
&lt;!-- Conclusion comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic summary and conclusion
# Insufficient as a cohesive summary of the best psychological theory and research about the topic
# Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words
# Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the edit summary.
# Highlights the importance of the problem or phenomenon of interest
# Highlight the importance of the problem or phenomenon of interest
&lt;!-- Conclusion – Key points --&gt;
# Key points are well summarised
# Key points are summarised in a basic way
# Summarise key points
&lt;!-- Conclusion – Focus questions --&gt;
# The focus questions are addressed
# The take-away messages for each focus question could be spelt out more clearly
# Address the focus questions
&lt;!-- Conclusion – Take-home messages --&gt;
# Clear take-home message(s)
# Add practical, take-home message(s)
&lt;!-- Conclusion – Word count --&gt;
# Not counted for marking purposes due to being over the maximum word count
|7=
&lt;!-- Written expression – Style comments... --&gt;
&lt;!-- Written expression – Written expression --&gt;
# Written expression
## The quality of written expression is excellent/very good/good/reasonably good/basic
## The quality of written expression is OK but there are several aspects which are below professional standard
## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills.
## Use active (e.g., &quot;this chapter explores&quot; or &quot;this chapter explored&quot;) rather than passive voice (e.g., &quot;this chapter will explore&quot; or &quot;this chapter has explored&quot;) [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/]
## The target audience is international, not domestic. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia].
## Reduce excessive use of bold font
&lt;!-- Written expression – Sentences --&gt;
## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression
## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+.
## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence.
&lt;!-- Written expression – Paragraphs --&gt;
## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences.
## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences.
## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs.
&lt;!-- Written expression – Language --&gt;
## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., &quot;it&quot;) instead of 1st (e.g., &quot;we&quot;) or 2nd person (e.g., &quot;you&quot;) in the main text. 1st or 2nd person can work well for case studies or feature boxes.
## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]].
## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]]
## &quot;Individuals&quot; is overused. &quot;People&quot; is usually a clearer term than &quot;individuals&quot;. Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally.
## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning
## Use permanent, rather than relative, time references. For example, instead of &quot;20 years ago&quot;, refer to something like &quot;at the beginning of the 21st century&quot;. In this way, the text will survive better into the future, without needing to be rewritten.
## Avoid overly emotive language (e.g,. *) in science-based communication
&lt;!-- Written expression – Layout --&gt;
# Layout
## The chapter is well structured, with major sections using sub-sections
## The headings could be more clearly aligned with the focus questions
## The structure is overly complicated; simplify and integrate
## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion
## The chapter structure is underdeveloped; expand by using subheadings
## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings
## Use the default heading style (e.g., remove additional numbers, italics, bold, and/or change in font size)
## See earlier comment about [[#Heading casing|heading casing]]
## Provide more descriptive headings
## Move links from headings into their first mention in text
## Remove abbreviations/citations from headings
## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags)
## Integrate learning features rather than having it as a stand-alone section
## The Overview and Conclusion should not have subheadings (fixed)
## Remove colons (:) from the ends of headings
&lt;!-- Written expression – Grammar --&gt;
# Grammar and spelling are excellent
# Grammar
## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback
## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas].
## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element
## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats')
## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who]
## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect]
## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)]
## Use past tense when describing research studies, although implications of findings could be in the present tense
&lt;!-- Written expression – Abbreviations --&gt;
## Abbreviations
### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out
### Check and correct formatting of abbreviations (such as e.g., i.e., etc.)
### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms.
### Spell out abbreviations on their first use, to explain them to the reader
### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards
### Only introduce abbreviations which are subsequently used
&lt;!-- Written expression – Spelling --&gt;
# Spelling
## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour)
## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages.
&lt;!-- Written expression – Proofreading --&gt;
# Proofreading
## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard
## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info]
&lt;!-- Written expression – APA style --&gt;
# APA style
## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY]
## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing for disorders, therapies, theories, etc.]
## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)]
&lt;!-- Written expression – APA style - Quotes --&gt;
## Use double (not single) quotation marks &quot;to introduce a word or phrase used ... as slang, or as an invented or coined expression&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## &quot;Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## Direct quotes need page numbers—even better, communicate about concepts in your own words
## Direct quotes are overused—it is better to communicate about concepts in your own words
&lt;!-- Written expression – Figures --&gt;
## Figures
### Very well/Well/Reasonably well captioned
### Brief captions; provide more detail to help connect the figure to the text
### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]].
### Add captions
&lt;!-- Written expression – Figures - Citations --&gt;
### Each Figure is referred to at least once within the main text using APA style
### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., &quot;(see Figure 1)&quot;; do not use bold, italics, check and correct capitalisation).
### Refer to each Figure at least once within the main text (e.g., &quot;(see Figure 1)&quot;)
&lt;!-- Written expression – Figures - Other --&gt;
### Some image uploads were removed because of a lack of sufficient/appropriate copyright information
### Numbering needs correcting
### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size)
&lt;!-- Written expression – Tables --&gt;
## Tables
### Very well/Well/Reasonably well captioned
### Brief caption(s); provide more explanatory detail about the table
### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]])
&lt;!-- Written expression – Tables - Citations --&gt;
### Each Table is referred to at least once within the main text using APA style
### Each Table is referred to at least once within the main text
### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation)
### Refer to each Table at least once within the main text (e.g., see Table 1)
&lt;!-- Written expression – Citations --&gt;
# Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags)
## If there are three or more authors, cite the first author followed by et al., then year. For example, either:
### in-text, Smith et al. (2020), or
### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020)
## Do not include author first name or initials
## Use ampersand (&amp;) inside [[w:Bracket#Parentheses|parentheses]] and &quot;and&quot; outside parentheses
## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra &amp; Aardvark, 2020)
## A full stop is needed after &quot;et al&quot; (i.e., &quot;et al.&quot;) because it is an abbreviation of [[wikt:et alii|et alii]]
## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]]
## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point)
## Check and correct placement of full-stops
## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois
## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources
# For citations, use APA style or wiki style, but not both
# Secondary citations are overused; strive to consult primary sources
&lt;!-- Written expression – References --&gt;
## References use excellent/very good/good/reasonably good/basic/poor APA style:
### Check and correct use of italicisation
### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization]
### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-)
### Include dois where available
### Hyperlink dois for 1-click access
### Provide the full titles of journals
### Remove &quot;Retrieved from &quot;
### Use alphabetical order
### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section
### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section
### Remove bullet-points; add hanging indent
&lt;!-- Feedback responsiveness ---&gt;
## No evidence of responsiveness to feedback on talk page
|8=
&lt;!-- Learning features comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features
&lt;!-- Learning features – Wikipedia embedded links --&gt;
# Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles
# Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
# Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
&lt;!-- Learning features – Wikiversity embedded links --&gt;
# Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]
# Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
# Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section
# Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
&lt;!-- Learning features – Figures, tables, feature boxes, scenarios --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s)
# Excellent/Very good/Good/Reasonably good/Basic/No use of table(s)
# Excellent/Very good/Good/Reasonably good/Basic use of feature box(es)
# No use of feature boxes other than the opening scenario
# Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples
# No use of scenarios, case studies, or examples, other than opening scenario
&lt;!-- Learning features – Quizzes --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s)
# The quiz questions could be improved by being more focused on the key points and/or take-home messages
# The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end
# The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]])
# No use of quiz(zes) and/or reflection question(s)
&lt;!-- Learning features – See also --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Also include links to related book chapters
## Also include links to related Wikipedia articles
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite
## Move external links into the [[{{PAGENAME}}#References|External links]] section
## Add more links
# [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count
&lt;!-- Learning features – External links --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section
## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite
## Target an international audience
## Add more links
## Link to the top 3-6 external resources about this topic
# [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count
|9=
&lt;!-- Social contribution comments... --&gt;
# ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]]
# ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence.
# Thanks for the Wiki Commons uploads
# Thanks very much for your extensive contributions
# Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# No logged contributions
}}
~~~~
&lt;/pre&gt;&lt;/small&gt;&lt;/small&gt;&lt;/small&gt;
gives
&lt;!-- Official book chapter feedback --&gt;
{{MEBF/2026
|1=
&lt;!-- Overall comments... --&gt;
# This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem
# This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem
# This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem
# This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a basic chapter
# This is an insufficient chapter
# The main area(s) for potential improvement:
#* use the best psychological theory about the topic
#* more detailed review of the best psychological research about the topic
#* quality of written expression
#* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]]
#* integrate more strongly with other chapters by using embedded links to related topics
#* overuse of unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] (watch out for [[w:AI slop|AI slop]])—express more in your own words
#* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter
&lt;!-- Overall - Edit summaries --&gt;
#* [[w:Help:Edit summary|Edit summaries]] are used to clearly communicated the changes made in most or all edits
#* Use more specific [[w:Help:Edit summary|edit summaries]] to clearly communicate the changes made in each edit
#* Use [[w:Help:Edit summary|edit summaries]] to briefly describe the changes made in each edit
&lt;!-- Overall - GenAI --&gt;
#* [[Motivation and emotion/Assessment/Using generative AI|genAI use]] is appropriately acknowledged
#* In some places, there is overreliance on genAI
#* In some places, there is overreliance on genAI, with insufficient acknowledged in edit summaries when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles
#* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in edit summaries with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]].
&lt;!-- Overall – Citations --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims
# Only cite sources that you consult
# All citations need to be in the References
&lt;!-- Overall – Word count --&gt;
# Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand
# Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes.
&lt;!-- Overall – Copyedits --&gt;
# For additional feedback, see the following comments and [ these copyedits]
|2=
&lt;!-- Overview – Comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped
&lt;!-- Overview – Scenario --&gt;
&lt;!-- Overview – Scenario - Description --&gt;
# Engaging scenario or case study
# Reasonably engaging scenario or case study
# Basic scenario or case study
# Use a more practical, real-life scenario; move review of research into a subsequent section
# Consider using an example that more people can relate to (less than 5% of the world population are university students)
# Add an engaging case study or scenario
&lt;!-- Overview – Scenario - Figure --&gt;
# Figure 1 is relevant to the scenario
# Figure 1 could be more relevant to the scenario
# Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section
# Include a relevant image
&lt;!-- Overview – Scenario - Feature box --&gt;
# The scenario uses an appropriate feature box
# Put the scenario in a feature box
&lt;!-- Overview – Explains problem --&gt;
# Clearly explains the psychological problem or phenomenon
# Explains the psychological problem or phenomenon reasonably well/in a basic way
# Briefly explains the psychological problem or phenomenon; provide more detail
# Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections.
# Clarity of written expression can be improved
&lt;!-- Overview – Focus questions --&gt;
# The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient
# The focus questions could be improved by:
## being more specific to the topic (i.e., the sub-title)
## matching the top-level headings more closely
## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]]
## splitting double-barrelled questions into separate questions
## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## being presented in a feature box to help guide the reader (fixed)
# Add focus questions in a feature box
# See copyedits for examples of possible improvements
|3=
&lt;!-- Theory comments... --&gt;
&lt;!-- Theory – Breadth --&gt;
# Excellent—key theories are very well explained and applied
# Very good—key theories are well explained and applied; minor areas for improvements
# Reasonably good—relevant theories are selected, described, and explained, with some room for improvement
# Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement
# A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic
# Insufficient use of relevant psychological theory about this topic
# Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question).
&lt;!-- Theory – Builds on --&gt;
# Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
&lt;!-- Theory – Depth --&gt;
# Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies)
&lt;!-- Theory – Tables/Figures/Lists --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information
&lt;!-- Theory – Citations --&gt;
# Key citations are well used
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
# If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source]
# If you didn't consult an original source, don't cite it
&lt;!-- Theory – Examples --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts
# Consider using more examples to illustrate theoretical concepts
# Use more examples to illustrate theoretical concepts
# Insufficient use of examples to illustrate theoretical concepts
|4=
&lt;!-- Research comments... --&gt;
&lt;!-- Research – Key findings --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research
# Excellent emphasis on systematic reviews and/or meta-analyses
# Greater emphasis on systematic reviews and/or meta-analyses would be ideal
# More detail about key studies would be ideal
# Claims are well referenced
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
&lt;!-- Research – Critical thinking --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident
# [[w:Critical thinking|Critical thinking]] about research could be further evidenced by:
## describing the methodology (e.g., sample, measures) in important studies
## considering the strength of relationships
## acknowledging limitations
## pointing out critiques/counterarguments
## suggesting ''specific'' directions for future research
|5=
&lt;!-- Integration comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research
# The chapter places more emphasis on theory than on research; strive for an integrated balance
# The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links
# Insufficient integration with related [[Motivation and emotion/Book|chapters]]
|6=
&lt;!-- Conclusion comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic summary and conclusion
# Insufficient as a cohesive summary of the best psychological theory and research about the topic
# Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words
# Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the edit summary.
# Highlights the importance of the problem or phenomenon of interest
# Highlight the importance of the problem or phenomenon of interest
&lt;!-- Conclusion – Key points --&gt;
# Key points are well summarised
# Key points are summarised in a basic way
# Summarise key points
&lt;!-- Conclusion – Focus questions --&gt;
# The focus questions are addressed
# The take-away messages for each focus question could be spelt out more clearly
# Address the focus questions
&lt;!-- Conclusion – Take-home messages --&gt;
# Clear take-home message(s)
# Add practical, take-home message(s)
&lt;!-- Conclusion – Word count --&gt;
# Not counted for marking purposes due to being over the maximum word count
|7=
&lt;!-- Written expression – Style comments... --&gt;
&lt;!-- Written expression – Written expression --&gt;
# Written expression
## The quality of written expression is excellent/very good/good/reasonably good/basic
## The quality of written expression is OK but there are several aspects which are below professional standard
## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills.
## Use active (e.g., &quot;this chapter explores&quot; or &quot;this chapter explored&quot;) rather than passive voice (e.g., &quot;this chapter will explore&quot; or &quot;this chapter has explored&quot;) [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/]
## The target audience is international, not domestic. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia].
## Reduce excessive use of bold font
&lt;!-- Written expression – Sentences --&gt;
## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression
## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+.
## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence.
&lt;!-- Written expression – Paragraphs --&gt;
## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences.
## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences.
## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs.
&lt;!-- Written expression – Language --&gt;
## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., &quot;it&quot;) instead of 1st (e.g., &quot;we&quot;) or 2nd person (e.g., &quot;you&quot;) in the main text. 1st of 2nd person can work well for case studies or feature boxes.
## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]].## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]]
## &quot;Individuals&quot; is overused. &quot;People&quot; is usually a clearer term than &quot;individuals&quot;. Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally.
## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning
## Use permanent, rather than relative, time references. For example, instead of &quot;20 years ago&quot;, refer to something like &quot;at the beginning of the 21st century&quot;. In this way, the text will survive better into the future, without needing to be rewritten.
## Avoid overly emotive language (e.g,. *) in science-based communication
&lt;!-- Written expression – Layout --&gt;
# Layout
## The chapter is well structured, with major sections using sub-sections
## The headings could be more clearly aligned with the focus questions
## The structure is overly complicated; simplify and integrate
## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion
## The chapter structure is underdeveloped; expand by using subheadings
## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings
## Use the default heading style (e.g.,  remove additional numbers, italics, bo]ld, and/or change in font size)
## See earlier comment about [[#Heading casing|heading casing]]
## Provide more descriptive headings
## Move links from headings into their first mention in text
## Remove abbreviations/citations from headings
## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags)
## Integrate learning features rather than having it as a stand-alone section
## The Overview and Conclusion should not have subheadings (fixed)
## Remove colons (:) from the ends of headings
&lt;!-- Written expression – Grammar --&gt;
# Grammar and spelling are excellent
# Grammar
## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback
## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas].
## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element
## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats')
## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who]
## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect]
## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)]
## Use past tense when describing research studies, although implications of findings could be in the present tense
&lt;!-- Written expression – Abbreviations --&gt;
## Abbreviations
### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out
### Check and correct formatting of abbreviations (such as e.g., i.e., etc.)
### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms.
### Spell out abbreviations on their first use, to explain them to the reader
### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards
### Only introduce abbreviations which are subsequently used
&lt;!-- Written expression – Spelling --&gt;
# Spelling
## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour)
## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages.
&lt;!-- Written expression – Proofreading --&gt;
# Proofreading
## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard
## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info]
&lt;!-- Written expression – APA style --&gt;
# APA style
## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY]
## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing for disorders, therapies, theories, etc.]
## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)]
&lt;!-- Written expression – APA style - Quotes --&gt;
## Use double (not single) quotation marks &quot;to introduce a word or phrase used ... as slang, or as an invented or coined expression&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## &quot;Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## Direct quotes need page numbers—even better, communicate about concepts in your own words
## Direct quotes are overused—it is better to communicate about concepts in your own words
&lt;!-- Written expression – Figures --&gt;
## Figures
### Very well/Well/Reasonably well captioned
### Brief captions; provide more detail to help connect the figure to the text
### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]].
### Add captions
&lt;!-- Written expression – Figures - Citations --&gt;
### Each Figure is referred to at least once within the main text using APA style
### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., &quot;(see Figure 1)&quot;; do not use bold, italics, check and correct capitalisation).
### Refer to each Figure at least once within the main text (e.g., &quot;(see Figure 1)&quot;)
&lt;!-- Written expression – Figures - Other --&gt;
### Some image uploads were removed because of a lack of sufficient/appropriate copyright information
### Numbering needs correcting
### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size)
&lt;!-- Written expression – Tables --&gt;
## Tables
### Very well/Well/Reasonably well captioned
### Brief caption(s); provide more explanatory detail about the table
### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]])
&lt;!-- Written expression – Tables - Citations --&gt;
### Each Table is referred to at least once within the main text using APA style
### Each Table is referred to at least once within the main text
### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation)
### Refer to each Table at least once within the main text (e.g., see Table 1)
&lt;!-- Written expression – Citations --&gt;
# Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags)
## If there are three or more authors, cite the first author followed by et al., then year. For example, either:
### in-text, Smith et al. (2020), or
### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020)
## Do not include author first name or initials
## Use ampersand (&amp;) inside [[w:Bracket#Parentheses|parentheses]] and &quot;and&quot; outside parentheses
## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra &amp; Aardvark, 2020)
## A full stop is needed after &quot;et al&quot; (i.e., &quot;et al.&quot;) because it is an abbreviation of [[wikt:et alii|et alii]]
## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]]
## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point)
## Check and correct placement of full-stops
## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois
## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources
# For citations, use APA style or wiki style, but not both
# Secondary citations are overused; strive to consult primary sources
&lt;!-- Written expression – References --&gt;
## References use excellent/very good/good/reasonably good/basic/poor APA style:
### Check and correct use of italicisation
### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization]
### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-)
### Include dois where available
### Hyperlink dois for 1-click access
### Provide the full titles of journals
### Remove &quot;Retrieved from &quot;
### Use alphabetical order
### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section
### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section
### Remove bullet-points; add hanging indent
&lt;!-- Feedback responsiveness ---&gt;
## No evidence of responsiveness to feedback on talk page
|8=
&lt;!-- Learning features comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features
&lt;!-- Learning features – Wikipedia embedded links --&gt;
# Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles
# Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
# Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
&lt;!-- Learning features – Wikiversity embedded links --&gt;
# Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]
# Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
# Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section
# Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
&lt;!-- Learning features – Figures, tables, feature boxes, scenarios --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s)
# Excellent/Very good/Good/Reasonably good/Basic/No use of table(s)
# Excellent/Very good/Good/Reasonably good/Basic use of feature box(es)
# No use of feature boxes other than the opening scenario
# Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples
# No use of scenarios, case studies, or examples, other than opening scenario
&lt;!-- Learning features – Quizzes --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s)
# The quiz questions could be improved by being more focused on the key points and/or take-home messages
# The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end
# The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]])
# No use of quiz(zes) and/or reflection question(s)
&lt;!-- Learning features – See also --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Also include links to related book chapters
## Also include links to related Wikipedia articles
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite
## Move external links into the [[{{PAGENAME}}#References|External links]] section
## Add more links
# [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count
&lt;!-- Learning features – External links --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section
## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite
## Target an international audience
## Add more links
## Link to the top 3-6 external resources about this topic
# [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count
|9=
&lt;!-- Social contribution comments... --&gt;
# ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]]
# ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence.
# Thanks for the Wiki Commons uploads
# Thanks very much for your extensive contributions
# Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# No logged contributions
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:47, 10 October 2026 (UTC)

==See also==
* [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]]
* [[Template:METF]]
* [[Template:MEMF]]

[[Category:Motivation and emotion/Admin/2026]]
[[Category:Motivation and emotion/Assessment/Chapter]]
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Designed to be [[Help:Transclusion|transcluded]] on a chapter [[Help:Talk page|talk page]].
__NOTOC__&lt;/noinclude&gt;&lt;includeonly&gt;
==[[Motivation and emotion/Assessment/Chapter|Book chapter]] review and feedback==
{{RoundBoxTop|theme=8}}
This chapter has been reviewed according to the [[Motivation and emotion/Assessment/Chapter/Marking criteria|marking criteria]]. Written feedback is provided below, plus there is a [[Motivation and emotion/Assessment/Chapter/Feedback|general feedback]] page. Please also check the chapter's [[Help:Page history|page history]] to check for editing changes made whilst reviewing through the chapter. Chapter marks will be available via {{Motivation and emotion/Canvas}} along with [[Motivation and emotion/Assessment/Social contribution|social contribution]] marks and feedback. Keep an eye on Announcements.
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===Overall===
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===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Overview (5%)|Overview]]===
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===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Conclusion (5%)|Conclusion]]===
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===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Style (20%)|Style]]===
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===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Learning features (5%)|Learning features]]===
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===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Social contribution (10%)|Social contribution]]===
{{{9|No comment}}}

{{RoundBoxBottom}}&lt;/includeonly&gt;&lt;noinclude&gt;{{collapse top|Simple example}}
==Simple example==
See also [[#Detailed example|detailed example]]
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-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:47, 10 October 2026 (UTC)
{{Collapse bottom}}
==Detailed example==
Example use of the template, with some common feedback comments:
&lt;small&gt;&lt;small&gt;&lt;small&gt;&lt;pre&gt;
&lt;!-- Official book chapter feedback --&gt;
{{MEBF/2026
|1=
&lt;!-- Overall comments... --&gt;
# This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem
# This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem
# This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem
# This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a basic chapter
# This is an insufficient chapter
# The main area(s) for potential improvement:
#* use the best psychological theory about the topic
#* more detailed review of the best psychological research about the topic
#* quality of written expression
#* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]]
#* integrate more strongly with other chapters by using embedded links to related topics
#* overuse of unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] (watch out for [[w:AI slop|AI slop]])—express more in your own words
#* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter
&lt;!-- Overall - Edit summaries --&gt;
#* [[w:Help:Edit summary|Edit summaries]] are used to clearly communicated the changes made in most or all edits
#* Use more specific [[w:Help:Edit summary|edit summaries]] to clearly communicate the changes made in each edit
#* Use [[w:Help:Edit summary|edit summaries]] to briefly describe the changes made in each edit
&lt;!-- Overall - GenAI --&gt;
#* [[Motivation and emotion/Assessment/Using generative AI|genAI use]] is appropriately acknowledged
#* In some places, there is overreliance on genAI
#* There is insufficient acknowledgement in edit summaries when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles
#* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in edit summaries with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]].
&lt;!-- Overall – Citations --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims
# Only cite sources that you consult
# All citations need to be in the References
&lt;!-- Overall – Word count --&gt;
# Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand
# Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes.
&lt;!-- Overall – Copyedits --&gt;
# For additional feedback, see the following comments and [ these copyedits]
|2=
&lt;!-- Overview – Comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped
&lt;!-- Overview – Scenario --&gt;
&lt;!-- Overview – Scenario - Description --&gt;
# Engaging scenario or case study
# Reasonably engaging scenario or case study
# Basic scenario or case study
# Use a more practical, real-life scenario; move review of research into a subsequent section
# Consider using an example that more people can relate to (less than 5% of the world population are university students)
# Add an engaging case study or scenario
&lt;!-- Overview – Scenario - Figure --&gt;
# Figure 1 is relevant to the scenario
# Figure 1 could be more relevant to the scenario
# Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section
# Include a relevant image
&lt;!-- Overview – Scenario - Feature box --&gt;
# The scenario uses an appropriate feature box
# Put the scenario in a feature box
&lt;!-- Overview – Explains problem --&gt;
# Clearly explains the psychological problem or phenomenon
# Explains the psychological problem or phenomenon reasonably well/in a basic way
# Briefly explains the psychological problem or phenomenon; provide more detail
# Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections.
# Clarity of written expression can be improved
&lt;!-- Overview – Focus questions --&gt;
# The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient
# The focus questions could be improved by:
## being more specific to the topic (i.e., the sub-title)
## matching the top-level headings more closely
## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]]
## splitting double-barrelled questions into separate questions
## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## being presented in a feature box to help guide the reader (fixed)
# Add focus questions in a feature box
# See copyedits for examples of possible improvements
|3=
&lt;!-- Theory comments... --&gt;
&lt;!-- Theory – Breadth --&gt;
# Excellent—key theories are very well explained and applied
# Very good—key theories are well explained and applied; minor areas for improvements
# Reasonably good—relevant theories are selected, described, and explained, with some room for improvement
# Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement
# A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic
# Insufficient use of relevant psychological theory about this topic
# Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question).
&lt;!-- Theory – Builds on --&gt;
# Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
&lt;!-- Theory – Depth --&gt;
# Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies)
&lt;!-- Theory – Tables/Figures/Lists --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information
&lt;!-- Theory – Citations --&gt;
# Key citations are well used
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
# If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source]
# If you didn't consult an original source, don't cite it
&lt;!-- Theory – Examples --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts
# Consider using more examples to illustrate theoretical concepts
# Use more examples to illustrate theoretical concepts
# Insufficient use of examples to illustrate theoretical concepts
|4=
&lt;!-- Research comments... --&gt;
&lt;!-- Research – Key findings --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research
# Excellent emphasis on systematic reviews and/or meta-analyses
# Greater emphasis on systematic reviews and/or meta-analyses would be ideal
# More detail about key studies would be ideal
# Claims are well referenced
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
&lt;!-- Research – Critical thinking --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident
# [[w:Critical thinking|Critical thinking]] about research could be further evidenced by:
## describing the methodology (e.g., sample, measures) in important studies
## considering the strength of relationships
## acknowledging limitations
## pointing out critiques/counterarguments
## suggesting ''specific'' directions for future research
|5=
&lt;!-- Integration comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research
# The chapter places more emphasis on theory than on research; strive for an integrated balance
# The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links
# Insufficient integration with related [[Motivation and emotion/Book|chapters]]
|6=
&lt;!-- Conclusion comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic summary and conclusion
# Insufficient as a cohesive summary of the best psychological theory and research about the topic
# Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words
# Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the edit summary.
# Highlights the importance of the problem or phenomenon of interest
# Highlight the importance of the problem or phenomenon of interest
&lt;!-- Conclusion – Key points --&gt;
# Key points are well summarised
# Key points are summarised in a basic way
# Summarise key points
&lt;!-- Conclusion – Focus questions --&gt;
# The focus questions are addressed
# The take-away messages for each focus question could be spelt out more clearly
# Address the focus questions
&lt;!-- Conclusion – Take-home messages --&gt;
# Clear take-home message(s)
# Add practical, take-home message(s)
&lt;!-- Conclusion – Word count --&gt;
# Not counted for marking purposes due to being over the maximum word count
|7=
&lt;!-- Written expression – Style comments... --&gt;
&lt;!-- Written expression – Written expression --&gt;
# Written expression
## The quality of written expression is excellent/very good/good/reasonably good/basic
## The quality of written expression is OK but there are several aspects which are below professional standard
## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills.
## Use active (e.g., &quot;this chapter explores&quot; or &quot;this chapter explored&quot;) rather than passive voice (e.g., &quot;this chapter will explore&quot; or &quot;this chapter has explored&quot;) [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/]
## The target audience is international, not domestic. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia].
## Reduce excessive use of bold font
&lt;!-- Written expression – Sentences --&gt;
## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression
## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+.
## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence.
&lt;!-- Written expression – Paragraphs --&gt;
## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences.
## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences.
## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs.
&lt;!-- Written expression – Language --&gt;
## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., &quot;it&quot;) instead of 1st (e.g., &quot;we&quot;) or 2nd person (e.g., &quot;you&quot;) in the main text. 1st or 2nd person can work well for case studies or feature boxes.
## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]].
## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]]
## &quot;Individuals&quot; is overused. &quot;People&quot; is usually a clearer term than &quot;individuals&quot;. Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally.
## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning
## Use permanent, rather than relative, time references. For example, instead of &quot;20 years ago&quot;, refer to something like &quot;at the beginning of the 21st century&quot;. In this way, the text will survive better into the future, without needing to be rewritten.
## Avoid overly emotive language (e.g,. *) in science-based communication
&lt;!-- Written expression – Layout --&gt;
# Layout
## The chapter is well structured, with major sections using sub-sections
## The headings could be more clearly aligned with the focus questions
## The structure is overly complicated; simplify and integrate
## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion
## The chapter structure is underdeveloped; expand by using subheadings
## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings
## Use the default heading style (e.g., remove additional numbers, italics, bold, and/or change in font size)
## See earlier comment about [[#Heading casing|heading casing]]
## Provide more descriptive headings
## Move links from headings into their first mention in text
## Remove abbreviations/citations from headings
## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags)
## Integrate learning features rather than having it as a stand-alone section
## The Overview and Conclusion should not have subheadings (fixed)
## Remove colons (:) from the ends of headings
&lt;!-- Written expression – Grammar --&gt;
# Grammar and spelling are excellent
# Grammar
## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback
## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas].
## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element
## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats')
## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who]
## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect]
## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)]
## Use past tense when describing research studies, although implications of findings could be in the present tense
&lt;!-- Written expression – Abbreviations --&gt;
## Abbreviations
### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out
### Check and correct formatting of abbreviations (such as e.g., i.e., etc.)
### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms.
### Spell out abbreviations on their first use, to explain them to the reader
### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards
### Only introduce abbreviations which are subsequently used
&lt;!-- Written expression – Spelling --&gt;
# Spelling
## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour)
## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages.
&lt;!-- Written expression – Proofreading --&gt;
# Proofreading
## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard
## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info]
&lt;!-- Written expression – APA style --&gt;
# APA style
## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY]
## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing for disorders, therapies, theories, etc.]
## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)]
&lt;!-- Written expression – APA style - Quotes --&gt;
## Use double (not single) quotation marks &quot;to introduce a word or phrase used ... as slang, or as an invented or coined expression&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## &quot;Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## Direct quotes need page numbers—even better, communicate about concepts in your own words
## Direct quotes are overused—it is better to communicate about concepts in your own words
&lt;!-- Written expression – Figures --&gt;
## Figures
### Very well/Well/Reasonably well captioned
### Brief captions; provide more detail to help connect the figure to the text
### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]].
### Add captions
&lt;!-- Written expression – Figures - Citations --&gt;
### Each Figure is referred to at least once within the main text using APA style
### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., &quot;(see Figure 1)&quot;; do not use bold, italics, check and correct capitalisation).
### Refer to each Figure at least once within the main text (e.g., &quot;(see Figure 1)&quot;)
&lt;!-- Written expression – Figures - Other --&gt;
### Some image uploads were removed because of a lack of sufficient/appropriate copyright information
### Numbering needs correcting
### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size)
&lt;!-- Written expression – Tables --&gt;
## Tables
### Very well/Well/Reasonably well captioned
### Brief caption(s); provide more explanatory detail about the table
### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]])
&lt;!-- Written expression – Tables - Citations --&gt;
### Each Table is referred to at least once within the main text using APA style
### Each Table is referred to at least once within the main text
### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation)
### Refer to each Table at least once within the main text (e.g., see Table 1)
&lt;!-- Written expression – Citations --&gt;
# Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags)
## If there are three or more authors, cite the first author followed by et al., then year. For example, either:
### in-text, Smith et al. (2020), or
### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020)
## Do not include author first name or initials
## Use ampersand (&amp;) inside [[w:Bracket#Parentheses|parentheses]] and &quot;and&quot; outside parentheses
## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra &amp; Aardvark, 2020)
## A full stop is needed after &quot;et al&quot; (i.e., &quot;et al.&quot;) because it is an abbreviation of [[wikt:et alii|et alii]]
## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]]
## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point)
## Check and correct placement of full-stops
## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois
## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources
# For citations, use APA style or wiki style, but not both
# Secondary citations are overused; strive to consult primary sources
&lt;!-- Written expression – References --&gt;
## References use excellent/very good/good/reasonably good/basic/poor APA style:
### Check and correct use of italicisation
### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization]
### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-)
### Include dois where available
### Hyperlink dois for 1-click access
### Provide the full titles of journals
### Remove &quot;Retrieved from &quot;
### Use alphabetical order
### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section
### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section
### Remove bullet-points; add hanging indent
&lt;!-- Feedback responsiveness ---&gt;
## No evidence of responsiveness to feedback on talk page
|8=
&lt;!-- Learning features comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features
&lt;!-- Learning features – Wikipedia embedded links --&gt;
# Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles
# Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
# Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
&lt;!-- Learning features – Wikiversity embedded links --&gt;
# Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]
# Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
# Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section
# Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
&lt;!-- Learning features – Figures, tables, feature boxes, scenarios --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s)
# Excellent/Very good/Good/Reasonably good/Basic/No use of table(s)
# Excellent/Very good/Good/Reasonably good/Basic use of feature box(es)
# No use of feature boxes other than the opening scenario
# Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples
# No use of scenarios, case studies, or examples, other than opening scenario
&lt;!-- Learning features – Quizzes --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s)
# The quiz questions could be improved by being more focused on the key points and/or take-home messages
# The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end
# The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]])
# No use of quiz(zes) and/or reflection question(s)
&lt;!-- Learning features – See also --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Also include links to related book chapters
## Also include links to related Wikipedia articles
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite
## Move external links into the [[{{PAGENAME}}#References|External links]] section
## Add more links
# [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count
&lt;!-- Learning features – External links --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section
## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite
## Target an international audience
## Add more links
## Link to the top 3-6 external resources about this topic
# [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count
|9=
&lt;!-- Social contribution comments... --&gt;
# ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]]
# ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence.
# Thanks for the Wiki Commons uploads
# Thanks very much for your extensive contributions
# Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# No logged contributions
}}
~~~~
&lt;/pre&gt;&lt;/small&gt;&lt;/small&gt;&lt;/small&gt;
gives
&lt;!-- Official book chapter feedback --&gt;
{{MEBF/2026
|1=
&lt;!-- Overall comments... --&gt;
# This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem
# This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem
# This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem
# This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a basic chapter
# This is an insufficient chapter
# The main area(s) for potential improvement:
#* use the best psychological theory about the topic
#* more detailed review of the best psychological research about the topic
#* quality of written expression
#* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]]
#* integrate more strongly with other chapters by using embedded links to related topics
#* overuse of unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] (watch out for [[w:AI slop|AI slop]])—express more in your own words
#* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter
&lt;!-- Overall - Edit summaries --&gt;
#* [[w:Help:Edit summary|Edit summaries]] are used to clearly communicated the changes made in most or all edits
#* Use more specific [[w:Help:Edit summary|edit summaries]] to clearly communicate the changes made in each edit
#* Use [[w:Help:Edit summary|edit summaries]] to briefly describe the changes made in each edit
&lt;!-- Overall - GenAI --&gt;
#* [[Motivation and emotion/Assessment/Using generative AI|genAI use]] is appropriately acknowledged
#* In some places, there is overreliance on genAI
#* There is insufficient acknowledgement in edit summaries when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles
#* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in edit summaries with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]].
&lt;!-- Overall – Citations --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims
# Only cite sources that you consult
# All citations need to be in the References
&lt;!-- Overall – Word count --&gt;
# Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand
# Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes.
&lt;!-- Overall – Copyedits --&gt;
# For additional feedback, see the following comments and [ these copyedits]
|2=
&lt;!-- Overview – Comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped
&lt;!-- Overview – Scenario --&gt;
&lt;!-- Overview – Scenario - Description --&gt;
# Engaging scenario or case study
# Reasonably engaging scenario or case study
# Basic scenario or case study
# Use a more practical, real-life scenario; move review of research into a subsequent section
# Consider using an example that more people can relate to (less than 5% of the world population are university students)
# Add an engaging case study or scenario
&lt;!-- Overview – Scenario - Figure --&gt;
# Figure 1 is relevant to the scenario
# Figure 1 could be more relevant to the scenario
# Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section
# Include a relevant image
&lt;!-- Overview – Scenario - Feature box --&gt;
# The scenario uses an appropriate feature box
# Put the scenario in a feature box
&lt;!-- Overview – Explains problem --&gt;
# Clearly explains the psychological problem or phenomenon
# Explains the psychological problem or phenomenon reasonably well/in a basic way
# Briefly explains the psychological problem or phenomenon; provide more detail
# Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections.
# Clarity of written expression can be improved
&lt;!-- Overview – Focus questions --&gt;
# The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient
# The focus questions could be improved by:
## being more specific to the topic (i.e., the sub-title)
## matching the top-level headings more closely
## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]]
## splitting double-barrelled questions into separate questions
## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## being presented in a feature box to help guide the reader (fixed)
# Add focus questions in a feature box
# See copyedits for examples of possible improvements
|3=
&lt;!-- Theory comments... --&gt;
&lt;!-- Theory – Breadth --&gt;
# Excellent—key theories are very well explained and applied
# Very good—key theories are well explained and applied; minor areas for improvements
# Reasonably good—relevant theories are selected, described, and explained, with some room for improvement
# Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement
# A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic
# Insufficient use of relevant psychological theory about this topic
# Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question).
&lt;!-- Theory – Builds on --&gt;
# Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
&lt;!-- Theory – Depth --&gt;
# Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies)
&lt;!-- Theory – Tables/Figures/Lists --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information
&lt;!-- Theory – Citations --&gt;
# Key citations are well used
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
# If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source]
# If you didn't consult an original source, don't cite it
&lt;!-- Theory – Examples --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts
# Consider using more examples to illustrate theoretical concepts
# Use more examples to illustrate theoretical concepts
# Insufficient use of examples to illustrate theoretical concepts
|4=
&lt;!-- Research comments... --&gt;
&lt;!-- Research – Key findings --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research
# Excellent emphasis on systematic reviews and/or meta-analyses
# Greater emphasis on systematic reviews and/or meta-analyses would be ideal
# More detail about key studies would be ideal
# Claims are well referenced
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
&lt;!-- Research – Critical thinking --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident
# [[w:Critical thinking|Critical thinking]] about research could be further evidenced by:
## describing the methodology (e.g., sample, measures) in important studies
## considering the strength of relationships
## acknowledging limitations
## pointing out critiques/counterarguments
## suggesting ''specific'' directions for future research
|5=
&lt;!-- Integration comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research
# The chapter places more emphasis on theory than on research; strive for an integrated balance
# The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links
# Insufficient integration with related [[Motivation and emotion/Book|chapters]]
|6=
&lt;!-- Conclusion comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic summary and conclusion
# Insufficient as a cohesive summary of the best psychological theory and research about the topic
# Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words
# Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the edit summary.
# Highlights the importance of the problem or phenomenon of interest
# Highlight the importance of the problem or phenomenon of interest
&lt;!-- Conclusion – Key points --&gt;
# Key points are well summarised
# Key points are summarised in a basic way
# Summarise key points
&lt;!-- Conclusion – Focus questions --&gt;
# The focus questions are addressed
# The take-away messages for each focus question could be spelt out more clearly
# Address the focus questions
&lt;!-- Conclusion – Take-home messages --&gt;
# Clear take-home message(s)
# Add practical, take-home message(s)
&lt;!-- Conclusion – Word count --&gt;
# Not counted for marking purposes due to being over the maximum word count
|7=
&lt;!-- Written expression – Style comments... --&gt;
&lt;!-- Written expression – Written expression --&gt;
# Written expression
## The quality of written expression is excellent/very good/good/reasonably good/basic
## The quality of written expression is OK but there are several aspects which are below professional standard
## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills.
## Use active (e.g., &quot;this chapter explores&quot; or &quot;this chapter explored&quot;) rather than passive voice (e.g., &quot;this chapter will explore&quot; or &quot;this chapter has explored&quot;) [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/]
## The target audience is international, not domestic. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia].
## Reduce excessive use of bold font
&lt;!-- Written expression – Sentences --&gt;
## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression
## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+.
## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence.
&lt;!-- Written expression – Paragraphs --&gt;
## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences.
## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences.
## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs.
&lt;!-- Written expression – Language --&gt;
## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., &quot;it&quot;) instead of 1st (e.g., &quot;we&quot;) or 2nd person (e.g., &quot;you&quot;) in the main text. 1st of 2nd person can work well for case studies or feature boxes.
## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]].## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]]
## &quot;Individuals&quot; is overused. &quot;People&quot; is usually a clearer term than &quot;individuals&quot;. Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally.
## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning
## Use permanent, rather than relative, time references. For example, instead of &quot;20 years ago&quot;, refer to something like &quot;at the beginning of the 21st century&quot;. In this way, the text will survive better into the future, without needing to be rewritten.
## Avoid overly emotive language (e.g,. *) in science-based communication
&lt;!-- Written expression – Layout --&gt;
# Layout
## The chapter is well structured, with major sections using sub-sections
## The headings could be more clearly aligned with the focus questions
## The structure is overly complicated; simplify and integrate
## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion
## The chapter structure is underdeveloped; expand by using subheadings
## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings
## Use the default heading style (e.g.,  remove additional numbers, italics, bo]ld, and/or change in font size)
## See earlier comment about [[#Heading casing|heading casing]]
## Provide more descriptive headings
## Move links from headings into their first mention in text
## Remove abbreviations/citations from headings
## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags)
## Integrate learning features rather than having it as a stand-alone section
## The Overview and Conclusion should not have subheadings (fixed)
## Remove colons (:) from the ends of headings
&lt;!-- Written expression – Grammar --&gt;
# Grammar and spelling are excellent
# Grammar
## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback
## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas].
## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element
## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats')
## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who]
## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect]
## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)]
## Use past tense when describing research studies, although implications of findings could be in the present tense
&lt;!-- Written expression – Abbreviations --&gt;
## Abbreviations
### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out
### Check and correct formatting of abbreviations (such as e.g., i.e., etc.)
### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms.
### Spell out abbreviations on their first use, to explain them to the reader
### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards
### Only introduce abbreviations which are subsequently used
&lt;!-- Written expression – Spelling --&gt;
# Spelling
## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour)
## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages.
&lt;!-- Written expression – Proofreading --&gt;
# Proofreading
## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard
## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info]
&lt;!-- Written expression – APA style --&gt;
# APA style
## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY]
## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing for disorders, therapies, theories, etc.]
## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)]
&lt;!-- Written expression – APA style - Quotes --&gt;
## Use double (not single) quotation marks &quot;to introduce a word or phrase used ... as slang, or as an invented or coined expression&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## &quot;Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## Direct quotes need page numbers—even better, communicate about concepts in your own words
## Direct quotes are overused—it is better to communicate about concepts in your own words
&lt;!-- Written expression – Figures --&gt;
## Figures
### Very well/Well/Reasonably well captioned
### Brief captions; provide more detail to help connect the figure to the text
### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]].
### Add captions
&lt;!-- Written expression – Figures - Citations --&gt;
### Each Figure is referred to at least once within the main text using APA style
### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., &quot;(see Figure 1)&quot;; do not use bold, italics, check and correct capitalisation).
### Refer to each Figure at least once within the main text (e.g., &quot;(see Figure 1)&quot;)
&lt;!-- Written expression – Figures - Other --&gt;
### Some image uploads were removed because of a lack of sufficient/appropriate copyright information
### Numbering needs correcting
### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size)
&lt;!-- Written expression – Tables --&gt;
## Tables
### Very well/Well/Reasonably well captioned
### Brief caption(s); provide more explanatory detail about the table
### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]])
&lt;!-- Written expression – Tables - Citations --&gt;
### Each Table is referred to at least once within the main text using APA style
### Each Table is referred to at least once within the main text
### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation)
### Refer to each Table at least once within the main text (e.g., see Table 1)
&lt;!-- Written expression – Citations --&gt;
# Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags)
## If there are three or more authors, cite the first author followed by et al., then year. For example, either:
### in-text, Smith et al. (2020), or
### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020)
## Do not include author first name or initials
## Use ampersand (&amp;) inside [[w:Bracket#Parentheses|parentheses]] and &quot;and&quot; outside parentheses
## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra &amp; Aardvark, 2020)
## A full stop is needed after &quot;et al&quot; (i.e., &quot;et al.&quot;) because it is an abbreviation of [[wikt:et alii|et alii]]
## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]]
## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point)
## Check and correct placement of full-stops
## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois
## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources
# For citations, use APA style or wiki style, but not both
# Secondary citations are overused; strive to consult primary sources
&lt;!-- Written expression – References --&gt;
## References use excellent/very good/good/reasonably good/basic/poor APA style:
### Check and correct use of italicisation
### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization]
### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-)
### Include dois where available
### Hyperlink dois for 1-click access
### Provide the full titles of journals
### Remove &quot;Retrieved from &quot;
### Use alphabetical order
### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section
### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section
### Remove bullet-points; add hanging indent
&lt;!-- Feedback responsiveness ---&gt;
## No evidence of responsiveness to feedback on talk page
|8=
&lt;!-- Learning features comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features
&lt;!-- Learning features – Wikipedia embedded links --&gt;
# Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles
# Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
# Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
&lt;!-- Learning features – Wikiversity embedded links --&gt;
# Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]
# Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
# Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section
# Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
&lt;!-- Learning features – Figures, tables, feature boxes, scenarios --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s)
# Excellent/Very good/Good/Reasonably good/Basic/No use of table(s)
# Excellent/Very good/Good/Reasonably good/Basic use of feature box(es)
# No use of feature boxes other than the opening scenario
# Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples
# No use of scenarios, case studies, or examples, other than opening scenario
&lt;!-- Learning features – Quizzes --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s)
# The quiz questions could be improved by being more focused on the key points and/or take-home messages
# The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end
# The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]])
# No use of quiz(zes) and/or reflection question(s)
&lt;!-- Learning features – See also --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Also include links to related book chapters
## Also include links to related Wikipedia articles
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite
## Move external links into the [[{{PAGENAME}}#References|External links]] section
## Add more links
# [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count
&lt;!-- Learning features – External links --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section
## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite
## Target an international audience
## Add more links
## Link to the top 3-6 external resources about this topic
# [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count
|9=
&lt;!-- Social contribution comments... --&gt;
# ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]]
# ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence.
# Thanks for the Wiki Commons uploads
# Thanks very much for your extensive contributions
# Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# No logged contributions
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:47, 10 October 2026 (UTC)

==See also==
* [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]]
* [[Template:METF]]
* [[Template:MEMF]]

[[Category:Motivation and emotion/Admin/2026]]
[[Category:Motivation and emotion/Assessment/Chapter]]
&lt;/noinclude&gt;</text>
      <sha1>eg4wrxgtuawrzo33qjlf3t8l36u8rw0</sha1>
    </revision>
    <revision>
      <id>2841495</id>
      <parentid>2841490</parentid>
      <timestamp>2026-10-19T11:10:35Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <comment>### genAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources</comment>
      <origin>2841495</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="65877" sha1="f87axm17jm4ti7uh08a50oq5mdwcz78" xml:space="preserve">&lt;noinclude&gt;Feedback [[wikiversity:FAQ/Template|template]] for the [[Motivation and emotion/Assessment/Chapter|book chapter]] exercise for the [[motivation and emotion]] unit.

Designed to be [[Help:Transclusion|transcluded]] on a chapter [[Help:Talk page|talk page]].
__NOTOC__&lt;/noinclude&gt;&lt;includeonly&gt;
==[[Motivation and emotion/Assessment/Chapter|Book chapter]] review and feedback==
{{RoundBoxTop|theme=8}}
This chapter has been reviewed according to the [[Motivation and emotion/Assessment/Chapter/Marking criteria|marking criteria]]. Written feedback is provided below, plus there is a [[Motivation and emotion/Assessment/Chapter/Feedback|general feedback]] page. Please also check the chapter's [[Help:Page history|page history]] to check for editing changes made whilst reviewing through the chapter. Chapter marks will be available via {{Motivation and emotion/Canvas}} along with [[Motivation and emotion/Assessment/Social contribution|social contribution]] marks and feedback. Keep an eye on Announcements.
{{RoundBoxBottom}}
{{RoundBoxTop|theme=}}[[File:Wikiuutiset logo typewriter.png|right|85px]]
===Overall===
{{{1|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Overview (5%)|Overview]]===
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===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Theory (20%)|Theory]]===
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===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Research (25%)|Research]]===
{{{4|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Integration (10%)|Integration]]===
{{{5|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Conclusion (5%)|Conclusion]]===
{{{6|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Style (20%)|Style]]===
{{{7|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Learning features (5%)|Learning features]]===
{{{8|No comment}}}
===[[Motivation and emotion/Assessment/Chapter/Marking criteria#Social contribution (10%)|Social contribution]]===
{{{9|No comment}}}

{{RoundBoxBottom}}&lt;/includeonly&gt;&lt;noinclude&gt;{{collapse top|Simple example}}
==Simple example==
See also [[#Detailed example|detailed example]]
&lt;pre&gt;
&lt;!-- Official feedback --&gt;
{{MEBF/2026
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~~~~
&lt;/pre&gt;
gives
&lt;!-- Official book chapter feedback --&gt;
{{MEBF/2026
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|3=
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-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:47, 10 October 2026 (UTC)
{{Collapse bottom}}
==Detailed example==
Example use of the template, with some common feedback comments:
&lt;small&gt;&lt;small&gt;&lt;small&gt;&lt;pre&gt;
&lt;!-- Official book chapter feedback --&gt;
{{MEBF/2026
|1=
&lt;!-- Overall comments... --&gt;
# This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem
# This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem
# This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem
# This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a basic chapter
# This is an insufficient chapter
# The main area(s) for potential improvement:
#* use the best psychological theory about the topic
#* more detailed review of the best psychological research about the topic
#* quality of written expression
#* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]]
#* integrate more strongly with other chapters by using embedded links to related topics
#* overuse of unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] (watch out for [[w:AI slop|AI slop]])—express more in your own words
#* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter
&lt;!-- Overall - Edit summaries --&gt;
#* [[w:Help:Edit summary|Edit summaries]] are used to clearly communicated the changes made in most or all edits
#* Use more specific [[w:Help:Edit summary|edit summaries]] to clearly communicate the changes made in each edit
#* Use [[w:Help:Edit summary|edit summaries]] to briefly describe the changes made in each edit
&lt;!-- Overall - GenAI --&gt;
#* [[Motivation and emotion/Assessment/Using generative AI|genAI use]] is appropriately acknowledged
#* In some places, there is overreliance on genAI
#* There is insufficient acknowledgement in edit summaries when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles
#* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in edit summaries with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]].
&lt;!-- Overall – Citations --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims
# Only cite sources that you consult
# All citations need to be in the References
&lt;!-- Overall – Word count --&gt;
# Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand
# Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes.
&lt;!-- Overall – Copyedits --&gt;
# For additional feedback, see the following comments and [ these copyedits]
|2=
&lt;!-- Overview – Comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped
&lt;!-- Overview – Scenario --&gt;
&lt;!-- Overview – Scenario - Description --&gt;
# Engaging scenario or case study
# Reasonably engaging scenario or case study
# Basic scenario or case study
# Use a more practical, real-life scenario; move review of research into a subsequent section
# Consider using an example that more people can relate to (less than 5% of the world population are university students)
# Add an engaging case study or scenario
&lt;!-- Overview – Scenario - Figure --&gt;
# Figure 1 is relevant to the scenario
# Figure 1 could be more relevant to the scenario
# Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section
# Include a relevant image
&lt;!-- Overview – Scenario - Feature box --&gt;
# The scenario uses an appropriate feature box
# Put the scenario in a feature box
&lt;!-- Overview – Explains problem --&gt;
# Clearly explains the psychological problem or phenomenon
# Explains the psychological problem or phenomenon reasonably well/in a basic way
# Briefly explains the psychological problem or phenomenon; provide more detail
# Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections.
# Clarity of written expression can be improved
&lt;!-- Overview – Focus questions --&gt;
# The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient
# The focus questions could be improved by:
## being more specific to the topic (i.e., the sub-title)
## matching the top-level headings more closely
## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]]
## splitting double-barrelled questions into separate questions
## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## being presented in a feature box to help guide the reader (fixed)
# Add focus questions in a feature box
# See copyedits for examples of possible improvements
|3=
&lt;!-- Theory comments... --&gt;
&lt;!-- Theory – Breadth --&gt;
# Excellent—key theories are very well explained and applied
# Very good—key theories are well explained and applied; minor areas for improvements
# Reasonably good—relevant theories are selected, described, and explained, with some room for improvement
# Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement
# A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic
# Insufficient use of relevant psychological theory about this topic
# Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question).
&lt;!-- Theory – Builds on --&gt;
# Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
&lt;!-- Theory – Depth --&gt;
# Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies)
&lt;!-- Theory – Tables/Figures/Lists --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information
&lt;!-- Theory – Citations --&gt;
# Key citations are well used
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
# If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source]
# If you didn't consult an original source, don't cite it
&lt;!-- Theory – Examples --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts
# Consider using more examples to illustrate theoretical concepts
# Use more examples to illustrate theoretical concepts
# Insufficient use of examples to illustrate theoretical concepts
|4=
&lt;!-- Research comments... --&gt;
&lt;!-- Research – Key findings --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research
# Excellent emphasis on systematic reviews and/or meta-analyses
# Greater emphasis on systematic reviews and/or meta-analyses would be ideal
# More detail about key studies would be ideal
# Claims are well referenced
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
&lt;!-- Research – Critical thinking --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident
# [[w:Critical thinking|Critical thinking]] about research could be further evidenced by:
## describing the methodology (e.g., sample, measures) in important studies
## considering the strength of relationships
## acknowledging limitations
## pointing out critiques/counterarguments
## suggesting ''specific'' directions for future research
|5=
&lt;!-- Integration comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research
# The chapter places more emphasis on theory than on research; strive for an integrated balance
# The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links
# Insufficient integration with related [[Motivation and emotion/Book|chapters]]
|6=
&lt;!-- Conclusion comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic summary and conclusion
# Insufficient as a cohesive summary of the best psychological theory and research about the topic
# Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words
# Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the edit summary.
# Highlights the importance of the problem or phenomenon of interest
# Highlight the importance of the problem or phenomenon of interest
&lt;!-- Conclusion – Key points --&gt;
# Key points are well summarised
# Key points are summarised in a basic way
# Summarise key points
&lt;!-- Conclusion – Focus questions --&gt;
# The focus questions are addressed
# The take-away messages for each focus question could be spelt out more clearly
# Address the focus questions
&lt;!-- Conclusion – Take-home messages --&gt;
# Clear take-home message(s)
# Add practical, take-home message(s)
&lt;!-- Conclusion – Word count --&gt;
# Not counted for marking purposes due to being over the maximum word count
|7=
&lt;!-- Written expression – Style comments... --&gt;
&lt;!-- Written expression – Written expression --&gt;
# Written expression
## The quality of written expression is excellent/very good/good/reasonably good/basic
## The quality of written expression is OK but there are several aspects which are below professional standard
## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills.
### genAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources
## Use active (e.g., &quot;this chapter explores&quot; or &quot;this chapter explored&quot;) rather than passive voice (e.g., &quot;this chapter will explore&quot; or &quot;this chapter has explored&quot;) [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/]
## The target audience is international, not domestic. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia].
## Reduce excessive use of bold font
&lt;!-- Written expression – Sentences --&gt;
## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression
## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+.
## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence.
&lt;!-- Written expression – Paragraphs --&gt;
## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences.
## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences.
## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs.
&lt;!-- Written expression – Language --&gt;
## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., &quot;it&quot;) instead of 1st (e.g., &quot;we&quot;) or 2nd person (e.g., &quot;you&quot;) in the main text. 1st or 2nd person can work well for case studies or feature boxes.
## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]].
## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]]
## &quot;Individuals&quot; is overused. &quot;People&quot; is usually a clearer term than &quot;individuals&quot;. Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally.
## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning
## Use permanent, rather than relative, time references. For example, instead of &quot;20 years ago&quot;, refer to something like &quot;at the beginning of the 21st century&quot;. In this way, the text will survive better into the future, without needing to be rewritten.
## Avoid overly emotive language (e.g,. *) in science-based communication
&lt;!-- Written expression – Layout --&gt;
# Layout
## The chapter is well structured, with major sections using sub-sections
## The headings could be more clearly aligned with the focus questions
## The structure is overly complicated; simplify and integrate
## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion
## The chapter structure is underdeveloped; expand by using subheadings
## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings
## Use the default heading style (e.g., remove additional numbers, italics, bold, and/or change in font size)
## See earlier comment about [[#Heading casing|heading casing]]
## Provide more descriptive headings
## Move links from headings into their first mention in text
## Remove abbreviations/citations from headings
## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags)
## Integrate learning features rather than having it as a stand-alone section
## The Overview and Conclusion should not have subheadings (fixed)
## Remove colons (:) from the ends of headings
&lt;!-- Written expression – Grammar --&gt;
# Grammar and spelling are excellent
# Grammar
## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback
## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas].
## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element
## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats')
## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who]
## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect]
## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)]
## Use past tense when describing research studies, although implications of findings could be in the present tense
&lt;!-- Written expression – Abbreviations --&gt;
## Abbreviations
### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out
### Check and correct formatting of abbreviations (such as e.g., i.e., etc.)
### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms.
### Spell out abbreviations on their first use, to explain them to the reader
### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards
### Only introduce abbreviations which are subsequently used
&lt;!-- Written expression – Spelling --&gt;
# Spelling
## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour)
## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages.
&lt;!-- Written expression – Proofreading --&gt;
# Proofreading
## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard
## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info]
&lt;!-- Written expression – APA style --&gt;
# APA style
## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY]
## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing for disorders, therapies, theories, etc.]
## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)]
&lt;!-- Written expression – APA style - Quotes --&gt;
## Use double (not single) quotation marks &quot;to introduce a word or phrase used ... as slang, or as an invented or coined expression&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## &quot;Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## Direct quotes need page numbers—even better, communicate about concepts in your own words
## Direct quotes are overused—it is better to communicate about concepts in your own words
&lt;!-- Written expression – Figures --&gt;
## Figures
### Very well/Well/Reasonably well captioned
### Brief captions; provide more detail to help connect the figure to the text
### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]].
### Add captions
&lt;!-- Written expression – Figures - Citations --&gt;
### Each Figure is referred to at least once within the main text using APA style
### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., &quot;(see Figure 1)&quot;; do not use bold, italics, check and correct capitalisation).
### Refer to each Figure at least once within the main text (e.g., &quot;(see Figure 1)&quot;)
&lt;!-- Written expression – Figures - Other --&gt;
### Some image uploads were removed because of a lack of sufficient/appropriate copyright information
### Numbering needs correcting
### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size)
&lt;!-- Written expression – Tables --&gt;
## Tables
### Very well/Well/Reasonably well captioned
### Brief caption(s); provide more explanatory detail about the table
### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]])
&lt;!-- Written expression – Tables - Citations --&gt;
### Each Table is referred to at least once within the main text using APA style
### Each Table is referred to at least once within the main text
### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation)
### Refer to each Table at least once within the main text (e.g., see Table 1)
&lt;!-- Written expression – Citations --&gt;
# Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags)
## If there are three or more authors, cite the first author followed by et al., then year. For example, either:
### in-text, Smith et al. (2020), or
### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020)
## Do not include author first name or initials
## Use ampersand (&amp;) inside [[w:Bracket#Parentheses|parentheses]] and &quot;and&quot; outside parentheses
## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra &amp; Aardvark, 2020)
## A full stop is needed after &quot;et al&quot; (i.e., &quot;et al.&quot;) because it is an abbreviation of [[wikt:et alii|et alii]]
## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]]
## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point)
## Check and correct placement of full-stops
## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois
## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources
# For citations, use APA style or wiki style, but not both
# Secondary citations are overused; strive to consult primary sources
&lt;!-- Written expression – References --&gt;
## References use excellent/very good/good/reasonably good/basic/poor APA style:
### Check and correct use of italicisation
### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization]
### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-)
### Include dois where available
### Hyperlink dois for 1-click access
### Provide the full titles of journals
### Remove &quot;Retrieved from &quot;
### Use alphabetical order
### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section
### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section
### Remove bullet-points; add hanging indent
&lt;!-- Feedback responsiveness ---&gt;
## No evidence of responsiveness to feedback on talk page
|8=
&lt;!-- Learning features comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features
&lt;!-- Learning features – Wikipedia embedded links --&gt;
# Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles
# Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
# Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
&lt;!-- Learning features – Wikiversity embedded links --&gt;
# Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]
# Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
# Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section
# Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
&lt;!-- Learning features – Figures, tables, feature boxes, scenarios --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s)
# Excellent/Very good/Good/Reasonably good/Basic/No use of table(s)
# Excellent/Very good/Good/Reasonably good/Basic use of feature box(es)
# No use of feature boxes other than the opening scenario
# Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples
# No use of scenarios, case studies, or examples, other than opening scenario
&lt;!-- Learning features – Quizzes --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s)
# The quiz questions could be improved by being more focused on the key points and/or take-home messages
# The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end
# The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]])
# No use of quiz(zes) and/or reflection question(s)
&lt;!-- Learning features – See also --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Also include links to related book chapters
## Also include links to related Wikipedia articles
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite
## Move external links into the [[{{PAGENAME}}#References|External links]] section
## Add more links
# [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count
&lt;!-- Learning features – External links --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section
## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite
## Target an international audience
## Add more links
## Link to the top 3-6 external resources about this topic
# [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count
|9=
&lt;!-- Social contribution comments... --&gt;
# ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]]
# ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence.
# Thanks for the Wiki Commons uploads
# Thanks very much for your extensive contributions
# Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# No logged contributions
}}
~~~~
&lt;/pre&gt;&lt;/small&gt;&lt;/small&gt;&lt;/small&gt;
gives
&lt;!-- Official book chapter feedback --&gt;
{{MEBF/2026
|1=
&lt;!-- Overall comments... --&gt;
# This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem
# This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem
# This is a very good chapter that makes very good use of psychological theory and research to address a real-world phenomenon or problem
# This is a good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a reasonably good chapter that makes good use of psychological theory and research to address a real-world phenomenon or problem
# This is a basic chapter
# This is an insufficient chapter
# The main area(s) for potential improvement:
#* use the best psychological theory about the topic
#* more detailed review of the best psychological research about the topic
#* quality of written expression
#* tackle the target topic more directly; this chapter [[wikt:beat around the bush|beats around the bush]]
#* integrate more strongly with other chapters by using embedded links to related topics
#* overuse of unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] (watch out for [[w:AI slop|AI slop]])—express more in your own words
#* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter
&lt;!-- Overall - Edit summaries --&gt;
#* [[w:Help:Edit summary|Edit summaries]] are used to clearly communicated the changes made in most or all edits
#* Use more specific [[w:Help:Edit summary|edit summaries]] to clearly communicate the changes made in each edit
#* Use [[w:Help:Edit summary|edit summaries]] to briefly describe the changes made in each edit
&lt;!-- Overall - GenAI --&gt;
#* [[Motivation and emotion/Assessment/Using generative AI|genAI use]] is appropriately acknowledged
#* In some places, there is overreliance on genAI
#* There is insufficient acknowledgement in edit summaries when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles
#* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in edit summaries with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]].
&lt;!-- Overall – Citations --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of academic, peer-reviewed citations to support claims
# Only cite sources that you consult
# All citations need to be in the References
&lt;!-- Overall – Word count --&gt;
# Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand
# Over the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]]. Content beyond 4,000 words has been ignored for marking purposes.
&lt;!-- Overall – Copyedits --&gt;
# For additional feedback, see the following comments and [ these copyedits]
|2=
&lt;!-- Overview – Comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped
&lt;!-- Overview – Scenario --&gt;
&lt;!-- Overview – Scenario - Description --&gt;
# Engaging scenario or case study
# Reasonably engaging scenario or case study
# Basic scenario or case study
# Use a more practical, real-life scenario; move review of research into a subsequent section
# Consider using an example that more people can relate to (less than 5% of the world population are university students)
# Add an engaging case study or scenario
&lt;!-- Overview – Scenario - Figure --&gt;
# Figure 1 is relevant to the scenario
# Figure 1 could be more relevant to the scenario
# Instead of a diagram, use an image which illustrates the scenario taking a place; use the diagram in a subsequent section
# Include a relevant image
&lt;!-- Overview – Scenario - Feature box --&gt;
# The scenario uses an appropriate feature box
# Put the scenario in a feature box
&lt;!-- Overview – Explains problem --&gt;
# Clearly explains the psychological problem or phenomenon
# Explains the psychological problem or phenomenon reasonably well/in a basic way
# Briefly explains the psychological problem or phenomenon; provide more detail
# Description of problem is too long/overly complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections.
# Clarity of written expression can be improved
&lt;!-- Overview – Focus questions --&gt;
# The focus questions are excellent (clear and relevant)/very good/good/reasonably good/basic/promising/insufficient
# The focus questions could be improved by:
## being more specific to the topic (i.e., the sub-title)
## matching the top-level headings more closely
## being [[w:Open-ended question|open-ended]] rather than [[w:Closed-ended question|closed-ended]]
## splitting double-barrelled questions into separate questions
## using bullet points as taught in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## being presented in a feature box to help guide the reader (fixed)
# Add focus questions in a feature box
# See copyedits for examples of possible improvements
|3=
&lt;!-- Theory comments... --&gt;
&lt;!-- Theory – Breadth --&gt;
# Excellent—key theories are very well explained and applied
# Very good—key theories are well explained and applied; minor areas for improvements
# Reasonably good—relevant theories are selected, described, and explained, with some room for improvement
# Basic—a basic range of relevant theories are selected, described, and explained; there is considerable room for improvement
# A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic
# Insufficient use of relevant psychological theory about this topic
# Reduce general theoretical background (e.g., definitions). Instead, summarise and link to related resources (i.e., other book chapters and/or Wikipedia articles). Increase emphasis on [[wikt:substantive|substantive]] aspects of theory that relate directly to the specific topic (i.e., the sub-title question).
&lt;!-- Theory – Builds on --&gt;
# Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds effectively on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds reasonably well on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds somewhat on other [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds in a basic way on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
# Doesn't build on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
&lt;!-- Theory – Depth --&gt;
# Insightful/Very good/Good/Reasonably good/Basic/Insufficient depth is provided about key theory(ies)
&lt;!-- Theory – Tables/Figures/Lists --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information
&lt;!-- Theory – Citations --&gt;
# Key citations are well used
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
# If you didn't consult an original source (e.g., ?), cite it as a [https://apastyle.apa.org/style-grammar-guidelines/citations/secondary-sources secondary source]
# If you didn't consult an original source, don't cite it
&lt;!-- Theory – Examples --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of examples to illustrate theoretical concepts
# Consider using more examples to illustrate theoretical concepts
# Use more examples to illustrate theoretical concepts
# Insufficient use of examples to illustrate theoretical concepts
|4=
&lt;!-- Research comments... --&gt;
&lt;!-- Research – Key findings --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient review of relevant research
# Excellent emphasis on systematic reviews and/or meta-analyses
# Greater emphasis on systematic reviews and/or meta-analyses would be ideal
# More detail about key studies would be ideal
# Claims are well referenced
# In some/many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic.
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
&lt;!-- Research – Critical thinking --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident
# [[w:Critical thinking|Critical thinking]] about research could be further evidenced by:
## describing the methodology (e.g., sample, measures) in important studies
## considering the strength of relationships
## acknowledging limitations
## pointing out critiques/counterarguments
## suggesting ''specific'' directions for future research
|5=
&lt;!-- Integration comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient integration between the most relevant theory(ies) and the best research
# The chapter places more emphasis on theory than on research; strive for an integrated balance
# The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links
# Insufficient integration with related [[Motivation and emotion/Book|chapters]]
|6=
&lt;!-- Conclusion comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic summary and conclusion
# Insufficient as a cohesive summary of the best psychological theory and research about the topic
# Reads like generic [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; write more compellingly in your own words
# Is this section based on [[Motivation and emotion/Assessment/Using generative AI|genAI output]]? If so, this was not acknowledged in the edit summary.
# Highlights the importance of the problem or phenomenon of interest
# Highlight the importance of the problem or phenomenon of interest
&lt;!-- Conclusion – Key points --&gt;
# Key points are well summarised
# Key points are summarised in a basic way
# Summarise key points
&lt;!-- Conclusion – Focus questions --&gt;
# The focus questions are addressed
# The take-away messages for each focus question could be spelt out more clearly
# Address the focus questions
&lt;!-- Conclusion – Take-home messages --&gt;
# Clear take-home message(s)
# Add practical, take-home message(s)
&lt;!-- Conclusion – Word count --&gt;
# Not counted for marking purposes due to being over the maximum word count
|7=
&lt;!-- Written expression – Style comments... --&gt;
&lt;!-- Written expression – Written expression --&gt;
# Written expression
## The quality of written expression is excellent/very good/good/reasonably good/basic
## The quality of written expression is OK but there are several aspects which are below professional standard
## The quality of written expression is below professional standard. [https://www.canberra.edu.au/current-students/study-skills UC Study Skills] assistance is recommended to help improve writing skills.
### genAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources
## Use active (e.g., &quot;this chapter explores&quot; or &quot;this chapter explored&quot;) rather than passive voice (e.g., &quot;this chapter will explore&quot; or &quot;this chapter has explored&quot;) [https://apastyle.apa.org/style-grammar-guidelines/grammar/active-passive-voice][https://www.grammarly.com/blog/active-vs-passive-voice/]
## The target audience is international, not domestic. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia].
## Reduce excessive use of bold font
&lt;!-- Written expression – Sentences --&gt;
## Some/Many sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression
## Some/Many sentences are overly long. Strive for the simplest expression. Consider splitting longer sentences into two shorter sentences. Shorter words and sentences are more [[w:Readability|readable]]. Try conducting a readability analysis such as via https://www.webfx.com/tools/read-able/. This chapter gets a score of . Aim for 50+.
## Avoid starting sentences with a citation unless the author is particularly pertinent. Instead, it is more interesting for the the content/key point to be communicated, with the citation included along the way or, more typically, in [[w:Bracket#Parentheses|parentheses]] at the end of the sentence.
&lt;!-- Written expression – Paragraphs --&gt;
## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences.
## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences.
## Bullet points are overused. Develop more of the bullet point statements into full sentences and paragraphs.
&lt;!-- Written expression – Language --&gt;
## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., &quot;it&quot;) instead of 1st (e.g., &quot;we&quot;) or 2nd person (e.g., &quot;you&quot;) in the main text. 1st of 2nd person can work well for case studies or feature boxes.
## Avoid phrases such as “as previously mentioned” or “as noted above,” as these add little value and can disrupt flow. If referencing another part of the chapter is necessary, use [[w:Help#Section linking|section linking]].## Embed direct quotes within sentences and paragraphs, rather than presenting them [[wikt:holus-bolus|holus-bolus]]
## &quot;Individuals&quot; is overused. &quot;People&quot; is usually a clearer term than &quot;individuals&quot;. Use ''individuals'' to highlight each person separately (e.g., “individual test scores”) and ''people'' when referring to humans more generally.
## Remove [[w:weasel words|weasel words]]—they add bulk without improving meaning
## Use permanent, rather than relative, time references. For example, instead of &quot;20 years ago&quot;, refer to something like &quot;at the beginning of the 21st century&quot;. In this way, the text will survive better into the future, without needing to be rewritten.
## Avoid overly emotive language (e.g,. *) in science-based communication
&lt;!-- Written expression – Layout --&gt;
# Layout
## The chapter is well structured, with major sections using sub-sections
## The headings could be more clearly aligned with the focus questions
## The structure is overly complicated; simplify and integrate
## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion
## The chapter structure is underdeveloped; expand by using subheadings
## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings
## Use the default heading style (e.g.,  remove additional numbers, italics, bo]ld, and/or change in font size)
## See earlier comment about [[#Heading casing|heading casing]]
## Provide more descriptive headings
## Move links from headings into their first mention in text
## Remove abbreviations/citations from headings
## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags)
## Integrate learning features rather than having it as a stand-alone section
## The Overview and Conclusion should not have subheadings (fixed)
## Remove colons (:) from the ends of headings
&lt;!-- Written expression – Grammar --&gt;
# Grammar and spelling are excellent
# Grammar
## The grammar for some/many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback
## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas].
## Check and make correct use of [https://www.merriam-webster.com/grammar/em-dash-en-dash-how-to-use em dashes (instead of hyphens)] to set off an amplifying or explanatory element
## [https://www.grammarly.com/blog/punctuation-capitalization/possessive-apostrophe/ Possessive apostrophes] are not used correctly (e.g., cats vs cat's vs cats')
## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who]
## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect]
## Check and correct use of [http://www.colonsemicolon.com/ semicolons (;) and colons (:)]
## Use past tense when describing research studies, although implications of findings could be in the present tense
&lt;!-- Written expression – Abbreviations --&gt;
## Abbreviations
### Only use abbreviations such as e.g., i.e., et al., etc. inside [[w:Bracket#Parentheses|parentheses]], otherwise spell them out
### Check and correct formatting of abbreviations (such as e.g., i.e., etc.)
### Use abbreviations sparingly. Do not use abbreviations for minor/infrequently used terms.
### Spell out abbreviations on their first use, to explain them to the reader
### Once an abbreviation has been established (e.g., PTSD), use it consistently afterwards
### Only introduce abbreviations which are subsequently used
&lt;!-- Written expression – Spelling --&gt;
# Spelling
## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour)
## Some words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages.
&lt;!-- Written expression – Proofreading --&gt;
# Proofreading
## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard
## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info]
&lt;!-- Written expression – APA style --&gt;
# APA style
## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should][https://www.youtube.com/watch?v=gBx8ooDupXY]
## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing for disorders, therapies, theories, etc.]
## [https://apastyle.apa.org/style-grammar-guidelines/numbers Express numbers under 10 using words (e.g., two) and 10 and over using numerals (e.g., 99)]
&lt;!-- Written expression – APA style - Quotes --&gt;
## Use double (not single) quotation marks &quot;to introduce a word or phrase used ... as slang, or as an invented or coined expression&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## &quot;Use quotation marks only for the first occurrence of the word or phrase, not for subsequent occurrences&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## Direct quotes need page numbers—even better, communicate about concepts in your own words
## Direct quotes are overused—it is better to communicate about concepts in your own words
&lt;!-- Written expression – Figures --&gt;
## Figures
### Very well/Well/Reasonably well captioned
### Brief captions; provide more detail to help connect the figure to the text
### Use this format for captions: '''Figure X'''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]].
### Add captions
&lt;!-- Written expression – Figures - Citations --&gt;
### Each Figure is referred to at least once within the main text using APA style
### Each Figure is referred to at least once within the main text. Refer to each Figure using APA style (e.g., &quot;(see Figure 1)&quot;; do not use bold, italics, check and correct capitalisation).
### Refer to each Figure at least once within the main text (e.g., &quot;(see Figure 1)&quot;)
&lt;!-- Written expression – Figures - Other --&gt;
### Some image uploads were removed because of a lack of sufficient/appropriate copyright information
### Numbering needs correcting
### Adjust some image sizes to make them easier to read (increase size) and/or less dominant (decrease size)
&lt;!-- Written expression – Tables --&gt;
## Tables
### Very well/Well/Reasonably well captioned
### Brief caption(s); provide more explanatory detail about the table
### Add an APA style caption to each table ([[Motivation and emotion/Assessment/Chapter/Tables|see example]])
&lt;!-- Written expression – Tables - Citations --&gt;
### Each Table is referred to at least once within the main text using APA style
### Each Table is referred to at least once within the main text
### Refer to each Table using APA style (e.g., do not use bold, italics, check and correct capitalisation)
### Refer to each Table at least once within the main text (e.g., see Table 1)
&lt;!-- Written expression – Citations --&gt;
# Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# Citations use very good/good/reasonably good/basic/poor [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# In some/many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags)
## If there are three or more authors, cite the first author followed by et al., then year. For example, either:
### in-text, Smith et al. (2020), or
### in [[w:Bracket#Parentheses|parentheses]] (Smith et al., 2020)
## Do not include author first name or initials
## Use ampersand (&amp;) inside [[w:Bracket#Parentheses|parentheses]] and &quot;and&quot; outside parentheses
## List multiple citations in alphabetical order by first author surname (e.g., Giraffe, 2024; Zebra &amp; Aardvark, 2020)
## A full stop is needed after &quot;et al&quot; (i.e., &quot;et al.&quot;) because it is an abbreviation of [[wikt:et alii|et alii]]
## Use a comma between the author(s) and year for citations in [[w:Bracket#Parentheses|parentheses]]
## Select up to a maximum of three citations per point (i.e., avoid citing four or more citations to support a single point)
## Check and correct placement of full-stops
## Move embedded links to academic peer-reviewed sources into the [[{{PAGENAME}}#References|References]] as APA style citations with hyperlinked dois
## Move embedded links to non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section; only cite peer-reviewed sources
# For citations, use APA style or wiki style, but not both
# Secondary citations are overused; strive to consult primary sources
&lt;!-- Written expression – References --&gt;
## References use excellent/very good/good/reasonably good/basic/poor APA style:
### Check and correct use of italicisation
### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization]
### Separate page numbers using an [[w:Dash#En dash|en dash]] (–) rather than a hyphen (-)
### Include dois where available
### Hyperlink dois for 1-click access
### Provide the full titles of journals
### Remove &quot;Retrieved from &quot;
### Use alphabetical order
### Move Wikipedia links into the [[{{PAGENAME}}#See also|See also]] section
### Move non-peer reviewed sources into the [[{{PAGENAME}}#External links|External links]] section
### Remove bullet-points; add hanging indent
&lt;!-- Feedback responsiveness ---&gt;
## No evidence of responsiveness to feedback on talk page
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&lt;!-- Learning features comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient use of learning features
&lt;!-- Learning features – Wikipedia embedded links --&gt;
# Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles
# Very good/Good/Reasonably good/Basic/One use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
# Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
&lt;!-- Learning features – Wikiversity embedded links --&gt;
# Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]
# Very good/Good/Reasonably good/Basic/One use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
# Use in-text [[m:Help:Interwiki linking|interwiki links]], rather than external links to Wikiversity chapters, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# Move embedded links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section
# Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
&lt;!-- Learning features – Figures, tables, feature boxes, scenarios --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of figure(s)
# Excellent/Very good/Good/Reasonably good/Basic/No use of table(s)
# Excellent/Very good/Good/Reasonably good/Basic use of feature box(es)
# No use of feature boxes other than the opening scenario
# Excellent/Very good/Good/Reasonably good/Basic use of scenarios, case studies, or examples
# No use of scenarios, case studies, or examples, other than opening scenario
&lt;!-- Learning features – Quizzes --&gt;
# Excellent/Very good/Good/Reasonably good/Basic use of quiz(zes) and/or reflection question(s)
# The quiz questions could be improved by being more focused on the key points and/or take-home messages
# The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end
# The reflection questions could be made more interactive by using a drop-down box that the reader can expand to see an answer/prompt to figure out the answers to the questions (e.g., see [[Motivation and emotion/Book/2026/Immersive therapy for PTSD treatment|this chapter]])
# No use of quiz(zes) and/or reflection question(s)
&lt;!-- Learning features – See also --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#See also|See also]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#See also|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use internal linking style per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Also include links to related book chapters
## Also include links to related Wikipedia articles
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move peer-reviewed articles into the [[{{PAGENAME}}#References|References]] section and cite
## Move external links into the [[{{PAGENAME}}#References|External links]] section
## Add more links
# [[{{PAGENAME}}#See also|See also]] section not counted for marking purposes due to being over the maximum word count
&lt;!-- Learning features – External links --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section
## Use the format shown in the [[Template:Motivation and emotion/Book chapter structure#External links|template]]
## Use bullet points per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Rename links per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
## Move Wikipedia/Wikiversity links to the [[{{PAGENAME}}#See also|See also]] section
## Move peer-reviewed articles to the [[{{PAGENAME}}#References|References]] section and cite
## Target an international audience
## Add more links
## Link to the top 3-6 external resources about this topic
# [[{{PAGENAME}}#External links|External links]] section not counted for marking purposes due to being over the maximum word count
|9=
&lt;!-- Social contribution comments... --&gt;
# ~ logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]]
# ~ logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence.
# Thanks for the Wiki Commons uploads
# Thanks very much for your extensive contributions
# Use a numbered list per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
# No logged contributions
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:47, 10 October 2026 (UTC)

==See also==
* [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]]
* [[Template:METF]]
* [[Template:MEMF]]

[[Category:Motivation and emotion/Admin/2026]]
[[Category:Motivation and emotion/Assessment/Chapter]]
&lt;/noinclude&gt;</text>
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    <title>The John Snow Prediabetes Institute</title>
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      <text bytes="6178" sha1="7p43urk9tvymtvwr8o6s0iepv59hy0l" xml:space="preserve">The John Snow prediabetes Institute is an international research network focused on evidence based prediabetes remission, early risk identification, and lifestyle health promotion. (https://w.wiki/Skm7).

'''Background:''' 
Millions are at increased risk of developing metabolic syndromes with prediabetes, diabetes type 2, high blood pressure and overweight (General Research Draft). &lt;ref&gt; https://www.dropbox.com/scl/fi/gau25oy5y1s57046icjt2/Research-protocol-draft.docx?cloud_editor=word&amp;dl=0&amp;rlkey=wat63e25ritmujwcpss8s4v0s &lt;/ref&gt; All can lower their risks by staying physical active and eating well. Early diagnosis and education of prediabetes is a cost-effective preventive strategy that can improve long-term health outcomes. Arteriosclerosis is developing in the prediabetes stage. The aim is to establish repeated Prediabetes prevalence studies based on data from the academic literature and in some cases from the seafarers`health clinics, the schools for seafarers, nurses and medical students. The 16-weeks '''intervention study''' include learnings by short video sequences and self-monitoring of blood sugar with glucometer &lt;ref&gt;https://www.sciencedirect.com/science/article/abs/pii/S1751991825001068 &lt;/ref&gt; and self-evaluation of diet and physical activity. Other intervention studies to be tested and developed include Digital lifestyle programs &lt;ref&gt; «Digital Lifestyle Program Cuts Diabetes Risk by 46% in Prediabetics, Study of 130k+ Adults Reveals». News-Medical, 14 de abril de 2025. https://www.news-medical.net/news/20250414/Digital-lifestyle-program-cuts-diabetes-risk-by-4625-in-prediabetics-study-of-130k2b-adults-reveals.aspx.&lt;/ref&gt; Educational materials come from the international diabetes organisations e.g the ADA:&lt;ref&gt;https://professional.diabetes.org/diabetes-support-resources&lt;/ref&gt; and the Health Promoting Schools.&lt;ref&gt; https://www.dropbox.com/scl/fi/0rm7honrezbjwrcy3h3yk/Health-promoting-schools.docx?cloud_editor=word&amp;dl=0&amp;rlkey=673jyzcmwbfw7k9ui9nmtp0zh &lt;/ref&gt;[[File:Lifestyle Medicine Pillars.png|250px|right|&lt;big&gt;
Lifestyle Medicine Pillars.png The focus of Lifestyle Medicine is on these 6 pillars&lt;/big&gt; ]]

===== &lt;big&gt;'''Prevalence studies'''  &lt;/big&gt; =====
[[/The Maritime Health database design // |1.1 The Maritime Health database design]] 

1.2  Nursing Students Health Database &lt;ref&gt; https://www.dropbox.com/scl/fi/tcznmmd2y3nona5e3h1ro/The-Nursing-students-health-database.docx?cloud_editor=word&amp;dl=0&amp;rlkey=onbjh4o8ko1lzdvgyi8nlrotk &lt;/ref&gt;

1.3. Medical student's Health Database &lt;ref&gt;https://www.dropbox.com/scl/fi/f16h9b60u4gxgt56un2jf/The-Medical-students-Health-database.docx?cloud_editor=word&amp;dl=0&amp;rlkey=xyfqen5trdc5lniaovipl548n &lt;/ref&gt;

1.4. School childrens` Health database &lt;ref&gt; https://www.dropbox.com/scl/fi/u6u50c8bxwhte9t2t6ck8/The-School-children-s-Health-database.docx?cloud_editor=word&amp;dl=0&amp;rlkey=zlyz5wn673wf7owettq3nx3h5 &lt;/ref&gt;

1.5  Excel recoding (pre diabetes, hypertension etc) &lt;ref&gt;https://www.dropbox.com/scl/fi/9qvqeccto2kbuqvx7mdkl?r=ACsntb2AuiFkJbEBLObVdo0HMD67UZBBUGCGl1RPCPy1X5Y3K3e9Lf4s7cG7i7E_iH0IK-WkynXw_FNCDWybHuCgaNl_OM8yche2w2aapJGk5BTHybbsLpLayBU8VKPPqxNa2zDaNslBdQg0MhmKTFSG&lt;/ref&gt;

'''Personal prevention''' Personal reversal of prediabetes relies on targeted lifestyle changes like eating a healthy diet, exercising regularly, and losing a modest amount of excess weight. (local Diabetes Associations)

&lt;span lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;&lt;small&gt;'''Core Institutional Strategies'''  Health authorities and organizations implement group-based or digital programs. The workplaces are prompted to make targeted interventions, including nutrition and exercise programs, to safeguard long-term cardiometabolic health in the workforces.&lt;/small&gt;&lt;/span&gt;

&lt;small&gt;16 weeks human caused Intervention studies: English 
&lt;ref&gt;https://www.dropbox.com/scl/fi/oi6cx6tlwwvoko3ed37tn/Invitation-to-the-course-English.docx?cloud_editor=word&amp;dl=0&amp;rlkey=7kzg91tqfgjskxf5aji8khicx &lt;/ref&gt; Danish
&lt;ref&gt;https://www.dropbox.com/scl/fi/2qahc3q9hmf4skbvk77ab/Invitation-to-the-course-in-Danish.docx?cloud_editor=word&amp;dl=0&amp;rlkey=x63w8oqvarz284zg2btq2johv &lt;/ref&gt; Spanish &lt;ref&gt; https://www.dropbox.com/scl/fi/bn71inqeeth4o4mc1fjth/Invitation-to-the-course-Spanish.docx?cloud_editor=word&amp;dl=0&amp;rlkey=popmr1fnodh1v951v9l7k9ezv &lt;/ref&gt;
and '''AI-Powered Lifestyle Intervention''' in the Diabetes Prevention
&lt;ref&gt;Mathioudakis, Nestoras, Benjamin Lalani, Mohammed S. Abusamaan, et al. «An AI-Powered Lifestyle Intervention vs Human Coaching in the Diabetes Prevention Program: A Randomized Clinical Trial». JAMA 334, n.º 23 (2025): 2079-89. https://doi.org/10.1001/jama.2025.19563.&lt;/ref&gt;&lt;/small&gt;

'''Organisation''' 

- [[/The John Snow Institute bylaws /]] 

- General research pr[[Category:Prediabetes ]]otoco[[Category:Prediabetes ]]l draft
&lt;ref&gt; https://www.dropbox.com/scl/fi/gau25oy5y1s57046icjt2/Research-protocol-draft.docx?cloud_editor=word&amp;dl=0&amp;rlkey=wat63e25ritmujwcpss8s4v0s &lt;/ref&gt;

- Health Promoting Schools &lt;ref&gt; https://www.dropbox.com/scl/fi/0rm7honrezbjwrcy3h3yk/Health-promoting-schools.docx?cloud_editor=word&amp;dl=0&amp;rlkey=673jyzcmwbfw7k9ui9nmtp0zh &lt;/ref&gt;

'''Publications'''
&lt;ref name=&quot;:0&quot;&gt; https://www.dropbox.com/scl/fi/mw7ft423lkkpjoxywd2bf &lt;/ref&gt;

'''The John Snow Prediabetes Institute Research Network:''' 
&lt;small&gt;Prof. Dr. Olaf Jensen, MD, MPH, PhD; Prof. Ing. MSc. Nailet Delgado Mujica; Prof. Magda Medir Mb, Tarragona Spain,  Prof. MSc.Ph.D. Bishal Gyawali SDU; MSc.PhD Vivi Just-Nørregaard; Prof. Dr. Johan Hviid Andersen MD, PhD. Århus University; Prof. MSc. Agnes Flores, UMECIT, Panama; Bruno Nørdam, Randers; Maritime Doctor. Erik Haarløv MD, Assens, Denmark; Dr. Maite Duque MD Venezuela; Dr. Indira Santos Panama MD; Med.Stud. Ashley Lezcano, Panama; Dr. Joseph Abesamis MD Filippines; Dr. Jen Mendoza, MD, Filippines; Dra.Marj Gab Huerte, MD, Filippines:&lt;/small&gt; 
&lt;small&gt;Dr. Andra Ergle MD, Latvia; Prof. MSc. Ingrid Morató, Tarragona and Cadiz, Spain; Dr. Alejandro Martinez, MD, MPH, Costa Rica; Christian Acheampong, MBA, New Jersey US; Dr. Med. Sci Finn Gyntelberg NFA.and Bispebj. Hosp. Denmark: Dr. Solomon Ching MD Filippines: Dr. Marcel Alcaraz MD Filippines;&lt;/small&gt; 
==References==</text>
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      <text bytes="6221" sha1="5iopjl3fgpyen2a2a9mp8y826c5pw6n" xml:space="preserve">The John Snow prediabetes Institute is an international research network focused on evidence based prediabetes remission, early risk identification, and lifestyle health promotion. (https://w.wiki/Skm7).

'''Background:''' 
Millions are at increased risk of developing metabolic syndromes with prediabetes, diabetes type 2, high blood pressure and overweight (General Research Draft). &lt;ref&gt; https://www.dropbox.com/scl/fi/gau25oy5y1s57046icjt2/Research-protocol-draft.docx?cloud_editor=word&amp;dl=0&amp;rlkey=wat63e25ritmujwcpss8s4v0s &lt;/ref&gt; All can lower their risks by staying physical active and eating well. Early diagnosis and education of prediabetes is a cost-effective preventive strategy that can improve long-term health outcomes. Arteriosclerosis is developing in the prediabetes stage. The aim is to establish repeated Prediabetes prevalence studies based on data from the academic literature in some cases by contact to the authors and in some cases from the seafarers`health clinics, the schools for seafarers, nurses and medical students. The 16-weeks '''intervention study''' include learnings by short video sequences and self-monitoring of blood sugar with glucometer &lt;ref&gt;https://www.sciencedirect.com/science/article/abs/pii/S1751991825001068 &lt;/ref&gt; and self-evaluation of diet and physical activity. Other intervention studies to be tested and developed include Digital lifestyle programs &lt;ref&gt; «Digital Lifestyle Program Cuts Diabetes Risk by 46% in Prediabetics, Study of 130k+ Adults Reveals». News-Medical, 14 de abril de 2025. https://www.news-medical.net/news/20250414/Digital-lifestyle-program-cuts-diabetes-risk-by-4625-in-prediabetics-study-of-130k2b-adults-reveals.aspx.&lt;/ref&gt; Educational materials come from the international diabetes organisations e.g the ADA:&lt;ref&gt;https://professional.diabetes.org/diabetes-support-resources&lt;/ref&gt; and the Health Promoting Schools.&lt;ref&gt; https://www.dropbox.com/scl/fi/0rm7honrezbjwrcy3h3yk/Health-promoting-schools.docx?cloud_editor=word&amp;dl=0&amp;rlkey=673jyzcmwbfw7k9ui9nmtp0zh &lt;/ref&gt;[[File:Lifestyle Medicine Pillars.png|250px|right|&lt;big&gt;
Lifestyle Medicine Pillars.png The focus of Lifestyle Medicine is on these 6 pillars&lt;/big&gt; ]]

===== &lt;big&gt;'''Prevalence studies'''  &lt;/big&gt; =====
[[/The Maritime Health database design // |1.1 The Maritime Health database design]] 

1.2  Nursing Students Health Database &lt;ref&gt; https://www.dropbox.com/scl/fi/tcznmmd2y3nona5e3h1ro/The-Nursing-students-health-database.docx?cloud_editor=word&amp;dl=0&amp;rlkey=onbjh4o8ko1lzdvgyi8nlrotk &lt;/ref&gt;

1.3. Medical student's Health Database &lt;ref&gt;https://www.dropbox.com/scl/fi/f16h9b60u4gxgt56un2jf/The-Medical-students-Health-database.docx?cloud_editor=word&amp;dl=0&amp;rlkey=xyfqen5trdc5lniaovipl548n &lt;/ref&gt;

1.4. School childrens` Health database &lt;ref&gt; https://www.dropbox.com/scl/fi/u6u50c8bxwhte9t2t6ck8/The-School-children-s-Health-database.docx?cloud_editor=word&amp;dl=0&amp;rlkey=zlyz5wn673wf7owettq3nx3h5 &lt;/ref&gt;

1.5  Excel recoding (pre diabetes, hypertension etc) &lt;ref&gt;https://www.dropbox.com/scl/fi/9qvqeccto2kbuqvx7mdkl?r=ACsntb2AuiFkJbEBLObVdo0HMD67UZBBUGCGl1RPCPy1X5Y3K3e9Lf4s7cG7i7E_iH0IK-WkynXw_FNCDWybHuCgaNl_OM8yche2w2aapJGk5BTHybbsLpLayBU8VKPPqxNa2zDaNslBdQg0MhmKTFSG&lt;/ref&gt;

&lt;big&gt;'''Personal prevention''' Personal reversal of prediabetes relies on targeted lifestyle changes like eating a healthy diet, exercising regularly, and losing a modest amount of excess weight. (local Diabetes Associations)&lt;/big&gt;

&lt;span lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;&lt;big&gt;'''Core Institutional Strategies'''  Health authorities and organizations implement group-based or digital programs. The workplaces are prompted to make targeted interventions, including nutrition and exercise programs, to safeguard long-term cardiometabolic health in the workforces.&lt;/big&gt;&lt;/span&gt;

&lt;big&gt;16 weeks human caused Intervention studies: English 
&lt;ref&gt;https://www.dropbox.com/scl/fi/oi6cx6tlwwvoko3ed37tn/Invitation-to-the-course-English.docx?cloud_editor=word&amp;dl=0&amp;rlkey=7kzg91tqfgjskxf5aji8khicx &lt;/ref&gt; Danish
&lt;ref&gt;https://www.dropbox.com/scl/fi/2qahc3q9hmf4skbvk77ab/Invitation-to-the-course-in-Danish.docx?cloud_editor=word&amp;dl=0&amp;rlkey=x63w8oqvarz284zg2btq2johv &lt;/ref&gt; Spanish &lt;ref&gt; https://www.dropbox.com/scl/fi/bn71inqeeth4o4mc1fjth/Invitation-to-the-course-Spanish.docx?cloud_editor=word&amp;dl=0&amp;rlkey=popmr1fnodh1v951v9l7k9ezv &lt;/ref&gt;
and '''AI-Powered Lifestyle Intervention''' in the Diabetes Prevention
&lt;ref&gt;Mathioudakis, Nestoras, Benjamin Lalani, Mohammed S. Abusamaan, et al. «An AI-Powered Lifestyle Intervention vs Human Coaching in the Diabetes Prevention Program: A Randomized Clinical Trial». JAMA 334, n.º 23 (2025): 2079-89. https://doi.org/10.1001/jama.2025.19563.&lt;/ref&gt;&lt;/big&gt;

'''Organisation''' 

- [[/The John Snow Institute bylaws /]] 

- General research pr[[Category:Prediabetes ]]otoco[[Category:Prediabetes ]]l draft
&lt;ref&gt; https://www.dropbox.com/scl/fi/gau25oy5y1s57046icjt2/Research-protocol-draft.docx?cloud_editor=word&amp;dl=0&amp;rlkey=wat63e25ritmujwcpss8s4v0s &lt;/ref&gt;

- Health Promoting Schools &lt;ref&gt; https://www.dropbox.com/scl/fi/0rm7honrezbjwrcy3h3yk/Health-promoting-schools.docx?cloud_editor=word&amp;dl=0&amp;rlkey=673jyzcmwbfw7k9ui9nmtp0zh &lt;/ref&gt;

'''Publications'''
&lt;ref name=&quot;:0&quot;&gt; https://www.dropbox.com/scl/fi/mw7ft423lkkpjoxywd2bf &lt;/ref&gt;

'''The John Snow Prediabetes Institute Research Network:''' 
&lt;small&gt;Prof. Dr. Olaf Jensen, MD, MPH, PhD; Prof. Ing. MSc. Nailet Delgado Mujica; Prof. Magda Medir Mb, Tarragona Spain,  Prof. MSc.Ph.D. Bishal Gyawali SDU; MSc.PhD Vivi Just-Nørregaard; Prof. Dr. Johan Hviid Andersen MD, PhD. Århus University; Prof. MSc. Agnes Flores, UMECIT, Panama; Bruno Nørdam, Randers; Maritime Doctor. Erik Haarløv MD, Assens, Denmark; Dr. Maite Duque MD Venezuela; Dr. Indira Santos Panama MD; Med.Stud. Ashley Lezcano, Panama; Dr. Joseph Abesamis MD Filippines; Dr. Jen Mendoza, MD, Filippines; Dra.Marj Gab Huerte, MD, Filippines:&lt;/small&gt; 
&lt;small&gt;Dr. Andra Ergle MD, Latvia; Prof. MSc. Ingrid Morató, Tarragona and Cadiz, Spain; Dr. Alejandro Martinez, MD, MPH, Costa Rica; Christian Acheampong, MBA, New Jersey US; Dr. Med. Sci Finn Gyntelberg NFA.and Bispebj. Hosp. Denmark: Dr. Solomon Ching MD Filippines: Dr. Marcel Alcaraz MD Filippines;&lt;/small&gt; 
==References==</text>
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      <text bytes="6518" sha1="el7hdwk7bptrw6h4wh1ylv94sk03cxr" xml:space="preserve">&lt;small&gt;The John Snow prediabetes Institute is an international research network focused on evidence based prediabetes remission, early risk identification, and lifestyle health promotion. (https://w.wiki/Skm7).&lt;/small&gt;

'''&lt;small&gt;Background:&lt;/small&gt;'''

&lt;small&gt;Millions are at increased risk of developing metabolic syndromes with prediabetes, diabetes type 2, high blood pressure and overweight (General Research Draft). &lt;ref&gt; https://www.dropbox.com/scl/fi/gau25oy5y1s57046icjt2/Research-protocol-draft.docx?cloud_editor=word&amp;dl=0&amp;rlkey=wat63e25ritmujwcpss8s4v0s &lt;/ref&gt; All can lower their risks by staying physical active and eating well. Early diagnosis and education of prediabetes is a cost-effective preventive strategy that can improve long-term health outcomes. Arteriosclerosis is developing in the prediabetes stage. The aim is to get repeated Prediabetes prevalence studies based on data from the academic literature in some cases by contact to the authors with request to reanalyse the data to identify the prediabetes prevalence. In some cases from the seafarers`health clinics, the schools for seafarers, nurses and medical students. The 16-weeks '''intervention study''' include learnings by short video sequences and self-monitoring of blood sugar with glucometer &lt;ref&gt;https://www.sciencedirect.com/science/article/abs/pii/S1751991825001068 &lt;/ref&gt; and self-evaluation of diet and physical activity. Other intervention studies to be tested and developed include Digital lifestyle programs &lt;ref&gt; «Digital Lifestyle Program Cuts Diabetes Risk by 46% in Prediabetics, Study of 130k+ Adults Reveals». News-Medical, 14 de abril de 2025. https://www.news-medical.net/news/20250414/Digital-lifestyle-program-cuts-diabetes-risk-by-4625-in-prediabetics-study-of-130k2b-adults-reveals.aspx.&lt;/ref&gt; Educational materials come from the international diabetes organisations e.g the ADA:&lt;ref&gt;https://professional.diabetes.org/diabetes-support-resources&lt;/ref&gt; and the Health Promoting Schools.&lt;ref&gt; https://www.dropbox.com/scl/fi/0rm7honrezbjwrcy3h3yk/Health-promoting-schools.docx?cloud_editor=word&amp;dl=0&amp;rlkey=673jyzcmwbfw7k9ui9nmtp0zh &lt;/ref&gt;&lt;/small&gt;[[File:Lifestyle Medicine Pillars.png|250px|right|
&lt;small&gt;Lifestyle Medicine Pillars.png The focus of Lifestyle Medicine is on these 6 pillars&lt;/small&gt;

]]&lt;small&gt;'''Prevalence studies'''&lt;/small&gt;  

[[/The Maritime Health database design // |&lt;small&gt;1.1 The Maritime Health database design&lt;/small&gt;]]

&lt;small&gt;1.2  Nursing Students Health Database &lt;ref&gt; https://www.dropbox.com/scl/fi/tcznmmd2y3nona5e3h1ro/The-Nursing-students-health-database.docx?cloud_editor=word&amp;dl=0&amp;rlkey=onbjh4o8ko1lzdvgyi8nlrotk &lt;/ref&gt;&lt;/small&gt;

&lt;small&gt;1.3. Medical student's Health Database &lt;ref&gt;https://www.dropbox.com/scl/fi/f16h9b60u4gxgt56un2jf/The-Medical-students-Health-database.docx?cloud_editor=word&amp;dl=0&amp;rlkey=xyfqen5trdc5lniaovipl548n &lt;/ref&gt;&lt;/small&gt;

&lt;small&gt;1.4. School childrens` Health database &lt;ref&gt; https://www.dropbox.com/scl/fi/u6u50c8bxwhte9t2t6ck8/The-School-children-s-Health-database.docx?cloud_editor=word&amp;dl=0&amp;rlkey=zlyz5wn673wf7owettq3nx3h5 &lt;/ref&gt;&lt;/small&gt;

&lt;small&gt;1.5  Excel recoding (pre diabetes, hypertension etc) &lt;ref&gt;https://www.dropbox.com/scl/fi/9qvqeccto2kbuqvx7mdkl?r=ACsntb2AuiFkJbEBLObVdo0HMD67UZBBUGCGl1RPCPy1X5Y3K3e9Lf4s7cG7i7E_iH0IK-WkynXw_FNCDWybHuCgaNl_OM8yche2w2aapJGk5BTHybbsLpLayBU8VKPPqxNa2zDaNslBdQg0MhmKTFSG&lt;/ref&gt;&lt;/small&gt;

&lt;small&gt;'''Personal prevention''' Personal reversal of prediabetes relies on targeted lifestyle changes like eating a healthy diet, exercising regularly, and losing a modest amount of excess weight. (local Diabetes Associations)&lt;/small&gt;

&lt;span lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;&lt;small&gt;'''Core Institutional Strategies'''  Health authorities and organizations implement group-based or digital programs. The workplaces are prompted to make targeted interventions, including nutrition and exercise programs, to safeguard long-term cardiometabolic health in the workforces.&lt;/small&gt;&lt;/span&gt;

&lt;small&gt;16 weeks human caused Intervention studies: English 
&lt;ref&gt;https://www.dropbox.com/scl/fi/oi6cx6tlwwvoko3ed37tn/Invitation-to-the-course-English.docx?cloud_editor=word&amp;dl=0&amp;rlkey=7kzg91tqfgjskxf5aji8khicx &lt;/ref&gt; Danish
&lt;ref&gt;https://www.dropbox.com/scl/fi/2qahc3q9hmf4skbvk77ab/Invitation-to-the-course-in-Danish.docx?cloud_editor=word&amp;dl=0&amp;rlkey=x63w8oqvarz284zg2btq2johv &lt;/ref&gt; Spanish &lt;ref&gt; https://www.dropbox.com/scl/fi/bn71inqeeth4o4mc1fjth/Invitation-to-the-course-Spanish.docx?cloud_editor=word&amp;dl=0&amp;rlkey=popmr1fnodh1v951v9l7k9ezv &lt;/ref&gt;
and '''AI-Powered Lifestyle Intervention''' in the Diabetes Prevention
&lt;ref&gt;Mathioudakis, Nestoras, Benjamin Lalani, Mohammed S. Abusamaan, et al. «An AI-Powered Lifestyle Intervention vs Human Coaching in the Diabetes Prevention Program: A Randomized Clinical Trial». JAMA 334, n.º 23 (2025): 2079-89. https://doi.org/10.1001/jama.2025.19563.&lt;/ref&gt;&lt;/small&gt;

'''&lt;small&gt;Organisation&lt;/small&gt;'''

&lt;small&gt;- [[/The John Snow Institute bylaws /|The John Snow Institute bylaws]]&lt;/small&gt;

&lt;small&gt;- General research protocol draft
&lt;ref&gt; https://www.dropbox.com/scl/fi/gau25oy5y1s57046icjt2/Research-protocol-draft.docx?cloud_editor=word&amp;dl=0&amp;rlkey=wat63e25ritmujwcpss8s4v0s &lt;/ref&gt;&lt;/small&gt;
[[Category:Prediabetes ]]
[[Category:Prediabetes ]]
&lt;small&gt;- Health Promoting Schools &lt;ref&gt; https://www.dropbox.com/scl/fi/0rm7honrezbjwrcy3h3yk/Health-promoting-schools.docx?cloud_editor=word&amp;dl=0&amp;rlkey=673jyzcmwbfw7k9ui9nmtp0zh &lt;/ref&gt;&lt;/small&gt;

&lt;small&gt;'''Publications'''
&lt;ref name=&quot;:0&quot;&gt; https://www.dropbox.com/scl/fi/mw7ft423lkkpjoxywd2bf &lt;/ref&gt;&lt;/small&gt;

'''The John Snow Prediabetes Institute Research Network:''' 
&lt;small&gt;Prof. Dr. Olaf Jensen, MD, MPH, PhD; Prof. Ing. MSc. Nailet Delgado Mujica; Prof. Magda Medir Mb, Tarragona Spain,  Prof. MSc.Ph.D. Bishal Gyawali SDU; MSc.PhD Vivi Just-Nørregaard; Prof. Dr. Johan Hviid Andersen MD, PhD. Århus University; Prof. MSc. Agnes Flores, UMECIT, Panama; Bruno Nørdam, Randers; Maritime Doctor. Erik Haarløv MD, Assens, Denmark; Dr. Maite Duque MD Venezuela; Dr. Indira Santos Panama MD; Med.Stud. Ashley Lezcano, Panama; Dr. Joseph Abesamis MD Filippines; Dr. Jen Mendoza, MD, Filippines; Dra.Marj Gab Huerte, MD, Filippines:&lt;/small&gt; 
&lt;small&gt;Dr. Andra Ergle MD, Latvia; Prof. MSc. Ingrid Morató, Tarragona and Cadiz, Spain; Dr. Alejandro Martinez, MD, MPH, Costa Rica; Christian Acheampong, MBA, New Jersey US; Dr. Med. Sci Finn Gyntelberg NFA.and Bispebj. Hosp. Denmark: Dr. Solomon Ching MD Filippines: Dr. Marcel Alcaraz MD Filippines;&lt;/small&gt; 
==References==</text>
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    <title>Motivation and emotion/Book/2026/Akrasia</title>
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      <text bytes="33225" sha1="cpkm803b0fjrolq61qcebo8pglu6jqy" xml:space="preserve">{{title|Akrasia:&lt;br&gt;Why do people act against their better judgement?}}
__TOC__

==Overview==
{{RoundBoxTop|theme=5}}'''Consider this scenario'''

Jordan signed up for a gym membership at the start of the year, determined to improve his physical and mental health. He bought new workout clothes, saved a list of routines and even told his friends he was committed to exercising. But when his alarm goes off at 6:30am, he hits snooze, telling himself he will simply go after work instead. By 5:00pm, he's too tired to go. The idea of lifting weights is too emotionally heavy and stress inducing for him, so Jordan chooses to stay home and watch a TV show. Each time Jordan's alarm goes off, he ignores it, even though he knows that going to the gym is a healthy option and helps him gain confidence although the short-term comfort of staying at home outweighs those feelings. 

Jordan isn't lazy; he is experiencing Akrasia, a predictable motivational and emotional conflict between long term goals and short-term impulses. {{RoundBoxBottom}}
[[File:Woman Stressed At Work Illustration.jpg|thumb|Figure 1. A women experiencing stressful situation with conflicting priorities. ]]
This chapter explains and explores why people act against their better judgment. It describes this through psychological explanations of self-control and regulation, motivational deficits, and emotional avoidance. This phenomenon has been named ''Akrasia''.   

Akrasia is a phenomenon many people experience. The problem with this is that it affects many areas of an individual's life such as academics, health choices, financial decisions, and relationships. This is because many people will intend to make choices that align with their values and goals yet often make choices that move them further away from them. This gap between intention and action can lead to issues with wellbeing and a sense of success in life.   

Having an understanding of akrasia is important because it describes an individual's ability to achieve goals and increase wellbeing through long term goal reinforcement. It demonstrates how an individual can have tension between reflective, value-based intentions and impulsive actions. Furthermore, understanding the psychological science that characterizes this concept is important because it provides tools for understanding the conflict by describing the internal and external factors that lead to akrasia. This chapter will examine self-control and regulation, motivational deficits, and emotional avoidance. This explanation will not only provide an understanding of why akrasia occurs but also ways to reduce this phenomenon, derived similarly from psychological sciences and salient research. 

{{RoundBoxTop|theme=5}}'''Focus questions''' [[File:Crystal Clear app ktip.svg|left|20px|]] 

* What is akrasia? 

* What psychological processes contribute to akrasia and the conflict between long term and short term impulses? 

* How do motivation and emotion interact to influence why people act against their better judgement ?  

* What evidence based strategies can help people reduce akrasia and act more consistently in line with their goals ? 
{{RoundBoxBottom}}
== Akrasia ==

==== What is Akrasia ====
The term akrasia refers to a psychological phenomenon of acting against one's better judgement. Current psychological research explains it as a product of predictable conflicts within human self-regulation systems. In psychological terms, Akrasia reflects a tension between reflective long-term intentions and immediate emotionally driven short term impulses. Research highlights that failures in goal monitoring, susceptibility to short term rewards and reduced sensitivity to long term consequences make an individual more likely to behave in ways that contradict their own considered goals. Research in motivational causes describe that Akrasia can be explained as a &quot;hedonic impulse&quot; which is when seeking comfort or avoiding discomfort can overpower reflective decision making, producing patterns of self-indulgence or avoidance. Akrasia is a multifactorial phenomenon driven by cognitive, emotional, and motivational sources (Bella, 2023). 

'''Historical background:''' [[File:Aristotle Altemps Inv8575.jpg|thumb|Figure 2. An image of Aristotle ]]Historically, akrasia has been recognized for thousands of years. The concept originates in ancient Greek philosophy, originally the idea came from Socrates who debated whether akrasia was even possible, suggesting that if someone acted wrongly, it must be because they misunderstood what was truly good. Aristotle however disagreed  who used the term akrasia to describe &quot;weakness of will&quot;. Aristotle argued that people sometimes fail to act in accordance with their rational understanding because emotions, desires, or impulses temporarily overpower reason. In his view, akrasia occurs when the rational part of the mind identifies the best course of action, but the non-rational part disrupts this judgment and pulls behavior toward short term gratification. This failure is not due to ignorance but to a momentary inability to manage or correctly interpret one's emotional and motivation states. He suggested that individuals often misjudge the force of their impulses, treating them as rational justifications at the moment. This historical debate helped lay the foundation for modern psychological explanations. As contemporary theories echo Aristotle's insight showing the people frequently experience a conflict between reflective, long-term reasoning and immediate affect driven impulses and behavior often follows whichever system is the strongest in the moment (Bobonich &amp; Destrée, 2007).  

== Akrasia as a motivational and emotional conflict ==
'''Focus question''': What psychological processes contribute to akrasia and the conflict between long term and short term impulses?

Akasia is framed as a psychological conflict between internal systems that operate according to different rules, time scales, and motivational priorities (Frederick et al., 2002). These systems are broken into two categories long term and short-term. The Long-term system refers to intention and goals that a person aims to reach and they are maintained by reflective value-based processes that rely on executive functioning, future planning and a coherent sense of identity, the part of the mind that says, &quot;finishing my degree matters for my future&quot;. These goals are cognitively effortful, meaning they require working memory, sustained attention, and the ability to tolerate discomfort in the service of a future outcome. In contrast short term refers to impulses that arise from fast, effect driven systems that priorates immediate emotional states. When someone feels tired, stressed, or bored, the short-term system generates urges like &quot;I just want to relax now&quot;. These impulses are not irrational, they are grounded in the brains' reward circuitry, which is highly sensitive to immediate relief and comfort (Sirois &amp; Pychyl, 2013). The reward system operates in a way that puts short term relief first over long term satisfaction with research showing that the most common cause of akrasia is when tasks evoke negative affect, so states of anxiety, frustration, or uncertainty. Under these conditions people tend to priories short term affective rewards, such as relief from discomfort, even when they consciously prefer the long-term outcomes. This means that akrasia can serve as a mood repair strategy, where avoidance temporarily improves emotional states at the cost of long-term goals (Steel, 2007).  

Similarly to the long term and short-term conflict Dual process models explain this dynamic by distinguishing between two interacting systems: a fast automatic emotionally reactive system called system 1 and a slower, reflective and future oriented system called system 2. Akrasia is when system 1 dominates the behavior in the moment, overpowering the deliberate reasoning of system 2.  Factors such as cognitive load, stress, and emotional discomfort weaken reflective control, making impulsive choices more likely (Inzlicht, 2021). All this to say, akrasia is the outcome of how human motivational and emotional systems compete for behavioral control (Hofmann et al., 2009).  

== Self‑regulation and self‑control ==

'''Failures in self‑regulation contribute to akrasia''':    

Above, long term and short-term systems were briefly discussed; in this section it will go more in depth into how these systems fall under self-regulation and control and failure within them. While there are many concepts and theories that can describe self-regulation failure, this section will only describe three. However, these three should provide you with a greater understanding of how self-regulation and control underpins how akrasia occurs.   

Self-regulation is a multifaceted process that describes an individual's ability to manage emotions, thoughts, and behaviors in a way that yields positive results. Failure of this is the inability to coordinate behaviors, emotions, or attention. This would create an inability to achieve a long-term goal (Bella, 2023). While there is no definitive cause for self-regulation failures, we can find patterns that produce failure (Baumeister &amp; Heatherton, 1996). Understating self-regulation is important because Self-regulation failure has the potential to cause undeniable harm to individuals by leading individuals to act in ways that may harm them or others financially, physically or emotionally. Self–regulation failure can be broken down into different conceptualization to describe how it occurs. It can be understood though the  feedback loop model proposed by Carver and Scheier (1981). This model suggests that to have successful self regulation depends on three components. The first part of the loop describes standards, the ideals and goals an individual aims to achieve, without proper standards self-regulation is hindered as behaviour lacks direction. The second part is monitoring, this is where individuals must account for their own actions in relation to their standards, meaning if one is not keeping themself accountable to meet their standards, this is where failure often starts. The third part is operating, which is where the monitoring phase falls short of the standards and the process is to change the goal or state is set in motion. Failure occurs when there is a discrepancy in a person's current state and their end goal, meaning they do not have the ability to either reduce their goal, expectations or potentially set a different goal entirely (Baumeister &amp; Heatherton, 1996).  
[[File:Feedback-Loop.-In-article-diagram.-Psychology-Fanatic-Image.webp|thumb|400x400px|Figure 3: Carver and Scheier feedback loop]]
Bella (2023) describes another way self-regulation failure can be caused with similar underlying factors to carvers and Scheier (1981). He argues that akrasia is best understood as a conflict between internal systems. Specifically, the reflective system that represents long term values and goals and the impulsive system responds to immediate emotional and motivational states. When these systems compete, behavior can becomes inconsistent, fragmented, and vulnerable to short term impulses. Self regulation failure indicates that the individual's ability to manage impulses, emotion, and maintain goal-directed behaviors is compromised. This vulnerability is not a character flaw, but a predictable psychological pattern that arises when an individuals regulatory processes are overloaded, undermined, and not integrated effectively. More specifically, akrasia occurs when the impulsive system becomes more dominant because short term impulses feel more compelling, and long-term goals feel more distant and effortful. This is what makes a person act against their better judgment, even when they fully understand the potential long term consequences (Bella, 2023). Understanding the causes of self-regulation failure demonstrate an ability to have value when it comes to finding solutions to acts of akrasia and other motivation conflicts. Understanding allows an individual to alter their own responses to a stimulus and change their response.  

=== Ego Depletion ===
A third concept that describes why akrasia might occur is [[wikipedia:Ego_depletion|ego depletion]].  Ego depletion is an idea that describes how self-control operates like a limited resource. When people excerpt self-control, they are displaying a regulation of their emotions, resisting temptations, making decisions, and forcing themselves to finish difficult tasks. Once this limited resource of self-control is depleted, their ability to persist, inhibit impulses, or act according to long term goals becomes significantly impaired (Inzlicht, 2012). 

Baumeister et al (1998) proposed that self-control relies on a single, general resource. Meaning any act of self-control consumes this resource, leaving a person temporally less capable of exerting further control. When individuals become depleted, they are more vulnerable to short term impulses, making akrasia more likely to occur. This is possible even when the long-term goal is important; they lack the regulatory strength to act on it.  

More recent work by Inzlicht and Schmeichel ( 2012) However, challenges this idea of self-control being a resource, arguing that instead ego depletion is a shift in motivation, attention and affect. After exerting self-control, people become less motivated to excerpt effort and less attentive to long term goals. This still supports the idea that akrasia is a regulatory system shift towards seeking short term rewards seeking over long-term intentions. These processes make akrasia more likely, as individuals who are depleted struggle to inhibit impulses or tolerate discomfort. In everyday life, ego depletion can be seen when a student intends to study after a long day but instead chooses to relax because their regulatory capacity is drained. In these moments the long-term goal remains valued but the ability to fulfil it is compromised.  

{{Robelbox|theme=5|width=60%|title=1.1 - Module overview|iconwidth=47px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
&lt;quiz display=simple&gt;
{ Which subject best explains how failures in self regulation contribute to akrasia? }

|type=&quot;()&quot;}

- Ego Depletion
- Feedback loop
+ Internal system conflict 

&lt;/quiz&gt;
&lt;/div&gt;
{{Robelbox-close}} 

== Motivational theories ==
[[File:Self-Determination-Theory-Visual 1.png|thumb|Figure 3: Self-Determination Theory visual diagram ]]

===== Self‑determination theory: =====
Akrasia is not only a self-regulatory system failure but also described as a motivational concept. Self-determination theory best describes this.   

[[Self-determination theory]] is a concept that explains innate psychological needs in relation to human motivation (Ryan &amp; Deci, 2000). It was developed by Edward Deci and Richard Ryan in 1985. The theory describes that humans have innate predisposition for psychological growth and development fueled by three basic psychological needs. Needs being defined as inherent desires that are motivating (Ryan &amp; Deci, 2017). Once the needs have been fulfilled, it will contribute to the health and wellbeing of the person.  

The first need identified is autonomy. Defined as, one's behavior is self-awarded and congruent with their personal interests and values. The satisfaction of this is that the actions of the individual fulfill their desires and that they feel authentic to themselves (Deci &amp; Ryan, 2015). The second is competence, the urge feel capable and develop a mastery of performing tasks. To satisfy this, an individual can challenge their skills and abilities (Vansteenkiste et al., 2020). Lastly, relatedness is the feeling of connection and belonging. It is fulfilled when an individual feels they have the capability to care for others and be cared for. When an individual's needs are not satisfied, however they can result in illness or discontent (Deci &amp; Ryan 2000). SDT proposes that not all motivation is equal meaning that the focus should be on how and why a person is motivated. To understand why akrasia occurs, understanding the difference between autonomous and controlled motivation is crucial.  

Autonomous motivation includes two forms, the first is intrinsic motivation, which refers to engaging in an act because it is personally meaningful and interesting. Integrated regulation refers to acting because it’s aligned with one’s values and sense of self (Deci, 1972).  Individuals must feel a sense of choice, volition, and psychological freedom, rather than pressure to perform. If these are all met, they have displayed satisfaction with the three needs. Akrasia becomes less likely when motivation is autonomous. When people genuinely value a goal, individuals are more likely to willingly tolerate discomfort, delay gratification, and persist even though difficult. This is because the action feels internally meaningful, the individuals feel capable of reaching their end goal, and they feel they have been supported through their action, so short term impulses have less power. An individual may still act in an autonomous manner even in accordance with any external expectation if they believe their behavior is still consistent with their own values and of their own volition (Ryan &amp; Deci 2017).  

Controlled motivation describes the feelings of pressure and tension. It occurs when behavior is driven not by personal values or genuine interest but by external demands, internal pressure or avoidance of guilt and shame.This is the opposite to autonomous motivation, meaning this can often be the cause of akrasia. Similar to autonomous motivation if breaks down into two main forms. External regulation is acting to obtain a reward or avoid punishment. Introjected regulation is acting to avoid guilt, anxiety, or maintain self-worth. In both cases, behavior tends to not be a fully self-endorsed action. Controlled motivation increases akrasia behavior; it makes tasks feel adverse, even when the individual knows the long-term goal is important.  Due to this creating an emotional friction, the tasks become associated with stress, guilt, or obligation. When an individual feels controlled, they are more likely to avoid the task, procrastinate, or act against their better judgement (Deci et al., 2012). 

{{RoundBoxTop|theme=5}}
''' Example scenario''' 
Sally knows she should be studying for her exam, but instead chooses to spend the evening watching netflix. even though she believes studying is the better choice she gives into the more enjoyable activity. Choosing immediate satisfaction over her long term goal. 

Self determination theory posits that sally is more likely to experience akrasia because studying feels pressured and stressful rather than personally meaning. This is that her need for autonomy and competence are not being fully met thus, reducing her motivation and self regulation. {{RoundBoxBottom}}

&lt;quiz display=&quot;simple&quot;&gt;
{SDT is primarly concerned with ? :} 
- How rewards increase performance
+ How basic psychological needs influence motivation
-  How motivation shapes decision making

{SDT views motivation as ?:}
- A simple intrinsic/extinsic split
- A set of unrelated catagories
+ A continuum from controlled to autonomous 
&lt;/quiz&gt;

== Reduction Techniques ==
'''Focus question''': what strategies are there to reduce to act of akrasia and act more consciously in line with their goals? 

We have now discussed how and why akrasia occurs. Let's move onto techniques you can use in your day-to-day life to reduce akrasia.   

Reducing [[wikipedia:Cognitive_load|cognitive load]] though targeted behavioral and environmental techniques is an effective method to decrease akrasia because these strategies simplify task demands and support sustained self-regulation. The techniques include task chunking, breaking up complex activates into smaller more cognitively manageable sections, lowering the initiation barrier, and reducing the likelihood of avoidance (Sweller, 1988). Externalizing memory, this is creating an organized method of reminder though planners and checklists in order to off load working memory demands, allowing the individual to maintain goal relevant information without experiencing cognitive strain, thereby improving follow through on intentions (Sweller et al., 2011). Environmental simplification is the process of reducing visual clutter and minimizing digital distractions. This will decrease extraneous cognitive load and help preserve attentional resources for goal-directed behavior. Similarly, decision reduction strategies which is the process of cutting down options such making an established routine or making default choices, this can limit the cognitive effort required for repeated decision making, protecting self-regulatory capacities from depletion (Baumeister &amp; Heatherton, 1996). Together, these techniques reduce unnecessary cognitive demands and help create conditions in which intentions are more likely to become actions.

'''Practical tip: Start small'''

When a task feels overwhelming, try committing to just five minutes instead of focusing on completing the entire task. For example, a student struggling to begin an assignment could start by reading one paragraph or writing a few sentences. Breaking tasks into smaller, manageable steps may reduce emotional discomfort and make it easier to begin working towards long-term goals (Sirois &amp; Pychyl, 2013).   

Another approach to reduce akrasia is through enhancing autonomous motivation. This is to shape the environment so that you individuals can experience volition, psychological freedom and personal endorsement. According to Reeve and Jang (2006), autonomy supportive environments help increase intrinsic motivation allowing an individual feel their behavior is self-initiated rather than externally pressurized. Their research demonstrated this by studying what teachers say and do during learning activities that helped increase student engagement and intrinsic motivation. One of the first things they recognized what that acknowledging that learners' thoughts, feelings and frustrations show respect for their internal experience. This works because it allows the individual to feel their task is not being controlled by others. A second finding shows that allowing oneself to explore, reflect and attempt the task without interruption this supports autonomy and competence. A third finding is that the feedback you give yourself should be informal and not controlling meaning changing the mindset to find alternative ways to think about a task, looking at an issue with a new more light perspective rather than a negative one such as &quot;this should be done this way&quot; to &quot;how many ways are there to reach this goal, task, problem&quot;. This helps enhance competence and strengthen motivation.  &lt;quiz display=&quot;simple&quot;&gt;
{Which technique would you use? :} 
-  Reduction of cognitive load
-  Autonomous motivation

&lt;/quiz&gt;

== The Importance Understanding of Psychological Science Of Akrasia and its limitations ==  

Empirical finding both support and refine theoretical models of akrasia by showing that it arises from multiple interaction processes, rather than simple tendency to put of work, reach on self-regulation failure (Bella, 2023), ego depletion (Baumeister et al., 1998; Inzlicht &amp; Schmeichel, 2012) and self-determination theory (Deci &amp; Ryan, 200) collectively demonstrate that akrasia reflects conflicts between long term, value based intentions and short term, affect driven impulses, that are shaped by motivational qualities, emotional avoidance and cognitive load. These findings challenge overly simplistic models that treat akrasia as simply procrastination or lack of willpower, and instead support integrative frameworks in which internal systems, basic psychological needs and situational demands jointly determine whether people act in line with their better judgement. This integrated knowledge has important implications for improving motivational and emotional lives. Understanding akrasia can help individuals view failures as not acts of laziness but as predictable psychological conflicts. This perspective can help promote self compassion and encourage the use of evidence based strategies such as reducing cognitive load and supporting autonomy. Interventions should not only focus on trying harder, but also support autonomous motivation and emotional regulation while reducing unnecessary control and guilt. By targeting these mechanisms, individuals are more likely to experience motivation that is self-endorsed, resilient to discomfort, and aligned with long-term goals (Sirois &amp; Pychyl, 2013).  

==== Limitations ====
Although current psychological theories provide beneficial explanations for akrasia, there is no single framework that can fully account for all displays of it. An example of this is the ego depletion model has faced several challenges regarding its reliability and applicability, this has caused some researcher to question whether self control operates as a limited resource in the way originally proposed by Baumeister et al (1998), (Lurquin, 2017). Additionally the majority of research has had a tendency to focus on the individual psychological processes , meaning less attention has been given to the influence of environmental constraints such as socioeconomic pressures or limited opportunities to act in accordance with ones goals. Furthermore much of the research relies on self report measures, this may not allow for an accurate real world behavior analysis. All this to mean that Akrasia is best understood as a multifactorial complex phenomenon that is influenced by multiple interacting cognitive, emotional, motivational and contextual factors (Bella, 2023)  

==Conclusion==
so why do people act against their better judgement? Psychological research suggest that akrasia occurs when an individuals long term goals and values conflict with their immediate emotional and motivational impulses, rather than a reflection of their laziness or weak character. Akrasia is a describe as a predictable psychological phenomenon, that is the cause of multiple converging sectors of an individual. This includes their ability to self regulate, emotional avoidance tendencies, cognitive load limits and the quality of their motivation. 

This chapter provided evidence as to how behaviour is shaped by the interaction of cognitive, emotional and motivation systems rather than simply by willpower. The self regulation theories describe how difficulties in the monitoring and maintenance of goals can undermine the intention of action. Self determination theory emphasis the importance of autonomy, competence, and relatedness in supporting meaningful and persistent motivation. It states that when motivation is autonomous and personally valued, individuals are more likely to tolerate discomfort and remain committed to long term objectives. 

Having an understanding of akrasia has important implications for personal growth and psychological welling. This is because recognising that an inability to reach or delay a goal is not due to a strength in will but because of predictable psychological causes can help reduce self blame and encourage more effective coping strategies. Strategies such as reducing cognitive load by breaking down tasks and supporting autonomy. To summarize, by acting in accordance with long term goals is not simply a matter of trying harder, but to creating an environment and conditions that help support motivation and self regulation.

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'''What did you learn?'''
* Key takeaway 1: ...
* Key takeaway 2: ...
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== See also ==
* [[Motivation and emotion/Book/2011/Self-determination theory|Self-determination theory]] (Book chapter, 2011)
* [[wikipedia:Goal_setting|Goal setting]] (Wikipedia) 
* [[wikipedia:Motivation|Motivation]] (Wikipedia)

==References==
{{Hanging indent|1=

Bobonich C., &amp;  Destrée, P. (2007). Akrasia in Greek Philosophy: From Socrates to Plotinus. BRILL .106, 1-11. https://books.google.com.au/books?id=so097j_jPBsC&amp;dq=akrasia+historical+background&amp;lr=&amp;source=gbs_navlinks_s

Bella, A. F. (2023). Psychological underpinnings of akrasia: A new integrative framework based on self-regulation vulnerabilities and failures. New Ideas in Psychology, 70, Article 101027. https://doi.org/10.1016/j.newideapsych.2023.101027)

Baumeister, R. F., et al. (1998). Ego depletion: Is the active self a limited resource? Journal of Personality and Social Psychology. DOI: https://doi.org/10.1037/0022-3514.74.5.1252

Baumeister, R. F., &amp; Heatherton, T. F. (1996). Self-Regulation Failure: An Overview. Psychological Inquiry, 7(1), 1–15. https://doi.org/10.1207/s15327965pli0701_1

Carver, C. S., &amp; Scheier, M. F. (1982). Control theory: A useful conceptual framework for personality-social, clinical, and health psychology. Psychological Bulletin, 92(1), 111–135. https://doi.org/10.1037/0033-2909.92.1.111

Deci, E. L., &amp; Ryan, R. M. (2000). The “What” and “Why” of Goal Pursuits: Human Needs and the Self-Determination of Behavior. Psychological Inquiry, 11(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01

Deci, E. L. (1972). Intrinsic motivation, extrinsic reinforcement, and inequity. Journal of Personality and Social Psychology, 22(1), 113–120. https://doi.org/10.1037/h0032355 

Deci, E. L., &amp; Ryan, R. M. (2015). Self-determination theory. In J. D. Wright (Ed.), International Encyclopedia of the Social &amp; Behavioral Sciences (2nd ed., pp. 486–491). Elsevier. https://doi.org/10.1016/B978-0-08-097086-8.26036-4 

De Castella, K., Platow, M. J., Tamir, M., &amp; Gross, J. J. (2018). Beliefs about emotion: implications for avoidance-based emotion regulation and psychological health. Cognition and Emotion, 32(4), 773–795. https://doi.org/10.1080/02699931.2017.1353485

Frederick, S., Loewenstein, G., &amp; O’Donoghue, T. (2002). Time discounting and time preference: A critical review. Journal of Economic Literature, 40(2), 351–401. https://doi.org/10.1257/002205102320161311 

Hofmann, W., Friese, M., &amp; Strack, F. (2009). Impulse and self-control from a dual-systems perspective. Perspectives on Psychological Science, 4(2), 162–176. https://doi.org/10.1111/j.1745-6924.2009.01116.x

Heatherton, T. F., &amp; Wagner, D. D. (2011). Cognitive neuroscience of self-regulation failure. Trends in cognitive sciences, 15(3), 132–139. https://doi.org/10.1016/j.tics.2010.12.005

Inzlicht, M., &amp; Schmeichel, B. J. (2012). What Is Ego Depletion? Toward a Mechanistic Revision of the Resource Model of Self-Control. Perspectives on Psychological Science, 7(5), 450–463. https://doi.org/10.1177/1745691612454134 

Inzlicht, M., Werner, K. M., Briskin, J. L., &amp; Roberts, B. W. (2021). Integrating Models of Self-Regulation. Annual Review of Psychology, 72(1), 319–345. https://doi.org/10.1146/annurev-psych-061020-105721

Lurquin, J. H., &amp; Miyake, A. (2017). Challenges to Ego-Depletion Research Go beyond the Replication Crisis: A Need for Tackling the Conceptual Crisis. Frontiers in Psychology, 8, 568. https://doi.org/10.3389/fpsyg.2017.00568

Ng, J. Y. Y., Ntoumanis, N., Thøgersen-Ntoumani, C., Deci, E. L., Ryan, R. M., Duda, J. L., &amp; Williams, G. C. (2012). Self-Determination Theory Applied to Health Contexts: A Meta-Analysis. Perspectives on Psychological Science, 7(4), 325–340. https://doi.org/10.1177/1745691612447309) 

Reeve, J., &amp; Jang, H. (2006). What Teachers Say and Do to Support Students’ Autonomy During a Learning Activity. Journal of Educational Psychology, 98(1), 209–218. https://doi.org/10.1037/0022-0663.98.1.209

Ryan, R. M., &amp; Deci, E. L. (2017). Self-determination theory: Basic psychological needs in motivation, development, and wellness (pp. xii, 756). The Guilford Press. https://doi.org/10.1037/0022-0663.98.1.209

Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257–285. https://doi.org/10.1207/s15516709cog1202_4

Sirois, F. M., &amp; Pychyl, T. A. (2013). Procrastination and the priority of short-term mood regulation: Consequences for future self. ''Social and Personality Psychology Compass, 7'' (2), 155-127. https://doi.org/10.1111/spc3.12011

Steel, P. (2007). The nature of procrastination: A meta-analytic and theoretical review of quintessential self-regulatory failure. Psychological Bulletin, 133(1), 65–94. https://doi.org/10.1037/0033-2909.133.1.65 

Vansteenkiste, M., Ryan, R. M., &amp; Soenens, B. (2020). Basic psychological need theory: Advancements, critical themes, and future directions. Motivation and Emotion, 44(1), 1–31. https://doi.org/10.1007/s11031-019-09818-1}}

==External links==

* [https://pmc.ncbi.nlm.nih.gov/articles/PMC3062191/ Cognitive neuroscience of self regulation failure] (National library of medicine) 
* [https://www.youtube.com/watch?v=jHGFlyHnhFQ Self control and Akrasia] (YouTube)

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== Overview ==
{{RoundBoxTop|theme=3}}
[[File:Sinclair Swimming.JPG|right|thumb|180px|'''Figure 1'''. Ash is a competitive swimmer and swims daily.]]

;Scenario

Ash is a swimmer training for a national competition. When asked to describe herself, being &quot;a swimmer&quot; is the first word Ash uses. She is eager to succeed at the upcoming swimming competition. Every morning, she wakes up at 4:00 a.m. to swim four kilometres (see Figure 1). Her friend Riley struggles to understand how Ash maintains this demanding schedule. Why is Ash able to do this when many would find this difficult?
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How can some people sustain long-term commitment to challenging goals while others lose momentum or experience fear of failure? Many popular explanations of motivation focus on [[Motivation and emotion/Book/2015/Willpower|willpower]], [[Motivation and emotion/Book/2019/Rewards, punishments, and social cooperation|rewards]], and [[Motivation and emotion/Book/2013/Needs|needs]]. However, motivation is also influenced by [[Motivation and emotion/Book/2010/Self-concept|self-concept]], a person's understanding of who they are and how they feel about themselves (Wehrle &amp; Fasbender, 2018). A person's self-concept helps them answer the question, ''who am I?'' and can act as a powerful motivational force which directs and energises human behaviour.

This chapter explores the reciprocal relationship between self-concept and motivation: how self-understanding motivates behaviour, and how motivated behaviour progressively shapes self-concept. Understanding this reciprocal relationship can help people develop motivation around meaningful identities while reducing the risk that failure becomes a threat to personal worth. 

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'''Focus questions'''

*What is self-concept? 
*How does self-concept influence motivation? 
*How does motivation shape self-concept?
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== What is self-concept? ==
Self-concept is a cognitive framework of self-knowledge including attitudes, beliefs, and judgements about oneself (Wehrle &amp; Fasbender, 2018). It is related, but unique to many of the popular “self-” constructs like [[self-esteem]], [[w:Self-efficacy|self-efficacy]], and [[w:Self-image|self-image]]. Each self-concept-relevant theory approaches the construct differently, but several common properties emerge and provide the foundation for understanding its motivational effects (see Table 1). Foundationally, [[wikipedia:William_James|James]] (1892, p. 176) conceptualised the self as having two parts which help people understand and describe themselves: “I”, the subjective thinker, and “me”, the material and social self. Cooley (1902) added the [[wikipedia:Looking-glass_self|looking-glass self,]] proposing that self-concept develops through perceived social evaluations. Modern frameworks, including identity-based motivation theory (Oyserman, 2024) and the multidimensional model (Marsh et al., 1992) suggest self-concept is hierarchical, multifaceted, and dynamic.

'''Table 1'''

''Self-Concept Properties and Their Significance for Motivation''
{| class=&quot;wikitable&quot; style=&quot;margin: auto;&quot;
!Property
!Key theory
!Significance for motivation
|-
|'''Descriptive  '''
|James' (1892) self-theory
|Identity beliefs set standards and expectations
|-
|'''Socially developed'''
|Looking-glass self (Cooley, 1902)
|Social feedback influences which behaviours are pursued 
|-
|'''Dynamic'''
|Identity-based motivation theory (Oyserman, 2024)
|Self-concept shifts situationally
|-
|'''Multidimensional'''
|Multidimensional model (Marsh et al., 1992)
|Domain-specific self-concepts motivate distinct behaviours
|-
|'''Hierarchical  '''
|Multidimensional model (Marsh et al., 1992)
|General and specific domains of the self influence each other and different behaviours
|}

== How does self-concept influence motivation? ==
With self-concept core to how people understand and navigate life, self-concept can act as a motivating force. This section explores how self-concept shapes and energises goal pursuit, and influences task engagement, responses to difficulty, and the threat of failure. 

=== How the self directs and energises behaviour ===
[[w:Self-discrepancy_theory|Self-discrepancy theory]] proposesthat people have three representations of the self: the actual (who one is), ideal (who one wants to become), and ought self (who one believes others want them to be; see Table 2; Higgins, 1987). Ideal and ought selves set standards for one to strive toward, laying a framework for goal direction. Discrepancies between actual and ideal or ought selves also generate emotional vulnerabilities (Table 2). Actual/ideal self-discrepancies result in dejection-related emotions (e.g., frustration, dissatisfaction; Higgins, 1987). Actual/ought self-discrepancies result in agitation-related emotions (e.g., anxiety, guilt). Greater discrepancies result in greater emotional discomfort and generate greater motivation to close the gap (Higgins, 1989).  

Mason et al.'s (2019) meta-analytic findings supported that greater self-discrepancies resulted in more negative emotions. However, they also found that both ideal and ought self-discrepancies correlated with dejection- and agitation-related emotions. This contrasts with self-discrepancy theory's proposition. Further, while the negative emotions resulting from discrepancies are proposed to motivate people to reduce discrepancies, MacIntyre and Vincze (2017) suggest positive emotions have greater motivating strength than negative emotions. This suggests that while self-concepts provide frameworks for goal selection and energise behaviour, self-discrepancies may not be the most powerful emotional source of motivation.

'''Table 2'''

''Dimensions of the Self and Emotional Effects of Discrepancies''   
{| class=&quot;wikitable&quot;
!Self dimension
!Examples
!Emotional effect of discrepancy
|-
|Actual
|Daily behaviours, beliefs
| -
|-
|Ideal
|Dreams, aspirations
|Dejection-related emotions
|-
|Ought
|Duties, obligations
|Agitation-related emotions
|}

[[w:Regulatory_focus_theory|Regulatory focus theory]] (Higgins, 1997) expands self-discrepancy theory to suggest that different self-representations produce different motivational orientations. Ideal-self goals generate a promotion focus, where people are motivated to seek positive outcomes (see Table 3). Ought-self goals generate a prevention focus, where people are motivated to avoid negative outcomes. These regulatory focuses positively correlated with intrinsic motivation in Wang et al.'s (2021) study of adolescent task engagement. Promotion focuses positively correlated with creativity and an innovative cognitive style, whereas prevention focuses negatively correlated with an innovative cognitive style and were characterised by error avoidance. This shows that while both promotion and prevention orientations generate motivation, they result in different approaches to tasks.                   

'''Table 3''' 

''Self-concept's Motivational Mechanisms''

{| class=&quot;wikitable&quot;
|+
!Self-discrepancy
!Motivational focus
!Motivational mechanism
!Task approach
|-
|Actual-ideal
|Promotion
|Seek positive outcomes
|Creativity, innovation
|-
|Actual-ought
|Prevention
|Avoid negative outcomes
|Reduced innovation, error avoidance
|}

[[wikipedia:Identity_based_motivation|Identity-based motivation theory]] (Oyserman, 2024) provides an alternative explanation of how self-concept directs behaviour. The theory proposes that situations influence which aspects of self-concept are active. Active identities change how people interpret difficulty, which influences motivation. When behaviour aligns with an active identity, people interpret difficulties in completing that behaviour as evidence that the behaviour is important (Oyserman, 2015). This is because identity-congruent behaviours provide information about who one is and who one wants to become, making difficulty meaningful rather than discouraging (Oyserman, 2024). Conversely, identity-incongruent actions that have the same challenges are interpreted as pointless. This means that identities mediate motivation and help goal selection and persistence through the process of difficulty interpretation.

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'''Scenario application'''
When Ash feels physically exhausted during her early morning swim sets, her identity as an elite athlete is active. This helps her interpret exhaustion as a meaningful challenge. For her non-swimmer friend, Riley, this exhaustion would be interpreted as evidence swimming is not for them.
{{RoundBoxBottom}}

Illustrating the motivating role of self-concept within this framework, Nurra and Oyserman (2018) found that motivation to pursue future identity-relevant goals in school children, and subsequent achievement, was influenced by how children thought about their future selves. Students were exposed to prompts that helped them think of their adult self as either near or far. Students in the adult-self-is-near group achieved significantly higher final grades than the adult-self-is-far group. These findings indicate that closely identifying with future selves and viewing future selves as attainable can motivate goal pursuit. Together, these results support identity-based motivation theory and detail that self-concept drives behaviour by defining desirable outcomes and shaping how challenges and opportunities are interpreted. 

Together, self-discrepancy and regulatory focus theory suggest that a person's perceived distance from a valued self can create motivational pressure to change, while identity-based motivation theory suggests active identities influence how people interpret challenges. In all three theories, self-concept is shown as central to motivation, driving goal selection and engagement. Thus, what motivates each person, and how they subsequently behave, is shaped by self-concept.

=== How self-concept can undermine motivation ===
While self-concept can energise and direct behaviour, it can also undermine motivation through self-worth contingencies. [[wikipedia:Contingent_self-esteem#Self-esteem_and_contingent_self-worth|Self-worth contingencies]] refer to the standards people feel they must meet to have personal value (Showers et al., 2015). When goals are tightly bound to self-worth, failure threatens self-concept. So, contingent self-worth can motivate the pursuit of identity-relevant goals, but can also result in avoidance and strong responses to failure.

{{RoundBoxTop|theme=11}}
&lt;quiz display=simple&gt; 
'''What are self-worth contingencies?'''
|type=&quot;()&quot;} 

- How people feel about themselves
+ Standards people feel they must meet to have value
- How people compare themselves to others
&lt;/quiz&gt;
{{RoundBoxBottom}}

Lietz et al. (2026) qualitatively studied 17 participants' identity-shaped goals and found that failing to achieve these goals resulted in negative and severe emotional responses. Further, participants tended to attribute failure to personal shortcomings because of how closely held the goal was to their self-concept. This resulted in reduced motivation to reattempt, or blind pursuit of the same goal without re-examining the approach. Despite the limited sample size, these findings are consistent with [[Motivation and emotion/Book/2024/Attribution theory and emotion|attribution theory]] (Weiner, 1985), which suggests that causal thinking processes, where people attribute outcomes to stable, uncontrollable factors, result in low motivation. Attributional styles affect self-evaluations and thus can undermine motivation when failure is attributed to stable aspects of the self (Bandhu et al., 2024). This can cause maladaptive behaviours to emerge.

One such response to the threat of failure is self-handicapping. [[w:Self-handicapping|Self-handicapping]] involves creating obstacles to one's own goal so that failure can be attributed to external, rather than personal factors (Török &amp; Szabó, 2018). This means people may increase the probability of failure to protect their self-concept (Coudevylle et al., 2020). Therefore, self-concept can impact motivation by hindering goal pursuit.

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'''Scenario application'''
Ash cares a lot about succeeding in her swimming competition. To protect her self-concept as a successful swimmer, Ash may fake a mild illness at the competition so that any failure can be attributed to her illness, rather than her competence.
{{RoundBoxBottom}}

[[File:Multidimensional_model_of_self-concept_diagram.png|thumb|536x536px|'''Figure 2.''' The hierarchical multidimensional model of self-concept (Marsh et al., 2019).]]

Illustrating the causes of self-handicapping, Schwinger et al. (2022) found a medium negative correlation between general self-evaluations and self-handicapping and a medium positive correlation between fear of failure and self-handicapping. With more negative general self-evaluations and greater fear of failure, people are more likely to self-handicap. This highlights self-concept as an antecedent to self-handicapping. However, in this study, general, rather than domain-specific, measures were used. According to the multidimensional model, self-concept is a hierarchical, multi-faceted construct, and more specific self-concepts are more closely related to actual behaviour (see Figure 2; Marsh et al., 2019). Accordingly, future research should investigate domain-specific measures of self-concept and fear of failure to understand domain-specific effects and illustrate the direct influence of self-concept domains on self-handicapping and task motivation.

Self-handicapping demonstrates that self-concept-driven motivation is not always directed towards achieving valued outcomes. Protecting self-worth can become more important than goal engagement. Together, this research suggests self-concept can act both as a motivational resource and a motivational vulnerability.

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'''Intervention application'''
To reduce self-handicapping, interventions should support people to separate self-worth and performance outcomes by building [[Motivation and emotion/Book/2025/Cultivating self-compassion|self-compassion]], diverse positive self-concepts, and [[Motivation_and_emotion/Book/2019/Growth_mindset_development|growth mindsets]].
{{RoundBoxBottom}}

== How does motivation shape self-concept? ==
The research and theories discussed so far have detailed how self-concept directs and motivates behaviour. The following section explores how, and whether, this relationship works in reverse.  

=== How internalising motivation shapes self-concept ===
[[Self-determination theory]] (Ryan &amp; Deci, 2020) proposes motivation exists on a continuum of self-determination, ranging from externally to increasingly internally regulated behaviour (see Table 4). Extrinsic motivation involves engaging in behaviour for an outcome that is separable from the activity itself (Morris et al., 2022). Types of extrinsic motivation include external, introjected, identified, and integrated regulation, capturing externally controlled to personally valued behaviour. Whereas intrinsic motivation refers to autonomous behaviours completed for enjoyment (Morris et al., 2022).

[[File:Self-determination theory psychological needs.jpg|thumb|413x413px|'''Figure 3.''' Self-determination theory psychological needs of autonomy, competence, and relatedness (Ryan &amp; Deci, 2020).]]

How self-determined people's motivations are depends on the extent to which one has internalised the values, beliefs, and perceptions of the behaviour into their self-concept. Self-determined motivation also depends on three innate needs: competence, autonomy, and relatedness (see Figure 3; Ryan &amp; Deci, 2020). Meeting these psychological needs supports motivation to become progressively internalised, and behaviour increasingly self-endorsed (Chiu, 2023). However, it should be noted that this process does not necessarily occur in a fixed sequence.

This framework illustrates how self-concept and motivation reciprocally form one another. The degree to which one identifies with a behaviour shapes their motivation to engage with the behaviour; when needs are met, motivated behaviours and psychological processes shape the self-concept. This internalisation process helps explain how Ash came to identify as a swimmer (see Table 4).  

'''Table 4'''

''Applying Self-Determination Theory to Ash's Motivation and Self-Concept Development''

{| class=&quot;wikitable&quot; style=&quot;margin: auto;&quot;
!Regulation type 
!Ash's self-concept and swimming progression example
!Motivational mechanism 
|-
|External 
|Ash received a lollipop after swimming lessons.  
|Rewards or punishments
|-
|Introjected 
|Ash wanted her parents to think she is dedicated to swimming. 
|Avoiding guilt
|-
|Identified 
|Ash continued swimming after recognising its health benefits.
|Consciously value goal 
|-
|Integrated 
|Ash starts to identify as a swimmer and with her swim team.  
|Congruence with self-concept 
|-
|Intrinsic 
|After the swimming competition, Ash continues swimming for the joy of it. 
|Inherent enjoyment 
|}

Chiu (2023) provided compelling evidence for how motivation shapes self-concept within the context of self-determination theory. In their study, 342 Hong Kong high school students completed STEM {{ic|explain abbreviation}} activities taught using either a standard teaching approach or a self-determination theory teaching method, focusing on supporting autonomy, competence, and relatedness needs (see Figure 3). Self-report measures reflected that the needs-supporting teaching approach increased students' feelings of autonomy, competence, and relatedness; and, consequently, increased STEM identity and interest. This supports that fulfilling core psychological needs promotes more autonomous motivation and develops identity.  

Further supporting this relationship, Yip et al.'s (2024) longitudinal study of 236 anti-poverty activists who completed self-reported social attitudes and personality measures at two time points found that increases in self-determined motivations positively correlated with group identification. However, non-self-determined motivations, such as external regulation, did not correlate with group identification. This suggests that self-determined motivation facilitates the incorporation of behaviour and group membership into one's self-concept. 

However, both Yip et al. (2024) and Chiu's (2023) studies employed self-report measures, which are vulnerable to [[w:Social-desirability_bias|social-desirability bias]]. This may have influenced results, particularly as these studies measured constructs of social satisfaction. Future studies should employ implicit and observational methods to better understand the influence of self-concept on motivation. Despite this limitation, considering these results alongside self-determination theory supports that self-concept develops as values and behaviours become progressively internalised. This demonstrates that motivation can be a mechanism through which self-concept develops and is not simply a motivating force.

{{RoundBoxTop|theme=11|title=Quiz}}
&lt;quiz display=simple&gt; 
'''Which statement best reflects how motivation shapes self-concept?'''
|type=&quot;()&quot;} 

- People are only motivated to engage in behaviours that are part of their self-concept.
- Self-concept does not change through motivational processes.
+ Repeated engagement with a behaviour and satisfaction of psychological needs gradually makes a behaviour part of one's self-concept.
&lt;/quiz&gt;
{{RoundBoxBottom}}

=== The cyclical process of motivation and self-concept development ===
The reciprocal effects model proposes that self-concept and achievement reinforce one another over time (Marsh et al., 2018). People with stronger self-concepts tend to achieve more highly, while achievement experiences subsequently shape self-concept. Motivation plays an important role in this process, influencing how people behave toward achievement experiences.  

There is a growing body of research investigating this model. For example, Sewasew et al.'s (2018) longitudinal study with 2,342 German high schoolers demonstrated that mathematics self-concept was positively correlated with mathematics achievement. Their study highlighted a mutually dependent relationship between academic self-concept and achievement, each mediated by motivation. However, Garn and Shen's (2015) longitudinal study of 329 participants' self-concept and motivation for exercise found that the psychological needs posited by self-determination theory (Ryan &amp; Deci, 2022) did not predict physical self-concept at follow-ups. Physical self-concept was only shown to shape, rather than be shaped by exercise motivation. This result conflicts with the reciprocal effects model and Sewasew et al.'s (2018) results, which may reflect the different self-concept domains examined: mathematics versus physical self-concept. This may indicate that reciprocal effects are domain-specific; the multidimensional model suggests academic and physical self-concepts function independently, meaning findings from one domain may not generalise to another (Marsh et al., 2019). Thus, future research should directly compare the reciprocal relationship between self-concept and motivation within different domains.  

However, there is further doubt regarding the validity of the reciprocal effects model. Sorjonen et al. (2024) reanalysed meta-analytic results that had provided evidence for the reciprocal effects model. They found that conclusions about the longitudinal relationship between achievement and academic self-concept changed depending on the statistical model used. This may indicate a spurious correlation that undermines the credibility of the reciprocal effects model. 

Taken together, these findings suggest that achievement can shape self-concept, but the strength and direction of this relationship may depend on the domain being examined and the methodological approach used. Although the reciprocal effects model remains influential, current evidence indicates that the relationship between motivation, achievement, and self-concept is more complex than originally proposed. 

== Conclusion ==
Self-concept is a multidimensional, dynamic framework of self-beliefs which acts as an internal compass for human behaviour. Self-concept shapes motivation by determining which goals feel meaningful, attainable, and identity-consistent. Self-discrepancy theory explains how perceived distance from ideal or ought selves creates motivational pressure for change, while identity-based motivation theory explains how active identities change the meaning of difficulty. Contrastingly, contingent self-worth can undermine motivation by making failure feel threatening to personal value. Together, these theories detail that self-concept influences goal direction and engagement through social, emotional, and cognitive processes. These theories provide insight that people can foster resilient motivation by aligning goals with valued identities and framing challenges as identity-building, rather than solely striving for behavioural discipline or external rewards.  

Motivation also influences self-concept. Self-determination theory details that motivation and subsequent behaviours form self-concept through internalisation processes when psychological needs are met. However, inconsistent support for the reciprocal effects model indicates that the extent to which motivation reshapes self-concept may vary across domains and statistical models. So, while the effect of motivation on self-concept requires further investigation, theoretical models suggest self-concept and motivation influence one another.  

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'''Take-home message'''

With self-concept and motivation inherently linked, who people believe they are shapes the goals they pursue, while motivations, behaviours, and experiences continually shape who people become. 

Ash's self-concept as a swimmer motivates her because swimming is identity-consistent and meaningful. Additionally, each time she swims, her identity as a swimmer is reinforced.
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{{RoundBoxTop|theme=11|title=Quiz}}
&lt;quiz display=simple&gt;
{'''Chapter comprehension check quiz:'''
Ash wakes up at 4:00 a.m. each day to train because being a swimmer is a central part of her identity. According to the chapter, what best explains Ash's motivation?
|type=&quot;()&quot;}

+Self-concept acts as an internal compass that guides goals and behaviour.
-Motivation is caused only by external rewards and punishment.
-Self-concept remains fixed and has little influence on actions.
&lt;/quiz&gt;
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== See also ==
* [[wikipedia:Self-concept|Self-concept]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Self-concept clarity|Self-concept clarity]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2014/Self-efficacy and motivation|Self-efficacy and motivation]] (Book chapter, 2014)

== References ==
{{Hanging indent|1=

Bandhu, D., Mohan, M., Nittala, N., Jadhav, P., Bhadauria, A., &amp; Saxena, K. K. (2024). Theories of motivation: A comprehensive analysis of human behavior drivers. ''Acta Psychologica, 244'', Article 104177. https://doi.org/10.1016/j.actpsy.2024.104177   

Chiu, T. K. (2023). Using self-determination theory (SDT) to explain student STEM interest and identity development. ''Instructional Science, 52'', 89–107. https://doi.org/10.1007/s11251-023-09642-8  

Cooley, C. H. (1902). The looking-glass self. ''The production of reality: Essays and readings on social interaction, 6''(1902), 126–128. https://doi.org/10.32376/3f8575cb.73d69f51 

Coudevylle, G. R., Boulley-Escriva, G., Finez, L., Eugène, K., &amp; Robin, N. (2020). An experimental investigation of claimed self-handicapping strategies across motivational climates based on achievement goal and self-determination theories. ''Educational Psychology, 40''(8), 1002–1021. https://doi.org/10.1080/01443410.2020.1746237 

Garn, A., &amp; Shen, B. (2015). Physical self-concept and basic psychological needs in exercise: Are there reciprocal effects? ''International Journal of Sport and Exercise Psychology, 13''(2), 169–181. https://doi.org/10.1080/1612197X.2014.940994  

Higgins, E. T. (1987). Self-discrepancy: A theory relating self and affect. ''Psychological Review, 94''(3), 319–340. https://doi.org/10.1037/0033-295X.94.3.319

Higgins, E. T. (1989). Self-discrepancy theory: What patterns of self-beliefs cause people to suffer? In L. Berkowitz (Ed.), ''Advances in experimental social psychology'' (Vol. 22, pp. 93–136). Academic Press. https://doi.org/10.1016/S0065-2601(08)60306-8

Higgins, E. T., Shah, J., &amp; Friedman, R. (1997). Emotional responses to goal attainment: Strength of regulatory focus as moderator. ''Journal of Personality and Social Psychology, 72''(3), 515–525. https://doi.org/10.1037/0022-3514.72.3.515

James, W. (1892). The self. In W. James (Ed.), ''Psychology: Briefer course'' (pp. 176–216). Macmillan and Co. https://doi.org/10.1037/11630-012

Lietz, R., Whittaker, S., &amp; Su, N. (2026). ‘It meant something about who I am’: What the lived experience of failure teaches us about designing for goal setting. ''Behaviour &amp; Information Technology,'' 1–27. https://doi.org/10.1080/0144929X.2026.2711023  

MacIntyre, P. D., &amp; Vincze, L. (2017). Positive and negative emotions in motivation for second language learning. ''Studies in Second Language Learning and Teaching, 7''(1), 61–88. https://doi.org/10.14746/ssllt.2017.7.1.4

Marsh, H. W., Byrne, B., &amp; Shavelson, R. J. (1992). A multidimensional, hierarchical self-concept. In T. Brinthaupt &amp; R. Lipka (Eds.), ''The self: Definitional and methodological issues'' (pp. 44–95). State University of New York Press. https://www.researchgate.net/publication/313711689_A_multidimensional_hierarchical_self-concept 

Marsh, H. W., Martin, A. J., Yeung, A. S., &amp; Craven, R. G. (2018). Chapter 6: Competence self-perceptions. In A. J. Elliot, C. S. Dweck, &amp; D. S. Yeager (Eds.), ''Handbook of competence and motivation: Theory and application'' (pp. 85–115). Guilford Publications. https://www.researchgate.net/publication/312491616_Competence_self-perceptions 

Marsh, H. W., Seaton, M., Dicke, T., Parker, P. D., &amp; Horwood, M. S. (2019). The centrality of academic self-concept to motivation and learning. In K. A. Renninger &amp; S. E. Hidi (Eds.), ''The Cambridge handbook of motivation and learning'' (pp. 36–62). Cambridge University Press. https://doi.org/10.1017/9781316823279.004  

Mason, T. B., Smith, K. E., Engwall, A., Lass, A., Mead, M., Sorby, M., Bjorlie, K., Strauman, T. J., &amp; Wonderlich, S. (2019). Self-discrepancy theory as a transdiagnostic framework: A meta-analysis of self-discrepancy and psychopathology. ''Psychological Bulletin, 145''(4), 372–389. https://doi.org/10.1037/bul0000186

Morris, L., Grehl, M., Rutter, S., Mehta, M., &amp; Westwater, M. (2022). On what motivates us: A detailed review of intrinsic v. extrinsic motivation. ''Psychological Medicine, 52''(10), 1801–1816. https://doi.org/10.1017/S0033291722001611

Nurra, C., &amp; Oyserman, D. (2018). From future self to current action: An identity-based motivation perspective. ''Self and Identity, 17''(3), 343–364. https://doi.org/10.1080/15298868.2017.1375003  

Oyserman, D. (2015). Identity-based motivation. ''Emerging Trends in the Social and Behavioral Sciences, 38'', 1–11. https://doi.org/10.1002/9781118900772.etrds0171  

Oyserman, D. (2024). Identity-based motivation and the motivational consequences of difficulty. ''Social and Personality Psychology Compass, 18'',  Article e70028. https://doi.org/10.1111/spc3.70028  

Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology, 61'', Article 101860. https://doi.org/10.1016/j.cedpsych.2020.101860  

Ryan, R. M., &amp; Deci, E. L. (2022). Self-determination theory. In F. Maggino (Ed.), ''Encyclopedia of quality of life and well-being research'' (pp. 1–7). Springer. https://doi.org/10.1007/978-3-319-69909-7_2630-2  

Schwinger, M., Trautner, M., Pütz, N., Fabianek, S., Lemmer, G., Lauermann, F., &amp; Wirthwein, L. (2022). Why do students use strategies that hurt their chances of academic success? A meta-analysis of antecedents of academic self-handicapping. ''Journal of Educational Psychology, 114''(3), 576–596. https://doi.org/10.1037/edu0000706  

Seaton, M., Parker, P. D., Marsh, H. W., Craven, R., &amp; Yeung, A. (2014). The reciprocal relations between self-concept, motivation and achievement: Juxtaposing academic self-concept and achievement goal orientations for mathematics success. ''Educational Psychology, 34''(1), 49–72. https://doi.org/10.1080/01443410.2013.825232  

Sewasew, D., Schroeders, U., Schiefer, I., Weirich, S., &amp; Artelt, C. (2018). Development of sex differences in math achievement, self-concept, and interest from grade 5 to 7. ''Contemporary Educational Psychology, 54'', 55–65. https://doi.org/10.1016/j.cedpsych.2018.05.003  

Showers, C., Ditzfeld, C., &amp; Zeigler-Hill, V. (2015). Self-concept structure and the quality of self-knowledge. ''Journal of Personality, 83''(5), 535–551. https://doi.org/10.1111/jopy.12130  

Sorjonen, K., Ingre, M., Melin, B., &amp; Nilsonne, G. (2024). Questioning the reciprocal effects model of academic self-concept and achievement: A reanalysis of a meta-analysis of longitudinal studies and a simulation. ''Sage Open, 14''(4). https://doi.org/10.1177/21582440241292826  

Török, L., &amp; Szabó, Z. (2018). The theory of self-handicapping: Forms, influencing factors and measurement. ''Ceskoslovenska Psychologie, 62''(2), 173–188. https://www.researchgate.net/publication/324913710_The_theory_of_self-handicapping_forms_influencing_factors_and_measurement

Wang, L., Cui, Y., Wang, X., Wang, J., Du, K., &amp; Luo, Z. (2021). Regulatory focus, motivation, and their relationship with creativity among adolescents. ''Frontiers in Psychology, 12'', Article 666071. https://doi.org/10.3389/fpsyg.2021.666071

Wehrle, K., &amp; Fasbender, U. (2018). Self-concept. In V. Zeigler-Hill &amp; T. Shackelford (Eds.), ''Encyclopedia of personality and individual differences'' (pp. 1–5). Springer. https://doi.org/10.1007/978-3-319-28099-8_2001-1  

Weiner, B. (1985). An attributional theory of achievement motivation and emotion. ''Psychological Review, 92''(4), 548–573. https://doi.org/10.1037/0033-295X.92.4.548  

Yip, L., Thomas, E. F., Amiot, C., Louis, W., &amp; McGarty, C. (2024). Autonomous motives foster sustained commitment to action: Integrating self-determination theory and the social identity approach. ''Personality and Social Psychology Bulletin, 50''(5), 750–765. https://doi.org/10.1177/01461672221148396  

}}

== External links ==
* [https://rickhanson.com/being-well-podcast-self-concept-the-secret-to-changing-who-you-are/ Self-concept: The secret to changing WHO you are] (Being Well Podcast)
* [https://www.youtube.com/watch?v=Nck7lP-6C2g Unlocking success: The power of self-efficacy and self-concept]  (TEDx Talks)
* [https://www.ted.com/talks/anil_ananthaswamy_where_does_your_sense_of_self_come_from_a_scientific_look Where does your sense of self come from? A scientific look] (TEDx Talks)

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== Overview ==
__TOC__
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[[File:Passeio de Buggy no Parque das Dunas de Genipabu, RN - 2.jpg| |thumb|right|150px| '''Figure 1'''. Teenagers Dangerously Driving]]

;Scenario

It is Friday night, and 16-year-old Mia is out with a group of friends. Someone suggests taking the family car for a late-night drive. Mia knows she does not have permission to drive, and knows that driving without a licence and with multiple people in the car could be dangerous. For a moment, she considers saying no. Her friends are excited, encouraging her, making the idea of doing something spontaneous and slightly dangerous feel thrilling. The idea of consequences seems distant and Mia eventually agrees to take the car.
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[[Adolescence]] is a developmental period characterised by increased  [https://www.sciencedirect.com/topics/immunology-and-microbiology/sensation-seeking sensation-seeking]  and risk-taking behaviours (Duell et al., 2018; Steinberg, 2007). Young people may be more likely to engage in behaviours that provide immediate rewards, such as experimenting with substances, risky driving (see figure 1), or seeking social approval, despite potential long-term consequences. Understanding why these behaviours increase during adolescence matters because risk-taking can contribute to negative health, social, and educational outcomes, while some exploration and novelty-seeking are also a normal part of development. One influential explanation is Steinberg's [https://pmc.ncbi.nlm.nih.gov/articles/PMC2396566/ Dual Systems Model], which proposes that adolescent risk-taking results from the interaction between a rapidly developing socioemotional reward system and a more gradually developing cognitive-control system (Steinberg, 2008). Similarly, the Maturational Imbalance Model suggests that reward-related regions become increasingly sensitive during adolescence before the brain systems responsible for regulating impulses and considering future consequences are fully mature (Casey et al., 2008). These theories suggest that adolescents do not lack self-control; rather, their developing reward and control systems can make immediate rewards particularly difficult to resist. Behavioural research indicates that sensation-seeking increases during adolescence, while impulse control develops more gradually (Steinberg et al., 2008). Other research has also shown that peers can increase adolescents' reward-related brain activity and risk-taking, highlighting the importance of social context (Chein et al., 2011). [[Psychological science]] therefore helps explain adolescent risk-taking by examining how reward sensitivity, cognitive control, impulsivity and social influences interact during brain development. Combining developmental theories with behavioural and neuroscience research provides a more comprehensive understanding of why adolescents may be particularly sensitive to rewarding experiences and how this can influence risky behaviours. 

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'''💡 Focus Questions''' 

* How does the reward-circuit maturation change the way adolescents respond to rewarding experiences? 
* How does increased reward sensitivity influence sensation-seeking? 
* How does the interaction between reward sensitivity and developing cognitive control influence risky behaviour? 
* How do social and environmental factors affect adolescents' reward processing and risk-taking behaviours? 
* When can sensation-seeking support positive development, and what factors increase the likelihood of harmful risk-taking? 
* How well do psychological theories and research explain the relationship between reward-system development and adolescent risk-taking? 

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==Adolescent risk-taking: the developmental problem ==

=== What is adolescent risk-taking? ===
Adolescent risk-taking refers to behaviour where there is some uncertainty regarding the possible outcome and the potential costs/rewards associated with an individual's physical, economic or psychological well-being (Trimpop, 2008). Adolescence, which is usually defined as the age of 10-19, represents a distinct developmental phase due to the extensive biological, psychological, and neurological changes occurring within an individual during this time (World Health Organisation, 2026). The alterations in an individual's brain sensitivity and responsiveness during adolescence can impact how they evaluate emotional responses to reward-related stimuli and the evaluation of the potential consequences of their actions (Jaworska &amp; MacQueen, 2015). Steinberg's Dual Systems Model explains that adolescent risk-taking results from the interaction of a developing socio-emotional system and a cognitive control system. As such, it is believed that adolescents are likely to be especially motivated to seek out exciting or immediately rewarding experiences, even if these experiences pose risks. For example, going on risky hikes would thrill adolescents and could pose as an opportunity for them to show off their braveness (see figure 2). Risk-taking is not necessarily negative. it can facilitate the formation of identity, independence, exploration, and the acquisition of real-world decision-making abilities. 
[[File:Gseng cliff 20200622.jpg|thumb|Figure 2. It Would Be Incredibly Risky To Stand On The Edge Of This Cliff]]
Therefore, understanding adolescent risk-taking is important so that parents, educators, and other professionals working with adolescents have the knowledge necessary to assist adolescents in pursuing constructive opportunities and reducing their exposure to behaviours that could cause harm. In Australia, adolescent well-being is also a major concern, with recent claims of increasing rates of suicidal ideation and attempts among adolescents, suggesting the need for evidence-based approaches to providing support to adolescents. Suicidal ideation and attempts are not equivalent to risk-taking and the relationship between them needs further investigation. 

Ultimately, an understanding of the developmental processes involved in risk-taking will enable us to develop healthier outcomes for adolescents while recognising adolescence as a period of both vulnerability and opportunity.

=== Why does reward matter? ===
Adolescence is a time of rapid developmental change in reward processing and emotional reactivity that makes rewarding, pleasurable, and socially-relevant experiences extremely attractive to adolescents (Spear, 2011). Sensitivity to reward refers to the degree to which an individual will respond to positive outcomes. Increased sensitivity to reward can contribute to risky decision-making when the short-term benefits of a behaviour, outweigh the potential long-term costs. Research conducted by Chein et al., (2011) demonstrated that adolescents took larger risks during a simulated driving task while their peers were observing them, and also had increased activity in brain areas associated with reward. Similarly, O'Brien et al., (2011) examined how social cues affected reward preferences in late adolescents ages 18-20, and found that social observation significantly impacted preferred rewards for immediate gratification. These findings collectively support the idea that reward sensitivity interacts with social influences to determine adolescent decision-making. If adolescents perceive immediate rewards to be more appealing than delayed ones, they are likely to engage in behaviours that provide them with a quick thrill without regard to the possible negative outcomes. The fact that adolescents are capable of evaluating the potential consequences of their actions is evident, however, the extent to which immediate rewards affects adolescent decision-making, varies based upon the individual and the circumstances. 

Therefore, understanding how reward sensitivity interacts with sensation-seeking, impulsivity and social context represents a critical component of understanding adolescent risk-taking behaviour. 

== The adolescent brain and reward-circuit development ==

=== Development of the adolescent brain ===
Adolescents experience substantial neural maturation during adolescence, especially with respect to those areas of the brain that regulate emotions, make decisions, and control impulses. The prefrontal cortex, which aids adolescents in thinking ahead, inhibits impulses and weighs the implications of their actions, will continue to mature until they reach adulthood (Casey et al., 2008). Additionally, maturation of the reward and emotional systems may contribute to adolescents' pursuit of instant gratification. According to the Dual Systems Model, because the reward and emotional systems are developing at different rates than the prefrontal cortex, adolescents may be more inclined to pursue rewards without considering the potential negative effects on their future. 

=== Reward-circuit maturation ===
The brains reward system is composed of several areas, including the ventral striatum which helps to create and process rewards. The brains ability to anticipate rewards, learn new behaviours to obtain them and motivate us to seek out those rewards, are all influenced by dopamine. Adolescents have developmentally immature reward systems that allow them to find novel, exciting and immediate rewards more appealing than adults. Crone and Dahl (2016) point out that being able to respond to rewards can be beneficial for adolescents in developing their exploratory skills, learning abilities, and social skills. Thus, while there is evidence that maturation of the reward system contributes to risk-taking, the effect will depend upon the interaction between an individuals level of reward sensitivity, their ability to regulate their behaviour through cognitive controls and the environment they live in. 

=== What does the research show? ===
Neuroimaging studies provide evidence that adolescents can show heightened responses to rewarding and emotionally significant cues. For example, Sommerville et al. (2010) examined developmental changes In response to appetitive and emotionally significant stimuli, highlighting how sensitivity to these cues can influence behaviour during adolescence. The results of their study indicate that adolescents' reactions to rewarding experiences can be very motivational at this stage of neural maturation. However, their reactions will depend upon the specific type of reward and the context in which it occurs. In general, this research provides a theoretical basis for why the maturation rates of reward sensitivity and behavioural control appear to differ among adolescents, which may help to explain some of the risk-taking behaviours observed in adolescence. &lt;quiz display=simple&gt;
{Which brain region is most closely associated with reward processing during adolescence?
|type=&quot;()&quot;}
+ ventral striatum.
- Cerebellum.
- Medulla.
-Occipital cortex.
&lt;/quiz&gt;

&lt;quiz display=simple&gt;
{What role does dopamine play in adolescent reward processing?
|type=&quot;()&quot;}
- It is responsible exclusively for cognitive control.
- It prevents adolescents from responding to rewards.
+ It contributes to motivation and sensitivity to rewarding experiences 
-It eliminates sensation-seeking.
&lt;/quiz&gt;

== Reward sensitivity, sensation-seeking and impulsivity ==

=== Reward sensitivity and adolescent sensation-seeking ===
Sensation-seeking describes individuals' tendencies to seek out new, stimulating and exciting experiences. Impulsivity is characterised by an individuals' inability to consider the potential consequences of their actions before taking action. Adolescent development includes neurological changes in how we process rewards which may contribute to the increased appeal of novel and immediately rewarding experiences. Dopamine is a neurotransmitter that has been linked to motivation, reward learning and predicting rewards. As such, adolescent developmental changes in reward-based neural circuitry can affect adolescents' behaviour (Galvan, 2010). Steinberg et al., (2008) discovered that sensation-seeking and impulsivity develop at different rates. This suggests that while adolescents may have a desire for exciting experiences, this doesn't mean that they will struggle with self-control. Crone &amp; Dahl (2016) further state that an increased sensitivity to both social and rewarding experiences may facilitate exploratory behaviours, learning and flexible goal setting. Therefore, sensation-seeking is not necessarily bad; the impacts will depend upon the type of experiences adolescents choose to participate in and the environments in which adolescents make these choices. 

=== Reward, cognitive-control and impulsive behaviour ===
Reward sensitivity develops during adolescence and is associated with the emergence of risk-taking behaviours (Steinberg, 2008). In addition, cognitive-control processes develop as adolescents age and these processes have been found to influence how they make decisions. According to Steinberg's Dual Systems Model, adolescent risk-taking can emerge from the interaction between a developing socioemotional system, which increases sensitivity to rewarding experiences and a cognitive-control system that develops more slowly. A similar idea has been proposed as the Maturational Imbalance Model (Casey et al., 2008) This model suggests that differences in the development of reward-related processes and cognitive-control may increase vulnerability to impulsive behaviour. Both models provide insight into why immediate rewards may at times outweigh consideration of long-term consequences, especially when adolescents are experiencing high levels of emotional stimulation. 

=== Social context and risk-taking ===
Evidence from real-world driving is consistent with the idea that peers amplify the reward value of risky choices. In a naturalistic study that monitored novice teenage drivers, risky driving was lower when an adult was in the car and higher among teens who reported having more risk-taking friends (Simons-Morton et al., 2011). This extends laboratory findings that peer presence increases reward-related brain activity and risk-taking (Chein et al., 2011). In Australia, young Queensland learner and provisional drivers described how rewards and punishments from friends, parents and police shaped their risky driving decisions, with drivers varying in how much they resisted their friends' influence (Scott-Parker et al., 2012). Together, these findings suggest that peer approval acts as a powerful social reward that can heighten sensation-seeking and impulsive choices, although its effect depends on the norms of the peer group and on individual differences in reward sensitivity.

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💻 What is the difference between sensation-seeking and impulse? 

'''Sensation-seeking''' is the active pursuit of novelty, thrills, and high intensity experiences, whereas '''impulsivity'''  is a lack of planning, reflection, and self-control that leads to rapid, uninhibited decision-making.
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== Implications for understanding adolescent risk-taking ==
=== Why are social rewards important? ===
Peer approval, social acceptance and status may become increasingly rewarding during adolescence as young people establish their identity, relationships and personal goals. The socially meaningful experiences during this period can trigger rewards that support motivation for behaviours that are socially approved by peers (Crone &amp; Dahl, 2012). 

=== Peer influence and reward processing ===
Evidence suggests that adolescents take increased risks during simulated driving tasks and peer monitoring is perceived to be occurring; this also correlates with increased activation in the brain areas involved in reward processing (Chein et al., 2011). Real-world driving studies demonstrate similar results. Simons-Morton et al. (2011) showed that the amount of risky driving by novice teen drivers was reduced if an adult was present, and the number of risky driving friends a driver had, correlated positively with the level of risky driving exhibited. In addition, Scott-Parker et al. (2012) examined the impact of peer groups, parental figures and law enforcement on young QLD learners and provisional drivers' risky driving decision-making processes, demonstrating differences in how adolescents respond to various types of social influences. 

=== When does reward-driven behaviour become risky? ===
When an adolescent is exposed to social environments that provide high levels of emotional stimulation through immediate rewards, their tendency towards sensation-seeking and/or impulsive behaviours may be particularly dangerous. In such situations, the immediate rewards of these behaviours may take precedence over a consideration of potential negative outcomes. However, adolescents are not all alike in how they will respond to social and reward cues. There are individual differences among adolescent regarding their sensitivity to rewards, ability to control themselves, personality traits, and past social experiences that can make them more or less vulnerable to being influenced by peers (Shulman et al., 2016; Kwon &amp; Telzer, 2022). 

Therefore, it is the combination of an adolescents increased desire for social approval and their exposure to peer groups with risky norms and little regard for long-term consequences, as opposed to simply seeking peer approval, that makes reward-driven behaviour more concerning. 

=== Psychological implications ===
It is important to note that a heightened level of reward sensitivity in teenagers does not reflect an underdeveloped brain. Romer et al. (2017) suggest that the tendency for adolescents to seek out exciting experiences may be better understood as part of a process of exploration; they have limited life experience and opportunity to learn from their experiences. Additionally, seeking out new experiences can provide teenagers with the opportunity to gain additional skills, increase their self-confidence and improve their decision-making abilities. An example would be when a teenager joins a high school football team, offers their opinion in class or creates new friendships. These can all positively affect an adolescent's well-being and growth. Duell and Steinberg (2019) emphasise the need to distinguish between risky behaviours that could potentially harm a teenager and those that create positive developmental opportunities. similarly, there is evidence that reward-related brain activity can also lead to positive outcomes. Telzer (2016) demonstrated that adolescents who demonstrated higher levels of activity in the ventral striatum while making prosocial decisions showed reduced levels of risk taking over time. In summary, reward sensitivity can lead to both positive and negative behaviours depending upon the circumstances and goals involved. 

'''Practical example: Positive risk-taking'''

Imagine a teenager who enjoys excitement and trying new experiences. Rather than engaging in dangerous driving to impress friends, they might choose to participate in a challenging sport, join a debating competition, or learn a new skill. These activities can provide excitement, social recognition, and a sense of achievement without the same level of potential harm. This illustrates how sensation-seeking can support confidence, independence, and personal development when adolescents have opportunities to take constructive risks (Duell &amp; Steinberg, 2019).

Understanding reward sensitivity helps explain why the same adolescent may behave differently depending on the rewards, emotions, and social pressures present in a situation. Interventions can redirect reward-seeking by providing adolescents with opportunities to experience excitement, achievement, independence, and social recognition through constructive activities such as sport or creative pursuits. Yeager et al. (2018) examined how adolescent sensitivity to social status and respect could inform interventions, supporting the importance of considering adolescents' social motivations when designing approaches to behaviour change. Much research supports the Dual Systems Model, suggesting that both reward sensitivity and cognitive control develop at varying rates throughout adolescence, however, the model is not an exhaustive explanation of adolescent risk taking (Shulman et al., 2016). In conclusion, understanding the role of reward sensitivity in explaining adolescent behaviour can inform interventions that help adolescents make safer decisions while promoting healthy developmental processes.

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Quick revision: 

🧭 Exploration: Seeking new experiences is a normal part of adolescent development 

🏗️ Development: Risk-taking can build skills, confidence and independence 

🧩 Context: Reward sensitivity can lead to positive or negative outcomes depending on the situation.

🤝 Intervention: Redirect reward-seeking towards constructive activities 

🧠 Theory: The Dual Systems Model helps explain adolescent risk-taking, but it is not a complete explanation. 
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==Conclusion==
Adolescents take risks due to the interactions of their developing reward systems, cognitive controls, sensation-seeking and social contexts. Reward-system development may create a strong attraction to new, exciting, and immediately rewarding experiences. Cognitive-control development, on the other hand, affects how adolescents assess consequences and manage their own behaviour (Steinberg, 2008). Chein et al.,(2011) and Simons-Morton et al., (2011) have demonstrated that peer influence contributes to the risky decisions and behaviours, especially in driving situations. The Dual Systems Model offers a helpful framework for understanding adolescent risk-taking, however, it does not provide a full explanation, as individual differences, emotional states and environmental factors also influence adolescents' behaviour. Reward-circuit maturation does not cause harmful behaviour; increased reward sensitivity can support exploration, learning, independence, and social development. Understanding these interactions helps explain adolescent sensation-seeking and impulsivity while informing interventions that promote safer decisions and positive development. Ultimately, reward-circuit maturation influences adolescent sensation-seeking and impulsive behaviours by increasing the motivational value of exciting, novel and immediately rewarding experiences, including peer approval and social acceptance. 

==See also==

*[[Behaviourism]] (Wikiversity)
*[[wikipedia:Dual_systems_model|Dual systems model]] (Wikipedia)
*[[Motivation and emotion/Book/2011/Peer influence in adolescence|Peer influence in adolescence]] (Book chapter, 2011)
*[[Influence and Persuasion|Peer pressure]]  (Wikiversity)
*[[Motivation and emotion/Book/2024/Adverse childhood experiences and risk-taking motivation|Risk-taking motivation]] (Book chapter, 2024)
==References==
{{Hanging indent|1=

Australian Institute of Family Studies. (2025, August 19). ''One-third of teens experience suicidal thoughts and behaviours''. Growing up in Australia. https://aifs.gov.au/growing-australia/media/one-third-teens-experience-suicidal-thoughts-and-behaviours

Casey, B. J., Jones, R. M., &amp; Hare, T. A. (2008). The adolescent brain. ''Annals of the New York Academy of Sciences, 1124''(1), 111–126. https://doi.org/10.1196/annals.1440.010

Casey, B. J., Getz, S., &amp; Galvan, A. (2008). The adolescent brain. Developmental review : DR, 28(1), 62–77. https://doi.org/10.1016/j.dr.2007.08.003

Castellanos-Ryan, N., &amp; Conrod, P. J. (2013). Personality and addiction processes. ''Principles of addiction: comprehensive addictive behaviours and disorders'', 211-224. https://doi.org/10.1016/B978-0-12-398336-7.00028-0

Chein, J., Albert, D., O'Brien, L., Uckert, K., &amp; Steinberg, L. (2011). Peers increase adolescent risk taking by enhancing activity in the brain's reward circuitry. ''Developmental Science, 14''(2), F1–F10. https://doi.org/10.1111/j.1467-7687.2010.01035.x

Crone, E. A., &amp; Dahl, R. E. (2012). Understanding adolescence as a period of social-affective engagement and goal flexibility. ''Nature reviews. Neuroscience, 13''(9), 636–650. https://doi.org/10.1038/nrn3313

Duell, N., &amp; Steinberg, L. (2019). Positive risk taking in adolescence. ''Child Development Perspectives, 13''(1), 48–52. https://doi.org/10.1111/cdep.12310

Duell, N., Steinberg, L., Icenogle, G., Chein, J., Chaudhary, N., Di Giunta, L., Dodge, K. A., Fanti, K. A., Lansford, J. E., Oburu, P., Pastorelli, C., Skinner, A. T., Sorbring, E., Tapanya, S., Uribe Tirado, L. M., Peña Alampay, L., Al-Hassan, S. M., Takash, H. M. S., Bacchini, D., &amp; Chang, L. (2018). Age patterns in risk taking across the world. ''Journal of Youth and Adolescence, 47''(5), 1052–1072. https://doi.org/10.1007/s10964-017-0752-y

Galván A. (2010). Neural plasticity of development and learning. ''Human brain mapping, 31''(6), 879–890. https://doi.org/10.1002/hbm.21029

Jaworska, N., &amp; MacQueen, G. (2015). Adolescence as a unique developmental period. ''Journal of psychiatry &amp; neuroscience : JPN, 40''(5), 291–293. https://doi.org/10.1503/jpn.150268

Kwon, SJ., Telzer, E.H. Social contextual risk taking in adolescence. ''Nat Rev Psychol 1'', 393–406 (2022). https://doi.org/10.1038/s44159-022-00060-0

Masten, S. V., Thomas, F. D., Korbelak, K. T., Peck, R. C., &amp; Blomberg, R. D. (2015). ''Meta-analysis of graduated driver licensing laws'' (Report No. DOT HS 812 211). National Highway Traffic Safety Administration. https://doi.org/10.21949/1525783

O'Brien, L., Albert, D., Chein, J., &amp; Steinberg, L. (2011). Adolescents prefer more immediate rewards when in the presence of their peers. ''Journal of Research on Adolescence, 21''(4), 747–753. https://doi.org/10.1111/j.1532-7795.2011.00738.x

Romer, D., Reyna, V. F., &amp; Satterthwaite, T. D. (2017). Beyond stereotypes of adolescent risk taking: Placing the adolescent brain in developmental context. ''Developmental Cognitive Neuroscience, 27'', 19–34. https://doi.org/10.1016/j.dcn.2017.07.007

Scott-Parker, B., Watson, B., King, M. J., &amp; Hyde, M. K. (2012). &quot;They're lunatics on the road&quot;: Exploring the normative influences of parents, friends, and police on young novices' risky driving decisions. ''Safety Science, 50''(9), 1917–1928. https://doi.org/10.1016/j.ssci.2012.05.014

Shulman, E. P., Smith, A. R., Silva, K., Icenogle, G., Duell, N., Chein, J., &amp; Steinberg, L. (2016). The dual systems model: Review, reappraisal, and reaffirmation. ''Developmental cognitive neuroscience, 17'', 103–117. https://doi.org/10.1016/j.dcn.2015.12.010

Simons-Morton, B., &amp; Ouimet, M. C. (2006). Parent involvement in novice teen driving: A review of the literature. ''Injury Prevention, 12''(Suppl 1), i30–i37. https://doi.org/10.1136/ip.2006.011569

Simons-Morton, B. G., Ouimet, M. C., Zhang, Z., Klauer, S. E., Lee, S. E., Wang, J., Chen, R., Albert, P., &amp; Dingus, T. A. (2011). The effect of passengers and risk-taking friends on risky driving and crashes/near crashes among novice teenagers. ''Journal of Adolescent Health, 49''(6), 587–593. https://doi.org/10.1016/j.jadohealth.2011.02.009

Somerville, L. H., Jones, R. M., &amp; Casey, B. J. (2010). A time of change: behavioral and neural correlates of adolescent sensitivity to appetitive and aversive environmental cues. ''Brain and cognition, 72''(1), 124–133. https://doi.org/10.1016/j.bandc.2009.07.003

Spear, L. P. (2011). Rewards, aversions and affect in adolescence: Emerging convergences across laboratory animal and human data. ''Developmental Cognitive Neuroscience, 1''(4), 390–403.https://doi.org/10.1016/j.dcn.2011.08.001

Steinberg, L. (2007). Risk taking in adolescence: New perspectives from brain and behavioral science. ''Current Directions in Psychological Science, 16''(2), 55–59. https://doi.org/10.1111/j.1467-8721.2007.00475.x

Steinberg, L. (2008). A social neuroscience perspective on adolescent risk-taking. ''Developmental Review, 28''(1), 78–106. https://doi.org/10.1016/j.dr.2007.08.002

Telzer, E. H. (2016). Dopaminergic reward sensitivity can promote adolescent health: A new perspective on the mechanism of ventral striatum activation. ''Developmental Cognitive Neuroscience, 17'', 57–67. https://doi.org/10.1016/j.dcn.2015.10.010

Wasserman, A. M., Mathias, C. W., Hill-Kapturczak, N., Karns-Wright, T. E., &amp; Dougherty, D. M. (2020). The Development of Impulsivity and Sensation Seeking: Associations with Substance Use among At-Risk Adolescents. ''Journal of research on adolescence : the official journal of the Society for Research on Adolescence, 30''(4), 1051–1066. https://doi.org/10.1111/jora.12579

Yeager, D. S., Dahl, R. E., &amp; Dweck, C. S. (2018). Why interventions to influence adolescent behavior often fail but could succeed. ''Perspectives on Psychological Science, 13''(1), 101–122. https://doi.org/10.1177/1745691617722620

}}

==External links==

*[https://youthrelationships.org/pages/adolescent-risk-behaviours Adolescent risk behaviours] (London family court clinic) 
*[https://www.youtube.com/watch?v=00BDx0bRalQ Speaking of psychology: understanding the teenage brain, with Eva Telzer, PhD] (American Psychological Association)
*[https://www.ted.com/talks/jennifer_pfeifer_the_surprising_science_of_adolescent_brains The surprising science of adolescent brains]   (TED talks)
*[https://www.abc.net.au/listen/programs/lifematters/risk-taking-in-teens-and-dylan-lewis-on-supporting-entertainers-/104340638 Risk taking in teens] (ABC listen) 
*[https://theconversation.com/of-course-parents-want-to-keep-tweens-and-teens-safe-heres-why-you-should-also-encourage-them-to-take-risks-289711 Why you should encourage teens to take risks] (The Conversation) 
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      <text bytes="30483" sha1="5e3sbip7cciwt6cffj1bs8b2a1tnb69" xml:space="preserve">{{title|Adolescent risk-taking and reward-system development:&lt;br&gt;How does reward circuit maturation influence adolescent sensation-seeking and impulsive behaviours?}}

== Overview ==
__TOC__
{{RoundBoxTop|theme=4}}
[[File:Passeio de Buggy no Parque das Dunas de Genipabu, RN - 2.jpg|thumb|right|150px| '''Figure 1'''. Teenagers driving dangerously]]

;Scenario

It is Friday night, and 16-year-old Mia is out with a group of friends. Someone suggests taking her family car for a late-night drive. Mia knows she does not have permission to drive, and knows that driving without a licence and with multiple people in the car could be dangerous. For a moment, she considers saying no. Her friends are excited, encouraging her, making the idea of doing something spontaneous and slightly dangerous feel thrilling. The idea of consequences seems distant and Mia eventually agrees to take the car.

{{RoundBoxBottom}}

[[Adolescence]] is a developmental period characterised by increased [https://www.sciencedirect.com/topics/immunology-and-microbiology/sensation-seeking sensation-seeking] and risk-taking behaviours (Duell et al., 2018; Steinberg, 2007). Young people may be more likely to engage in behaviours that provide immediate rewards, such as experimenting with substances, risky driving (see figure 1), or seeking social approval, despite potential long-term consequences. Understanding why these behaviours increase during adolescence matters because risk-taking can contribute to negative health, social, and educational outcomes, while some exploration and novelty-seeking are also a normal part of development.

One influential explanation is Steinberg's [https://pmc.ncbi.nlm.nih.gov/articles/PMC2396566/ Dual Systems Model], which proposes that adolescent risk-taking results from the interaction between a rapidly developing socioemotional reward system and a more gradually developing cognitive-control system (Steinberg, 2008). Similarly, the Maturational Imbalance Model suggests that reward-related regions become increasingly sensitive during adolescence before the brain systems responsible for regulating impulses and considering future consequences are fully mature (Casey et al., 2008). These theories suggest that adolescents do not lack self-control; rather, their developing reward and control systems can make immediate rewards particularly difficult to resist. Behavioural research indicates that sensation-seeking increases during adolescence, while impulse control develops more gradually (Steinberg et al., 2008). Other research has also shown that peers can increase adolescents' reward-related brain activity and risk-taking, highlighting the importance of social context (Chein et al., 2011). [[Psychological science]] therefore helps explain adolescent risk-taking by examining how reward sensitivity, cognitive control, impulsivity and social influences interact during brain development. Combining developmental theories with behavioural and neuroscience research provides a psychological understanding of why adolescents may be particularly sensitive to rewarding experiences and how this can influence risky behaviours.

{{RoundBoxTop|theme=4}}
'''💡 Focus Questions''' 

* How does the reward-circuit maturation change the way adolescents respond to rewarding experiences? 
* How does increased reward sensitivity influence sensation-seeking? 
* How does the interaction between reward sensitivity and developing cognitive control influence risky behaviour? 
* How do social and environmental factors affect adolescents' reward processing and risk-taking behaviours? 
* When can sensation-seeking support positive development, and what factors increase the likelihood of harmful risk-taking? 
* How well do psychological theories and research explain the relationship between reward-system development and adolescent risk-taking? 

{{RoundBoxBottom}}

==Adolescent risk-taking: the developmental problem ==
{{expand}}

=== What is adolescent risk-taking? ===
Adolescent risk-taking refers to behaviour where there is some uncertainty regarding the possible outcome and the potential costs/rewards associated with an individual's physical, economic or psychological well-being (Trimpop, 2008). Adolescence, which is usually defined as the age of 10-19 years, represents a distinct developmental phase due to the extensive biological, psychological, and neurological changes occurring within an individual during this time (World Health Organisation, 2026). The alterations in an individual's brain sensitivity and responsiveness during adolescence can impact how they evaluate emotional responses to reward-related stimuli and the evaluation of the potential consequences of their actions (Jaworska &amp; MacQueen, 2015). 

Steinberg's Dual Systems Model explains that adolescent risk-taking results from the interaction of a developing socio-emotional system and a cognitive control system. As such, it is believed that adolescents are likely to be especially motivated to seek out exciting or immediately rewarding experiences, even if these experiences pose risks. For example, going on risky hikes would thrill adolescents and could pose as an opportunity for them to show off their bravery (see Figure 2). Risk-taking is not necessarily negative; it can facilitate the formation of identity, independence, exploration, and the acquisition of real-world decision-making abilities.

[[File:Gseng cliff 20200622.jpg|thumb|'''Figure 2'''. It would be incredibly risky to stand on the edge of this cliff]]

Therefore, understanding adolescent risk-taking is important so that parents, educators, and other professionals working with adolescents have the knowledge necessary to assist adolescents in pursuing constructive opportunities and reducing their exposure to behaviours that could cause harm. In Australia, adolescent well-being is also a major concern, with recent claims of increasing rates of suicidal ideation and attempts among adolescents, suggesting the need for evidence-based approaches to providing support to adolescents {{f}}. Suicidal ideation and attempts are not equivalent to risk-taking and the relationship between them needs further investigation. 

Ultimately, an understanding of the developmental processes involved in risk-taking will enable us to develop healthier outcomes for adolescents while recognising adolescence as a period of both vulnerability and opportunity.

=== Why does reward matter? ===
Adolescence is a time of rapid developmental change in reward processing and emotional reactivity that makes rewarding, pleasurable, and socially-relevant experiences extremely attractive to adolescents (Spear, 2011). Sensitivity to reward refers to the degree to which an individual will respond to positive outcomes. Increased sensitivity to reward can contribute to risky decision-making when the short-term benefits of a behaviour, {{g}} outweigh the potential long-term costs. Research conducted by Chein et al., (2011) demonstrated that adolescents took larger risks during a simulated driving task while their peers were observing them, and also had increased activity in brain areas associated with reward.

Similarly, O'Brien et al., (2011) examined how social cues affected reward preferences in late adolescents aged 18-20 years, and found that social observation significantly impacted preferred rewards for immediate gratification. These findings collectively support the idea that reward sensitivity interacts with social influences to determine adolescent decision-making. If adolescents perceive immediate rewards to be more appealing than delayed ones, they are likely to engage in behaviours that provide them with a quick thrill without regard to the possible negative outcomes. The fact that adolescents are capable of evaluating the potential consequences of their actions is evident {{f}}, however, the extent to which immediate rewards affects adolescent decision-making, varies based upon the individual and the circumstances {{f}}. 

Therefore, understanding how reward sensitivity interacts with sensation-seeking, impulsivity and social context represents a critical component of understanding adolescent risk-taking behaviour. 

== The adolescent brain and reward-circuit development ==
{{expand}}

=== Development of the adolescent brain ===
Adolescents experience substantial neural maturation during adolescence, especially with respect to those areas of the brain that regulate emotions, make decisions, and control impulses {{f}}. The prefrontal cortex, which aids adolescents in thinking ahead, inhibits impulses and weighs the implications of their actions, will continue to mature until they reach adulthood (Casey et al., 2008). Additionally, maturation of the reward and emotional systems may contribute to adolescents' pursuit of instant gratification {{f}}. According to the Dual Systems Model, because the reward and emotional systems are developing at different rates than the prefrontal cortex, adolescents may be more inclined to pursue rewards without considering the potential negative effects on their future {{f}}. 

=== Reward-circuit maturation ===
The brains {{g}} reward system is composed of several areas, including the ventral striatum which helps to create and process rewards. The brains {{g}} ability to anticipate rewards, learn new behaviours to obtain them and motivate us to seek out those rewards, are all influenced by dopamine {{f}}. Adolescents have developmentally immature reward systems that allow them to find novel, exciting and immediate rewards more appealing than adults {{f}}. Crone and Dahl (2016) point out that being able to respond to rewards can be beneficial for adolescents in developing their exploratory skills, learning abilities, and social skills. Thus, while there is evidence {{f}} that maturation of the reward system contributes to risk-taking, the effect will depend upon the interaction between an individuals level of reward sensitivity, their ability to regulate their behaviour through cognitive controls and the environment they live in. 

=== What does the research show? ===
Neuroimaging studies {{f}} provide evidence that adolescents can show heightened responses to rewarding and emotionally significant cues. For example, Sommerville et al. (2010) examined {{how}} developmental changes in response to appetitive and emotionally significant stimuli, highlighting how sensitivity to these cues can influence behaviour during adolescence {{vague}}. The results of their study indicate that adolescents' reactions to rewarding experiences can be very motivational at this stage of neural maturation. However, their reactions will depend upon the specific type of reward and the context in which it occurs. In general, this research provides a theoretical basis for why the maturation rates of reward sensitivity and behavioural control appear to differ among adolescents, which may help to explain some of the risk-taking behaviours observed in adolescence.

&lt;quiz display=simple&gt;
{Which brain region is most closely associated with reward processing during adolescence?
|type=&quot;()&quot;}
+ ventral striatum
- cerebellum
- medulla
- occipital cortex
&lt;/quiz&gt;

&lt;quiz display=simple&gt;
{What role does dopamine play in adolescent reward processing?
|type=&quot;()&quot;}
- It is responsible exclusively for cognitive control.
- It prevents adolescents from responding to rewards.
+ It contributes to motivation and sensitivity to rewarding experiences 
-It eliminates sensation-seeking.
&lt;/quiz&gt;

== Reward sensitivity, sensation-seeking and impulsivity ==
{{expand}}

=== Reward sensitivity and adolescent sensation-seeking ===
Sensation-seeking describes individuals' tendencies to seek out new, stimulating and exciting experiences. Impulsivity is characterised by an individuals' inability to consider the potential consequences of their actions before taking action. Adolescent development includes neurological changes in how we process rewards which may contribute to the increased appeal of novel and immediately rewarding experiences {{f}}. Dopamine is a neurotransmitter that has been linked to motivation, reward learning and predicting rewards {{f}}. As such, adolescent developmental changes in reward-based neural circuitry can affect adolescents' behaviour (Galvan, 2010).

Steinberg et al., (2008) discovered that sensation-seeking and impulsivity develop at different rates. This suggests that while adolescents may have a desire for exciting experiences, this doesn't mean that they will struggle with self-control. Crone &amp; Dahl (2016) further state that an increased sensitivity to both social and rewarding experiences may facilitate exploratory behaviours, learning and flexible goal setting. Therefore, sensation-seeking is not necessarily bad; the impacts will depend upon the type of experiences adolescents choose to participate in and the environments in which adolescents make these choices. 

=== Reward, cognitive-control and impulsive behaviour ===
Reward sensitivity develops during adolescence and is associated with the emergence of risk-taking behaviours (Steinberg, 2008). In addition, cognitive-control processes develop as adolescents age and these processes have been found to influence how they make decisions. According to Steinberg's Dual Systems Model {{f}}, adolescent risk-taking can emerge from the interaction between a developing socioemotional system, which increases sensitivity to rewarding experiences, and a cognitive-control system that develops more slowly. A similar idea has been proposed as the Maturational Imbalance Model (Casey et al., 2008) This model suggests that differences in the development of reward-related processes and cognitive-control may increase vulnerability to impulsive behaviour. Both models provide insight into why immediate rewards may at times outweigh consideration of long-term consequences, especially when adolescents are experiencing high levels of emotional stimulation. 

=== Social context and risk-taking ===
Evidence from real-world driving is consistent with the idea that peers amplify the reward value of risky choices. In a naturalistic study that monitored novice teenage drivers {{where}}, risky driving was lower when an adult was in the car and higher among teens who reported having more risk-taking friends (Simons-Morton et al., 2011). This extends laboratory findings that peer presence increases reward-related brain activity and risk-taking (Chein et al., 2011). In Australia, young Queensland learner and provisional drivers described how rewards and punishments from friends, parents and police shaped their risky driving decisions, with drivers varying in how much they resisted their friends' influence (Scott-Parker et al., 2012). Together, these findings suggest that peer approval acts as a powerful social reward that can heighten sensation-seeking and impulsive choices, although its effect depends on the norms of the peer group and on individual differences in reward sensitivity.

{{RoundBoxTop|theme=4}}
💻 What is the difference between sensation-seeking and impulsivity? 

'''Sensation-seeking''' is the active pursuit of novelty, thrills, and high intensity experiences, whereas '''impulsivity'''  is a lack of planning, reflection, and self-control that leads to rapid, uninhibited decision-making.
{{RoundBoxBottom}}

== Implications for understanding adolescent risk-taking ==
{{expand}}

=== Why are social rewards important? ===
Peer approval, social acceptance and status may become increasingly rewarding during adolescence as young people establish their identity, relationships and personal goals. The socially meaningful experiences during this period can trigger rewards that support motivation for behaviours that are socially approved by peers (Crone &amp; Dahl, 2012). 

=== Peer influence and reward processing ===
Evidence {{f}} suggests that adolescents take increased risks during simulated driving tasks and peer monitoring is perceived to be occurring; this also correlates with increased activation in the brain areas involved in reward processing (Chein et al., 2011). Real-world driving studies demonstrate similar results. Simons-Morton et al. (2011) showed that the amount of risky driving by novice teen drivers was reduced if an adult was present, and the number of risky driving friends a driver had, correlated positively with the level of risky driving exhibited. In addition, Scott-Parker et al. (2012) examined the impact of peer groups, parental figures and law enforcement on young QLD learners and provisional drivers' risky driving decision-making processes, demonstrating differences in how adolescents respond to various types of social influences. {{ic|seems repetitive of previous paragraph - consider removing/integrating}}

=== When does reward-driven behaviour become risky? ===
When an adolescent is exposed to social environments that provide high levels of emotional stimulation through immediate rewards, their tendency towards sensation-seeking and/or impulsive behaviours may be particularly dangerous {{f}}. In such situations, the immediate rewards of these behaviours may take precedence over a consideration of potential negative outcomes {{f}}. However, adolescents are not all alike in how they will respond to social and reward cues {{f}}. There are individual differences among adolescent regarding their sensitivity to rewards, ability to control themselves, personality traits, and past social experiences that can make them more or less vulnerable to being influenced by peers (Shulman et al., 2016; Kwon &amp; Telzer, 2022). 

Therefore, it is the combination of an adolescents {{g}} increased desire for social approval and their exposure to peer groups with risky norms and little regard for long-term consequences, as opposed to simply seeking peer approval, that makes reward-driven behaviour more concerning. 

=== Psychological implications ===
It is important to note that a heightened level of reward sensitivity in teenagers does not reflect an underdeveloped brain. Romer et al. (2017) suggest that the tendency for adolescents to seek out exciting experiences may be better understood as part of a process of exploration; they have limited life experience and opportunity to learn from their experiences. Additionally, seeking out new experiences can provide teenagers with the opportunity to gain additional skills, increase their self-confidence and improve their decision-making abilities. An example would be when a teenager joins a high school football team, offers their opinion in class or creates new friendships. These can all positively affect an adolescent's well-being and growth. Duell and Steinberg (2019) emphasise the need to distinguish between risky behaviours that could potentially harm a teenager and those that create positive developmental opportunities. similarly, there is evidence that reward-related brain activity can also lead to positive outcomes. Telzer (2016) demonstrated that adolescents who demonstrated higher levels of activity in the ventral striatum while making prosocial decisions showed reduced levels of risk taking over time {{explain}}. In summary, reward sensitivity can lead to both positive and negative behaviours depending upon the circumstances and goals involved. 

{{RoundBoxTop|theme=3}}
'''Practical example: Positive risk-taking'''

Imagine a teenager who enjoys excitement and trying new experiences. Rather than engaging in dangerous driving to impress friends, they might choose to participate in a challenging sport, join a debating competition, or learn a new skill. These activities can provide excitement, social recognition, and a sense of achievement without the same level of potential harm. This illustrates how sensation-seeking can support confidence, independence, and personal development when adolescents have opportunities to take constructive risks (Duell &amp; Steinberg, 2019).
{{RoundBoxBottom}}

Understanding reward sensitivity helps explain why the same adolescent may behave differently depending on the rewards, emotions, and social pressures present in a situation. Interventions can redirect reward-seeking by providing adolescents with opportunities to experience excitement, achievement, independence, and social recognition through constructive activities such as sport or creative pursuits. Yeager et al. (2018) examined how adolescent sensitivity to social status and respect could inform interventions, supporting the importance of considering adolescents' social motivations when designing approaches to behaviour change. Much research supports the Dual Systems Model, suggesting that both reward sensitivity and cognitive control develop at varying rates throughout adolescence, however, the model is not an exhaustive explanation of adolescent risk taking (Shulman et al., 2016).

{{RoundBoxTop|theme=4}}
Quick revision: 

🧭 Exploration: Seeking new experiences is a normal part of adolescent development 

🏗️ Development: Risk-taking can build skills, confidence and independence 

🧩 Context: Reward sensitivity can lead to positive or negative outcomes depending on the situation.

🤝 Intervention: Redirect reward-seeking towards constructive activities 

🧠 Theory: The Dual Systems Model helps explain adolescent risk-taking, but it is not a complete explanation. 
{{RoundBoxBottom}}

==Conclusion==
Understanding the role of reward sensitivity in explaining adolescent behaviour can inform interventions that help adolescents make safer decisions while promoting healthy developmental processes. Adolescents take risks due to the interactions of their developing reward systems, cognitive controls, sensation-seeking and social contexts.

Reward-system development may create a strong attraction to new, exciting, and immediately rewarding experiences. Cognitive-control development, on the other hand, affects how adolescents assess consequences and manage their own behaviour (Steinberg, 2008). C

hein et al.,(2011) and Simons-Morton et al., (2011) have demonstrated that peer influence contributes to the risky decisions and behaviours, especially in driving situations. The Dual Systems Model offers a helpful framework for understanding adolescent risk-taking, however, it does not provide a full explanation, as individual differences, emotional states and environmental factors also influence adolescents' behaviour.

Reward-circuit maturation does not cause harmful behaviour; increased reward sensitivity can support exploration, learning, independence, and social development. Understanding these interactions helps explain adolescent sensation-seeking and impulsivity while informing interventions that promote safer decisions and positive development. Ultimately, reward-circuit maturation influences adolescent sensation-seeking and impulsive behaviours by increasing the motivational value of exciting, novel and immediately rewarding experiences, including peer approval and social acceptance. 

==See also==
*[[Behaviourism]] (Wikiversity)
*[[wikipedia:Dual_systems_model|Dual systems model]] (Wikipedia)
*[[Motivation and emotion/Book/2011/Peer influence in adolescence|Peer influence in adolescence]] (Book chapter, 2011)
*[[Influence and Persuasion|Peer pressure]]  (Wikiversity)
*[[Motivation and emotion/Book/2024/Adverse childhood experiences and risk-taking motivation|Risk-taking motivation]] (Book chapter, 2024)

==References==
{{Hanging indent|1=

Australian Institute of Family Studies. (2025, August 19). ''One-third of teens experience suicidal thoughts and behaviours''. Growing up in Australia. https://aifs.gov.au/growing-australia/media/one-third-teens-experience-suicidal-thoughts-and-behaviours

Casey, B. J., Jones, R. M., &amp; Hare, T. A. (2008). The adolescent brain. ''Annals of the New York Academy of Sciences, 1124''(1), 111–126. https://doi.org/10.1196/annals.1440.010

Casey, B. J., Getz, S., &amp; Galvan, A. (2008). The adolescent brain. Developmental review : DR, 28(1), 62–77. https://doi.org/10.1016/j.dr.2007.08.003

Castellanos-Ryan, N., &amp; Conrod, P. J. (2013). Personality and addiction processes. ''Principles of addiction: comprehensive addictive behaviours and disorders'', 211-224. https://doi.org/10.1016/B978-0-12-398336-7.00028-0

Chein, J., Albert, D., O'Brien, L., Uckert, K., &amp; Steinberg, L. (2011). Peers increase adolescent risk taking by enhancing activity in the brain's reward circuitry. ''Developmental Science, 14''(2), F1–F10. https://doi.org/10.1111/j.1467-7687.2010.01035.x

Crone, E. A., &amp; Dahl, R. E. (2012). Understanding adolescence as a period of social-affective engagement and goal flexibility. ''Nature reviews. Neuroscience, 13''(9), 636–650. https://doi.org/10.1038/nrn3313

Duell, N., &amp; Steinberg, L. (2019). Positive risk taking in adolescence. ''Child Development Perspectives, 13''(1), 48–52. https://doi.org/10.1111/cdep.12310

Duell, N., Steinberg, L., Icenogle, G., Chein, J., Chaudhary, N., Di Giunta, L., Dodge, K. A., Fanti, K. A., Lansford, J. E., Oburu, P., Pastorelli, C., Skinner, A. T., Sorbring, E., Tapanya, S., Uribe Tirado, L. M., Peña Alampay, L., Al-Hassan, S. M., Takash, H. M. S., Bacchini, D., &amp; Chang, L. (2018). Age patterns in risk taking across the world. ''Journal of Youth and Adolescence, 47''(5), 1052–1072. https://doi.org/10.1007/s10964-017-0752-y

Galván A. (2010). Neural plasticity of development and learning. ''Human brain mapping, 31''(6), 879–890. https://doi.org/10.1002/hbm.21029

Jaworska, N., &amp; MacQueen, G. (2015). Adolescence as a unique developmental period. ''Journal of psychiatry &amp; neuroscience : JPN, 40''(5), 291–293. https://doi.org/10.1503/jpn.150268

Kwon, SJ., Telzer, E.H. Social contextual risk taking in adolescence. ''Nat Rev Psychol 1'', 393–406 (2022). https://doi.org/10.1038/s44159-022-00060-0

Masten, S. V., Thomas, F. D., Korbelak, K. T., Peck, R. C., &amp; Blomberg, R. D. (2015). ''Meta-analysis of graduated driver licensing laws'' (Report No. DOT HS 812 211). National Highway Traffic Safety Administration. https://doi.org/10.21949/1525783

O'Brien, L., Albert, D., Chein, J., &amp; Steinberg, L. (2011). Adolescents prefer more immediate rewards when in the presence of their peers. ''Journal of Research on Adolescence, 21''(4), 747–753. https://doi.org/10.1111/j.1532-7795.2011.00738.x

Romer, D., Reyna, V. F., &amp; Satterthwaite, T. D. (2017). Beyond stereotypes of adolescent risk taking: Placing the adolescent brain in developmental context. ''Developmental Cognitive Neuroscience, 27'', 19–34. https://doi.org/10.1016/j.dcn.2017.07.007

Scott-Parker, B., Watson, B., King, M. J., &amp; Hyde, M. K. (2012). &quot;They're lunatics on the road&quot;: Exploring the normative influences of parents, friends, and police on young novices' risky driving decisions. ''Safety Science, 50''(9), 1917–1928. https://doi.org/10.1016/j.ssci.2012.05.014

Shulman, E. P., Smith, A. R., Silva, K., Icenogle, G., Duell, N., Chein, J., &amp; Steinberg, L. (2016). The dual systems model: Review, reappraisal, and reaffirmation. ''Developmental cognitive neuroscience, 17'', 103–117. https://doi.org/10.1016/j.dcn.2015.12.010

Simons-Morton, B., &amp; Ouimet, M. C. (2006). Parent involvement in novice teen driving: A review of the literature. ''Injury Prevention, 12''(Suppl 1), i30–i37. https://doi.org/10.1136/ip.2006.011569

Simons-Morton, B. G., Ouimet, M. C., Zhang, Z., Klauer, S. E., Lee, S. E., Wang, J., Chen, R., Albert, P., &amp; Dingus, T. A. (2011). The effect of passengers and risk-taking friends on risky driving and crashes/near crashes among novice teenagers. ''Journal of Adolescent Health, 49''(6), 587–593. https://doi.org/10.1016/j.jadohealth.2011.02.009

Somerville, L. H., Jones, R. M., &amp; Casey, B. J. (2010). A time of change: behavioral and neural correlates of adolescent sensitivity to appetitive and aversive environmental cues. ''Brain and cognition, 72''(1), 124–133. https://doi.org/10.1016/j.bandc.2009.07.003

Spear, L. P. (2011). Rewards, aversions and affect in adolescence: Emerging convergences across laboratory animal and human data. ''Developmental Cognitive Neuroscience, 1''(4), 390–403.https://doi.org/10.1016/j.dcn.2011.08.001

Steinberg, L. (2007). Risk taking in adolescence: New perspectives from brain and behavioral science. ''Current Directions in Psychological Science, 16''(2), 55–59. https://doi.org/10.1111/j.1467-8721.2007.00475.x

Steinberg, L. (2008). A social neuroscience perspective on adolescent risk-taking. ''Developmental Review, 28''(1), 78–106. https://doi.org/10.1016/j.dr.2007.08.002

Telzer, E. H. (2016). Dopaminergic reward sensitivity can promote adolescent health: A new perspective on the mechanism of ventral striatum activation. ''Developmental Cognitive Neuroscience, 17'', 57–67. https://doi.org/10.1016/j.dcn.2015.10.010

Wasserman, A. M., Mathias, C. W., Hill-Kapturczak, N., Karns-Wright, T. E., &amp; Dougherty, D. M. (2020). The Development of Impulsivity and Sensation Seeking: Associations with Substance Use among At-Risk Adolescents. ''Journal of research on adolescence : the official journal of the Society for Research on Adolescence, 30''(4), 1051–1066. https://doi.org/10.1111/jora.12579

Yeager, D. S., Dahl, R. E., &amp; Dweck, C. S. (2018). Why interventions to influence adolescent behavior often fail but could succeed. ''Perspectives on Psychological Science, 13''(1), 101–122. https://doi.org/10.1177/1745691617722620

}}

==External links==
*[https://youthrelationships.org/pages/adolescent-risk-behaviours Adolescent risk behaviours] (London family court clinic) 
*[https://www.youtube.com/watch?v=00BDx0bRalQ Speaking of psychology: understanding the teenage brain, with Eva Telzer, PhD] (American Psychological Association)
*[https://www.ted.com/talks/jennifer_pfeifer_the_surprising_science_of_adolescent_brains The surprising science of adolescent brains]   (TED talks)
*[https://www.abc.net.au/listen/programs/lifematters/risk-taking-in-teens-and-dylan-lewis-on-supporting-entertainers-/104340638 Risk taking in teens] (ABC listen) 
*[https://theconversation.com/of-course-parents-want-to-keep-tweens-and-teens-safe-heres-why-you-should-also-encourage-them-to-take-risks-289711 Why you should encourage teens to take risks] (The Conversation) 

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[[Category:Motivation and emotion/Book/Adolescence]]
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__TOC__

==Overview==
This book chapter will be addressing the role that melatonin plays in seasonal mood changes through, seasonal changes, light pattern changes within seasonal changes as well as the correlation of melatonin production within these conditions.{{RoundBoxTop|theme=3}}
[[File:A picture is worth a thousand words.jpg|right|thumb|150px|'''Figure 1'''. Use a captioned image to illustrate the scenario]]

; Case study: Seasonal levels of melatonin near the Arctic Circle

Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study{{fact}} was conducted on why this would be the case. 

Circumpolar environments have been known for its changes in day night cycles as well as its temperature. 

Explorers within these research stations have reported increases in depressive symptoms. 

There was a hypothesis on being a link between melatonin production and the effects of the Arctic's seasonal characteristics. Especially the link of the light intensity and its suppression in producing melatonin{{g}}. 

{{RoundBoxBottom}}


{{expand}}

The Overview section should provide:
# '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above)
# '''Explanation of the problem, issue, or topic''': Briefly explain the problem, why it is important, and outline how psychological science can help
# '''Focus questions''': Unpack the sub-title into focus questions in a feature box

Recommended length: 180 to 330 words.

{{RoundBoxTop|theme=3}}
'''Focus questions'''

Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions.
* How is Melatonin produced?
* What seasonal effects have been shown on mood?
* Does irregular melatonin production have an impact on Seasonal Mood Disorders and if so why?

Ask [[w:Open-ended question|open-ended]] focus questions. For example:
* Is there a relationship between weather and criminal behaviour? (closed-ended)
* What is the relationship between weather and criminal behaviour? (open-ended)
{{RoundBoxBottom}}

==Melatonin==
[[File:Melatonin.svg|center|thumb|350x350px|Figure 1. Melatonin Chemical Structure]]

[[w:Melatonin|Melatonin]] is a hormone, best know through its function of regulating circadian rhythms. (Megha, et al, 2024)

* Indolamines, a family of neurotransmitters, that share a common molecular structure
* Produced in the Pineal Gland 
** For vertabres melatonin is produced in the dark
** Melatonin is a key signaling molecule that connects changes in external light conditions with changes
*** After the retina receives a light signal, it transmits the signal to the pineal gland which then transforms the light signal into melatonin.
*Circulars through the blood stream 
*Various tissues and oragans can secrete melatonin 
**but only the reinal tissue of the pineal glad and eyes show periodic secretory activity
**linking the biosysynthesis of melatonin shows that circidian rhythm and seasonal characteristics associated with external light conditions
** Meliska et al (2013)

=== Functions ===

* Sleep (regulates circadian changes)
*linked with light
*proctective effects on the nervous system
*Broad spectrum and antibacterial and immunoregularory functions 
*Even looking into melatonin's relations with fertility and reproduction 

=== Melatonin Synthesis and secretion ===
[[File:Melatonin mechanism.jpg|thumb|Figure 2. Mechanism of melatonin biosynthesis]]

* tryptohan excreted from the small instestine into the blood circulation and actively taken up by pineal cells
* AANAT converts the tryptohan hydroxlase into ASMT 
* catalyzes into melatonin
* cAMP-catalyzed proteins promotates formation of a complex 
* reduces the K (m) of serotonin, enhancing melatonin production
* Melatonin is released into the blood and spinal fluid
* blinds into plasma proteins
* Distructed throughout most tissues 

[[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 3. Melatonin production in 24 hour cycle]]

=== Melatonin Fluctuations/Imbalance ===

* Melatonin release cycles over time 
* Temperature
* Circandian cycle and daylight changes

&lt;quiz display=&quot;simple&quot;&gt;
{1. Melatonin is produced by the?
|type=&quot;()&quot;}
+ Pineal Gland
- Cerebral Cortex
- Brain Stem 
- Retina 
 &lt;/quiz&gt;

== Seasonal Mood Disorders ==
Seasonal Affective Disorder (SAD)

* Part of the depression and bipolar family
*Combination of biological and mood disturbances through out different seasonal patterns
**Most commonly occurring during autumn and winter but cases have shown in the other seasons too ( Kurlanksik &amp; Ibay, 2012) 
*Light therapy has been shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment ( Kurlanksik &amp; Ibay, 2012)  

Polar triiodothyronine syndrome

One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. 

Bipolar effects with mood.  

*

== Studies ==

* Artic Study on melatonin and light 
* Effect on controlled-release melatonin on sleep quality, mood and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour (2003)
* polar triiodothyronine syndrome
** Double-blind trial
*** Group A Melatonin
*** Group B placebo
** Connected with the photoperiod not the weather-related aspect of the seasons

==Key points==
For the topic development, for each heading and sub-heading:
* Provide at least three bullet-points, including for the Overview and Conclusion
* Include key citations

;Quizzes
* Using one or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=simple&gt;
{The purpose of quizzes is to provide an interactive learning feature:
|type=&quot;()&quot;}
+ True
- False

{Long and complex quiz questions are recommended:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[w:Melatonin|Melatonin]] (Wikipedia)
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)
* [[w:Self determination theory|Self determination theory]] (Wikipedia)

{{tip|Suggestions for this section:
* Only select links to major internal resources about the topic
* Include the source in parentheses
}}

==References==
This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]].

APA style example:
{{Hanging indent|1=

Kurlansik, Stuart &amp; Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. 

Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0

Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., &amp; Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652

Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., &amp; Rintamäki, H., Ruokonen, A., Hassi, J., &amp; Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. 

}}

{{tip|Suggestions for this section:
* Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]:
** Use &quot;Edit source&quot;
** &lt;nowiki&gt;{{Hanging indent|1= the full list of references}}&lt;/nowiki&gt;
* Important aspects of APA referencing style
** Author surname, followed by a comma, then the author initials separated by full stops and spaces
** Year of publication in parentheses
** Title of work in lower case (except first letter and proper names), ending in a full-stop
** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop
** doi as a URL which is a working hyperlink (i.e., clickable)
* The most common mistakes include:
** Incorrect capitalisation
** Incorrect italicisation
** dois which aren't clickable as working hyperlinks
** Citing sources that haven't been consulted
}}

==External links==
Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)
* Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity
* Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour
* Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle 
* Melatonin as a treatment for mood disorders: a systematic review
* Melatonin and agomelatine for preventing seasonal affective disorder
* Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   
* Melatonin Biosynthesis and regulation in reproduction 
* Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 
* Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects 

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Mood]]
[[Category:Motivation and emotion/Book/Environment]]</text>
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__TOC__

==Overview==
This book chapter will be addressing the role that melatonin plays in seasonal mood changes through, seasonal changes, light pattern changes within seasonal changes as well as the correlation of melatonin production within these conditions.{{RoundBoxTop|theme=3}}
[[File:A picture is worth a thousand words.jpg|right|thumb|150px|'''Figure 1'''. Use a captioned image to illustrate the scenario]]

; Case study: Seasonal levels of melatonin near the Arctic Circle

Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study{{fact}} was conducted on why this would be the case. 

Circumpolar environments have been known for its changes in day night cycles as well as its temperature. 

Explorers within these research stations have reported increases in depressive symptoms. 

There was a hypothesis on being a link between melatonin production and the effects of the Arctic's seasonal characteristics. Especially the link of the light intensity and its suppression in producing melatonin{{g}}. 

{{RoundBoxBottom}}


{{expand}}

The Overview section should provide:
# '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above)
# '''Explanation of the problem, issue, or topic''': Briefly explain the problem, why it is important, and outline how psychological science can help
# '''Focus questions''': Unpack the sub-title into focus questions in a feature box

Recommended length: 180 to 330 words.

{{RoundBoxTop|theme=3}}
'''Focus questions'''

Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions.
* How is Melatonin produced?
* What seasonal effects have been shown on mood?
* Does irregular melatonin production have an impact on Seasonal Mood Disorders and if so why?

Ask [[w:Open-ended question|open-ended]] focus questions. For example:
* Is there a relationship between weather and criminal behaviour? (closed-ended)
* What is the relationship between weather and criminal behaviour? (open-ended)
{{RoundBoxBottom}}

==Melatonin==
[[File:Melatonin.svg|center|thumb|350x350px|Figure 1. Melatonin Chemical Structure]]

[[w:Melatonin|Melatonin]] is a hormone, best know through its function of regulating circadian rhythms. (Megha, et al, 2024)

* Indolamines, a family of neurotransmitters, that share a common molecular structure
* Produced in the Pineal Gland 
** For vertabres melatonin is produced in the dark
** Melatonin is a key signaling molecule that connects changes in external light conditions with changes
*** After the retina receives a light signal, it transmits the signal to the pineal gland which then transforms the light signal into melatonin.
*Circulars through the blood stream 
*Various tissues and oragans can secrete melatonin 
**but only the reinal tissue of the pineal glad and eyes show periodic secretory activity
**linking the biosysynthesis of melatonin shows that circidian rhythm and seasonal characteristics associated with external light conditions
** Meliska et al (2013)

=== Functions ===

* Sleep (regulates circadian changes)
*linked with light
*proctective effects on the nervous system
*Broad spectrum and antibacterial and immunoregularory functions 
*Even looking into melatonin's relations with fertility and reproduction 

=== Melatonin Synthesis and secretion ===
[[File:Melatonin mechanism.jpg|thumb|Figure 2. Mechanism of melatonin biosynthesis]]

* tryptohan excreted from the small instestine into the blood circulation and actively taken up by pineal cells
* AANAT converts the tryptohan hydroxlase into ASMT 
* catalyzes into melatonin
* cAMP-catalyzed proteins promotates formation of a complex 
* reduces the K (m) of serotonin, enhancing melatonin production
* Melatonin is released into the blood and spinal fluid
* blinds into plasma proteins
* Distructed throughout most tissues 

[[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 3. Melatonin production in 24 hour cycle]]

=== Melatonin Fluctuations/Imbalance ===

* Melatonin release cycles over time 
* Temperature
* Circandian cycle and daylight changes

&lt;quiz display=&quot;simple&quot;&gt;
{1. Melatonin is produced by the?
|type=&quot;()&quot;}
+ Pineal Gland
- Cerebral Cortex
- Brain Stem 
- Retina 
 &lt;/quiz&gt;

== Seasonal Mood Disorders ==
Seasonal Affective Disorder (SAD)

* Part of the depression and bipolar family
*Combination of biological and mood disturbances through out different seasonal patterns
**Most commonly occurring during autumn and winter but cases have shown in the other seasons too ( Kurlanksik &amp; Ibay, 2012) 
*Light therapy has been shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment ( Kurlanksik &amp; Ibay, 2012)  

Polar triiodothyronine syndrome

One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. 

Bipolar effects with mood.  

*

== Studies ==

* Arctic Study on melatonin and light
* Effect on controlled-release melatonin on sleep quality, mood and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour (2003)
* polar triiodothyronine syndrome
** Double-blind trial
*** Group A Melatonin
*** Group B placebo
** Connected with the photoperiod not the weather-related aspect of the seasons

==Key points==
For the topic development, for each heading and sub-heading:
* Provide at least three bullet-points, including for the Overview and Conclusion
* Include key citations

;Quizzes
* Using one or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[w:Melatonin|Melatonin]] (Wikipedia)
* [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia)
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)
* [[w:Self determination theory|Self determination theory]] (Wikipedia)

==References==
This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]].

APA style example:
{{Hanging indent|1=

Kurlansik, Stuart &amp; Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. 

Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0

Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., &amp; Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652

Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., &amp; Rintamäki, H., Ruokonen, A., Hassi, J., &amp; Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. 

}}

==External links==
Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)
* Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity
* Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour
* Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle 
* Melatonin as a treatment for mood disorders: a systematic review
* Melatonin and agomelatine for preventing seasonal affective disorder
* Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   
* Melatonin Biosynthesis and regulation in reproduction 
* Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 
* Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects 

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Mood]]
[[Category:Motivation and emotion/Book/Environment]]</text>
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__TOC__

==Overview==
This book chapter will be addressing the role that melatonin plays in seasonal mood changes through, seasonal changes, light pattern changes within seasonal changes as well as the correlation of melatonin production within these conditions.{{RoundBoxTop|theme=3}}
[[File:|right|thumb|150px|'''Figure 1'''. Use a captioned image to illustrate the scenario]]

; Case study: Seasonal levels of melatonin near the Arctic Circle

Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study was conducted on why this would be the case. 

Circumpolar environments have been known for its changes in day night cycles as well as its temperature. 

Explorers within these research stations have reported increases in depressive symptoms. 

There was a hypothesis on being a link between melatonin production and the effects of the Arctic's seasonal characteristics. In particular the link of the light intensity and its suppression of producing melatonin.

{{RoundBoxBottom}}


{{expand}}

The Overview section should provide:
# '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above)
# '''Explanation of the problem, issue, or topic''': Briefly explain the problem, why it is important, and outline how psychological science can help
# '''Focus questions''': Unpack the sub-title into focus questions in a feature box

Recommended length: 180 to 330 words.

{{RoundBoxTop|theme=3}}
'''Focus questions'''


* How is Melatonin produced?
* What seasonal effects have been shown on mood?
* Does irregular melatonin production have an impact on Seasonal Mood Disorders and if so why?


==Melatonin==
[[File:Melatonin.svg|center|thumb|350x350px|Figure 1. Melatonin Chemical Structure]]

[[w:Melatonin|Melatonin]] is a hormone, best know through its function of regulating circadian rhythms. (Megha, et al, 2024)

* Indolamines, a family of neurotransmitters, that share a common molecular structure
* Produced in the Pineal Gland 
** For vertabres melatonin is produced in the dark
** Melatonin is a key signaling molecule that connects changes in external light conditions with changes
*** After the retina receives a light signal, it transmits the signal to the pineal gland which then transforms the light signal into melatonin.
*Circulars through the blood stream 
*Various tissues and oragans can secrete melatonin 
**but only the reinal tissue of the pineal glad and eyes show periodic secretory activity
**linking the biosysynthesis of melatonin shows that circidian rhythm and seasonal characteristics associated with external light conditions
** Meliska et al (2013)

=== Functions ===

* Sleep (regulates circadian changes)
*linked with light
*proctective effects on the nervous system
*Broad spectrum and antibacterial and immunoregularory functions 
*Even looking into melatonin's relations with fertility and reproduction 

=== Melatonin Synthesis and secretion ===
[[File:Melatonin mechanism.jpg|thumb|Figure 2. Mechanism of melatonin biosynthesis]]

* tryptohan excreted from the small instestine into the blood circulation and actively taken up by pineal cells
* AANAT converts the tryptohan hydroxlase into ASMT 
* catalyzes into melatonin
* cAMP-catalyzed proteins promotates formation of a complex 
* reduces the K (m) of serotonin, enhancing melatonin production
* Melatonin is released into the blood and spinal fluid
* blinds into plasma proteins
* Distructed throughout most tissues 

[[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 3. Melatonin production in 24 hour cycle]]

=== Melatonin Fluctuations/Imbalance ===

* Melatonin release cycles over time 
* Temperature
* Circandian cycle and daylight changes

&lt;quiz display=&quot;simple&quot;&gt;
{1. Melatonin is produced by the?
|type=&quot;()&quot;}
+ Pineal Gland
- Cerebral Cortex
- Brain Stem 
- Retina 
 &lt;/quiz&gt;

== Seasonal Mood Disorders ==
Seasonal Affective Disorder (SAD)

* Part of the depression and bipolar family
*Combination of biological and mood disturbances through out different seasonal patterns
**Most commonly occurring during autumn and winter but cases have shown in the other seasons too ( Kurlanksik &amp; Ibay, 2012) 
*Light therapy has been shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment ( Kurlanksik &amp; Ibay, 2012)  

Polar triiodothyronine syndrome

One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. 

Bipolar effects with mood.  

*

== Studies ==

* Arctic Study on melatonin and light
* Effect on controlled-release melatonin on sleep quality, mood and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour (2003)
* polar triiodothyronine syndrome
** Double-blind trial
*** Group A Melatonin
*** Group B placebo
** Connected with the photoperiod not the weather-related aspect of the seasons

==Key points==
For the topic development, for each heading and sub-heading:
* Provide at least three bullet-points, including for the Overview and Conclusion
* Include key citations

;Quizzes
* Using one or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[w:Melatonin|Melatonin]] (Wikipedia)
* [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia)
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)
* [[w:Self determination theory|Self determination theory]] (Wikipedia)

==References==
This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]].

APA style example:
{{Hanging indent|1=

Kurlansik, Stuart &amp; Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. 

Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0

Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., &amp; Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652

Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., &amp; Rintamäki, H., Ruokonen, A., Hassi, J., &amp; Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. 

}}

==External links==
Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)
* Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity
* Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour
* Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle 
* Melatonin as a treatment for mood disorders: a systematic review
* Melatonin and agomelatine for preventing seasonal affective disorder
* Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   
* Melatonin Biosynthesis and regulation in reproduction 
* Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 
* Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects 

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Mood]]
[[Category:Motivation and emotion/Book/Environment]]</text>
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__TOC__

==Overview==
This book chapter will be addressing the role that melatonin plays in seasonal mood changes through, seasonal changes, light pattern changes within seasonal changes as well as the correlation of melatonin production within these conditions.{{RoundBoxTop|theme=3}}

; Case study: Seasonal levels of melatonin near the Arctic Circle

Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, multiple studies&lt;ref&gt;Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., &amp; Rintamäki, H., Ruokonen, A., Hassi, J., &amp; Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.&lt;/ref&gt; have been conducted on why this would be the case. 

Circumpolar environments have been known for its changes in day night cycles as well as its temperature. 

Explorers within these research stations have reported increases in depressive symptoms. 

There was a hypothesis on being a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion.

{{RoundBoxBottom}}


{{expand}}

The Overview section should provide:
# '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above)
# '''Explanation of the problem, issue, or topic''': Briefly explain the problem, why it is important, and outline how psychological science can help
# '''Focus questions''': Unpack the sub-title into focus questions in a feature box

Recommended length: 180 to 330 words.

{{RoundBoxTop|theme=3}}
'''Focus questions'''


* How is Melatonin produced?
* What seasonal effects have been shown on mood?
* Does irregular melatonin production have an impact on Seasonal Mood Disorders and if so why?


==Melatonin==
[[File:Melatonin.svg|center|thumb|350x350px|Figure 1. Melatonin Chemical Structure]]

[[w:Melatonin|Melatonin]] is a hormone, best know through its function of regulating circadian rhythms. (Megha, et al, 2024)

* Indolamines, a family of neurotransmitters, that share a common molecular structure
* Produced in the Pineal Gland 
** For vertabres melatonin is produced in the dark
** Melatonin is a key signaling molecule that connects changes in external light conditions with changes
*** After the retina receives a light signal, it transmits the signal to the pineal gland which then transforms the light signal into melatonin.
*Circulars through the blood stream 
*Various tissues and oragans can secrete melatonin 
**but only the reinal tissue of the pineal glad and eyes show periodic secretory activity
**linking the biosysynthesis of melatonin shows that circidian rhythm and seasonal characteristics associated with external light conditions
** Meliska et al (2013)

=== Functions ===

* Sleep (regulates circadian changes)
*linked with light
*proctective effects on the nervous system
*Broad spectrum and antibacterial and immunoregularory functions 
*Even looking into melatonin's relations with fertility and reproduction 

=== Melatonin Synthesis and secretion ===
[[File:Melatonin mechanism.jpg|thumb|Figure 2. Mechanism of melatonin biosynthesis]]

* tryptohan excreted from the small instestine into the blood circulation and actively taken up by pineal cells
* AANAT converts the tryptohan hydroxlase into ASMT 
* catalyzes into melatonin
* cAMP-catalyzed proteins promotates formation of a complex 
* reduces the K (m) of serotonin, enhancing melatonin production
* Melatonin is released into the blood and spinal fluid
* blinds into plasma proteins
* Distructed throughout most tissues 

[[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 3. Melatonin production in 24 hour cycle]]

=== Melatonin Fluctuations/Imbalance ===

* Melatonin release cycles over time 
* Temperature
* Circandian cycle and daylight changes

&lt;quiz display=&quot;simple&quot;&gt;
{1. Melatonin is produced by the?
|type=&quot;()&quot;}
+ Pineal Gland
- Cerebral Cortex
- Brain Stem 
- Retina 
 &lt;/quiz&gt;

== Seasonal Mood Disorders ==
Seasonal Affective Disorder (SAD)

* Part of the depression and bipolar family
*Combination of biological and mood disturbances through out different seasonal patterns
**Most commonly occurring during autumn and winter but cases have shown in the other seasons too ( Kurlanksik &amp; Ibay, 2012) 
*Light therapy has been shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment ( Kurlanksik &amp; Ibay, 2012)  

Polar triiodothyronine syndrome

One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. 

Bipolar effects with mood.  

*

== Studies ==

* Arctic Study on melatonin and light
* Effect on controlled-release melatonin on sleep quality, mood and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour (2003)
* polar triiodothyronine syndrome
** Double-blind trial
*** Group A Melatonin
*** Group B placebo
** Connected with the photoperiod not the weather-related aspect of the seasons

==Key points==
For the topic development, for each heading and sub-heading:
* Provide at least three bullet-points, including for the Overview and Conclusion
* Include key citations

;Quizzes
* Using one or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[w:Melatonin|Melatonin]] (Wikipedia)
* [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia)
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)
* [[w:Self determination theory|Self determination theory]] (Wikipedia)

==References==
This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]].

APA style example:
{{Hanging indent|1=

Kurlansik, Stuart &amp; Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. 

Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0

Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., &amp; Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652

Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., &amp; Rintamäki, H., Ruokonen, A., Hassi, J., &amp; Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. 

}}

==External links==
Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)
* Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity
* Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour
* Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle 
* Melatonin as a treatment for mood disorders: a systematic review
* Melatonin and agomelatine for preventing seasonal affective disorder
* Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   
* Melatonin Biosynthesis and regulation in reproduction 
* Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 
* Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects 

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Mood]]
[[Category:Motivation and emotion/Book/Environment]]</text>
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__TOC__

==Overview==
This book chapter will be addressing the role that melatonin plays in seasonal mood changes through, seasonal changes, light pattern changes within seasonal changes as well as the correlation of melatonin production within these conditions.{{RoundBoxTop|theme=3}}

; Case study: Seasonal levels of melatonin near the Arctic Circle

Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study&lt;ref&gt;Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., &amp; Rintamäki, H., Ruokonen, A., Hassi, J., &amp; Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.&lt;/ref&gt; have been conducted on why this would be the case. 

Circumpolar environments have been known for its changes in day night cycles as well as its temperature. 

Explorers within these research stations have reported increases in depressive symptoms. 

There was a hypothesis on being a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion.

{{RoundBoxBottom}}


{{expand}}

The Overview section should provide:
# '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above)
# '''Explanation of the problem, issue, or topic''': Briefly explain the problem, why it is important, and outline how psychological science can help
# '''Focus questions''': Unpack the sub-title into focus questions in a feature box

Recommended length: 180 to 330 words.

{{RoundBoxTop|theme=3}}
'''Focus questions'''


* How is Melatonin produced?
* What seasonal effects have been shown on mood?
* Does irregular melatonin production have an impact on Seasonal Mood Disorders and if so why?

==Melatonin==
[[File:Melatonin.svg|center|thumb|350x350px|Figure 1. Melatonin Chemical Structure]]

[[w:Melatonin|Melatonin]] is a hormone, best know through its function of regulating circadian rhythms. (Megha, et al, 2024)

* Indolamines, a family of neurotransmitters, that share a common molecular structure
* Produced in the Pineal Gland 
** For vertabres melatonin is produced in the dark
** Melatonin is a key signaling molecule that connects changes in external light conditions with changes
*** After the retina receives a light signal, it transmits the signal to the pineal gland which then transforms the light signal into melatonin.
*Circulars through the blood stream 
*Various tissues and oragans can secrete melatonin 
**but only the reinal tissue of the pineal glad and eyes show periodic secretory activity
**linking the biosysynthesis of melatonin shows that circidian rhythm and seasonal characteristics associated with external light conditions
** Meliska et al (2013)

=== Functions ===

* Sleep (regulates circadian changes)
*linked with light
*proctective effects on the nervous system
*Broad spectrum and antibacterial and immunoregularory functions 
*Even looking into melatonin's relations with fertility and reproduction 

=== Melatonin Synthesis and secretion ===
[[File:Melatonin mechanism.jpg|thumb|Figure 2. Mechanism of melatonin biosynthesis]]

* tryptohan excreted from the small instestine into the blood circulation and actively taken up by pineal cells
* AANAT converts the tryptohan hydroxlase into ASMT 
* catalyzes into melatonin
* cAMP-catalyzed proteins promotates formation of a complex 
* reduces the K (m) of serotonin, enhancing melatonin production
* Melatonin is released into the blood and spinal fluid
* blinds into plasma proteins
* Distructed throughout most tissues 

[[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 3. Melatonin production in 24 hour cycle]]

=== Melatonin Fluctuations/Imbalance ===

* Melatonin release cycles over time 
* Temperature
* Circandian cycle and daylight changes

&lt;quiz display=&quot;simple&quot;&gt;
{1. Melatonin is produced by the?
|type=&quot;()&quot;}
+ Pineal Gland
- Cerebral Cortex
- Brain Stem 
- Retina 
 &lt;/quiz&gt;

== Seasonal Mood Disorders ==
Seasonal Affective Disorder (SAD)

* Part of the depression and bipolar family
*Combination of biological and mood disturbances through out different seasonal patterns
**Most commonly occurring during autumn and winter but cases have shown in the other seasons too ( Kurlanksik &amp; Ibay, 2012) 
*Light therapy has been shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment ( Kurlanksik &amp; Ibay, 2012)  

Polar triiodothyronine syndrome

One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. 

Bipolar effects with mood.  

*

== Studies ==

* Arctic Study on melatonin and light
* Effect on controlled-release melatonin on sleep quality, mood and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour (2003)
* polar triiodothyronine syndrome
** Double-blind trial
*** Group A Melatonin
*** Group B placebo
** Connected with the photoperiod not the weather-related aspect of the seasons

==Key points==
For the topic development, for each heading and sub-heading:
* Provide at least three bullet-points, including for the Overview and Conclusion
* Include key citations

;Quizzes
* Using one or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[w:Melatonin|Melatonin]] (Wikipedia)
* [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia)
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)
* [[w:Self determination theory|Self determination theory]] (Wikipedia)

==References==
This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]].

APA style example:
{{Hanging indent|1=

Kurlansik, Stuart &amp; Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. 

Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0

Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., &amp; Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652

Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., &amp; Rintamäki, H., Ruokonen, A., Hassi, J., &amp; Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. 

}}

==External links==
Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)
* Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity
* Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour
* Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle 
* Melatonin as a treatment for mood disorders: a systematic review
* Melatonin and agomelatine for preventing seasonal affective disorder
* Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   
* Melatonin Biosynthesis and regulation in reproduction 
* Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 
* Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects 

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Mood]]
[[Category:Motivation and emotion/Book/Environment]]</text>
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__TOC__

==Overview==
This book chapter will be addressing the role that melatonin plays in seasonal mood changes through, seasonal changes, light pattern changes within seasonal changes as well as the correlation of melatonin production within these conditions.{{RoundBoxTop|theme=3}}

; Case study: Seasonal levels of melatonin near the Arctic Circle

Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study&lt;ref&gt;Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., &amp; Rintamäki, H., Ruokonen, A., Hassi, J., &amp; Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.&lt;/ref&gt; have been conducted on why this would be the case. 

Circumpolar environments have been known for its changes in day night cycles as well as its temperature. 

Explorers within these research stations have reported increases in depressive symptoms. 

There was a hypothesis on being a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion.

{{RoundBoxBottom}}


{{expand}}

The Overview section should provide:
# '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above)
# '''Explanation of the problem, issue, or topic''': Briefly explain the problem, why it is important, and outline how psychological science can help
# '''Focus questions''': Unpack the sub-title into focus questions in a feature box

Recommended length: 180 to 330 words.

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* How is Melatonin produced?
* What seasonal effects have been shown on mood?
* Does irregular melatonin production have an impact on Seasonal Mood Disorders and if so why?
{{RoundBoxBottom}}

==Melatonin==
[[File:Melatonin.svg|center|thumb|350x350px|Figure 1. Melatonin Chemical Structure]]

[[w:Melatonin|Melatonin]] is a hormone, best know through its function of regulating circadian rhythms. (Megha, et al, 2024)

* Indolamines, a family of neurotransmitters, that share a common molecular structure
* Produced in the Pineal Gland 
** For vertabres melatonin is produced in the dark
** Melatonin is a key signaling molecule that connects changes in external light conditions with changes
*** After the retina receives a light signal, it transmits the signal to the pineal gland which then transforms the light signal into melatonin.
*Circulars through the blood stream 
*Various tissues and oragans can secrete melatonin 
**but only the reinal tissue of the pineal glad and eyes show periodic secretory activity
**linking the biosysynthesis of melatonin shows that circidian rhythm and seasonal characteristics associated with external light conditions
** Meliska et al (2013)

=== Functions ===

* Sleep (regulates circadian changes)
*linked with light
*proctective effects on the nervous system
*Broad spectrum and antibacterial and immunoregularory functions 
*Even looking into melatonin's relations with fertility and reproduction 

=== Melatonin Synthesis and secretion ===
[[File:Melatonin mechanism.jpg|thumb|Figure 2. Mechanism of melatonin biosynthesis]]

* tryptohan excreted from the small instestine into the blood circulation and actively taken up by pineal cells
* AANAT converts the tryptohan hydroxlase into ASMT 
* catalyzes into melatonin
* cAMP-catalyzed proteins promotates formation of a complex 
* reduces the K (m) of serotonin, enhancing melatonin production
* Melatonin is released into the blood and spinal fluid
* blinds into plasma proteins
* Distructed throughout most tissues 

[[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 3. Melatonin production in 24 hour cycle]]

=== Melatonin Fluctuations/Imbalance ===

* Melatonin release cycles over time 
* Temperature
* Circandian cycle and daylight changes

&lt;quiz display=&quot;simple&quot;&gt;
{1. Melatonin is produced by the?
|type=&quot;()&quot;}
+ Pineal Gland
- Cerebral Cortex
- Brain Stem 
- Retina 
 &lt;/quiz&gt;

== Seasonal Mood Disorders ==
Seasonal Affective Disorder (SAD)

* Part of the depression and bipolar family
*Combination of biological and mood disturbances through out different seasonal patterns
**Most commonly occurring during autumn and winter but cases have shown in the other seasons too ( Kurlanksik &amp; Ibay, 2012) 
*Light therapy has been shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment ( Kurlanksik &amp; Ibay, 2012)  

Polar triiodothyronine syndrome

One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. 

Bipolar effects with mood.  

*

== Studies ==

* Arctic Study on melatonin and light
* Effect on controlled-release melatonin on sleep quality, mood and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour (2003)
* polar triiodothyronine syndrome
** Double-blind trial
*** Group A Melatonin
*** Group B placebo
** Connected with the photoperiod not the weather-related aspect of the seasons

==Key points==
For the topic development, for each heading and sub-heading:
* Provide at least three bullet-points, including for the Overview and Conclusion
* Include key citations

;Quizzes
* Using one or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[w:Melatonin|Melatonin]] (Wikipedia)
* [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia)
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)
* [[w:Self determination theory|Self determination theory]] (Wikipedia)

==References==
This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]].

APA style example:
{{Hanging indent|1=

Kurlansik, Stuart &amp; Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. 

Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0

Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., &amp; Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652

Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., &amp; Rintamäki, H., Ruokonen, A., Hassi, J., &amp; Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. 

}}

==External links==
Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)
* Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity
* Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour
* Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle 
* Melatonin as a treatment for mood disorders: a systematic review
* Melatonin and agomelatine for preventing seasonal affective disorder
* Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   
* Melatonin Biosynthesis and regulation in reproduction 
* Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 
* Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects 

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Mood]]
[[Category:Motivation and emotion/Book/Environment]]</text>
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__TOC__

==Overview==
This book chapter will be addressing the role that melatonin plays in seasonal mood changes through, seasonal changes, light pattern changes within seasonal changes as well as the correlation of melatonin production within these conditions.{{RoundBoxTop|theme=3}}

; Case study: Seasonal levels of melatonin near the Arctic Circle

Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study&lt;ref&gt;Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., &amp; Rintamäki, H., Ruokonen, A., Hassi, J., &amp; Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.&lt;/ref&gt; have been conducted on why this would be the case. 

Circumpolar environments have been known for its changes in day night cycles as well as its temperature. 

Explorers within these research stations have reported increases in depressive symptoms. 

There was a hypothesis on being a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion.

{{RoundBoxBottom}}


Through at correlations of melatonin and seasonal mood changes, we may be able to tie a link and pursue treatment of [[wikipedia:Seasonal_affective_disorder|Seasonal affective depression]], [[wikipedia:Winter-over_syndrome|Winter-over syndrome]] and other seasonal mood discrepancies. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* How is Melatonin produced?
* What seasonal effects have been shown on mood?
* Does irregular melatonin production have an impact on Seasonal Mood Disorders and if so why?
{{RoundBoxBottom}}

==Melatonin==
[[File:Melatonin.svg|center|thumb|350x350px|Figure 1. Melatonin Chemical Structure]]

[[w:Melatonin|Melatonin]] is a [[wikipedia:Hormone|hormone]], best know through its function of regulating circadian rhythms (Megha, et al, 2024). It is also a type of [[wikipedia:Neurotransmitter|neurotransmitter]] as it is a type of [[wikipedia:Indolamines|indolamines]] causing melatonin to function as both a hormone and a neurotransmitter. It has the nickname 'hormone of darkness' as it is primary function of sleep regulation through maintaining our bodies' biological clock though a physiological process in response to darkness.  

Melatonin is produced within the [[wikipedia:Pineal_gland|pineal gland]] 

* Produced in the Pineal Gland 
** For vertabres melatonin is produced in the dark
** Melatonin is a key signaling molecule that connects changes in external light conditions with changes
*** After the retina receives a light signal, it transmits the signal to the pineal gland which then transforms the light signal into melatonin.
*Circulars through the blood stream
*Various tissues and organs can secrete melatonin 
**but only the reinal tissue of the pineal glad and eyes show periodic secretory activity
**linking the biosysynthesis of melatonin shows that circidian rhythm and seasonal characteristics associated with external light conditions
** Meliska et al (2013)

=== Functions ===

* Sleep (regulates circadian changes)
*linked with light
*proctective effects on the nervous system
*Broad spectrum and antibacterial and immunoregularory functions 
*Even looking into melatonin's relations with fertility and reproduction 

=== Melatonin Synthesis and secretion ===
[[File:Melatonin mechanism.jpg|thumb|Figure 2. Mechanism of melatonin biosynthesis]]

* tryptohan excreted from the small instestine into the blood circulation and actively taken up by pineal cells
* AANAT converts the tryptohan hydroxlase into ASMT 
* catalyzes into melatonin
* cAMP-catalyzed proteins promotates formation of a complex 
* reduces the K (m) of serotonin, enhancing melatonin production
* Melatonin is released into the blood and spinal fluid
* blinds into plasma proteins
* Distructed throughout most tissues 

[[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 3. Melatonin production in 24 hour cycle]]

=== Melatonin Fluctuations/Imbalance ===

* Melatonin release cycles over time 
* Temperature
* Circandian cycle and daylight changes

&lt;quiz display=&quot;simple&quot;&gt;
{1. Melatonin is produced by the?
|type=&quot;()&quot;}
+ Pineal Gland
- Cerebral Cortex
- Brain Stem 
- Retina 
 &lt;/quiz&gt;

== Seasonal Mood Disorders ==
Seasonal Affective Disorder (SAD)

* Part of the depression and bipolar family
*Combination of biological and mood disturbances through out different seasonal patterns
**Most commonly occurring during autumn and winter but cases have shown in the other seasons too ( Kurlanksik &amp; Ibay, 2012) 
*Light therapy has been shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment ( Kurlanksik &amp; Ibay, 2012)  

Polar triiodothyronine syndrome

One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. 

Bipolar effects with mood.  

*

== Studies ==

* Arctic Study on melatonin and light
* Effect on controlled-release melatonin on sleep quality, mood and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour (2003)
* polar triiodothyronine syndrome
** Double-blind trial
*** Group A Melatonin
*** Group B placebo
** Connected with the photoperiod not the weather-related aspect of the seasons

==Key points==
For the topic development, for each heading and sub-heading:
* Provide at least three bullet-points, including for the Overview and Conclusion
* Include key citations

;Quizzes
* Using one or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[w:Melatonin|Melatonin]] (Wikipedia)
* [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia)
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)
* [[w:Self determination theory|Self determination theory]] (Wikipedia)

==References==
This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]].

APA style example:
{{Hanging indent|1=

Kurlansik, Stuart &amp; Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. 

Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0

Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., &amp; Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652

Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., &amp; Rintamäki, H., Ruokonen, A., Hassi, J., &amp; Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. 

}}

==External links==
Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)
* Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity
* Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour
* Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle 
* Melatonin as a treatment for mood disorders: a systematic review
* Melatonin and agomelatine for preventing seasonal affective disorder
* Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   
* Melatonin Biosynthesis and regulation in reproduction 
* Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 
* Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects 

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Mood]]
[[Category:Motivation and emotion/Book/Environment]]</text>
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__TOC__

==Overview==
This book chapter will be addressing the role that melatonin plays in seasonal mood changes through, seasonal changes, light pattern changes within seasonal changes as well as the correlation of melatonin production within these conditions.{{RoundBoxTop|theme=3}}

; Case study: Seasonal levels of melatonin near the Arctic Circle

Through explorations of the Arctic circle and the effects on mood and cognitive performance has on explorers, a study&lt;ref&gt;Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., &amp; Rintamäki, H., Ruokonen, A., Hassi, J., &amp; Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008.&lt;/ref&gt; have been conducted on why this would be the case. 

Circumpolar environments have been known for its changes in day night cycles as well as its temperature. 

Explorers within these research stations have reported increases in depressive symptoms. 

There was a hypothesis on being a link between melatonin production and the effects of the Arctic's seasonal characteristics, in particular the link of the light intensity and its suppression of melatonin secretion.

{{RoundBoxBottom}}


Through at correlations of melatonin and seasonal mood changes, we may be able to tie a link and pursue treatment of [[wikipedia:Seasonal_affective_disorder|Seasonal affective depression]], [[wikipedia:Winter-over_syndrome|Winter-over syndrome]] and other seasonal mood discrepancies. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* How is Melatonin produced?
* What seasonal effects have been shown on mood?
* Does irregular melatonin production have an impact on seasonal mood disorders and if so why?
{{RoundBoxBottom}}

==Melatonin==
[[File:Melatonin.svg|center|thumb|350x350px|Figure 1. Melatonin Chemical Structure]]

[[w:Melatonin|Melatonin]] is a [[wikipedia:Hormone|hormone]], best know through its function of regulating circadian rhythms (Megha, et al, 2024). It is also a type of [[wikipedia:Neurotransmitter|neurotransmitter]] as it is a type of [[wikipedia:Indolamines|indolamines]] causing melatonin to function as both a hormone and a neurotransmitter. It has the nickname 'hormone of darkness' as it is primary function of sleep regulation through maintaining our bodies' biological clock though a physiological process in response to darkness.  

Melatonin is produced within the [[wikipedia:Pineal_gland|pineal gland]] 

* Produced in the Pineal Gland 
** For vertabres melatonin is produced in the dark
** Melatonin is a key signaling molecule that connects changes in external light conditions with changes
*** After the retina receives a light signal, it transmits the signal to the pineal gland which then transforms the light signal into melatonin.
*Circulars through the blood stream
*Various tissues and organs can secrete melatonin 
**but only the reinal tissue of the pineal glad and eyes show periodic secretory activity
**linking the biosysynthesis of melatonin shows that circidian rhythm and seasonal characteristics associated with external light conditions
** Meliska et al (2013)

=== Functions ===

* Sleep (regulates circadian changes)
*linked with light
*proctective effects on the nervous system
*Broad spectrum and antibacterial and immunoregularory functions 
*Even looking into melatonin's relations with fertility and reproduction 

=== Melatonin Synthesis and secretion ===
[[File:Melatonin mechanism.jpg|thumb|Figure 2. Mechanism of melatonin biosynthesis]]

* tryptohan excreted from the small instestine into the blood circulation and actively taken up by pineal cells
* AANAT converts the tryptohan hydroxlase into ASMT 
* catalyzes into melatonin
* cAMP-catalyzed proteins promotates formation of a complex 
* reduces the K (m) of serotonin, enhancing melatonin production
* Melatonin is released into the blood and spinal fluid
* blinds into plasma proteins
* Distructed throughout most tissues 

[[File:Melatonin production in 24 hour cycle.jpg|center|thumb|431x431px|Figure 3. Melatonin production in 24 hour cycle]]

=== Melatonin Fluctuations/Imbalance ===

* Melatonin release cycles over time 
* Temperature
* Circandian cycle and daylight changes

&lt;quiz display=&quot;simple&quot;&gt;
{1. Melatonin is produced by the?
|type=&quot;()&quot;}
+ Pineal Gland
- Cerebral Cortex
- Brain Stem 
- Retina 
 &lt;/quiz&gt;

== Seasonal Mood Disorders ==
Seasonal Affective Disorder (SAD)

* Part of the depression and bipolar family
*Combination of biological and mood disturbances through out different seasonal patterns
**Most commonly occurring during autumn and winter but cases have shown in the other seasons too ( Kurlanksik &amp; Ibay, 2012) 
*Light therapy has been shown to be effective for most patients showing clinical improvements within one to two weeks after the start of treatment ( Kurlanksik &amp; Ibay, 2012)  

Polar triiodothyronine syndrome

One of the clearest links of mood disparities and melatonin levels is through arctic reports. With the high light levels throughout the day disrupting the circadian rhythms and therefore melatonin secreting. 

Bipolar effects with mood.  

*

== Studies ==

* Arctic Study on melatonin and light
* Effect on controlled-release melatonin on sleep quality, mood and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour (2003)
* polar triiodothyronine syndrome
** Double-blind trial
*** Group A Melatonin
*** Group B placebo
** Connected with the photoperiod not the weather-related aspect of the seasons

==Key points==
For the topic development, for each heading and sub-heading:
* Provide at least three bullet-points, including for the Overview and Conclusion
* Include key citations

;Quizzes
* Using one or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[w:Melatonin|Melatonin]] (Wikipedia)
* [[wikipedia:Light_therapy|Light Therapy]] (Wikipedia)
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)
* [[w:Self determination theory|Self determination theory]] (Wikipedia)

==References==
This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]].

APA style example:
{{Hanging indent|1=

Kurlansik, Stuart &amp; Ibay, Annamarie. (2012). Seasonal affective disorder. American family physician. 86. 1037-41. 

Megha, K.B., Arathi, A., Shikha, S. et al. Significance of Melatonin in the Regulation of Circadian Rhythms and Disease Management. Mol Neurobiol 61, 5541–5571 (2024). https://doi.org/10.1007/s12035-024-03915-0

Meliska, C. J., Martínez, L. F., López, A. M., Sorenson, D. L., Nowakowski, S., Kripke, D. F., Elliott, J., &amp; Parry, B. L. (2013). Antepartum depression severity is increased during seasonally longer nights: relationship to melatonin and cortisol timing and quantity. Chronobiology international, 30(9), 1160–1173. https://doi.org/10.3109/07420528.2013.808652

Pääkkönen,T., Leppäluoto, J., Ikäheimo, T., &amp; Rintamäki, H., Ruokonen, A., Hassi, J., &amp; Palinkas, L., (2008). Seasonal Levels of Melatonin, Thyroid Hormones, Mood, and Cognition Near the Arctic Circle. Aviation, space, and environmental medicine. 79. 695-9. https://doi.org/10.3357/ASEM.2148.2008. 

}}

==External links==
Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)
* Antepartum Depression Severity is Increased During Seasonally Longer Nights: Relationship to Melatonin and Cortisol Timing and Quantity
* Effect of controlled-release melatonin on sleep quality, mood, and quality of life in subjects with seasonal or weather-associated changes in mood and behaviour
* Seasonal levels of melatonin, thyroid hormones, mood, and cognition near the Arctic Circle 
* Melatonin as a treatment for mood disorders: a systematic review
* Melatonin and agomelatine for preventing seasonal affective disorder
* Seasonal rhythms in mental health: a narrative scoping review of neurobiological mechanisms and therapeutic interventions   
* Melatonin Biosynthesis and regulation in reproduction 
* Seasonal changes in mood and behavior: A cluster analytic approach https://www.sciencedirect.com/science/article/abs/pii/0165178189900498 
* Ngiam, Alicia. (2022). Light Deprivation and Its Effects. https://www.researchgate.net/publication/365021664_Light_Deprivation_and_Its_Effects 

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== Overview ==
{{RoundBoxTop|theme=3}}Picture this: A missed breakfast

The student oversleeps, hurries to university without having breakfast or drinking water. Listening to the instructor in class initially poses no challenge. Then the appetite, coupled with dry mouth, starts growing and becomes an incessant torment. A student might start thinking about where to get food and coffee in the vicinity. Why are basic physiological urges hard to ignore?

This common scenario is an example of homeostatic motivation: the process of how physiological needs affect attention, emotions, and behavior. The hypothalamus is a small part of the brain involved in integration of information regarding the state of the organism's energy, hydration and other variables. This structure works together with sensory, endocrine and broader brain mechanisms coordinating responses to protect survival (Timper &amp; Brüning, 2017; Zimmerman et al., 2017).

This chapter will explore how hunger and thirst arise as a result of the activity of specific but interacting brain circuits. It will also cover why the nature of motivation is more complicated than just the process of turning on the biological mechanism.

{{RoundBoxBottom}}

The hypothalamus is a small region of the brain that plays an important role in maintaining homeostasis, which is the body's ability to keep its internal conditions relatively stable. Biological needs such as hunger and thirst can become powerful sources of motivation when the body's internal conditions move away from balance. Hypothalamic and related neural circuits detect and integrate physiological information and contribute to behaviours such as eating and drinking that help restore energy and fluid balance (Timper &amp; Brüning, 2017; Zimmerman et al., 2017).

Understanding these processes is important because hunger and thirst are fundamental survival-related motivations that can strongly influence behaviour. Neuroscience research indicates that these motivations involve specialised and interconnected neural circuits that respond to physiological need and help generate appropriate consumption behaviours (Augustine et al., 2020).

{{RoundBoxTop|theme=3}}Focus questions

1. What is homeostasis, and how does the hypothalamus contribute to it?

2. How do hypothalamic circuits influence hunger and eating?

3. How do neural circuits detect thirst and control drinking?

4. How do hormones and bodily signals communicate needs to the brain?

5. How do biological needs become motivated behaviour?
{{RoundBoxBottom}}

== Homeostasis and the hypothalamus ==
Homeostasis refers to the systems of the body to regulate its internal conditions. These conditions change. However, there is a set of body processes that keep them in a functioning state. One example is the desire to drink water that comes when the supply is low. The desire for food also varies. These systems work through a feedback loop that returns things to the state they were in before an outside influence. The system that carries this out is regulated by the hypothalamus. This system relies on different signals that include hormones, nerves, and processes of metabolism. The different processes have different systems located in it. These systems are known as nuclei. An example of a nucleus is the arcuate nucleus which regulates energy. The parts of the hypothalamus, along with forebrain structures, control fluid. Other parts of the system regulate temperature, stress, and endocrine systems. While individual systems have their own tasks, none of them fully govern the processes needed to survive. There are different physical regulation and motivation. Some processes happen involuntarily. Others involve a person's motivation. For example, a person's motivation might guide them to drink water. A need leads a person to formulate a planned or chosen response. A person may experience a need and then have to decide what response to use based on many different factors. A person may feel the need to eat, but for many different reasons, may choose not to. An important concept to learn is how different bodily needs lead a person to do many different things. For example, consider the factors that cause a person to feel hungry. There are many bodily signals that lead a person to feel hungry. One reason may be low blood glucose levels. What could be another? Think about that and reflect on it. Homeostasis is the process by which an organism maintains a stable environment despite shifting circumstances. Body temperature can change to respond to outside stress and return to normal after the stressor is removed. Water can become unavailable. Body energy can become low. Food interest changes to adjust the need to restore that energy. Body systems work in the same way to maintain the needed conditions for life.

The hypothalamus takes care of a lot of these shifting systems. There are distinct nuclei in it which play different roles in homeostasis. For instance, energy regulation is handled by the arcuate nucleus. Other regions and nuclei help control other functions such as stress response, fluid regulation, endocrine secretion, and body temperature. No individual nucleus handles every single survival-oriented process, either (Timper &amp; Brüning, 2017; Augustine et al., 2020). There is a division between regulation and motivation. Many processes, such as hormone changes, happen without choice. But a person can have the motivation to do something, for instance, to seek out water. Motivation provides a bridge from recognizing a need to implementing a solution. Having said this, there is often more than one way to achieve the goal of a specific need. For example, a particular need can manifest differently in different situations based on availability and/or other factors.
* Even when the body or the surroundings change, homeostasis aims to hold things steady.
* The hypothalamus also gathers input from more than one source. It uses signals from nerves, hormones, and metabolic processes.
* Not all parts of the hypothalamus do the same job. Different nuclei and groups of neurons link to different functions. Some shifts affect bodily regulation, while others shape motivation
* When balance is disrupted, motivation can rise. Those urges steer actions that help bring the body back toward the right conditions.

[[File:Hypothalamus in coronal view.jpg|thumb|140x140px|'''Figure 2'''. Sagittal diagram of the hypothalamus showing major nuclei involved in regulating physiological and survival-related processes, including the arcuate, ventromedial, paraventricular, supraoptic, anterior, posterior, and dorsomedial nuclei.]]

== Homeostasis and the hypothalamus ==
Homeostasis means your body keeps its internal conditions within a safe range. This helps you work the way you should.  The hypothalamus is key here. It takes in data about what is going on inside the body. Then it helps set off the right body actions. Those actions can include shifts in body functions and changes in behaviour.  If things drift too far from the normal range, the body does not just “notice” it. Homeostatic systems can also push you toward certain urges. Those urges can lead to actions like eating or drinking.

* Homeostasis helps maintain relatively stable internal conditions despite changes within the body or environment.
* The hypothalamus integrates neural, hormonal, and metabolic information involved in homeostatic regulation (Timper &amp; Brüning, 2017).
* The hypothalamus contains several specialised nuclei that contribute to different aspects of physiological and homeostatic regulation (see Figure 2).
* Homeostatic disturbances can produce motivational states that encourage behaviours capable of restoring biological balance (Augustine et al., 2020).

=== Hypothalamic regulation of hunger ===
Hunger is a mental state that encourages you to seek out and eat food. Energy balance depends on the needs of the body, energy storage, and nutrition. While the hypothalamus does play a part in regulating both energy expenditure and food intake, eating is complex. For example, eating can be a response to the way a food is presented or even a response to social eating. Eating can also be conditioned. All of this makes hunger a good example of how psychological and biological factors can interact (Liu &amp; Kanoski, 2018).

The arcuate nucleus contains a population of AgRP/NPY neurons that when stimulated promotes the consumption of food, while POMC neurons, named for pro-opiomelanocortin, work to suppress the consumption of food through the melanocortin system. These two populations act to create a feedback loop that works against an all or nothing control mechanism of feeding. (Timper &amp; Brüning, 2017).

==== Hunger and energy balance ====
* Your central nervous system gets signals about how much energy is available. It does this using nutrients, nerve messages, and hormones in the blood.
* Part of the hypothalamus helps steer both eating and how fast the body uses energy. This work supports a stable energy balance, as described by Timper and Brüning in 2017.
* When you feel hunger, food may start to feel more valuable. That feeling can push you toward actions like looking for food, moving toward it, and eating it.

* Biology matters, but it is not the only thing. Food choice and eating can also shift with reward, past experiences, learning, and cues from the food around you. Liu and Kanoski discuss this in 2018.

==== The arcuate nucleus ====
* The arcuate nucleus of the hypothalamus contains important neuronal populations involved in the regulation of appetite and energy balance (Timper &amp; Brüning, 2017).
* AgRP/NPY-related {{ic|explain technical terms}} neurons are associated with hunger and can promote feeding when energy availability is low.
* POMC-related neurons contribute to signalling involved in reduced food intake and energy regulation.

* These neuronal populations interact with other hypothalamic and extra-hypothalamic regions, showing that feeding is 
* regulated by an interconnected neural network rather than one isolated brain structure.

==== Ghrelin and leptin ====
* Hormones allow peripheral organs and tissues to communicate information about energy availability to the brain {{ic|hypothalamus?}}.
* Ghrelin is associated with hunger signalling and can influence neural systems involved in food intake.
* Leptin is produced primarily by adipose tissue and provides the brain with information related to stored energy.
* Metabolic and hormonal signals such as leptin act on hypothalamic neuronal populations involved in appetite and energy homeostasis (Timper &amp; Brüning, 2017).
'''What experimental research shows'''

Aponte and colleagues (2011) used optogenetics. They used light to switch on AgRP neurons in mice. When the neurons were turned on, the animals ate faster right away. This result points to a direct link between these cells and eating. One strong point is the method. It did not just look at patterns in data. It changed a defined group of cells. That said, the setup is also limited. Light-driven stimulation in mice is not the same as the many parts of human hunger.

Betley et al. (2015) added an important psychological dimension. In mouse experiments, activity in hunger-related AgRP neurons carried a negative-valence signal: animals learned preferences for cues associated with reduction of this activity. The results point to a simple idea. When a need is eased, learning can follow. This means food seeking is not only driven by lack of energy. The brain can also pick up which places and signals mean relief is coming. These new findings fit with older homeostatic views.

They do not swap them out. Instead, they spell out brain pathways that turn body signals into action. They also show that what drives the person is shaped by what is expected and what has been learned before. It would be an overstatement to conclude that the same neural manipulations produce identical subjective experiences in humans.

'''Hormonal communication'''

The brain does not have to inspect the body's energy stores directly. It receives chemical messages from peripheral tissues. Ghrelin comes out mostly from the stomach. It is linked to hunger cues. Leptin is made mainly in fat tissue. It reflects how much energy the body has stored. These hormones act on hypothalamic cells and other neural routes. They affect appetite and how the body handles energy (Timper &amp; Brüning, 2017). One issue with a simple story about hormones is this. The amount of a hormone in the body does not fully tell you when someone eats. A person might eat because the food looks good. Or it might be because it is midday. Sometimes it is because other people are eating. Also, someone can wait to eat even if there is a physical pull to eat. A stronger view uses both body signals and mental, outside, and reward factors together (Liu &amp; Kanoski, 2018).

'''Why research methods matter'''

Optogenetic work can be very useful. In these studies, scientists turn on a chosen set of neurons. Then they watch what the animal does next. That link between cell activity and behaviour helps with causal claims. Aponte and colleagues in 2011 reported a clear shift in feeding. When they stimulated AgRP neurons in mice that were well fed, the animals began to eat fast. In the same study, activating POMC neurons lowered eating.

That change was tied to melanocortin signalling. Still, this does not prove that these neuron groups are the only drivers of appetite. Their impact can vary. It may depend on what the signals do after leaving the neurons. It also depends on the body state of the animal and on the way the stimulation is set up.

Betley and co-workers in 2015 took a different approach. They combined neuronal control with learning tasks. Their results pointed to need sensitive neurons acting as an unpleasant teaching cue. So hunger can be read in another way. Food intake is not always just about pleasure. Animals can also learn steps that ease an unpleasant need state. Yet negative valence in a mouse task should not be equated directly with a person's conscious experience of hunger. Taken together, the studies are strongest as mechanistic evidence and less decisive as explanations of everyday human food choices.

=== Quiz ===
&lt;quiz display=&quot;simple&quot;&gt;
{The hypothalamus contains specialised neural circuits that help regulate homeostatic processes such as hunger and thirst:
|type=&quot;()&quot;}
+ True
- False

{Hunger and thirst are each controlled by a single hypothalamic “switch” that turns the motivation on or off:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

=== Hypothalamic regulation of thirst ===
Thirst is a powerful homeostatic motivation that encourages drinking when the body's fluid balance is disturbed. Neural circuits continuously monitor physiological signals related to hydration and generate behavioural and hormonal responses that help restore fluid balance (Zimmerman et al., 2017).

==== Detecting fluid imbalance ====
The presence of thirst signals the need for hydration in the body. When a person is thirsty, they seek and drink water. This happens due to the body’s state of having a disrupted fluid balance. The body monitors a few key signals regarding hydration. One signal is blood osmolality. Other signals include sodium levels, blood volume, and blood pressure. Key sensory organs of the body for hydration signals are the subfornical organ and the organum vasculosum of the lamina terminalis (OVLT), both of which are located close to the hypothalamus. These sites can detect signals carried in the blood. They then pass information into linked brain circuits, such as the median preoptic nucleus.

Together, these pathways help set up drinking and hormone related responses (Zimmerman et al., 2017). From this, a key point follows. Thirst is not a function of the hypothalamus on its own. While some mechanisms do exist in this part of the brain, other brain functions play a role and contribute significantly to thirst. The mechanisms involved are complex and cannot be reduced to just one area of the brain. That is why it would be a mistake to call the hypothalamus a single thirst center.
* Your body’s hydration status shows up in several blood measurements. Blood osmolality, sodium levels, blood volume, and blood pressure all shift when you are getting more or less fluid.
* The brain also has special sensory areas. Two of them are the subfornical organ, or SFO, and the organum vasculosum of the lamina terminalis, the OVLT. These regions help pick up changes linked to fluid balance (Zimmerman et al., 2017).
* After that, these cues reach the hypothalamus and nearby pathways. Those networks help drive thirst. They also push you toward finding and drinking water.

* Thirst therefore demonstrates how a physiological imbalance can be transformed into a powerful motivational state.
'''Why thirst can disappear before water is absorbed'''

A model that is only reactive and based on homeostasis says thirst should drop only after the swallowed water fixes the fluid mix inside the body. But normal day to day life does not match that. When people drink, the feeling can ease right away. Zimmerman and colleagues in 2016 tested this issue in mice. They tracked brain activity linked to thirst. Their findings showed rapid responses to drinking-related sensory information before full physiological restoration occurred.

This is called anticipatory regulation. The brain reads signals that come up during drinking. It uses those cues to guess what will happen next in the body. It does not wait for every inner change to fully settle first. This may help prevent excessive consumption while allowing timely correction of fluid imbalance (Zimmerman et al., 2017).

The research strengthens homeostatic theory by showing that regulation is predictive as well as reactive. A lot of the circuit level evidence is built from animal studies. Turning those single cell responses into what people actually feel as thirst is not simple. It needs more careful work and extra checks.

'''Comparing reactive and anticipatory explanations'''

Classic negative feedback stories say a lack of fluid should push someone to drink. Still, they do not fit one key observation. Thirst related nerve activity can shift within seconds after drinking starts. At that point, the water in the gut has not yet changed blood chemistry. Zimmerman and colleagues in 2016 studied mice. They watched neurons linked to thirst and saw fast changes right after oral cues. This pattern fits an idea where the brain uses what is happening now and also expects what the next steps will bring.

Grove and Knight wrote a review in 2024 that puts these results into a wider circuit. That circuit seems to cover both water and salt drives. They also point out gaps. Some body sensors are not fully known. They also ask why drinking happens when there is no clear fluid drop, like during meals. So this work does not swap out homeostasis for prediction. It argues that good control may use both direct signals and expected effects. This matters because a simple rule like “drink only when dehydrated” misses much of normal daily behavior.

==== Drinking and anticipatory regulation ====
* Thirst can begin decreasing before consumed water has been fully absorbed and restored the body's fluid balance.
* Sensory information associated with drinking provides rapid feedback to neural circuits involved in thirst (Zimmerman &amp; Knight, 2020).
* This anticipatory regulation allows the brain to predict how ongoing drinking will affect the body's future physiological state.

* These mechanisms help prevent excessive water consumption while still allowing fluid balance to be restored.

=== Other Survival-Related Motivations ===
Although hunger and thirst provide clear examples of homeostatic motivation, the hypothalamus contributes to several other processes necessary for survival. Different hypothalamic nuclei and neural populations participate in coordinating physiological and behavioural responses according to the body's current needs.

* The hypothalamus helps control body temperature, sleep, daily cycles, mating patterns, hormone balance, and reactions to stress.
* Not every part of the hypothalamus does the same job. Each nucleus has its own role, and they link up with each other. So it is not one single “motivation hub” that drives everything.
* When something goes wrong in the body, the priorities can shift. A person may feel a strong, short-term need, and that need can override other aims.
* That is what hunger and thirst show. Signals from inside the body can create drive states. Those drives then shape actions that keep a person alive.
'''How bodily needs become motivated behaviour'''

Need for food and need for water start with different body messages. Still, they follow many of the same rules. In both cases, the brain has to sense what is going on inside. It also pulls in specific nerve paths. Then it shifts focus toward things that can help. After that, the brain uses new sensory input to adjust what the person does next. Both systems also change with experience. A cafe sign can feel more important when someone is hungry.

A bottle of water can stand out more after hard exercise. Betley and colleagues in 2015 showed this in mice. They changed neural groups linked to hunger and thirst. Those changes then altered what the animals later preferred or tried to avoid. The result fits the view that these need circuits do more than just drive eating or drinking. They may also set the worth of cues tied to relief. When this is put together with work on thirst control before dehydration, the picture becomes clearer. Survival drives seem to rely on forecasts, feedback, and learning. It is not only a late response to bodily lack.
{| class=&quot;wikitable&quot;
|+Table 1: Comparison of hunger and thirst as homeostatic motivations
!Biological need
!Example signals
!Key neural systems
!Motivated behaviour
|-
|Hunger
|Energy availability, ghrelin, leptin
|Arcuate and interconnected hypothalamic circuits
|Food seeking and eating
|-
|Thirst
|Osmolality, sodium and blood-volume signals
|SFO, OVLT, MnPO {{ic|explain abbreviations}} and hypothalamic circuits
|Water seeking and drinking
|}

As shown in Table 1, hunger and thirst involve different physiological signals and specialised neural systems, but both demonstrate how disturbances in homeostasis can generate motivated behaviour (Augustine et al., 2020; Zimmerman et al., 2017).
----'''Other survival-related motivations'''

The hypothalamus has many roles, including the regulation of temperature, time, sleep, stress and even reproduction. These separate functions require unique and distinct paths that traverse the brain, though they intersect with one another, sometimes leading to split or diverted attention. A person may opt to seek shade if they feel excessively hot over continuing to eat. In general, body state changes what feels urgent. Surroundings then decide what can actually be done.

In this chapter, the best support is for hunger and thirst. It is not true that every survival drive follows the same pattern. There are differences, and it would be good to see further study into how the brain makes decisions to address multiple needs when they arise.

'''What the evidence can and cannot tell us'''

Differentiated clusters of neurons have added depth and dimension to earlier descriptions of the hypothalamus as a group of fundamental points of drive. Researchers are able to turn specific neural circuits off and on and see how this impacts an animal’s behavior. The results of the stimulation work are enhanced when paired with observations that show the rapid shift in an animal’s neural signaling when it comes into proximity of its food and water. These studies begin to illustrate the connection of neural signals to needs, expectations, and subsequent behaviors (Aponte et al., 2011; Betley et al., 2015; Zimmerman et al., 2016).

Still, there are clear drawbacks. A lot of cause and effect work uses mice. In managed environments such as a laboratory, life differs greatly for animals from how it is for us. Scientists often artificially manipulate neuronal firing. Natural stimuli do not always equal artificial neuronal firing patterns. Research measuring consumption does not reveal how an individual feels internally. There is a need to conduct more research and to make cross-species comparisons. There is a need to study how social and cultural context plays a role.

A combined picture is useful. While I understand why some think the body controls behavior through signals that exert a push and a pull (and that’s one interpretation), that view has blind spots. Without discounting homeostasis, there’s an entire system of factors, including anticipated outcomes and external stimuli, that guides behavior, too. The view explains how it is possible to think that an intense feeling of hunger or thirst might not compel you to eat or drink.

'''Practical implications and future directions'''

The study helps explain how internal drive changes what we focus on. For instance, people who have not eaten will quickly spot food, whereas people who have worked out in very hot weather will become focused on finding things to drink. In both cases, the subjects are focused, but neither example shows that a particular set of cells in the brain directs us on what we are going to do. What someone is likely to do is driven by factors such as: how available certain things are, their habits, medications they might be on, their social lives, and how someone’s personality might manifest.

Next work should pair clear human behaviour tasks with neuroimaging and body measures that fit ethical rules. It should also use animal work to probe what happens inside brain circuits. Researchers should look at cases where more than one need is active at the same time. A prime example is balancing food consumption and hydration needs. When a researcher achieves this, the field learns a lot about how closely lab research correlates with reality. This also shines a lot of light on how well lab results translate to real life with people and how they differ between different demographics and communities.

==Conclusion==
There is an emotional aspect to the physical processes in the body. That aspect originates in the hypothalamus. Circuits within this brain area and its connected structures receive input concerning energy and water levels. The hypothalamus drives actions to maintain homeostasis. Feeding and drinking behaviors along with many other actions of the organism also occur due to inputs. Body processes can also signal through hormones. Ghrelin and leptin are two examples. Sensory areas, such as the SFO and OVLT, help track cues tied to hydration.

This is not just a set of on or off actions. AgRP neurons are important for hunger, as demonstrated in mice. The neurobiology of hunger and thirst control suggests the mechanism is flexible. Hunger and thirst processes also involve advanced warning, and learning as well as the absence of a response (relief). While providing important data on homeostasis and body control in support of motivational theories of prediction, these studies cannot yet be generalized to people.

=== Key take-home points ===
·       Homeostasis involves flexible regulation, not perfect physiological constancy.

·       Hunger and thirst depend on specialised, interconnected neural networks.

·       Hormonal and sensory signals communicate the body's changing needs.

·       Motivation involves learning, anticipation and environmental context as well as physiological need.

·       Animal neuroscience provides important mechanistic evidence, but human generalisation requires further research.{{tip|Take-home message:The hypothalamus helps maintain homeostasis by detecting biological needs and motivating behaviours that restore balance. Specialised neural circuits regulate hunger, thirst, and other survival-related processes, showing how changes within the body can strongly influence motivation and behaviour.
}}

==See also==
* [[Motivation and emotion/Brain structures|Brain structures]] (Wikiversity)
* [[Motivation and emotion/Book/2025/Homeostasis and basic drives|Homeostasis and basic drives]] (Book chapter, 2025)
* [[Motivation and emotion/Book/2017/Hypothalamus and motivation|Hypothalamus and motivation]] (Book chapter, 2017)
* [[w:Homeostasis|Homeostasis]] (Wikipedia)
* [[w:Hypothalamus|Hypothalamus]] (Wikipedia)

==References==
{{Hanging indent|1=

Augustine, V., Lee, S., &amp; Oka, Y. (2020). Neural control and modulation of thirst, sodium appetite, and hunger. Cell, 180(1), 25–32. https://doi.org/10.1016/j.cell.2019.11.040

Aponte, Y., Atasoy, D., &amp; Sternson, S. M. (2011). AGRP neurons are sufficient to orchestrate feeding behavior rapidly and without training. Nature Neuroscience, 14, 351–355. https://doi.org/10.1038/nn.2739

Betley, J. N., Xu, S., Cao, Z. F. H., Gong, R., Magnus, C. J., Yu, Y., &amp; Sternson, S. M. (2015). Neurons for hunger and thirst transmit a negative-valence teaching signal. Nature, 521, 180–185. https://doi.org/10.1038/nature14416

Grove, J. C. R., &amp; Knight, Z. A. (2024). The neurobiology of thirst and salt appetite. Neuron, 112(24), 3999–4016. https://doi.org/10.1016/j.neuron.2024.10.028

Liu, C. M., &amp; Kanoski, S. E. (2018). Homeostatic and non-homeostatic controls of feeding behavior: Distinct vs. common neural systems. Physiology &amp; Behavior, 193, 223–231. https://doi.org/10.1016/j.physbeh.2018.02.011

Timper, K., &amp; Brüning, J. C. (2017). Hypothalamic circuits regulating appetite and energy homeostasis: Pathways to obesity. Disease Models &amp; Mechanisms, 10(6), 679–689. https://doi.org/10.1242/dmm.026609

Williams, G., Bing, C., Cai, X. J., Harrold, J. A., King, P. J., &amp; Liu, X. H. (2001). The hypothalamus and the control of energy homeostasis: Different circuits, different purposes. Physiology &amp; Behavior, 74(4–5), 683–701. https://doi.org/10.1016/S0031-9384(01)00612-6

Zimmerman, C. A., Leib, D. E., &amp; Knight, Z. A. (2017). Neural circuits underlying thirst and fluid homeostasis. Nature Reviews Neuroscience, 18(8), 459–469. https://doi.org/10.1038/nrn.2017.71

Zimmerman, C. A., &amp; Knight, Z. A. (2020). Layers of signals that regulate appetite. Current Opinion in Neurobiology, 64, 79–88. https://doi.org/10.1016/j.conb.2020.03.007

}}

==External links==
* [https://www.brainfacts.org/3d-brain 3D Brain] (BrainFacts)
* [https://my.clevelandclinic.org/health/body/22566-hypothalamus Hypothalamus] (Cleveland Clinic)

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally understood to be a positive, high-arousal emotional state that prepares an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2021). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014). 

=== Early views on excitement ===
Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect, which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situatuion or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational Dimensional Model of Affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural Activation System (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable. Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional picture. From this data, the study developed a three-axial model integrating valence, arousal and a cognitive dimension of expectation/anticipation of which demonstrated that expectation/anticipation is significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball, and hates crowds, might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}
;Physiological responses
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) suggests that excitement involves increased physiological arousal, including increased heart rate, alertness and energy with reduced heart rate variability signalling a heightened sympathetic nervous system (Ketonen et al., 2022).
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}
;Psychological processes
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought actions encouraging problem-solving, and exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}
;Approach motivation and goal pursuit
High affective states have been linked to more approach-oriented behaviour. That is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states also can have goal directed behaviour, however, as excitement is a high positive affect (valence) state and is anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}
;Excitments affect on cognition
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (1998, 2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

=== Excitement on performance ===
According to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor and sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., springint and football tacking) whereas, fine motor tasks &amp; decision-making was impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.  

While excitement can increase motivation and engagement, heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others.


* (Self-note:Look into more below) affective arousal has been shown to affect judgement, learning and memory (Storbeck &amp; Clore, 2008).
* Attention
* Decision-making
* Positive arousal increases people's risk-taking (GAlentino, Bonini, &amp; Savadori, 2017)
* Creativity
* Performance
* Exploration

{{anchor|Does excitement help or hinder behaviour?}}
;Does excitement help or hinder behaviour?
With helpful excitement, an individual might move towards a goal by preparing, practiising, engaging and performing with said goal.

However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision.

(Find proper citation for this.

Add possible learning task here?)

==Excitement and its influence on well-being==
*Excitement is a positive emotional experience.
*Experiencing positive emotions can contribute to subjective well-being.
* Excitement can make activities feel more engaging and rewarding.
* Anticipating positive experiences can contribute to motvaiton and enjoyment.
* research shows the re-appraisal for anxiety inducing tasks as exciting can lead to greater overall positive experience and performance increase in performance activities (Brooks, 2014).

{{anchor|Excitement, goals and engagement}}
;Excitement goals and engagement
* Excitement can encourage individuals to pursue personally meaningful goals.
* Goal pursuit can contribute to competence, engagement and satisfaction.
* Excitement may help people initiate activities they might otherwise avoid.
* Excitement can therefore indirectly contribute to well-being through behaviour.
* Positive affect has been shown to increase life satisfaction and relationships over time (Liu, 2026).

Case study check: Excitement doesn't necessarily improve well-being simply because they &quot;feel good&quot;, Rather, the emotion may encourage preparation, engagement and goal pursuit, which can subsequently cotnribute to a sense of accomplishment

{{anchor|When excitement becomes unhelpful}}
;When excitement becomes unhelpful

* Extremely high emotional arousal may become overwhelming.
* Excitement may sometimes contribute to impulsive decisions or risk-taking.
* The consequences of excitement depend on the context and the individual's ability to regulate their behaviour.
* Therefore, excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion.

Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depend on intensity, context and behavioural regulation.

==Conclusion==
Excitement is a positive, high-arousal emotional state characterised by anticipation and readiness for action. It can influence behaviour through increased approach motivation, attention and goal-directed action.

Excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes alternatively, the reappraisal of similar physiological emotions into excitement, can allow for greater outcomes in life as well as performance of specific tasks.

Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

So, do what excites!

==Figures==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]]

* For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure; this can be the figure in the scenario
* For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples
* Images must be embedded from [[commons:|Wikimedia Commons]] which hosts free-to-use media such as photos, diagrams, graphs, video, and audio
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text)
* Cite each figure at least once in the main text (e.g., see Figure 2)

==Learning features==
Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options:

{{anchor|Scenarios}}
;Scenarios
* Scenarios, case studies, or examples that illustrate concepts in action
* Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages)
* Can be real or fictional; if real, provide citation(s)

{{anchor|Feature box}}
;Feature boxes
* Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect
* Consider using feature boxes for:
** [[#Scenarios|Scenarios]], case studies, or examples
** Focus questions
** Tips
** Quiz questions
** Take-home messages

;Embedded links
* When key words are introduced, use [[Help:Links|interwiki links]] to:
** Wikipedia articles (e.g., &quot;An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]&quot;) or
** Related book chapters (e.g., &quot;If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]&quot;)

{{anchor|Tables}}
;Tables
* Use tables to organise and summarise information
* Cite each table at least once in the main text (e.g., see Table 1)
* Tables should be captioned
* [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted

'''Table 1''' 

A Descriptive Caption Explains The Table Contents and its Relevance to the Text e.g., 

The 2 x 2 Johari Window Model Showing the Relationship Between Known/Unknown and Self/Other

{| class=&quot;wikitable&quot; style=&quot;margin: auto;
|-
! !! Known to self !! Not known to self
|-
| '''Known to others''' || Open area || Blind spot
|-
| '''Not known to others''' || Hidden area || Unknown
|}

;Quizzes
* One or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=simple&gt;
{The purpose of quizzes is to provide an interactive learning feature:
|type=&quot;()&quot;}
+ True
- False

{Long and complex quiz questions are recommended:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

==Conclusion==
* Arguably the most important section
* Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking
* For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
{{tip|Suggestions for this section:
* Link to the most relevant internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

 Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. Journal of Experimental Psychology. General, 143(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. The American Psychologist, 56(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. Current Opinion in Behavioral Sciences, 39, 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. Frontiers in Psychology, 8, Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. British Journal of Educational Psychology, 93(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. The Journal of Positive Psychology, (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. Social and Personality Psychology Compass, 2(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. Psychological Review, 35(5), 351–366. https://doi.org/10.1037/h0071406

}}

{{tip|Suggestions for this section:
* Important aspects of APA referencing style
** Author surname, followed by a comma, then the author initials separated by full stops and spaces
** Year of publication in parentheses
** Title of work in lower case (except first letter and proper names), ending in a full-stop
** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop
** doi as a URL which is a working hyperlink (i.e., clickable)
** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]:
*** Use &quot;Edit source&quot;
*** &lt;nowiki&gt;{{Hanging indent|1= the full list of references}}&lt;/nowiki&gt;
* The most common mistakes include:
** Incorrect capitalisation
** Incorrect italicisation
** dois which aren't clickable as working hyperlinks
** Citing sources that haven't been consulted
}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)

{{tip|Suggestions for this section:
* Link to the most relevant external resources about the topic
* Include the source in parentheses after the link
}}

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally understood to be a positive, high-arousal emotional state that prepares an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2021). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014). 

=== Early views on excitement ===
Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect, which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situatuion or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational Dimensional Model of Affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural Activation System (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable. Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional picture. From this data, the study developed a three-axial model integrating valence, arousal and a cognitive dimension of expectation/anticipation of which demonstrated that expectation/anticipation is significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball, and hates crowds, might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}
;Physiological responses
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) suggests that excitement involves increased physiological arousal, including increased heart rate, alertness and energy with reduced heart rate variability signalling a heightened sympathetic nervous system (Ketonen et al., 2022).
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}
;Psychological processes
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought actions encouraging problem-solving, and exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}
;Approach motivation and goal pursuit
High affective states have been linked to more approach-oriented behaviour. That is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states also can have goal directed behaviour, however, as excitement is a high positive affect (valence) state and is anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}
;Excitments affect on cognition
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (1998, 2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

=== Excitement on performance ===
According to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor and sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., springint and football tacking) whereas, fine motor tasks &amp; decision-making was impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.  

=== Excitement on impulsivity and risk taking ===
Unregulated excitement can lead to behavioural overshooting. Galentino et al. (2017) demonstrated that positive emotional arousal significantly increases preferences for monetary risks by accentuating reward salience over potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets, over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude, driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (cite). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing said goal. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an understimation of risks, and form impulsive decisions (cite).

While excitement can increase motivation and engagement, heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others.


* (Self-note:Look into more below) affective arousal has been shown to affect judgement, learning and memory (Storbeck &amp; Clore, 2008).
* Attention
* Decision-making
* Positive arousal increases people's risk-taking (GAlentino, Bonini, &amp; Savadori, 2017)
* Creativity
* Performance
* Exploration

{{anchor|Does excitement help or hinder behaviour?}}
;Does excitement help or hinder behaviour?
With helpful excitement, an individual might move towards a goal by preparing, practiising, engaging and performing with said goal.

However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision.

(Find proper citation for this.

Add possible learning task here?)

==Excitement and its influence on well-being==
*Excitement is a positive emotional experience.
*Experiencing positive emotions can contribute to subjective well-being.
* Excitement can make activities feel more engaging and rewarding.
* Anticipating positive experiences can contribute to motvaiton and enjoyment.
* research shows the re-appraisal for anxiety inducing tasks as exciting can lead to greater overall positive experience and performance increase in performance activities (Brooks, 2014).

{{anchor|Excitement, goals and engagement}}
;Excitement goals and engagement
* Excitement can encourage individuals to pursue personally meaningful goals.
* Goal pursuit can contribute to competence, engagement and satisfaction.
* Excitement may help people initiate activities they might otherwise avoid.
* Excitement can therefore indirectly contribute to well-being through behaviour.
* Positive affect has been shown to increase life satisfaction and relationships over time (Liu, 2026).

Case study check: Excitement doesn't necessarily improve well-being simply because they &quot;feel good&quot;, Rather, the emotion may encourage preparation, engagement and goal pursuit, which can subsequently cotnribute to a sense of accomplishment

{{anchor|When excitement becomes unhelpful}}
;When excitement becomes unhelpful

* Extremely high emotional arousal may become overwhelming.
* Excitement may sometimes contribute to impulsive decisions or risk-taking.
* The consequences of excitement depend on the context and the individual's ability to regulate their behaviour.
* Therefore, excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion.

Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depend on intensity, context and behavioural regulation.

==Conclusion==
Excitement is a positive, high-arousal emotional state characterised by anticipation and readiness for action. It can influence behaviour through increased approach motivation, attention and goal-directed action.

Excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes alternatively, the reappraisal of similar physiological emotions into excitement, can allow for greater outcomes in life as well as performance of specific tasks.

Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

So, do what excites!

==Figures==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]]

* For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure; this can be the figure in the scenario
* For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples
* Images must be embedded from [[commons:|Wikimedia Commons]] which hosts free-to-use media such as photos, diagrams, graphs, video, and audio
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text)
* Cite each figure at least once in the main text (e.g., see Figure 2)

==Learning features==
Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options:

{{anchor|Scenarios}}
;Scenarios
* Scenarios, case studies, or examples that illustrate concepts in action
* Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages)
* Can be real or fictional; if real, provide citation(s)

{{anchor|Feature box}}
;Feature boxes
* Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect
* Consider using feature boxes for:
** [[#Scenarios|Scenarios]], case studies, or examples
** Focus questions
** Tips
** Quiz questions
** Take-home messages

;Embedded links
* When key words are introduced, use [[Help:Links|interwiki links]] to:
** Wikipedia articles (e.g., &quot;An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]&quot;) or
** Related book chapters (e.g., &quot;If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]&quot;)

{{anchor|Tables}}
;Tables
* Use tables to organise and summarise information
* Cite each table at least once in the main text (e.g., see Table 1)
* Tables should be captioned
* [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted

'''Table 1''' 

A Descriptive Caption Explains The Table Contents and its Relevance to the Text e.g., 

The 2 x 2 Johari Window Model Showing the Relationship Between Known/Unknown and Self/Other

{| class=&quot;wikitable&quot; style=&quot;margin: auto;
|-
! !! Known to self !! Not known to self
|-
| '''Known to others''' || Open area || Blind spot
|-
| '''Not known to others''' || Hidden area || Unknown
|}

;Quizzes
* One or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=simple&gt;
{The purpose of quizzes is to provide an interactive learning feature:
|type=&quot;()&quot;}
+ True
- False

{Long and complex quiz questions are recommended:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

==Conclusion==
* Arguably the most important section
* Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking
* For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
{{tip|Suggestions for this section:
* Link to the most relevant internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

 Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. Journal of Experimental Psychology. General, 143(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. The American Psychologist, 56(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. Current Opinion in Behavioral Sciences, 39, 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. Frontiers in Psychology, 8, Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. British Journal of Educational Psychology, 93(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. The Journal of Positive Psychology, (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. Social and Personality Psychology Compass, 2(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. Psychological Review, 35(5), 351–366. https://doi.org/10.1037/h0071406

}}

{{tip|Suggestions for this section:
* Important aspects of APA referencing style
** Author surname, followed by a comma, then the author initials separated by full stops and spaces
** Year of publication in parentheses
** Title of work in lower case (except first letter and proper names), ending in a full-stop
** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop
** doi as a URL which is a working hyperlink (i.e., clickable)
** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]:
*** Use &quot;Edit source&quot;
*** &lt;nowiki&gt;{{Hanging indent|1= the full list of references}}&lt;/nowiki&gt;
* The most common mistakes include:
** Incorrect capitalisation
** Incorrect italicisation
** dois which aren't clickable as working hyperlinks
** Citing sources that haven't been consulted
}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)

{{tip|Suggestions for this section:
* Link to the most relevant external resources about the topic
* Include the source in parentheses after the link
}}

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally understood to be a positive, high-arousal emotional state that prepares an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2021). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014). 

=== Early views on excitement ===
Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect, which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situatuion or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational Dimensional Model of Affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural Activation System (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable. Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional picture. From this data, the study developed a three-axial model integrating valence, arousal and a cognitive dimension of expectation/anticipation of which demonstrated that expectation/anticipation is significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball, and hates crowds, might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}
;Physiological responses
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) suggests that excitement involves increased physiological arousal, including increased heart rate, alertness and energy with reduced heart rate variability signalling a heightened sympathetic nervous system (Ketonen et al., 2022).
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}
;Psychological processes
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought actions encouraging problem-solving, and exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}
;Approach motivation and goal pursuit
High affective states have been linked to more approach-oriented behaviour. That is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states also can have goal directed behaviour, however, as excitement is a high positive affect (valence) state and is anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}
;Excitments affect on cognition
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (1998, 2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

=== Excitement on performance ===
According to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor and sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., springint and football tacking) whereas, fine motor tasks &amp; decision-making was impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.  

=== Excitement on impulsivity and risk taking ===
Unregulated excitement can lead to behavioural overshooting. Galentino et al. (2017) demonstrated that positive emotional arousal significantly increases preferences for monetary risks by accentuating reward salience over potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets, over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude, driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (cite). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing said goal. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an understimation of risks, and form impulsive decisions (cite).

While excitement can increase motivation and engagement, heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Brooks (2014) found that excitement and anxiety share similar high-arousal physiological profiles. With attempting to suppress arousal as difficult, Brooks tested participants cognitive strategies under high-presusre tasks with 90% believing the best strategy was some variation of 'calming down'. Brooks showed that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in heart rate. When simply employing this cognitive restrucuture, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Lie et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, found that pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as those than energised positive affect. Lie et al. summates that pleasant positive affect may regulate hedonic stability whereas energised positive affect may operate in the gap between current and desired states, driving personal growth, agency, and goal adaptation rather than baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

=== Excitement as viewed cross-culturally ===
Jeanne Tsai (2007) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm. This maybe due to an 'ideal affect' that is to say, the desire to assert personal autononmy and influence others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. 
* (Self-note:Look into more below) affective arousal has been shown to affect judgement, learning and memory (Storbeck &amp; Clore, 2008).
* Attention
* Decision-making
* Positive arousal increases people's risk-taking (GAlentino, Bonini, &amp; Savadori, 2017)
* Creativity
* Performance
* Exploration

{{anchor|Does excitement help or hinder behaviour?}}
;Does excitement help or hinder behaviour?
With helpful excitement, an individual might move towards a goal by preparing, practiising, engaging and performing with said goal.

However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision.

(Find proper citation for this.

Add possible learning task here?)

==Excitement and its influence on well-being==
*Excitement is a positive emotional experience.
*Experiencing positive emotions can contribute to subjective well-being.
* Excitement can make activities feel more engaging and rewarding.
* Anticipating positive experiences can contribute to motvaiton and enjoyment.
* research shows the re-appraisal for anxiety inducing tasks as exciting can lead to greater overall positive experience and performance increase in performance activities (Brooks, 2014).

{{anchor|Excitement, goals and engagement}}
;Excitement goals and engagement
* Excitement can encourage individuals to pursue personally meaningful goals.
* Goal pursuit can contribute to competence, engagement and satisfaction.
* Excitement may help people initiate activities they might otherwise avoid.
* Excitement can therefore indirectly contribute to well-being through behaviour.
* Positive affect has been shown to increase life satisfaction and relationships over time (Liu, 2026).

Case study check: Excitement doesn't necessarily improve well-being simply because they &quot;feel good&quot;, Rather, the emotion may encourage preparation, engagement and goal pursuit, which can subsequently cotnribute to a sense of accomplishment

{{anchor|When excitement becomes unhelpful}}
;When excitement becomes unhelpful

* Extremely high emotional arousal may become overwhelming.
* Excitement may sometimes contribute to impulsive decisions or risk-taking.
* The consequences of excitement depend on the context and the individual's ability to regulate their behaviour.
* Therefore, excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion.

Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depend on intensity, context and behavioural regulation.

==Conclusion==
Excitement is a positive, high-arousal emotional state characterised by anticipation and readiness for action. It can influence behaviour through increased approach motivation, attention and goal-directed action.

Excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes alternatively, the reappraisal of similar physiological emotions into excitement, can allow for greater outcomes in life as well as performance of specific tasks.

Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

So, do what excites!

==Figures==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]]

* For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure; this can be the figure in the scenario
* For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples
* Images must be embedded from [[commons:|Wikimedia Commons]] which hosts free-to-use media such as photos, diagrams, graphs, video, and audio
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text)
* Cite each figure at least once in the main text (e.g., see Figure 2)

==Learning features==
Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options:

{{anchor|Scenarios}}
;Scenarios
* Scenarios, case studies, or examples that illustrate concepts in action
* Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages)
* Can be real or fictional; if real, provide citation(s)

{{anchor|Feature box}}
;Feature boxes
* Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect
* Consider using feature boxes for:
** [[#Scenarios|Scenarios]], case studies, or examples
** Focus questions
** Tips
** Quiz questions
** Take-home messages

;Embedded links
* When key words are introduced, use [[Help:Links|interwiki links]] to:
** Wikipedia articles (e.g., &quot;An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]&quot;) or
** Related book chapters (e.g., &quot;If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]&quot;)

{{anchor|Tables}}
;Tables
* Use tables to organise and summarise information
* Cite each table at least once in the main text (e.g., see Table 1)
* Tables should be captioned
* [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted

'''Table 1''' 

A Descriptive Caption Explains The Table Contents and its Relevance to the Text e.g., 

The 2 x 2 Johari Window Model Showing the Relationship Between Known/Unknown and Self/Other

{| class=&quot;wikitable&quot; style=&quot;margin: auto;
|-
! !! Known to self !! Not known to self
|-
| '''Known to others''' || Open area || Blind spot
|-
| '''Not known to others''' || Hidden area || Unknown
|}

;Quizzes
* One or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=simple&gt;
{The purpose of quizzes is to provide an interactive learning feature:
|type=&quot;()&quot;}
+ True
- False

{Long and complex quiz questions are recommended:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

==Conclusion==
* Arguably the most important section
* Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking
* For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
{{tip|Suggestions for this section:
* Link to the most relevant internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

 Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. Journal of Experimental Psychology. General, 143(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. The American Psychologist, 56(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. Current Opinion in Behavioral Sciences, 39, 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. Frontiers in Psychology, 8, Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. British Journal of Educational Psychology, 93(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. The Journal of Positive Psychology, (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. Social and Personality Psychology Compass, 2(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. Psychological Review, 35(5), 351–366. https://doi.org/10.1037/h0071406

}}

{{tip|Suggestions for this section:
* Important aspects of APA referencing style
** Author surname, followed by a comma, then the author initials separated by full stops and spaces
** Year of publication in parentheses
** Title of work in lower case (except first letter and proper names), ending in a full-stop
** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop
** doi as a URL which is a working hyperlink (i.e., clickable)
** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]:
*** Use &quot;Edit source&quot;
*** &lt;nowiki&gt;{{Hanging indent|1= the full list of references}}&lt;/nowiki&gt;
* The most common mistakes include:
** Incorrect capitalisation
** Incorrect italicisation
** dois which aren't clickable as working hyperlinks
** Citing sources that haven't been consulted
}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)

{{tip|Suggestions for this section:
* Link to the most relevant external resources about the topic
* Include the source in parentheses after the link
}}

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally understood to be a positive, high-arousal emotional state that prepares an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2021). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014). 

=== Early views on excitement ===
Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect, which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situatuion or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational Dimensional Model of Affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural Activation System (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable. Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional picture. From this data, the study developed a three-axial model integrating valence, arousal and a cognitive dimension of expectation/anticipation of which demonstrated that expectation/anticipation is significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball, and hates crowds, might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}
;Physiological responses
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) suggests that excitement involves increased physiological arousal, including increased heart rate, alertness and energy with reduced heart rate variability signalling a heightened sympathetic nervous system (Ketonen et al., 2022).
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}
;Psychological processes
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought actions encouraging problem-solving, and exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}
;Approach motivation and goal pursuit
High affective states have been linked to more approach-oriented behaviour. That is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states also can have goal directed behaviour, however, as excitement is a high positive affect (valence) state and is anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}
;Excitments affect on cognition
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (1998, 2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

=== Excitement on performance ===
According to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor and sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., springint and football tacking) whereas, fine motor tasks &amp; decision-making was impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.  

=== Excitement on impulsivity and risk taking ===
Unregulated excitement can lead to behavioural overshooting. Galentino et al. (2017) demonstrated that positive emotional arousal significantly increases preferences for monetary risks by accentuating reward salience over potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets, over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude, driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (cite). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing said goal. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an understimation of risks, and form impulsive decisions (cite).

While excitement can increase motivation and engagement, heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Brooks (2014) found that excitement and anxiety share similar high-arousal physiological profiles. With attempting to suppress arousal as difficult, Brooks tested participants cognitive strategies under high-presusre tasks with 90% believing the best strategy was some variation of 'calming down'. Brooks showed that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in heart rate. When simply employing this cognitive restrucuture, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Lie et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, found that pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as those than energised positive affect. Lie et al. summates that pleasant positive affect may regulate hedonic stability whereas energised positive affect may operate in the gap between current and desired states, driving personal growth, agency, and goal adaptation rather than baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

Despite this, Li et al. (2016) found that positive affect in general has been shown to to increase life satisfaction and relationships over time. As excitement is a positive emotional experience, these can contribute to ones subjective well-being. As this emotional state can make activities feel more engaging and rewarding, so to can this anticipation lead to more engagement and possibly reward. Excitement may not necessarily improve well-being simply because it is a positive emotional state, rather, the emotion may encourage preparation, engagement and goal pursuit which can further contributue to a sense of accomplishment (cite).

=== Excitement as viewed cross-culturally ===
Jeanne Tsai (2007) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm. This maybe due to an 'ideal affect' that is to say, the desire to assert personal autononmy and influence others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. 

{{anchor|Does excitement help or hinder behaviour?}}
;Does excitement help or hinder behaviour?
With helpful excitement, an individual might move towards a goal by preparing, practising, engaging and performing behaviours that lead to a desired outcome. However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision (Galentino et al., 2017).

Extremely high emotional arousal may become overwhelming, with the consequences of excitement dependent on the context and the individual's ability to regulate their behaviour. Excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion. Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depend on intnsity, context and behavioural regulation.

{{anchor|Excitement, goals and engagement}}
==Conclusion==
Excitement is a positive, high-arousal emotional state characterised by anticipation and readiness for action. It can influence behaviour through increased approach motivation, attention and goal-directed action.

Excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes alternatively, the reappraisal of similar physiological emotions into excitement, can allow for greater outcomes in life as well as performance of specific tasks.

Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

So, do what excites!

==Figures==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]]

* For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure; this can be the figure in the scenario
* For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples
* Images must be embedded from [[commons:|Wikimedia Commons]] which hosts free-to-use media such as photos, diagrams, graphs, video, and audio
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text)
* Cite each figure at least once in the main text (e.g., see Figure 2)

==Learning features==
Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options:

{{anchor|Scenarios}}
;Scenarios
* Scenarios, case studies, or examples that illustrate concepts in action
* Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages)
* Can be real or fictional; if real, provide citation(s)

{{anchor|Feature box}}
;Feature boxes
* Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect
* Consider using feature boxes for:
** [[#Scenarios|Scenarios]], case studies, or examples
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;Embedded links
* When key words are introduced, use [[Help:Links|interwiki links]] to:
** Wikipedia articles (e.g., &quot;An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]&quot;) or
** Related book chapters (e.g., &quot;If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]&quot;)

{{anchor|Tables}}
;Tables
* Use tables to organise and summarise information
* Cite each table at least once in the main text (e.g., see Table 1)
* Tables should be captioned
* [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted

'''Table 1''' 

A Descriptive Caption Explains The Table Contents and its Relevance to the Text e.g., 

The 2 x 2 Johari Window Model Showing the Relationship Between Known/Unknown and Self/Other

{| class=&quot;wikitable&quot; style=&quot;margin: auto;
|-
! !! Known to self !! Not known to self
|-
| '''Known to others''' || Open area || Blind spot
|-
| '''Not known to others''' || Hidden area || Unknown
|}

;Quizzes
* One or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=simple&gt;
{The purpose of quizzes is to provide an interactive learning feature:
|type=&quot;()&quot;}
+ True
- False

{Long and complex quiz questions are recommended:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

==Conclusion==
* Arguably the most important section
* Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking
* For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
{{tip|Suggestions for this section:
* Link to the most relevant internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

 Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. Journal of Experimental Psychology. General, 143(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. The American Psychologist, 56(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. Current Opinion in Behavioral Sciences, 39, 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. Frontiers in Psychology, 8, Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. British Journal of Educational Psychology, 93(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. The Journal of Positive Psychology, (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. Social and Personality Psychology Compass, 2(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. Psychological Review, 35(5), 351–366. https://doi.org/10.1037/h0071406

}}

{{tip|Suggestions for this section:
* Important aspects of APA referencing style
** Author surname, followed by a comma, then the author initials separated by full stops and spaces
** Year of publication in parentheses
** Title of work in lower case (except first letter and proper names), ending in a full-stop
** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop
** doi as a URL which is a working hyperlink (i.e., clickable)
** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]:
*** Use &quot;Edit source&quot;
*** &lt;nowiki&gt;{{Hanging indent|1= the full list of references}}&lt;/nowiki&gt;
* The most common mistakes include:
** Incorrect capitalisation
** Incorrect italicisation
** dois which aren't clickable as working hyperlinks
** Citing sources that haven't been consulted
}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)

{{tip|Suggestions for this section:
* Link to the most relevant external resources about the topic
* Include the source in parentheses after the link
}}

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally understood to be a positive, high-arousal emotional state that prepares an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2021). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014). 

=== Early views on excitement ===
Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect, which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situatuion or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational Dimensional Model of Affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural Activation System (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable (. Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional picture. From this data, the study developed a three-axial model integrating valence, arousal and a cognitive dimension of expectation/anticipation of which demonstrated that expectation/anticipation is significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball, and hates crowds, might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}
;Physiological responses
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) suggests that excitement involves increased physiological arousal, including increased heart rate, alertness and energy with reduced heart rate variability signalling a heightened sympathetic nervous system (Ketonen et al., 2022).
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}
;Psychological processes
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought actions encouraging problem-solving, and exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}
;Approach motivation and goal pursuit
High affective states have been linked to more approach-oriented behaviour. That is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states also can have goal directed behaviour, however, as excitement is a high positive affect (valence) state and is anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}
;Excitments affect on cognition
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (1998, 2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

=== Excitement on performance ===
According to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor and sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., springint and football tacking) whereas, fine motor tasks &amp; decision-making was impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.  

=== Excitement on impulsivity and risk taking ===
Unregulated excitement can lead to behavioural overshooting. Galentino et al. (2017) demonstrated that positive emotional arousal significantly increases preferences for monetary risks by accentuating reward salience over potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets, over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude, driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (cite). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing said goal. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an understimation of risks, and form impulsive decisions (cite).

While excitement can increase motivation and engagement, heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Brooks (2014) found that excitement and anxiety share similar high-arousal physiological profiles. With attempting to suppress arousal as difficult, Brooks tested participants cognitive strategies under high-presusre tasks with 90% believing the best strategy was some variation of 'calming down'. Brooks showed that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in heart rate. When simply employing this cognitive restrucuture, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Lie et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, found that pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as those than energised positive affect. Lie et al. summates that pleasant positive affect may regulate hedonic stability whereas energised positive affect may operate in the gap between current and desired states, driving personal growth, agency, and goal adaptation rather than baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

Despite this, Li et al. (2016) found that positive affect in general has been shown to to increase life satisfaction and relationships over time. As excitement is a positive emotional experience, these can contribute to ones subjective well-being. As this emotional state can make activities feel more engaging and rewarding, so to can this anticipation lead to more engagement and possibly reward. Excitement may not necessarily improve well-being simply because it is a positive emotional state, rather, the emotion may encourage preparation, engagement and goal pursuit which can further contributue to a sense of accomplishment (cite).

=== Excitement as viewed cross-culturally ===
Jeanne Tsai (2007) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm. This maybe due to an 'ideal affect' that is to say, the desire to assert personal autononmy and influence others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. 

{{anchor|Does excitement help or hinder behaviour?}}
;Does excitement help or hinder behaviour?
With helpful excitement, an individual might move towards a goal by preparing, practising, engaging and performing behaviours that lead to a desired outcome. However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision (Galentino et al., 2017).

Extremely high emotional arousal may become overwhelming, with the consequences of excitement dependent on the context and the individual's ability to regulate their behaviour. Excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion. Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depend on intnsity, context and behavioural regulation.

{{anchor|Excitement, goals and engagement}}
==Conclusion==
Excitement is a positive, high-arousal emotional state characterised by anticipation and readiness for action. It can influence behaviour through increased approach motivation, attention and goal-directed action.

Excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes alternatively, the reappraisal of similar physiological emotions into excitement, can allow for greater outcomes in life as well as performance of specific tasks.

Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

So, do what excites!

==Figures==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]]

* For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure; this can be the figure in the scenario
* For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples
* Images must be embedded from [[commons:|Wikimedia Commons]] which hosts free-to-use media such as photos, diagrams, graphs, video, and audio
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text)
* Cite each figure at least once in the main text (e.g., see Figure 2)

==Learning features==
Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options:

{{anchor|Scenarios}}
;Scenarios
* Scenarios, case studies, or examples that illustrate concepts in action
* Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages)
* Can be real or fictional; if real, provide citation(s)

{{anchor|Feature box}}
;Feature boxes
* Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect
* Consider using feature boxes for:
** [[#Scenarios|Scenarios]], case studies, or examples
** Focus questions
** Tips
** Quiz questions
** Take-home messages

;Embedded links
* When key words are introduced, use [[Help:Links|interwiki links]] to:
** Wikipedia articles (e.g., &quot;An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]&quot;) or
** Related book chapters (e.g., &quot;If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]&quot;)

{{anchor|Tables}}
;Tables
* Use tables to organise and summarise information
* Cite each table at least once in the main text (e.g., see Table 1)
* Tables should be captioned
* [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted

'''Table 1''' 

A Descriptive Caption Explains The Table Contents and its Relevance to the Text e.g., 

The 2 x 2 Johari Window Model Showing the Relationship Between Known/Unknown and Self/Other

{| class=&quot;wikitable&quot; style=&quot;margin: auto;
|-
! !! Known to self !! Not known to self
|-
| '''Known to others''' || Open area || Blind spot
|-
| '''Not known to others''' || Hidden area || Unknown
|}

;Quizzes
* One or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=simple&gt;
{The purpose of quizzes is to provide an interactive learning feature:
|type=&quot;()&quot;}
+ True
- False

{Long and complex quiz questions are recommended:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

==Conclusion==
* Arguably the most important section
* Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking
* For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
{{tip|Suggestions for this section:
* Link to the most relevant internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

 Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. Journal of Experimental Psychology. General, 143(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. The American Psychologist, 56(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. Current Opinion in Behavioral Sciences, 39, 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. Frontiers in Psychology, 8, Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. British Journal of Educational Psychology, 93(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. The Journal of Positive Psychology, (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. Social and Personality Psychology Compass, 2(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. Psychological Review, 35(5), 351–366. https://doi.org/10.1037/h0071406

}}

{{tip|Suggestions for this section:
* Important aspects of APA referencing style
** Author surname, followed by a comma, then the author initials separated by full stops and spaces
** Year of publication in parentheses
** Title of work in lower case (except first letter and proper names), ending in a full-stop
** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop
** doi as a URL which is a working hyperlink (i.e., clickable)
** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]:
*** Use &quot;Edit source&quot;
*** &lt;nowiki&gt;{{Hanging indent|1= the full list of references}}&lt;/nowiki&gt;
* The most common mistakes include:
** Incorrect capitalisation
** Incorrect italicisation
** dois which aren't clickable as working hyperlinks
** Citing sources that haven't been consulted
}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)

{{tip|Suggestions for this section:
* Link to the most relevant external resources about the topic
* Include the source in parentheses after the link
}}

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally understood to be a positive, high-arousal emotional state that prepares an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2021). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014). 

=== Early views on excitement ===
Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect, which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situatuion or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational Dimensional Model of Affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural Activation System (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable (. Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional picture. From this data, the study developed a three-axial model integrating valence, arousal and a cognitive dimension of expectation/anticipation of which demonstrated that expectation/anticipation is significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball, and hates crowds, might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}

=== Physiological responses ===
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) suggests that excitement involves increased physiological arousal, including increased heart rate, alertness and energy with reduced heart rate variability signalling a heightened sympathetic nervous system (Ketonen et al., 2022).
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}

=== Psychological processes ===
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought actions encouraging problem-solving, and exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}

=== Approach motivation and goal pursuit ===
High affective states have been linked to more approach-oriented behaviour. That is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states also can have goal directed behaviour, however, as excitement is a high positive affect (valence) state and is anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}

=== Excitments affect on cognition ===
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (1998, 2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

=== Excitement on performance ===
According to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor and sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., springint and football tacking) whereas, fine motor tasks &amp; decision-making was impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.  

=== Excitement on impulsivity and risk taking ===
Unregulated excitement can lead to behavioural overshooting. Galentino et al. (2017) demonstrated that positive emotional arousal significantly increases preferences for monetary risks by accentuating reward salience over potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets, over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude, driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (cite). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing said goal. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an understimation of risks, and form impulsive decisions (cite).

While excitement can increase motivation and engagement, heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Brooks (2014) found that excitement and anxiety share similar high-arousal physiological profiles. With attempting to suppress arousal as difficult, Brooks tested participants cognitive strategies under high-presusre tasks with 90% believing the best strategy was some variation of 'calming down'. Brooks showed that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in heart rate. When simply employing this cognitive restrucuture, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Lie et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, found that pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as those than energised positive affect. Lie et al. summates that pleasant positive affect may regulate hedonic stability whereas energised positive affect may operate in the gap between current and desired states, driving personal growth, agency, and goal adaptation rather than baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

Despite this, Li et al. (2016) found that positive affect in general has been shown to to increase life satisfaction and relationships over time. As excitement is a positive emotional experience, these can contribute to ones subjective well-being. As this emotional state can make activities feel more engaging and rewarding, so to can this anticipation lead to more engagement and possibly reward. Excitement may not necessarily improve well-being simply because it is a positive emotional state, rather, the emotion may encourage preparation, engagement and goal pursuit which can further contributue to a sense of accomplishment (cite).

=== Excitement as viewed cross-culturally ===
Jeanne Tsai (2007) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm. This maybe due to an 'ideal affect' that is to say, the desire to assert personal autononmy and influence others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. 

{{anchor|Does excitement help or hinder behaviour?}}

=== Does excitement help or hinder behaviour? ===
With helpful excitement, an individual might move towards a goal by preparing, practising, engaging and performing behaviours that lead to a desired outcome. However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision (Galentino et al., 2017).

Extremely high emotional arousal may become overwhelming, with the consequences of excitement dependent on the context and the individual's ability to regulate their behaviour. Excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion. Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depend on intnsity, context and behavioural regulation.

{{anchor|Excitement, goals and engagement}}
==Conclusion==
Excitement is a positive, high-arousal emotional state characterised by anticipation and readiness for action. It can influence behaviour through increased approach motivation, attention and goal-directed action.

Excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes alternatively, the reappraisal of similar physiological emotions into excitement, can allow for greater outcomes in life as well as performance of specific tasks.

Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

So, do what excites!

==Figures==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]]

* For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure; this can be the figure in the scenario
* For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples
* Images must be embedded from [[commons:|Wikimedia Commons]] which hosts free-to-use media such as photos, diagrams, graphs, video, and audio
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text)
* Cite each figure at least once in the main text (e.g., see Figure 2)

==Learning features==
Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options:

{{anchor|Scenarios}}
;Scenarios
* Scenarios, case studies, or examples that illustrate concepts in action
* Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages)
* Can be real or fictional; if real, provide citation(s)

{{anchor|Feature box}}
;Feature boxes
* Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect
* Consider using feature boxes for:
** [[#Scenarios|Scenarios]], case studies, or examples
** Focus questions
** Tips
** Quiz questions
** Take-home messages

;Embedded links
* When key words are introduced, use [[Help:Links|interwiki links]] to:
** Wikipedia articles (e.g., &quot;An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]&quot;) or
** Related book chapters (e.g., &quot;If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]&quot;)

{{anchor|Tables}}
;Tables
* Use tables to organise and summarise information
* Cite each table at least once in the main text (e.g., see Table 1)
* Tables should be captioned
* [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted

'''Table 1''' 

A Descriptive Caption Explains The Table Contents and its Relevance to the Text e.g., 

The 2 x 2 Johari Window Model Showing the Relationship Between Known/Unknown and Self/Other

{| class=&quot;wikitable&quot; style=&quot;margin: auto;
|-
! !! Known to self !! Not known to self
|-
| '''Known to others''' || Open area || Blind spot
|-
| '''Not known to others''' || Hidden area || Unknown
|}

;Quizzes
* One or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=simple&gt;
{The purpose of quizzes is to provide an interactive learning feature:
|type=&quot;()&quot;}
+ True
- False

{Long and complex quiz questions are recommended:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

==Conclusion==
* Arguably the most important section
* Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking
* For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
{{tip|Suggestions for this section:
* Link to the most relevant internal resources about the topic
* Include the source in parentheses
}}

==References==
{{Hanging indent|1=

 Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. Journal of Experimental Psychology. General, 143(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. The American Psychologist, 56(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. Current Opinion in Behavioral Sciences, 39, 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. Frontiers in Psychology, 8, Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. British Journal of Educational Psychology, 93(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. The Journal of Positive Psychology, (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. Social and Personality Psychology Compass, 2(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. Psychological Review, 35(5), 351–366. https://doi.org/10.1037/h0071406

}}

{{tip|Suggestions for this section:
* Important aspects of APA referencing style
** Author surname, followed by a comma, then the author initials separated by full stops and spaces
** Year of publication in parentheses
** Title of work in lower case (except first letter and proper names), ending in a full-stop
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* The most common mistakes include:
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}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)

{{tip|Suggestions for this section:
* Link to the most relevant external resources about the topic
* Include the source in parentheses after the link
}}

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally understood to be a positive, high-arousal emotional state that prepares an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2021). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014). 

=== Early views on excitement ===
Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect, which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situatuion or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational Dimensional Model of Affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural Activation System (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable (. Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional picture. From this data, the study developed a three-axial model integrating valence, arousal and a cognitive dimension of expectation/anticipation of which demonstrated that expectation/anticipation is significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball, and hates crowds, might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}

=== Physiological responses ===
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) suggests that excitement involves increased physiological arousal, including increased heart rate, alertness and energy with reduced heart rate variability signalling a heightened sympathetic nervous system (Ketonen et al., 2022).
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}

=== Psychological processes ===
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought actions encouraging problem-solving, and exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}

=== Approach motivation and goal pursuit ===
High affective states have been linked to more approach-oriented behaviour. That is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states also can have goal directed behaviour, however, as excitement is a high positive affect (valence) state and is anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}

=== Excitments affect on cognition ===
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (1998, 2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

=== Excitement on performance ===
According to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor and sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., springint and football tacking) whereas, fine motor tasks &amp; decision-making was impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.  

=== Excitement on impulsivity and risk taking ===
Unregulated excitement can lead to behavioural overshooting. Galentino et al. (2017) demonstrated that positive emotional arousal significantly increases preferences for monetary risks by accentuating reward salience over potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets, over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude, driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (cite). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing said goal. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an understimation of risks, and form impulsive decisions (cite).

While excitement can increase motivation and engagement, heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Brooks (2014) found that excitement and anxiety share similar high-arousal physiological profiles. With attempting to suppress arousal as difficult, Brooks tested participants cognitive strategies under high-presusre tasks with 90% believing the best strategy was some variation of 'calming down'. Brooks showed that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in heart rate. When simply employing this cognitive restrucuture, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Lie et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, found that pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as those than energised positive affect. Lie et al. summates that pleasant positive affect may regulate hedonic stability whereas energised positive affect may operate in the gap between current and desired states, driving personal growth, agency, and goal adaptation rather than baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

Despite this, Li et al. (2016) found that positive affect in general has been shown to to increase life satisfaction and relationships over time. As excitement is a positive emotional experience, these can contribute to ones subjective well-being. As this emotional state can make activities feel more engaging and rewarding, so to can this anticipation lead to more engagement and possibly reward. Excitement may not necessarily improve well-being simply because it is a positive emotional state, rather, the emotion may encourage preparation, engagement and goal pursuit which can further contributue to a sense of accomplishment (cite).

=== Excitement as viewed cross-culturally ===
Jeanne Tsai (2007) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm. This maybe due to an 'ideal affect' that is to say, the desire to assert personal autononmy and influence others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. 

{{anchor|Does excitement help or hinder behaviour?}}

=== Does excitement help or hinder behaviour? ===
With helpful excitement, an individual might move towards a goal by preparing, practising, engaging and performing behaviours that lead to a desired outcome. However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision (Galentino et al., 2017).

Extremely high emotional arousal may become overwhelming, with the consequences of excitement dependent on the context and the individual's ability to regulate their behaviour. Excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion. Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depend on intnsity, context and behavioural regulation.

{{anchor|Excitement, goals and engagement}}
==Conclusion==
Excitement is a positive, high-arousal emotional state characterised by anticipation and readiness for action. It can influence behaviour through increased approach motivation, attention and goal-directed action.

Excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes alternatively, the reappraisal of similar physiological emotions into excitement, can allow for greater outcomes in life as well as performance of specific tasks.

Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

So, do what excites!

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
==References==
{{Hanging indent|1=

 Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. Journal of Experimental Psychology. General, 143(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. The American Psychologist, 56(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. Current Opinion in Behavioral Sciences, 39, 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. Frontiers in Psychology, 8, Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. British Journal of Educational Psychology, 93(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. The Journal of Positive Psychology, (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. Social and Personality Psychology Compass, 2(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. Psychological Review, 35(5), 351–366. https://doi.org/10.1037/h0071406

}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally understood to be a positive, high-arousal emotional state that prepares an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2021). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014). 

=== Early views on excitement ===
Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect, which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situatuion or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational Dimensional Model of Affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural Activation System (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable (. Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional picture. From this data, the study developed a three-axial model integrating valence, arousal and a cognitive dimension of expectation/anticipation of which demonstrated that expectation/anticipation is significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball, and hates crowds, might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}

=== Physiological responses ===
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) suggests that excitement involves increased physiological arousal, including increased heart rate, alertness and energy with reduced heart rate variability signalling a heightened sympathetic nervous system (Ketonen et al., 2022).
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}

=== Psychological processes ===
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought actions encouraging problem-solving, and exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}

=== Approach motivation and goal pursuit ===
High affective states have been linked to more approach-oriented behaviour. That is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states also can have goal directed behaviour, however, as excitement is a high positive affect (valence) state and is anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}

=== Excitments affect on cognition ===
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (1998, 2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

=== Excitement on performance ===
According to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor and sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., springint and football tacking) whereas, fine motor tasks &amp; decision-making was impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.  

=== Excitement on impulsivity and risk taking ===
Unregulated excitement can lead to behavioural overshooting. Galentino et al. (2017) demonstrated that positive emotional arousal significantly increases preferences for monetary risks by accentuating reward salience over potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets, over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude, driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (cite). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing said goal. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an understimation of risks, and form impulsive decisions (cite).

While excitement can increase motivation and engagement, heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Brooks (2014) found that excitement and anxiety share similar high-arousal physiological profiles. With attempting to suppress arousal as difficult, Brooks tested participants cognitive strategies under high-presusre tasks with 90% believing the best strategy was some variation of 'calming down'. Brooks showed that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in heart rate. When simply employing this cognitive restrucuture, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Lie et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, found that pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as those than energised positive affect. Lie et al. summates that pleasant positive affect may regulate hedonic stability whereas energised positive affect may operate in the gap between current and desired states, driving personal growth, agency, and goal adaptation rather than baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

Despite this, Li et al. (2016) found that positive affect in general has been shown to to increase life satisfaction and relationships over time. As excitement is a positive emotional experience, these can contribute to ones subjective well-being. As this emotional state can make activities feel more engaging and rewarding, so to can this anticipation lead to more engagement and possibly reward. Excitement may not necessarily improve well-being simply because it is a positive emotional state, rather, the emotion may encourage preparation, engagement and goal pursuit which can further contributue to a sense of accomplishment (cite).

=== Excitement as viewed cross-culturally ===
Jeanne Tsai (2007) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm. This maybe due to an 'ideal affect' that is to say, the desire to assert personal autononmy and influence others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. 

{{anchor|Does excitement help or hinder behaviour?}}

=== Does excitement help or hinder behaviour? ===
With helpful excitement, an individual might move towards a goal by preparing, practising, engaging and performing behaviours that lead to a desired outcome. However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision (Galentino et al., 2017).

Extremely high emotional arousal may become overwhelming, with the consequences of excitement dependent on the context and the individual's ability to regulate their behaviour. Excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion. Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depend on intnsity, context and behavioural regulation.

{{anchor|Excitement, goals and engagement}}
==Conclusion==
Excitement is a positive, high-arousal emotional state characterised by anticipation and readiness for action. It can influence behaviour through increased approach motivation, attention and goal-directed action.

Excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes alternatively, the reappraisal of similar physiological emotions into excitement, can allow for greater outcomes in life as well as performance of specific tasks.

Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

So, do what excites!

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
==References==
{{Hanging indent|1=

Andrade, E. B., Odean, T., &amp; Lin, S. (2016). Bubbling with Excitement: An Experiment. ''Review of Finance, 20''(2), 447–466. https://doi.org/10.1093/rof/rfv016

Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. ''Journal of Experimental Psychology. General, 143''(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. ''The American Psychologist, 56''(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. ''Current Opinion in Behavioral Sciences, 39'', 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Gable, P., &amp; Harmon-Jones, E. (2010). The motivational dimensional model of affect: Implications for breadth of attention, memory, and cognitive categorisation. ''Cognition and Emotion, 24''(2), 322–337. https://doi.org/10.1080/02699930903378305

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. ''Frontiers in Psychology, 8'', Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Hasada, R. (1994). ''The semantic aspects of onomatopoeia: focusing on Japanese psychomimes'' [Master's thesis, The Australian National University]. ANU Open Research. https://doi.org/10.25911/5d723cb12c49c 

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. ''British Journal of Educational Psychology, 93''(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Lim, N. (2016). Cultural differences in emotion: differences in emotional arousal level between the East and the West. ''Integrative Medicine Research, 5''(2), 105–109. https://doi.org/10.1016/j.imr.2016.03.004

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. ''The Journal of Positive Psychology'', (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Machizawa, M. G., Lisi, G., Kanayama, N., Mizuochi, R., Makita, K., Sasaoka, T., &amp; Yamawaki, S. (2020). Quantification of anticipation of excitement with a three-axial model of emotion with EEG. ''Journal of Neural Engineering, 17''(3). https://doi.org/10.1088/1741-2552/ab93b4

Oxendine, J. B. (1970). Emotional Arousal and Motor Performance. ''Quest (National Association for Kinesiology in Higher Education), 13''(1), 23–32. https://doi.org/10.1080/00336297.1970.10519673

Piira, O.-P., Huikuri, H. V., &amp; Tulppo, M. P. (2011). Effects of emotional excitement on heart rate and blood pressure dynamics in patients with coronary artery disease. ''Autonomic Neuroscience, 160''(1–2), 107–114. https://doi.org/10.1016/j.autneu.2010.11.011

Posner, J., Russell, J. A., &amp; Peterson, B. S. (2005). The circumplex model of affect: An integrative approach to affective neuroscience, cognitive development, and psychopathology. ''Development and Psychopathology, 17''(3), 715–734. https://doi.org/10.1017/S0954579405050340

Robinson, M. D., &amp; Irvin, R. L. (2022). Out of the shell, into the world: preferences for openness as a substrate of approach motivation and positive affect. ''Motivation and Emotion, 46''(3), 307–318. https://doi.org/10.1007/s11031-022-09934-5

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Schachter, S., &amp; Singer, J. (1962). Cognitive, social, and physiological determinants of emotional state. ''Psychological Review, 69''(5), 379–399. https://doi.org/10.1037/h0046234

Smith, K. E., Woodard, K., &amp; Pollak, S. D. (2025). Arousal May Not Be Anything to Get Excited About. ''Emotion Review, 17''(1), 3–15. https://doi.org/10.1177/17540739241303499

Sohn, J.-H., Kim, H.-E., Sohn, S., Seok, J.-W., Choi, D., &amp; Watanuki, S. (2015). Effect of emotional arousal on inter-temporal decision-making: an fMRI study. ''Journal of Physiological Anthropology, 34''(1), Article 8. https://doi.org/10.1186/s40101-015-0047-5

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. ''Social and Personality Psychology Compass, 2''(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. ''Psychological Review, 35''(5), 351–366. https://doi.org/10.1037/h0071406

Tugade, M. M., Shiota, M. N., &amp; Kirby, L. D. (Eds.). (2014). ''Handbook of positive emotions'' (1st ed.). Guilford Press.


}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally understood to be a positive, high-arousal emotional state that prepares an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2021). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014). 

=== Early views on excitement ===
Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect, which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situatuion or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational Dimensional Model of Affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural Activation System (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable (. Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional picture. From this data, the study developed a three-axial model integrating valence, arousal and a cognitive dimension of expectation/anticipation of which demonstrated that expectation/anticipation is significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball, and hates crowds, might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}

=== Physiological responses ===
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) suggests that excitement involves increased physiological arousal, including increased heart rate, alertness and energy with reduced heart rate variability signalling a heightened sympathetic nervous system (Ketonen et al., 2022).
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}

=== Psychological processes ===
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought actions encouraging problem-solving, and exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}

=== Approach motivation and goal pursuit ===
High affective states have been linked to more approach-oriented behaviour. That is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states also can have goal directed behaviour, however, as excitement is a high positive affect (valence) state and is anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}

=== Excitments affect on cognition ===
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (1998, 2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

=== Excitement on performance ===
According to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor and sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., springint and football tacking) whereas, fine motor tasks &amp; decision-making was impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.  

=== Excitement on impulsivity and risk taking ===
Unregulated excitement can lead to behavioural overshooting. Galentino et al. (2017) demonstrated that positive emotional arousal significantly increases preferences for monetary risks by accentuating reward salience over potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets, over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude, driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (cite). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing said goal. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an understimation of risks, and form impulsive decisions (cite).

While excitement can increase motivation and engagement, heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Brooks (2014) found that excitement and anxiety share similar high-arousal physiological profiles. With attempting to suppress arousal as difficult, Brooks tested participants cognitive strategies under high-presusre tasks with 90% believing the best strategy was some variation of 'calming down'. Brooks showed that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in heart rate. When simply employing this cognitive restrucuture, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Lie et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, found that pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as those than energised positive affect. Lie et al. summates that pleasant positive affect may regulate hedonic stability whereas energised positive affect may operate in the gap between current and desired states, driving personal growth, agency, and goal adaptation rather than baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

Despite this, Li et al. (2016) found that positive affect in general has been shown to to increase life satisfaction and relationships over time. As excitement is a positive emotional experience, these can contribute to ones subjective well-being. As this emotional state can make activities feel more engaging and rewarding, so to can this anticipation lead to more engagement and possibly reward. Excitement may not necessarily improve well-being simply because it is a positive emotional state, rather, the emotion may encourage preparation, engagement and goal pursuit which can further contributue to a sense of accomplishment (cite).

=== Excitement as viewed cross-culturally ===
Jeanne Tsai (2007) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm. This maybe due to an 'ideal affect' that is to say, the desire to assert personal autononmy and influence others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. 

{{anchor|Does excitement help or hinder behaviour?}}

=== Does excitement help or hinder behaviour? ===
With helpful excitement, an individual might move towards a goal by preparing, practising, engaging and performing behaviours that lead to a desired outcome. However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision (Galentino et al., 2017).

Extremely high emotional arousal may become overwhelming, with the consequences of excitement dependent on the context and the individual's ability to regulate their behaviour. Excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion. Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depend on intnsity, context and behavioural regulation.

{{anchor|Excitement, goals and engagement}}
==Conclusion==
Excitement is a positive, high-arousal emotional state characterised by anticipation and readiness for action. It can influence behaviour through increased approach motivation, attention and goal-directed action.

Excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes alternatively, the reappraisal of similar physiological emotions into excitement, can allow for greater outcomes in life as well as performance of specific tasks.

Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

So, do what excites!

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
==References==
{{Hanging indent|1=

Andrade, E. B., Odean, T., &amp; Lin, S. (2016). Bubbling with Excitement: An Experiment. ''Review of Finance, 20''(2), 447–466. https://doi.org/10.1093/rof/rfv016

Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. ''Journal of Experimental Psychology. General, 143''(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. ''The American Psychologist, 56''(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. ''Current Opinion in Behavioral Sciences, 39'', 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Gable, P., &amp; Harmon-Jones, E. (2010). The motivational dimensional model of affect: Implications for breadth of attention, memory, and cognitive categorisation. ''Cognition and Emotion, 24''(2), 322–337. https://doi.org/10.1080/02699930903378305

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. ''Frontiers in Psychology, 8'', Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Hasada, R. (1994). ''The semantic aspects of onomatopoeia: focusing on Japanese psychomimes'' [Master's thesis, The Australian National University]. ANU Open Research. https://doi.org/10.25911/5d723cb12c49c 

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. ''British Journal of Educational Psychology, 93''(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Lim, N. (2016). Cultural differences in emotion: differences in emotional arousal level between the East and the West. ''Integrative Medicine Research, 5''(2), 105–109. https://doi.org/10.1016/j.imr.2016.03.004

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. ''The Journal of Positive Psychology'', (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Machizawa, M. G., Lisi, G., Kanayama, N., Mizuochi, R., Makita, K., Sasaoka, T., &amp; Yamawaki, S. (2020). Quantification of anticipation of excitement with a three-axial model of emotion with EEG. ''Journal of Neural Engineering, 17''(3). https://doi.org/10.1088/1741-2552/ab93b4

Oxendine, J. B. (1970). Emotional Arousal and Motor Performance. ''Quest (National Association for Kinesiology in Higher Education), 13''(1), 23–32. https://doi.org/10.1080/00336297.1970.10519673

Piira, O.-P., Huikuri, H. V., &amp; Tulppo, M. P. (2011). Effects of emotional excitement on heart rate and blood pressure dynamics in patients with coronary artery disease. ''Autonomic Neuroscience, 160''(1–2), 107–114. https://doi.org/10.1016/j.autneu.2010.11.011

Posner, J., Russell, J. A., &amp; Peterson, B. S. (2005). The circumplex model of affect: An integrative approach to affective neuroscience, cognitive development, and psychopathology. ''Development and Psychopathology, 17''(3), 715–734. https://doi.org/10.1017/S0954579405050340

Robinson, M. D., &amp; Irvin, R. L. (2022). Out of the shell, into the world: preferences for openness as a substrate of approach motivation and positive affect. ''Motivation and Emotion, 46''(3), 307–318. https://doi.org/10.1007/s11031-022-09934-5

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Schachter, S., &amp; Singer, J. (1962). Cognitive, social, and physiological determinants of emotional state. ''Psychological Review, 69''(5), 379–399. https://doi.org/10.1037/h0046234

Smith, K. E., Woodard, K., &amp; Pollak, S. D. (2025). Arousal May Not Be Anything to Get Excited About. ''Emotion Review, 17''(1), 3–15. https://doi.org/10.1177/17540739241303499

Sohn, J.-H., Kim, H.-E., Sohn, S., Seok, J.-W., Choi, D., &amp; Watanuki, S. (2015). Effect of emotional arousal on inter-temporal decision-making: an fMRI study. ''Journal of Physiological Anthropology, 34''(1), Article 8. https://doi.org/10.1186/s40101-015-0047-5

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. ''Social and Personality Psychology Compass, 2''(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. ''Psychological Review, 35''(5), 351–366. https://doi.org/10.1037/h0071406

Tugade, M. M., Shiota, M. N., &amp; Kirby, L. D. (Eds.). (2014). ''Handbook of positive emotions'' (1st ed.). Guilford Press.


}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)
* Cognitive Reappraisal for Anxiety: Evidence-Based Strategies That Work (

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally understood to be a positive, high-arousal emotional state that prepares an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2021). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014). 

=== Early views on excitement ===
Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect, which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situatuion or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational Dimensional Model of Affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural Activation System (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable (. Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional picture. From this data, the study developed a three-axial model integrating valence, arousal and a cognitive dimension of expectation/anticipation of which demonstrated that expectation/anticipation is significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball, and hates crowds, might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}

=== Physiological responses ===
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) suggests that excitement involves increased physiological arousal, including increased heart rate, alertness and energy with reduced heart rate variability signalling a heightened sympathetic nervous system (Ketonen et al., 2022).
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}

=== Psychological processes ===
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought actions encouraging problem-solving, and exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}

=== Approach motivation and goal pursuit ===
High affective states have been linked to more approach-oriented behaviour. That is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states also can have goal directed behaviour, however, as excitement is a high positive affect (valence) state and is anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}

=== Excitments affect on cognition ===
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (1998, 2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

=== Excitement on performance ===
According to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor and sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., springint and football tacking) whereas, fine motor tasks &amp; decision-making was impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.  

=== Excitement on impulsivity and risk taking ===
Unregulated excitement can lead to behavioural overshooting. Galentino et al. (2017) demonstrated that positive emotional arousal significantly increases preferences for monetary risks by accentuating reward salience over potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets, over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude, driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (cite). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing said goal. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an understimation of risks, and form impulsive decisions (cite).

While excitement can increase motivation and engagement, heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Brooks (2014) found that excitement and anxiety share similar high-arousal physiological profiles. With attempting to suppress arousal as difficult, Brooks tested participants cognitive strategies under high-presusre tasks with 90% believing the best strategy was some variation of 'calming down'. Brooks showed that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in heart rate. When simply employing this cognitive restrucuture, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Lie et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, found that pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as those than energised positive affect. Lie et al. summates that pleasant positive affect may regulate hedonic stability whereas energised positive affect may operate in the gap between current and desired states, driving personal growth, agency, and goal adaptation rather than baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

Despite this, Li et al. (2016) found that positive affect in general has been shown to to increase life satisfaction and relationships over time. As excitement is a positive emotional experience, these can contribute to ones subjective well-being. As this emotional state can make activities feel more engaging and rewarding, so to can this anticipation lead to more engagement and possibly reward. Excitement may not necessarily improve well-being simply because it is a positive emotional state, rather, the emotion may encourage preparation, engagement and goal pursuit which can further contributue to a sense of accomplishment (cite).

=== Excitement as viewed cross-culturally ===
Jeanne Tsai (2007) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm. This maybe due to an 'ideal affect' that is to say, the desire to assert personal autononmy and influence others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. 

{{anchor|Does excitement help or hinder behaviour?}}

=== Does excitement help or hinder behaviour? ===
With helpful excitement, an individual might move towards a goal by preparing, practising, engaging and performing behaviours that lead to a desired outcome. However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision (Galentino et al., 2017).

Extremely high emotional arousal may become overwhelming, with the consequences of excitement dependent on the context and the individual's ability to regulate their behaviour. Excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion. Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depend on intnsity, context and behavioural regulation.

{{anchor|Excitement, goals and engagement}}
==Conclusion==
Excitement is a positive, high-arousal emotional state characterised by anticipation and readiness for action. It can influence behaviour through increased approach motivation, attention and goal-directed action.

Excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes alternatively, the reappraisal of similar physiological emotions into excitement, can allow for greater outcomes in life as well as performance of specific tasks.

Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

So, do what excites!

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
==References==
{{Hanging indent|1=

Andrade, E. B., Odean, T., &amp; Lin, S. (2016). Bubbling with Excitement: An Experiment. ''Review of Finance, 20''(2), 447–466. https://doi.org/10.1093/rof/rfv016

Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. ''Journal of Experimental Psychology. General, 143''(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. ''The American Psychologist, 56''(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. ''Current Opinion in Behavioral Sciences, 39'', 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Gable, P., &amp; Harmon-Jones, E. (2010). The motivational dimensional model of affect: Implications for breadth of attention, memory, and cognitive categorisation. ''Cognition and Emotion, 24''(2), 322–337. https://doi.org/10.1080/02699930903378305

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. ''Frontiers in Psychology, 8'', Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Hasada, R. (1994). ''The semantic aspects of onomatopoeia: focusing on Japanese psychomimes'' [Master's thesis, The Australian National University]. ANU Open Research. https://doi.org/10.25911/5d723cb12c49c 

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. ''British Journal of Educational Psychology, 93''(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Lim, N. (2016). Cultural differences in emotion: differences in emotional arousal level between the East and the West. ''Integrative Medicine Research, 5''(2), 105–109. https://doi.org/10.1016/j.imr.2016.03.004

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. ''The Journal of Positive Psychology'', (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Machizawa, M. G., Lisi, G., Kanayama, N., Mizuochi, R., Makita, K., Sasaoka, T., &amp; Yamawaki, S. (2020). Quantification of anticipation of excitement with a three-axial model of emotion with EEG. ''Journal of Neural Engineering, 17''(3). https://doi.org/10.1088/1741-2552/ab93b4

Oxendine, J. B. (1970). Emotional Arousal and Motor Performance. ''Quest (National Association for Kinesiology in Higher Education), 13''(1), 23–32. https://doi.org/10.1080/00336297.1970.10519673

Piira, O.-P., Huikuri, H. V., &amp; Tulppo, M. P. (2011). Effects of emotional excitement on heart rate and blood pressure dynamics in patients with coronary artery disease. ''Autonomic Neuroscience, 160''(1–2), 107–114. https://doi.org/10.1016/j.autneu.2010.11.011

Posner, J., Russell, J. A., &amp; Peterson, B. S. (2005). The circumplex model of affect: An integrative approach to affective neuroscience, cognitive development, and psychopathology. ''Development and Psychopathology, 17''(3), 715–734. https://doi.org/10.1017/S0954579405050340

Robinson, M. D., &amp; Irvin, R. L. (2022). Out of the shell, into the world: preferences for openness as a substrate of approach motivation and positive affect. ''Motivation and Emotion, 46''(3), 307–318. https://doi.org/10.1007/s11031-022-09934-5

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Schachter, S., &amp; Singer, J. (1962). Cognitive, social, and physiological determinants of emotional state. ''Psychological Review, 69''(5), 379–399. https://doi.org/10.1037/h0046234

Smith, K. E., Woodard, K., &amp; Pollak, S. D. (2025). Arousal May Not Be Anything to Get Excited About. ''Emotion Review, 17''(1), 3–15. https://doi.org/10.1177/17540739241303499

Sohn, J.-H., Kim, H.-E., Sohn, S., Seok, J.-W., Choi, D., &amp; Watanuki, S. (2015). Effect of emotional arousal on inter-temporal decision-making: an fMRI study. ''Journal of Physiological Anthropology, 34''(1), Article 8. https://doi.org/10.1186/s40101-015-0047-5

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. ''Social and Personality Psychology Compass, 2''(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. ''Psychological Review, 35''(5), 351–366. https://doi.org/10.1037/h0071406

Tugade, M. M., Shiota, M. N., &amp; Kirby, L. D. (Eds.). (2014). ''Handbook of positive emotions'' (1st ed.). Guilford Press.


}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)
* [https://www.simplypsychology.com/articles/anxiety-reappraisal-strategies Cognitive Reappraisal for Anxiety: Evidence-Based Strategies That Work] (Simply Psychology)

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally characterised to be a positive, high-arousal emotional state associated with preparing an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2023). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014; Russel, 1980). 

Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situation or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring) (Tugade et al., 2014)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal (Gable &amp; Dreisbach, 2021)
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural activation system (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable (Hasada, 1994). Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional image. From this data, the study developed a three-axial model integrating valence, arousal and a new cognitive dimension of expectation/anticipation. Through this study, Macahizawa found that the this added temporal dimension was significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball and hates crowds might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}

=== Physiological responses ===
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) found that after controlling for physical activity, self-reported excitement was associated with increased physiological arousal. This included increased heart rate, alertness and energy with reduced heart rate variability, signalling a heightened sympathetic nervous system (Ketonen et al., 2023). The corresponding associations for anxiety and calmness were not found to be signficant thus possibly signalling excitement as a unique emotional experience despite ununique physiological responses.
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}

=== Psychological processes ===
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought-actions encouraging problem-solving, and exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}

=== Approach motivation and goal pursuit ===
High affective states have been linked to more approach-oriented behaviour, that is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach (2021) suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states can also have goal directed behaviour, however, as excitement is a high positive affect (valence) state and anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}

=== Excitements affect on cognition ===
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (1998, 2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

The consequences of positive emotion on cognition may depend partly on motivational intensity and not always translate into greater performance. Excitement may help in focusing in on a task, but an overly narrow focus may make it more difficult to take in necessary information and stimuli.

ADD TABLE.

Furthermore, according to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., sprinting and football tacking) whereas, fine motor tasks &amp; decision-making were impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.  

=== Excitement on behaviour ===

==== Impulsivity and risk taking ====
Unregulated excitement can lead to a sort of behavioural overshooting. Galentino et al. (2017) demonstrates that positive emotional arousal significantly increases preferences for monetary risks by over-valuing rewards over their potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (Sohn et al., 2015; Galentino, Bonini, &amp; Savadori, 2017; Andrade, Odean, &amp; Lin, 2016). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an underestimation of risks and causing impulsive decisions.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Excitement and anxiety share similar high-arousal physiological profiles. A study by Brooks (2014) identified that these similar profiles were difficult to suppress and 90% of participants believed a variation of 'calming down' was the best cognitive strategy under high-pressure tasks. This research demonstrated that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in heart rate. When simply employing this cognitive restrucuture, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

INTERVENTION APPLICATION

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Liu et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as energised positive affect. Liu et al. (2026) proposed that pleasant positive affect may stabilise life satisfaction whereas more energised positive affect may be present in individuals with gaps between a current and desired states. These may drive personal growth, agency, and goal adaptation as opposed to baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

Overall, positive affect in general has been shown to increase life satisfaction and relationships over time. As excitement is a positive emotional experience, these can contribute to ones subjective well-being. As this emotional state can make activities feel more engaging and rewarding, so too can this anticipation lead to more engagement and possibly reward. Excitement may not necessarily improve well-being simply because it is a positive emotional state, rather, the emotion may encourage preparation, engagement and goal pursuit which can further contributue to a sense of accomplishment (Liu et al. 2026).

=== Excitement as viewed cross-culturally ===
Jeanne Tsai (2007) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with some individualistic Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm. This maybe due to an 'ideal affect' that is to say, the desire to assert personal autononmy and influence others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. 

{{anchor|Does excitement help or hinder behaviour?}}

=== Does excitement help or hinder behaviour? ===
With helpful excitement, an individual might move towards a goal by preparing, practising, engaging and performing behaviours that lead to a desired outcome. However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision (Galentino et al., 2017).

Extremely high emotional arousal may become overwhelming, with the consequences of excitement dependent on the context and the individual's ability to regulate their behaviour. Excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion. Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depends on intensity, context and behavioural regulation.

FIGURE FOR HELP.

{{anchor|Excitement, goals and engagement}}
==Conclusion==
Excitement is a positively valenced, high-arousal emotional state associated with anticipation, approach motivation and readiness to act. It can encourage preparation, persistence and engagement with meaningful goals.


Pschological theories help explain these different outcomes. Russell's circumplex model describes excitement in terms of positive valence and high arousal, whilte moti

It can influence behaviour through increased approach motivation, attention and goal-directed action.

Excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes alternatively, the reappraisal of similar physiological emotions into excitement, can allow for greater outcomes in life as well as performance of specific tasks.

Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

So, do what excites!

TAKE HOME MESSAGE

CHAPTER COMPREHENSION QUIZ

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
==References==
{{Hanging indent|1=

Andrade, E. B., Odean, T., &amp; Lin, S. (2016). Bubbling with Excitement: An Experiment. ''Review of Finance, 20''(2), 447–466. https://doi.org/10.1093/rof/rfv016

Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. ''Journal of Experimental Psychology. General, 143''(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. ''The American Psychologist, 56''(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. ''Current Opinion in Behavioral Sciences, 39'', 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Gable, P., &amp; Harmon-Jones, E. (2010). The motivational dimensional model of affect: Implications for breadth of attention, memory, and cognitive categorisation. ''Cognition and Emotion, 24''(2), 322–337. https://doi.org/10.1080/02699930903378305

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. ''Frontiers in Psychology, 8'', Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Hasada, R. (1994). ''The semantic aspects of onomatopoeia: focusing on Japanese psychomimes'' [Master's thesis, The Australian National University]. ANU Open Research. https://doi.org/10.25911/5d723cb12c49c 

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. ''British Journal of Educational Psychology, 93''(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Lim, N. (2016). Cultural differences in emotion: differences in emotional arousal level between the East and the West. ''Integrative Medicine Research, 5''(2), 105–109. https://doi.org/10.1016/j.imr.2016.03.004

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. ''The Journal of Positive Psychology'', (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Machizawa, M. G., Lisi, G., Kanayama, N., Mizuochi, R., Makita, K., Sasaoka, T., &amp; Yamawaki, S. (2020). Quantification of anticipation of excitement with a three-axial model of emotion with EEG. ''Journal of Neural Engineering, 17''(3). https://doi.org/10.1088/1741-2552/ab93b4

Oxendine, J. B. (1970). Emotional Arousal and Motor Performance. ''Quest (National Association for Kinesiology in Higher Education), 13''(1), 23–32. https://doi.org/10.1080/00336297.1970.10519673

Piira, O.-P., Huikuri, H. V., &amp; Tulppo, M. P. (2011). Effects of emotional excitement on heart rate and blood pressure dynamics in patients with coronary artery disease. ''Autonomic Neuroscience, 160''(1–2), 107–114. https://doi.org/10.1016/j.autneu.2010.11.011

Posner, J., Russell, J. A., &amp; Peterson, B. S. (2005). The circumplex model of affect: An integrative approach to affective neuroscience, cognitive development, and psychopathology. ''Development and Psychopathology, 17''(3), 715–734. https://doi.org/10.1017/S0954579405050340

Robinson, M. D., &amp; Irvin, R. L. (2022). Out of the shell, into the world: preferences for openness as a substrate of approach motivation and positive affect. ''Motivation and Emotion, 46''(3), 307–318. https://doi.org/10.1007/s11031-022-09934-5

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Schachter, S., &amp; Singer, J. (1962). Cognitive, social, and physiological determinants of emotional state. ''Psychological Review, 69''(5), 379–399. https://doi.org/10.1037/h0046234

Smith, K. E., Woodard, K., &amp; Pollak, S. D. (2025). Arousal May Not Be Anything to Get Excited About. ''Emotion Review, 17''(1), 3–15. https://doi.org/10.1177/17540739241303499

Sohn, J.-H., Kim, H.-E., Sohn, S., Seok, J.-W., Choi, D., &amp; Watanuki, S. (2015). Effect of emotional arousal on inter-temporal decision-making: an fMRI study. ''Journal of Physiological Anthropology, 34''(1), Article 8. https://doi.org/10.1186/s40101-015-0047-5

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. ''Social and Personality Psychology Compass, 2''(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. ''Psychological Review, 35''(5), 351–366. https://doi.org/10.1037/h0071406

Tugade, M. M., Shiota, M. N., &amp; Kirby, L. D. (Eds.). (2014). ''Handbook of positive emotions'' (1st ed.). Guilford Press.


}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)
* [https://www.simplypsychology.com/articles/anxiety-reappraisal-strategies Cognitive Reappraisal for Anxiety: Evidence-Based Strategies That Work] (Simply Psychology)

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally characterised to be a positive, high-arousal emotional state associated with preparing an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2023). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014; Russel, 1980). 

Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situation or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring) (Tugade et al., 2014)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal (Gable &amp; Dreisbach, 2021)
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural activation system (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable (Hasada, 1994). Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional image. From this data, the study developed a three-axial model integrating valence, arousal and a new cognitive dimension of expectation/anticipation. Through this study, Macahizawa found that the this added temporal dimension was significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball and hates crowds might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}

=== Physiological responses ===
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) found that after controlling for physical activity, self-reported excitement was associated with increased physiological arousal. This included increased heart rate, alertness and energy with reduced heart rate variability, signalling a heightened sympathetic nervous system (Ketonen et al., 2023). The corresponding associations for anxiety and calmness were not found to be signficant thus possibly signalling excitement as a unique emotional experience despite ununique physiological responses.
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}

=== Psychological processes ===
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought-actions encouraging problem-solving, and affecting exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}

=== Approach motivation and goal pursuit ===
High affective states have been linked to more approach-oriented behaviour, that is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach (2021) suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states can also have goal directed behaviour, however, as excitement is a high positive affect (valence) state and anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}

=== Excitements affect on cognition ===
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

The consequences of positive emotion on cognition may depend partly on motivational intensity and not always translate into greater performance. Excitement may help in focusing in on a task, but an overly narrow focus may make it more difficult to take in necessary information and stimuli.

ADD TABLE.

Furthermore, according to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., sprinting and football tacking) whereas, fine motor tasks &amp; decision-making were impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.  

=== Excitement on behaviour ===

==== Impulsivity and risk taking ====
Unregulated excitement can lead to a sort of behavioural overshooting. Galentino et al. (2017) demonstrates that positive emotional arousal significantly increases preferences for monetary risks by over-valuing rewards over their potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (Sohn et al., 2015; Galentino, Bonini, &amp; Savadori, 2017; Andrade, Odean, &amp; Lin, 2016). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an underestimation of risks and causing impulsive decisions.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Excitement and anxiety share similar high-arousal physiological profiles. A study by Brooks (2014) identified that these similar profiles were difficult to suppress and 90% of participants believed a variation of 'calming down' was the best cognitive strategy under high-pressure tasks. This research demonstrated that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in heart rate. When simply employing this cognitive restrucuture, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

INTERVENTION APPLICATION

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Liu et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as energised positive affect. Liu et al. (2026) proposed that pleasant positive affect may stabilise life satisfaction whereas more energised positive affect may be present in individuals with gaps between a current and desired states. These may drive personal growth, agency, and goal adaptation as opposed to baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

Overall, positive affect in general has been shown to increase life satisfaction and relationships over time. As excitement is a positive emotional experience, these can contribute to ones subjective well-being. As this emotional state can make activities feel more engaging and rewarding, so too can this anticipation lead to more engagement and possibly reward. Excitement may not necessarily improve well-being simply because it is a positive emotional state, rather, the emotion may encourage preparation, engagement and goal pursuit which can further contributue to a sense of accomplishment (Liu et al. 2026).

=== Excitement as viewed cross-culturally ===
Jeanne Tsai (2007) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with some individualistic Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm. This maybe due to an 'ideal affect' that is to say, the desire to assert personal autononmy and influence others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. 

{{anchor|Does excitement help or hinder behaviour?}}

=== Does excitement help or hinder behaviour? ===
With helpful excitement, an individual might move towards a goal by preparing, practising, engaging and performing behaviours that lead to a desired outcome. However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision (Galentino et al., 2017).

Extremely high emotional arousal may become overwhelming, with the consequences of excitement dependent on the context and the individual's ability to regulate their behaviour. Excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion. Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depends on intensity, context and behavioural regulation.

FIGURE FOR HELP.

{{anchor|Excitement, goals and engagement}}
==Conclusion==
Excitement is a positively valenced, high-arousal emotional state associated with anticipation, approach motivation and readiness to act. It can encourage preparation, persistence and engagement with meaningful goals. Although, following in similar physiological traits to other emotions such as anxiety, excitement may differ from other emotions due to its combination of positive valence, high activation/arousal, approach to goals and anticipatory nature (Russell, 1980; Gable &amp; Harmon-Jones, 2010; Macahizawa et al., 2020). Excitement as a state triggers activation of the autonomic nervous system, preparing itself for some kind of action (Oxendine, 1970). Commonm physiological responses include elevated heart rate, alertness, energy and rise of blood pressure (Ketonen et al., 2023). Psychologically, excitement can boost an individual's readiness to act, perceived self-efficacy, and cognitive scope (Brooks, 2014; Fredrickson, 2001).

As a catalyst to engaging with actions towards a certain goal, excitement can effect ones cognition, narrowing or widening its scope (Fredrickson, 2001), and possibly leading to greater impulsive or risk taking behaviours (e.g., Galentino et al., 2017). Excitement can also be a powerful tool in restructuring other emotions, and as a positive emotion, may increase satisfaction across the lifespan (Liu et al., 2016). With its value differing across culture, excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes. Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

TAKE HOME MESSAGE

CHAPTER COMPREHENSION QUIZ

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
==References==
{{Hanging indent|1=

Andrade, E. B., Odean, T., &amp; Lin, S. (2016). Bubbling with Excitement: An Experiment. ''Review of Finance, 20''(2), 447–466. https://doi.org/10.1093/rof/rfv016

Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. ''Journal of Experimental Psychology. General, 143''(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. ''The American Psychologist, 56''(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. ''Current Opinion in Behavioral Sciences, 39'', 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Gable, P., &amp; Harmon-Jones, E. (2010). The motivational dimensional model of affect: Implications for breadth of attention, memory, and cognitive categorisation. ''Cognition and Emotion, 24''(2), 322–337. https://doi.org/10.1080/02699930903378305

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. ''Frontiers in Psychology, 8'', Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Hasada, R. (1994). ''The semantic aspects of onomatopoeia: focusing on Japanese psychomimes'' [Master's thesis, The Australian National University]. ANU Open Research. https://doi.org/10.25911/5d723cb12c49c 

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. ''British Journal of Educational Psychology, 93''(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Lim, N. (2016). Cultural differences in emotion: differences in emotional arousal level between the East and the West. ''Integrative Medicine Research, 5''(2), 105–109. https://doi.org/10.1016/j.imr.2016.03.004

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. ''The Journal of Positive Psychology'', (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Machizawa, M. G., Lisi, G., Kanayama, N., Mizuochi, R., Makita, K., Sasaoka, T., &amp; Yamawaki, S. (2020). Quantification of anticipation of excitement with a three-axial model of emotion with EEG. ''Journal of Neural Engineering, 17''(3). https://doi.org/10.1088/1741-2552/ab93b4

Oxendine, J. B. (1970). Emotional Arousal and Motor Performance. ''Quest (National Association for Kinesiology in Higher Education), 13''(1), 23–32. https://doi.org/10.1080/00336297.1970.10519673

Piira, O.-P., Huikuri, H. V., &amp; Tulppo, M. P. (2011). Effects of emotional excitement on heart rate and blood pressure dynamics in patients with coronary artery disease. ''Autonomic Neuroscience, 160''(1–2), 107–114. https://doi.org/10.1016/j.autneu.2010.11.011

Posner, J., Russell, J. A., &amp; Peterson, B. S. (2005). The circumplex model of affect: An integrative approach to affective neuroscience, cognitive development, and psychopathology. ''Development and Psychopathology, 17''(3), 715–734. https://doi.org/10.1017/S0954579405050340

Robinson, M. D., &amp; Irvin, R. L. (2022). Out of the shell, into the world: preferences for openness as a substrate of approach motivation and positive affect. ''Motivation and Emotion, 46''(3), 307–318. https://doi.org/10.1007/s11031-022-09934-5

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Schachter, S., &amp; Singer, J. (1962). Cognitive, social, and physiological determinants of emotional state. ''Psychological Review, 69''(5), 379–399. https://doi.org/10.1037/h0046234

Smith, K. E., Woodard, K., &amp; Pollak, S. D. (2025). Arousal May Not Be Anything to Get Excited About. ''Emotion Review, 17''(1), 3–15. https://doi.org/10.1177/17540739241303499

Sohn, J.-H., Kim, H.-E., Sohn, S., Seok, J.-W., Choi, D., &amp; Watanuki, S. (2015). Effect of emotional arousal on inter-temporal decision-making: an fMRI study. ''Journal of Physiological Anthropology, 34''(1), Article 8. https://doi.org/10.1186/s40101-015-0047-5

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. ''Social and Personality Psychology Compass, 2''(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. ''Psychological Review, 35''(5), 351–366. https://doi.org/10.1037/h0071406

Tugade, M. M., Shiota, M. N., &amp; Kirby, L. D. (Eds.). (2014). ''Handbook of positive emotions'' (1st ed.). Guilford Press.


}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)
* [https://www.simplypsychology.com/articles/anxiety-reappraisal-strategies Cognitive Reappraisal for Anxiety: Evidence-Based Strategies That Work] (Simply Psychology)

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally characterised to be a positive, high-arousal emotional state associated with preparing an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2023). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014; Russel, 1980). 

Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situation or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring) (Tugade et al., 2014)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal (Gable &amp; Dreisbach, 2021)
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural activation system (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable (Hasada, 1994). Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional image. From this data, the study developed a three-axial model integrating valence, arousal and a new cognitive dimension of expectation/anticipation. Through this study, Macahizawa found that the this added temporal dimension was significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball and hates crowds might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}

=== Physiological responses ===
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) found that after controlling for physical activity, self-reported excitement was associated with increased physiological arousal. This included increased heart rate, alertness and energy with reduced heart rate variability, signalling a heightened sympathetic nervous system (Ketonen et al., 2023). The corresponding associations for anxiety and calmness were not found to be signficant thus possibly signalling excitement as a unique emotional experience despite ununique physiological responses.
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}

=== Psychological processes ===
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought-actions encouraging problem-solving, and affecting exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}

=== Approach motivation and goal pursuit ===
High affective states have been linked to more approach-oriented behaviour, that is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach (2021) suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states can also have goal directed behaviour, however, as excitement is a high positive affect (valence) state and anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}

=== Excitements affect on cognition ===
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

The consequences of positive emotion on cognition may depend partly on motivational intensity and not always translate into greater performance. Excitement may help in focusing in on a task, but an overly narrow focus may make it more difficult to take in necessary information and stimuli.

'''Table 2'''

''Excitement and positive affect on cognitive scope (Fredrickson, 2001; Gable &amp; Dreisbach, 2021)''
{| class=&quot;wikitable&quot; style=&quot;margin: auto;&quot;
!
!Low-intensity positive affect
!High-intensity positive affect
|-
|'''Cognitive scope'''
|Broadens attention to access wider range of stimuli and information.
|Narrows attention towards central goal potentially filtering out relevant information.
|-
|'''Potential benefits'''
|Encourages creative exploration, flexible thinking, alternative ideas.
|Focused processing of goal-related information, persistencen and performance on tasks with focused attention. 
|-
|'''Potential limitations'''
|Broad focus may cause less action towards specific goal required, or lack intense concentration needed towards target.
|Narrow focus may cause important stimuli to be lost or peripheral information to be overlooked.
|}

Furthermore, according to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., sprinting and football tacking) whereas, fine motor tasks &amp; decision-making were impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.

=== Excitement on behaviour ===

==== Impulsivity and risk taking ====
Unregulated excitement can lead to a sort of behavioural overshooting. Galentino et al. (2017) demonstrates that positive emotional arousal significantly increases preferences for monetary risks by over-valuing rewards over their potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (Sohn et al., 2015; Galentino, Bonini, &amp; Savadori, 2017; Andrade, Odean, &amp; Lin, 2016). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an underestimation of risks and causing impulsive decisions.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Excitement and anxiety share similar high-arousal physiological profiles. A study by Brooks (2014) identified that these similar profiles were difficult to suppress and 90% of participants believed a variation of 'calming down' was the best cognitive strategy under high-pressure tasks. This research demonstrated that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in heart rate. When simply employing this cognitive restrucuture, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

INTERVENTION APPLICATION

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Liu et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as energised positive affect. Liu et al. (2026) proposed that pleasant positive affect may stabilise life satisfaction whereas more energised positive affect may be present in individuals with gaps between a current and desired states. These may drive personal growth, agency, and goal adaptation as opposed to baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

Overall, positive affect in general has been shown to increase life satisfaction and relationships over time. As excitement is a positive emotional experience, these can contribute to ones subjective well-being. As this emotional state can make activities feel more engaging and rewarding, so too can this anticipation lead to more engagement and possibly reward. Excitement may not necessarily improve well-being simply because it is a positive emotional state, rather, the emotion may encourage preparation, engagement and goal pursuit which can further contributue to a sense of accomplishment (Liu et al. 2026).

=== Excitement as viewed cross-culturally ===
Jeanne Tsai (2007) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with some individualistic Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm. This maybe due to an 'ideal affect' that is to say, the desire to assert personal autononmy and influence others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. 

{{anchor|Does excitement help or hinder behaviour?}}

=== Does excitement help or hinder behaviour? ===
With helpful excitement, an individual might move towards a goal by preparing, practising, engaging and performing behaviours that lead to a desired outcome. However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision (Galentino et al., 2017).

Extremely high emotional arousal may become overwhelming, with the consequences of excitement dependent on the context and the individual's ability to regulate their behaviour. Excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion. Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depends on intensity, context and behavioural regulation.

FIGURE FOR HELP.

{{anchor|Excitement, goals and engagement}}
==Conclusion==
Excitement is a positively valenced, high-arousal emotional state associated with anticipation, approach motivation and readiness to act. It can encourage preparation, persistence and engagement with meaningful goals. Although, following in similar physiological traits to other emotions such as anxiety, excitement may differ from other emotions due to its combination of positive valence, high activation/arousal, approach to goals and anticipatory nature (Russell, 1980; Gable &amp; Harmon-Jones, 2010; Macahizawa et al., 2020). Excitement as a state triggers activation of the autonomic nervous system, preparing itself for some kind of action (Oxendine, 1970). Commonm physiological responses include elevated heart rate, alertness, energy and rise of blood pressure (Ketonen et al., 2023). Psychologically, excitement can boost an individual's readiness to act, perceived self-efficacy, and cognitive scope (Brooks, 2014; Fredrickson, 2001).

As a catalyst to engaging with actions towards a certain goal, excitement can effect ones cognition, narrowing or widening its scope (Fredrickson, 2001), and possibly leading to greater impulsive or risk taking behaviours (e.g., Galentino et al., 2017). Excitement can also be a powerful tool in restructuring other emotions, and as a positive emotion, may increase satisfaction across the lifespan (Liu et al., 2016). With its value differing across culture, excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes. Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

TAKE HOME MESSAGE

CHAPTER COMPREHENSION QUIZ

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
==References==
{{Hanging indent|1=

Andrade, E. B., Odean, T., &amp; Lin, S. (2016). Bubbling with Excitement: An Experiment. ''Review of Finance, 20''(2), 447–466. https://doi.org/10.1093/rof/rfv016

Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. ''Journal of Experimental Psychology. General, 143''(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. ''The American Psychologist, 56''(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. ''Current Opinion in Behavioral Sciences, 39'', 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Gable, P., &amp; Harmon-Jones, E. (2010). The motivational dimensional model of affect: Implications for breadth of attention, memory, and cognitive categorisation. ''Cognition and Emotion, 24''(2), 322–337. https://doi.org/10.1080/02699930903378305

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. ''Frontiers in Psychology, 8'', Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Hasada, R. (1994). ''The semantic aspects of onomatopoeia: focusing on Japanese psychomimes'' [Master's thesis, The Australian National University]. ANU Open Research. https://doi.org/10.25911/5d723cb12c49c 

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. ''British Journal of Educational Psychology, 93''(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Lim, N. (2016). Cultural differences in emotion: differences in emotional arousal level between the East and the West. ''Integrative Medicine Research, 5''(2), 105–109. https://doi.org/10.1016/j.imr.2016.03.004

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. ''The Journal of Positive Psychology'', (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Machizawa, M. G., Lisi, G., Kanayama, N., Mizuochi, R., Makita, K., Sasaoka, T., &amp; Yamawaki, S. (2020). Quantification of anticipation of excitement with a three-axial model of emotion with EEG. ''Journal of Neural Engineering, 17''(3). https://doi.org/10.1088/1741-2552/ab93b4

Oxendine, J. B. (1970). Emotional Arousal and Motor Performance. ''Quest (National Association for Kinesiology in Higher Education), 13''(1), 23–32. https://doi.org/10.1080/00336297.1970.10519673

Piira, O.-P., Huikuri, H. V., &amp; Tulppo, M. P. (2011). Effects of emotional excitement on heart rate and blood pressure dynamics in patients with coronary artery disease. ''Autonomic Neuroscience, 160''(1–2), 107–114. https://doi.org/10.1016/j.autneu.2010.11.011

Posner, J., Russell, J. A., &amp; Peterson, B. S. (2005). The circumplex model of affect: An integrative approach to affective neuroscience, cognitive development, and psychopathology. ''Development and Psychopathology, 17''(3), 715–734. https://doi.org/10.1017/S0954579405050340

Robinson, M. D., &amp; Irvin, R. L. (2022). Out of the shell, into the world: preferences for openness as a substrate of approach motivation and positive affect. ''Motivation and Emotion, 46''(3), 307–318. https://doi.org/10.1007/s11031-022-09934-5

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Schachter, S., &amp; Singer, J. (1962). Cognitive, social, and physiological determinants of emotional state. ''Psychological Review, 69''(5), 379–399. https://doi.org/10.1037/h0046234

Smith, K. E., Woodard, K., &amp; Pollak, S. D. (2025). Arousal May Not Be Anything to Get Excited About. ''Emotion Review, 17''(1), 3–15. https://doi.org/10.1177/17540739241303499

Sohn, J.-H., Kim, H.-E., Sohn, S., Seok, J.-W., Choi, D., &amp; Watanuki, S. (2015). Effect of emotional arousal on inter-temporal decision-making: an fMRI study. ''Journal of Physiological Anthropology, 34''(1), Article 8. https://doi.org/10.1186/s40101-015-0047-5

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. ''Social and Personality Psychology Compass, 2''(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. ''Psychological Review, 35''(5), 351–366. https://doi.org/10.1037/h0071406

Tugade, M. M., Shiota, M. N., &amp; Kirby, L. D. (Eds.). (2014). ''Handbook of positive emotions'' (1st ed.). Guilford Press.


}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)
* [https://www.simplypsychology.com/articles/anxiety-reappraisal-strategies Cognitive Reappraisal for Anxiety: Evidence-Based Strategies That Work] (Simply Psychology)

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally characterised to be a positive, high-arousal emotional state associated with preparing an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2023). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014; Russel, 1980). 

Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situation or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring) (Tugade et al., 2014)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal (Gable &amp; Dreisbach, 2021)
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural activation system (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable (Hasada, 1994). Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional image. From this data, the study developed a three-axial model integrating valence, arousal and a new cognitive dimension of expectation/anticipation. Through this study, Macahizawa found that the this added temporal dimension was significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball and hates crowds might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}

=== Physiological responses ===
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) found that after controlling for physical activity, self-reported excitement was associated with increased physiological arousal. This included increased heart rate, alertness and energy with reduced heart rate variability, signalling a heightened sympathetic nervous system (Ketonen et al., 2023). The corresponding associations for anxiety and calmness were not found to be signficant thus possibly signalling excitement as a unique emotional experience despite ununique physiological responses.
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}

=== Psychological processes ===
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought-actions encouraging problem-solving, and affecting exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}

=== Approach motivation and goal pursuit ===
High affective states have been linked to more approach-oriented behaviour, that is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach (2021) suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states can also have goal directed behaviour, however, as excitement is a high positive affect (valence) state and anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}

=== Excitements affect on cognition ===
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

The consequences of positive emotion on cognition may depend partly on motivational intensity and not always translate into greater performance. Excitement may help in focusing in on a task, but an overly narrow focus may make it more difficult to take in necessary information and stimuli; see Table 2.

'''Table 2'''

''Comparison of low-intensity positive affect on cognitive scope versus high (Fredrickson, 2001; Gable &amp; Dreisbach, 2021)''
{| class=&quot;wikitable&quot; style=&quot;margin: auto;&quot;
!
!Low-intensity positive affect
!High-intensity positive affect
|-
|'''Cognitive scope'''
|Broadens attention to access wider range of stimuli and information.
|Narrows attention towards central goal potentially filtering out relevant information.
|-
|'''Potential benefits'''
|Encourages creative exploration, flexible thinking, alternative ideas.
|Focused processing of goal-related information, persistence and performance on tasks with focused attention. 
|-
|'''Potential limitations'''
|Broad focus may cause less action towards specific goal required, or lack intense concentration needed towards target.
|Narrow focus may cause important stimuli to be lost or peripheral information to be overlooked.
|}

Furthermore, according to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., sprinting and football tacking) whereas, fine motor tasks &amp; decision-making were impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.

=== Excitement on behaviour ===

==== Impulsivity and risk taking ====
Unregulated excitement can lead to a sort of behavioural overshooting. Galentino et al. (2017) demonstrates that positive emotional arousal significantly increases preferences for monetary risks by over-valuing rewards over their potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (Sohn et al., 2015; Galentino, Bonini, &amp; Savadori, 2017; Andrade, Odean, &amp; Lin, 2016). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an underestimation of risks and causing impulsive decisions.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Excitement and anxiety share similar high-arousal physiological profiles. A study by Brooks (2014) identified that these similar profiles were difficult to suppress and 90% of participants believed a variation of 'calming down' was the best cognitive strategy under high-pressure tasks. This research demonstrated that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in heart rate. When simply employing this cognitive restrucuture, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Liu et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as energised positive affect. Liu et al. (2026) proposed that pleasant positive affect may stabilise life satisfaction whereas more energised positive affect may be present in individuals with gaps between a current and desired states. These may drive personal growth, agency, and goal adaptation as opposed to baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

Overall, positive affect in general has been shown to increase life satisfaction and relationships over time. As excitement is a positive emotional experience, these can contribute to ones subjective well-being. As this emotional state can make activities feel more engaging and rewarding, so too can this anticipation lead to more engagement and possibly reward. Excitement may not necessarily improve well-being simply because it is a positive emotional state, rather, the emotion may encourage preparation, engagement and goal pursuit which can further contributue to a sense of accomplishment (Liu et al. 2026).

=== Excitement as viewed cross-culturally ===
Jeanne Tsai (2007) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with some individualistic Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm. This maybe due to an 'ideal affect' that is to say, the desire to assert personal autononmy and influence others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. 

{{anchor|Does excitement help or hinder behaviour?}}

=== Does excitement help or hinder behaviour? ===
With helpful excitement, an individual might move towards a goal by preparing, practising, engaging and performing behaviours that lead to a desired outcome. However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision (Galentino et al., 2017).

Extremely high emotional arousal may become overwhelming, with the consequences of excitement dependent on the context and the individual's ability to regulate their behaviour. Excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion. Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depends on intensity, context and behavioural regulation.
==Conclusion==
Excitement is a positively valenced, high-arousal emotional state associated with anticipation, approach motivation and readiness to act. It can encourage preparation, persistence and engagement with meaningful goals. Although, following in similar physiological traits to other emotions such as anxiety, excitement may differ from other emotions due to its combination of positive valence, high activation/arousal, approach to goals and anticipatory nature (Russell, 1980; Gable &amp; Harmon-Jones, 2010; Macahizawa et al., 2020). Excitement as a state triggers activation of the autonomic nervous system, preparing itself for some kind of action (Oxendine, 1970). Commonm physiological responses include elevated heart rate, alertness, energy and rise of blood pressure (Ketonen et al., 2023). Psychologically, excitement can boost an individual's readiness to act, perceived self-efficacy, and cognitive scope (Brooks, 2014; Fredrickson, 2001).

As a catalyst to engaging with actions towards a certain goal, excitement can effect ones cognition, narrowing or widening its scope (Fredrickson, 2001), and possibly leading to greater impulsive or risk taking behaviours (e.g., Galentino et al., 2017). Excitement can also be a powerful tool in restructuring other emotions, and as a positive emotion, may increase satisfaction across the lifespan (Liu et al., 2016). With its value differing across culture, excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes. Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

TAKE HOME MESSAGE

CHAPTER COMPREHENSION QUIZ

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
==References==
{{Hanging indent|1=

Andrade, E. B., Odean, T., &amp; Lin, S. (2016). Bubbling with Excitement: An Experiment. ''Review of Finance, 20''(2), 447–466. https://doi.org/10.1093/rof/rfv016

Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. ''Journal of Experimental Psychology. General, 143''(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. ''The American Psychologist, 56''(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. ''Current Opinion in Behavioral Sciences, 39'', 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Gable, P., &amp; Harmon-Jones, E. (2010). The motivational dimensional model of affect: Implications for breadth of attention, memory, and cognitive categorisation. ''Cognition and Emotion, 24''(2), 322–337. https://doi.org/10.1080/02699930903378305

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. ''Frontiers in Psychology, 8'', Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Hasada, R. (1994). ''The semantic aspects of onomatopoeia: focusing on Japanese psychomimes'' [Master's thesis, The Australian National University]. ANU Open Research. https://doi.org/10.25911/5d723cb12c49c 

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. ''British Journal of Educational Psychology, 93''(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Lim, N. (2016). Cultural differences in emotion: differences in emotional arousal level between the East and the West. ''Integrative Medicine Research, 5''(2), 105–109. https://doi.org/10.1016/j.imr.2016.03.004

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. ''The Journal of Positive Psychology'', (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Machizawa, M. G., Lisi, G., Kanayama, N., Mizuochi, R., Makita, K., Sasaoka, T., &amp; Yamawaki, S. (2020). Quantification of anticipation of excitement with a three-axial model of emotion with EEG. ''Journal of Neural Engineering, 17''(3). https://doi.org/10.1088/1741-2552/ab93b4

Oxendine, J. B. (1970). Emotional Arousal and Motor Performance. ''Quest (National Association for Kinesiology in Higher Education), 13''(1), 23–32. https://doi.org/10.1080/00336297.1970.10519673

Piira, O.-P., Huikuri, H. V., &amp; Tulppo, M. P. (2011). Effects of emotional excitement on heart rate and blood pressure dynamics in patients with coronary artery disease. ''Autonomic Neuroscience, 160''(1–2), 107–114. https://doi.org/10.1016/j.autneu.2010.11.011

Posner, J., Russell, J. A., &amp; Peterson, B. S. (2005). The circumplex model of affect: An integrative approach to affective neuroscience, cognitive development, and psychopathology. ''Development and Psychopathology, 17''(3), 715–734. https://doi.org/10.1017/S0954579405050340

Robinson, M. D., &amp; Irvin, R. L. (2022). Out of the shell, into the world: preferences for openness as a substrate of approach motivation and positive affect. ''Motivation and Emotion, 46''(3), 307–318. https://doi.org/10.1007/s11031-022-09934-5

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Schachter, S., &amp; Singer, J. (1962). Cognitive, social, and physiological determinants of emotional state. ''Psychological Review, 69''(5), 379–399. https://doi.org/10.1037/h0046234

Smith, K. E., Woodard, K., &amp; Pollak, S. D. (2025). Arousal May Not Be Anything to Get Excited About. ''Emotion Review, 17''(1), 3–15. https://doi.org/10.1177/17540739241303499

Sohn, J.-H., Kim, H.-E., Sohn, S., Seok, J.-W., Choi, D., &amp; Watanuki, S. (2015). Effect of emotional arousal on inter-temporal decision-making: an fMRI study. ''Journal of Physiological Anthropology, 34''(1), Article 8. https://doi.org/10.1186/s40101-015-0047-5

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. ''Social and Personality Psychology Compass, 2''(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. ''Psychological Review, 35''(5), 351–366. https://doi.org/10.1037/h0071406

Tugade, M. M., Shiota, M. N., &amp; Kirby, L. D. (Eds.). (2014). ''Handbook of positive emotions'' (1st ed.). Guilford Press.


}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)
* [https://www.simplypsychology.com/articles/anxiety-reappraisal-strategies Cognitive Reappraisal for Anxiety: Evidence-Based Strategies That Work] (Simply Psychology)

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally characterised to be a positive, high-arousal emotional state associated with preparing an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2023). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014; Russel, 1980). 

Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situation or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring) (Tugade et al., 2014)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal (Gable &amp; Dreisbach, 2021)
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural activation system (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable (Hasada, 1994). Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional image. From this data, the study developed a three-axial model integrating valence, arousal and a new cognitive dimension of expectation/anticipation. Through this study, Macahizawa found that the this added temporal dimension was significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball and hates crowds might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}

=== Physiological responses ===
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) found that after controlling for physical activity, self-reported excitement was associated with increased physiological arousal. This included increased heart rate, alertness and energy with reduced heart rate variability, signalling a heightened sympathetic nervous system (Ketonen et al., 2023). The corresponding associations for anxiety and calmness were not found to be signficant thus possibly signalling excitement as a unique emotional experience despite ununique physiological responses.
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}

=== Psychological processes ===
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought-actions encouraging problem-solving, and affecting exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}

=== Approach motivation and goal pursuit ===
High affective states have been linked to more approach-oriented behaviour, that is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach (2021) suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states can also have goal directed behaviour, however, as excitement is a high positive affect (valence) state and anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}

=== Excitements affect on cognition ===
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

The consequences of positive emotion on cognition may depend partly on motivational intensity and not always translate into greater performance. Excitement may help in focusing in on a task, but an overly narrow focus may make it more difficult to take in necessary information and stimuli; see Table 2.

'''Table 2'''

''Comparison of low-intensity positive affect on cognitive scope versus high (Fredrickson, 2001; Gable &amp; Dreisbach, 2021)''
{| class=&quot;wikitable&quot; style=&quot;margin: auto;&quot;
!
!Low-intensity positive affect
!High-intensity positive affect
|-
|'''Cognitive scope'''
|Broadens attention to access wider range of stimuli and information.
|Narrows attention towards central goal potentially filtering out relevant information.
|-
|'''Potential benefits'''
|Encourages creative exploration, flexible thinking, alternative ideas.
|Focused processing of goal-related information, persistence and performance on tasks with focused attention. 
|-
|'''Potential limitations'''
|Broad focus may cause less action towards specific goal required, or lack intense concentration needed towards target.
|Narrow focus may cause important stimuli to be lost or peripheral information to be overlooked.
|}

Furthermore, according to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., sprinting and football tacking) whereas, fine motor tasks &amp; decision-making were impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.

=== Excitement on behaviour ===

==== Impulsivity and risk taking ====
Unregulated excitement can lead to a sort of behavioural overshooting. Galentino et al. (2017) demonstrates that positive emotional arousal significantly increases preferences for monetary risks by over-valuing rewards over their potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (Sohn et al., 2015; Galentino, Bonini, &amp; Savadori, 2017; Andrade, Odean, &amp; Lin, 2016). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an underestimation of risks and causing impulsive decisions.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Excitement and anxiety share similar high-arousal physiological profiles. A study by Brooks (2014) identified that these similar profiles were difficult to suppress and 90% of participants believed a variation of 'calming down' was the best cognitive strategy under high-pressure tasks. This research demonstrated that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in heart rate. When simply employing this cognitive restrucuture, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

{{RoundBoxTop|theme=3}}'''Scenario application'''
During the finals game, Steve continues to make mistakes and he starts to get anxious. Under this high pressure environment, Steve starts to reframe his mistakes as opprtunities to learn and chances to adjust to his competition. He uses some simple self-statements which he feels helps him connect to his game. His teammates notice his performance improve.{{RoundBoxBottom}}

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Liu et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as energised positive affect. Liu et al. (2026) proposed that pleasant positive affect may stabilise life satisfaction whereas more energised positive affect may be present in individuals with gaps between a current and desired states. These may drive personal growth, agency, and goal adaptation as opposed to baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

Overall, positive affect in general has been shown to increase life satisfaction and relationships over time. As excitement is a positive emotional experience, these can contribute to ones subjective well-being. As this emotional state can make activities feel more engaging and rewarding, so too can this anticipation lead to more engagement and possibly reward. Excitement may not necessarily improve well-being simply because it is a positive emotional state, rather, the emotion may encourage preparation, engagement and goal pursuit which can further contributue to a sense of accomplishment (Liu et al. 2026).

=== Excitement as viewed cross-culturally ===
Jeanne Tsai (2007) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with some individualistic Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm. This maybe due to an 'ideal affect' that is to say, the desire to assert personal autononmy and influence others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. 

{{anchor|Does excitement help or hinder behaviour?}}

=== Does excitement help or hinder behaviour? ===
With helpful excitement, an individual might move towards a goal by preparing, practising, engaging and performing behaviours that lead to a desired outcome. However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision (Galentino et al., 2017).

Extremely high emotional arousal may become overwhelming, with the consequences of excitement dependent on the context and the individual's ability to regulate their behaviour. Excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion. Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depends on intensity, context and behavioural regulation.
==Conclusion==
Excitement is a positively valenced, high-arousal emotional state associated with anticipation, approach motivation and readiness to act. It can encourage preparation, persistence and engagement with meaningful goals. Although, following in similar physiological traits to other emotions such as anxiety, excitement may differ from other emotions due to its combination of positive valence, high activation/arousal, approach to goals and anticipatory nature (Russell, 1980; Gable &amp; Harmon-Jones, 2010; Macahizawa et al., 2020). Excitement as a state triggers activation of the autonomic nervous system, preparing itself for some kind of action (Oxendine, 1970). Commonm physiological responses include elevated heart rate, alertness, energy and rise of blood pressure (Ketonen et al., 2023). Psychologically, excitement can boost an individual's readiness to act, perceived self-efficacy, and cognitive scope (Brooks, 2014; Fredrickson, 2001).

As a catalyst to engaging with actions towards a certain goal, excitement can effect ones cognition, narrowing or widening its scope (Fredrickson, 2001), and possibly leading to greater impulsive or risk taking behaviours (e.g., Galentino et al., 2017). Excitement can also be a powerful tool in restructuring other emotions, and as a positive emotion, may increase satisfaction across the lifespan (Liu et al., 2016). With its value differing across culture, excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes. Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

TAKE HOME MESSAGE

CHAPTER COMPREHENSION QUIZ

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
==References==
{{Hanging indent|1=

Andrade, E. B., Odean, T., &amp; Lin, S. (2016). Bubbling with Excitement: An Experiment. ''Review of Finance, 20''(2), 447–466. https://doi.org/10.1093/rof/rfv016

Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. ''Journal of Experimental Psychology. General, 143''(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. ''The American Psychologist, 56''(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. ''Current Opinion in Behavioral Sciences, 39'', 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Gable, P., &amp; Harmon-Jones, E. (2010). The motivational dimensional model of affect: Implications for breadth of attention, memory, and cognitive categorisation. ''Cognition and Emotion, 24''(2), 322–337. https://doi.org/10.1080/02699930903378305

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. ''Frontiers in Psychology, 8'', Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Hasada, R. (1994). ''The semantic aspects of onomatopoeia: focusing on Japanese psychomimes'' [Master's thesis, The Australian National University]. ANU Open Research. https://doi.org/10.25911/5d723cb12c49c 

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. ''British Journal of Educational Psychology, 93''(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Lim, N. (2016). Cultural differences in emotion: differences in emotional arousal level between the East and the West. ''Integrative Medicine Research, 5''(2), 105–109. https://doi.org/10.1016/j.imr.2016.03.004

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. ''The Journal of Positive Psychology'', (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Machizawa, M. G., Lisi, G., Kanayama, N., Mizuochi, R., Makita, K., Sasaoka, T., &amp; Yamawaki, S. (2020). Quantification of anticipation of excitement with a three-axial model of emotion with EEG. ''Journal of Neural Engineering, 17''(3). https://doi.org/10.1088/1741-2552/ab93b4

Oxendine, J. B. (1970). Emotional Arousal and Motor Performance. ''Quest (National Association for Kinesiology in Higher Education), 13''(1), 23–32. https://doi.org/10.1080/00336297.1970.10519673

Piira, O.-P., Huikuri, H. V., &amp; Tulppo, M. P. (2011). Effects of emotional excitement on heart rate and blood pressure dynamics in patients with coronary artery disease. ''Autonomic Neuroscience, 160''(1–2), 107–114. https://doi.org/10.1016/j.autneu.2010.11.011

Posner, J., Russell, J. A., &amp; Peterson, B. S. (2005). The circumplex model of affect: An integrative approach to affective neuroscience, cognitive development, and psychopathology. ''Development and Psychopathology, 17''(3), 715–734. https://doi.org/10.1017/S0954579405050340

Robinson, M. D., &amp; Irvin, R. L. (2022). Out of the shell, into the world: preferences for openness as a substrate of approach motivation and positive affect. ''Motivation and Emotion, 46''(3), 307–318. https://doi.org/10.1007/s11031-022-09934-5

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Schachter, S., &amp; Singer, J. (1962). Cognitive, social, and physiological determinants of emotional state. ''Psychological Review, 69''(5), 379–399. https://doi.org/10.1037/h0046234

Smith, K. E., Woodard, K., &amp; Pollak, S. D. (2025). Arousal May Not Be Anything to Get Excited About. ''Emotion Review, 17''(1), 3–15. https://doi.org/10.1177/17540739241303499

Sohn, J.-H., Kim, H.-E., Sohn, S., Seok, J.-W., Choi, D., &amp; Watanuki, S. (2015). Effect of emotional arousal on inter-temporal decision-making: an fMRI study. ''Journal of Physiological Anthropology, 34''(1), Article 8. https://doi.org/10.1186/s40101-015-0047-5

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. ''Social and Personality Psychology Compass, 2''(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. ''Psychological Review, 35''(5), 351–366. https://doi.org/10.1037/h0071406

Tugade, M. M., Shiota, M. N., &amp; Kirby, L. D. (Eds.). (2014). ''Handbook of positive emotions'' (1st ed.). Guilford Press.


}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)
* [https://www.simplypsychology.com/articles/anxiety-reappraisal-strategies Cognitive Reappraisal for Anxiety: Evidence-Based Strategies That Work] (Simply Psychology)

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally characterised to be a positive, high-arousal emotional state associated with preparing an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2023). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014; Russel, 1980). 

Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situation or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring) (Tugade et al., 2014)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal (Gable &amp; Dreisbach, 2021)
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural activation system (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable (Hasada, 1994). Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional image. From this data, the study developed a three-axial model integrating valence, arousal and a new cognitive dimension of expectation/anticipation. Through this study, Macahizawa found that the this added temporal dimension was significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball and hates crowds might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}

=== Physiological responses ===
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) found that after controlling for physical activity, self-reported excitement was associated with increased physiological arousal. This included increased heart rate, alertness and energy with reduced heart rate variability, signalling a heightened sympathetic nervous system (Ketonen et al., 2023). The corresponding associations for anxiety and calmness were not found to be signficant thus possibly signalling excitement as a unique emotional experience despite ununique physiological responses.
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}

=== Psychological processes ===
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought-actions encouraging problem-solving, and affecting exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}

=== Approach motivation and goal pursuit ===
High affective states have been linked to more approach-oriented behaviour, that is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach (2021) suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states can also have goal directed behaviour, however, as excitement is a high positive affect (valence) state and anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}

=== Excitements affect on cognition ===
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

The consequences of positive emotion on cognition may depend partly on motivational intensity and not always translate into greater performance. Excitement may help in focusing in on a task, but an overly narrow focus may make it more difficult to take in necessary information and stimuli; see Table 2.

'''Table 2'''

''Comparison of low-intensity positive affect on cognitive scope versus high (Fredrickson, 2001; Gable &amp; Dreisbach, 2021)''
{| class=&quot;wikitable&quot; style=&quot;margin: auto;&quot;
!
!Low-intensity positive affect
!High-intensity positive affect
|-
|'''Cognitive scope'''
|Broadens attention to access wider range of stimuli and information.
|Narrows attention towards central goal potentially filtering out relevant information.
|-
|'''Potential benefits'''
|Encourages creative exploration, flexible thinking, alternative ideas.
|Focused processing of goal-related information, persistence and performance on tasks with focused attention. 
|-
|'''Potential limitations'''
|Broad focus may cause less action towards specific goal required, or lack intense concentration needed towards target.
|Narrow focus may cause important stimuli to be lost or peripheral information to be overlooked.
|}

Furthermore, according to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., sprinting and football tacking) whereas, fine motor tasks &amp; decision-making were impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.

=== Excitement on behaviour ===

==== Impulsivity and risk taking ====
Unregulated excitement can lead to a sort of behavioural overshooting. Galentino et al. (2017) demonstrates that positive emotional arousal significantly increases preferences for monetary risks by over-valuing rewards over their potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (Sohn et al., 2015; Galentino, Bonini, &amp; Savadori, 2017; Andrade, Odean, &amp; Lin, 2016). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an underestimation of risks and causing impulsive decisions.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Excitement and anxiety share similar high-arousal physiological profiles. A study by Brooks (2014) identified that these similar profiles were difficult to suppress and 90% of participants believed a variation of 'calming down' was the best cognitive strategy under high-pressure tasks. This research demonstrated that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in heart rate. When simply employing this cognitive restrucuture, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

{{RoundBoxTop|theme=3}}'''Scenario application'''
During the finals game, Steve continues to make mistakes and he starts to get anxious. Under this high pressure environment, Steve starts to reframe his mistakes as opprtunities to learn and chances to adjust to his competition. He uses some simple self-statements which he feels helps him connect to his game. His teammates notice his performance improve.{{RoundBoxBottom}}

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Liu et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as energised positive affect. Liu et al. (2026) proposed that pleasant positive affect may stabilise life satisfaction whereas more energised positive affect may be present in individuals with gaps between a current and desired states. These may drive personal growth, agency, and goal adaptation as opposed to baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

Overall, positive affect in general has been shown to increase life satisfaction and relationships over time. As excitement is a positive emotional experience, these can contribute to ones subjective well-being. As this emotional state can make activities feel more engaging and rewarding, so too can this anticipation lead to more engagement and possibly reward. Excitement may not necessarily improve well-being simply because it is a positive emotional state, rather, the emotion may encourage preparation, engagement and goal pursuit which can further contributue to a sense of accomplishment (Liu et al. 2026).

=== Excitement as viewed cross-culturally ===
Tsai (2024) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with some individualistic Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm. This maybe due to an 'ideal affect' that is to say, the desire to assert personal autononmy and influence others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. 

{{anchor|Does excitement help or hinder behaviour?}}

=== Does excitement help or hinder behaviour? ===
With helpful excitement, an individual might move towards a goal by preparing, practising, engaging and performing behaviours that lead to a desired outcome. However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision (Galentino et al., 2017).

Extremely high emotional arousal may become overwhelming, with the consequences of excitement dependent on the context and the individual's ability to regulate their behaviour. Excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion. Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depends on intensity, context and behavioural regulation.
==Conclusion==
Excitement is a positively valenced, high-arousal emotional state associated with anticipation, approach motivation and readiness to act. It can encourage preparation, persistence and engagement with meaningful goals. Although, following in similar physiological traits to other emotions such as anxiety, excitement may differ from other emotions due to its combination of positive valence, high activation/arousal, approach to goals and anticipatory nature (Russell, 1980; Gable &amp; Harmon-Jones, 2010; Macahizawa et al., 2020). Excitement as a state triggers activation of the autonomic nervous system, preparing itself for some kind of action (Oxendine, 1970). Commonm physiological responses include elevated heart rate, alertness, energy and rise of blood pressure (Ketonen et al., 2023). Psychologically, excitement can boost an individual's readiness to act, perceived self-efficacy, and cognitive scope (Brooks, 2014; Fredrickson, 2001).

As a catalyst to engaging with actions towards a certain goal, excitement can effect ones cognition, narrowing or widening its scope (Fredrickson, 2001), and possibly leading to greater impulsive or risk taking behaviours (e.g., Galentino et al., 2017). Excitement can also be a powerful tool in restructuring other emotions, and as a positive emotion, may increase satisfaction across the lifespan (Liu et al., 2016). With its value differing across culture, excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes. Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

TAKE HOME MESSAGE

CHAPTER COMPREHENSION QUIZ

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
==References==
{{Hanging indent|1=

Andrade, E. B., Odean, T., &amp; Lin, S. (2016). Bubbling with Excitement: An Experiment. ''Review of Finance, 20''(2), 447–466. https://doi.org/10.1093/rof/rfv016

Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. ''Journal of Experimental Psychology. General, 143''(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. ''The American Psychologist, 56''(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. ''Current Opinion in Behavioral Sciences, 39'', 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Gable, P., &amp; Harmon-Jones, E. (2010). The motivational dimensional model of affect: Implications for breadth of attention, memory, and cognitive categorisation. ''Cognition and Emotion, 24''(2), 322–337. https://doi.org/10.1080/02699930903378305

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. ''Frontiers in Psychology, 8'', Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Hasada, R. (1994). ''The semantic aspects of onomatopoeia: focusing on Japanese psychomimes'' [Master's thesis, The Australian National University]. ANU Open Research. https://doi.org/10.25911/5d723cb12c49c 

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. ''British Journal of Educational Psychology, 93''(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Lim, N. (2016). Cultural differences in emotion: differences in emotional arousal level between the East and the West. ''Integrative Medicine Research, 5''(2), 105–109. https://doi.org/10.1016/j.imr.2016.03.004

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. ''The Journal of Positive Psychology'', (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Machizawa, M. G., Lisi, G., Kanayama, N., Mizuochi, R., Makita, K., Sasaoka, T., &amp; Yamawaki, S. (2020). Quantification of anticipation of excitement with a three-axial model of emotion with EEG. ''Journal of Neural Engineering, 17''(3). https://doi.org/10.1088/1741-2552/ab93b4

Oxendine, J. B. (1970). Emotional Arousal and Motor Performance. ''Quest (National Association for Kinesiology in Higher Education), 13''(1), 23–32. https://doi.org/10.1080/00336297.1970.10519673

Piira, O.-P., Huikuri, H. V., &amp; Tulppo, M. P. (2011). Effects of emotional excitement on heart rate and blood pressure dynamics in patients with coronary artery disease. ''Autonomic Neuroscience, 160''(1–2), 107–114. https://doi.org/10.1016/j.autneu.2010.11.011

Posner, J., Russell, J. A., &amp; Peterson, B. S. (2005). The circumplex model of affect: An integrative approach to affective neuroscience, cognitive development, and psychopathology. ''Development and Psychopathology, 17''(3), 715–734. https://doi.org/10.1017/S0954579405050340

Robinson, M. D., &amp; Irvin, R. L. (2022). Out of the shell, into the world: preferences for openness as a substrate of approach motivation and positive affect. ''Motivation and Emotion, 46''(3), 307–318. https://doi.org/10.1007/s11031-022-09934-5

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Schachter, S., &amp; Singer, J. (1962). Cognitive, social, and physiological determinants of emotional state. ''Psychological Review, 69''(5), 379–399. https://doi.org/10.1037/h0046234

Smith, K. E., Woodard, K., &amp; Pollak, S. D. (2025). Arousal May Not Be Anything to Get Excited About. ''Emotion Review, 17''(1), 3–15. https://doi.org/10.1177/17540739241303499

Sohn, J.-H., Kim, H.-E., Sohn, S., Seok, J.-W., Choi, D., &amp; Watanuki, S. (2015). Effect of emotional arousal on inter-temporal decision-making: an fMRI study. ''Journal of Physiological Anthropology, 34''(1), Article 8. https://doi.org/10.1186/s40101-015-0047-5

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. ''Social and Personality Psychology Compass, 2''(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. ''Psychological Review, 35''(5), 351–366. https://doi.org/10.1037/h0071406

Tugade, M. M., Shiota, M. N., &amp; Kirby, L. D. (Eds.). (2014). ''Handbook of positive emotions'' (1st ed.). Guilford Press.


}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)
* [https://www.simplypsychology.com/articles/anxiety-reappraisal-strategies Cognitive Reappraisal for Anxiety: Evidence-Based Strategies That Work] (Simply Psychology)

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally characterised to be a positive, high-arousal emotional state associated with preparing an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2023). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014; Russel, 1980). 

Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situation or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring) (Tugade et al., 2014)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal (Gable &amp; Dreisbach, 2021)
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural activation system (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable (Hasada, 1994). Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional image. From this data, the study developed a three-axial model integrating valence, arousal and a new cognitive dimension of expectation/anticipation. Through this study, Macahizawa found that the this added temporal dimension was significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball and hates crowds might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}

=== Physiological responses ===
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) found that after controlling for physical activity, self-reported excitement was associated with increased physiological arousal. This included increased heart rate, alertness and energy with reduced heart rate variability, signalling a heightened sympathetic nervous system (Ketonen et al., 2023). The corresponding associations for anxiety and calmness were not found to be signficant thus possibly signalling excitement as a unique emotional experience despite ununique physiological responses.
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}

=== Psychological processes ===
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought-actions encouraging problem-solving, and affecting exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}

=== Approach motivation and goal pursuit ===
High affective states have been linked to more approach-oriented behaviour, that is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach (2021) suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states can also have goal directed behaviour, however, as excitement is a high positive affect (valence) state and anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}

=== Excitements affect on cognition ===
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

The consequences of positive emotion on cognition may depend partly on motivational intensity and not always translate into greater performance. Excitement may help in focusing in on a task, but an overly narrow focus may make it more difficult to take in necessary information and stimuli; see Table 2.

'''Table 2'''

''Comparison of low-intensity positive affect on cognitive scope versus high (Fredrickson, 2001; Gable &amp; Dreisbach, 2021)''
{| class=&quot;wikitable&quot; style=&quot;margin: auto;&quot;
!
!Low-intensity positive affect
!High-intensity positive affect
|-
|'''Cognitive scope'''
|Broadens attention to access wider range of stimuli and information.
|Narrows attention towards central goal potentially filtering out relevant information.
|-
|'''Potential benefits'''
|Encourages creative exploration, flexible thinking, alternative ideas.
|Focused processing of goal-related information, persistence and performance on tasks with focused attention. 
|-
|'''Potential limitations'''
|Broad focus may cause less action towards specific goal required, or lack intense concentration needed towards target.
|Narrow focus may cause important stimuli to be lost or peripheral information to be overlooked.
|}

Furthermore, according to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., sprinting and football tacking) whereas, fine motor tasks &amp; decision-making were impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.

=== Excitement on behaviour ===

==== Impulsivity and risk taking ====
Unregulated excitement can lead to a sort of behavioural overshooting. Galentino et al. (2017) demonstrates that positive emotional arousal significantly increases preferences for monetary risks by over-valuing rewards over their potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (Sohn et al., 2015; Galentino, Bonini, &amp; Savadori, 2017; Andrade, Odean, &amp; Lin, 2016). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an underestimation of risks and causing impulsive decisions.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Excitement and anxiety share similar high-arousal physiological profiles. A study by Brooks (2014) identified that these similar profiles were difficult to suppress and 90% of participants believed a variation of 'calming down' was the best cognitive strategy under high-pressure tasks. This research demonstrated that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in heart rate. When simply employing this cognitive restrucuture, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

{{RoundBoxTop|theme=3}}'''Scenario application'''
During the finals game, Steve continues to make mistakes and he starts to get anxious. Under this high pressure environment, Steve starts to reframe his mistakes as opprtunities to learn and chances to adjust to his competition. He uses some simple self-statements which he feels helps him connect to his game. His teammates notice his performance improve.{{RoundBoxBottom}}

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Liu et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as energised positive affect. Liu et al. (2026) proposed that pleasant positive affect may stabilise life satisfaction whereas more energised positive affect may be present in individuals with gaps between a current and desired states. These may drive personal growth, agency, and goal adaptation as opposed to baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

Overall, positive affect in general has been shown to increase life satisfaction and relationships over time. As excitement is a positive emotional experience, these can contribute to ones subjective well-being. As this emotional state can make activities feel more engaging and rewarding, so too can this anticipation lead to more engagement and possibly reward. Excitement may not necessarily improve well-being simply because it is a positive emotional state, rather, the emotion may encourage preparation, engagement and goal pursuit which can further contributue to a sense of accomplishment (Liu et al. 2026).

=== Excitement as viewed cross-culturally ===
Tsai (2024) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with some individualistic Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm. This maybe due to an 'ideal affect' that is to say, the desire to assert personal autononmy and influence others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. 

{{anchor|Does excitement help or hinder behaviour?}}

=== Does excitement help or hinder behaviour? ===
With helpful excitement, an individual might move towards a goal by preparing, practising, engaging and performing behaviours that lead to a desired outcome. However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision (Galentino et al., 2017).

Extremely high emotional arousal may become overwhelming, with the consequences of excitement dependent on the context and the individual's ability to regulate their behaviour. Excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion. Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depends on intensity, context and behavioural regulation.
==Conclusion==
Excitement is a positively valenced, high-arousal emotional state associated with anticipation, approach motivation and readiness to act. It can encourage preparation, persistence and engagement with meaningful goals. Although, following in similar physiological traits to other emotions such as anxiety, excitement may differ from other emotions due to its combination of positive valence, high activation/arousal, approach to goals and anticipatory nature (Russell, 1980; Gable &amp; Harmon-Jones, 2010; Macahizawa et al., 2020). Excitement as a state triggers activation of the autonomic nervous system, preparing itself for some kind of action (Oxendine, 1970). Commonm physiological responses include elevated heart rate, alertness, energy and rise of blood pressure (Ketonen et al., 2023). Psychologically, excitement can boost an individual's readiness to act, perceived self-efficacy, and cognitive scope (Brooks, 2014; Fredrickson, 2001).

As a catalyst to engaging with actions towards a certain goal, excitement can effect ones cognition, narrowing or widening its scope (Fredrickson, 2001), and possibly leading to greater impulsive or risk taking behaviours (e.g., Galentino et al., 2017). Excitement can also be a powerful tool in restructuring other emotions, and as a positive emotion, may increase satisfaction across the lifespan (Liu et al., 2016). With its value differing across culture, excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes. Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

TAKE HOME MESSAGE

CHAPTER COMPREHENSION QUIZ

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
==References==
{{Hanging indent|1=

Andrade, E. B., Odean, T., &amp; Lin, S. (2016). Bubbling with Excitement: An Experiment. ''Review of Finance, 20''(2), 447–466. https://doi.org/10.1093/rof/rfv016

Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. ''Journal of Experimental Psychology. General, 143''(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. ''The American Psychologist, 56''(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. ''Current Opinion in Behavioral Sciences, 39'', 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Gable, P., &amp; Harmon-Jones, E. (2010). The motivational dimensional model of affect: Implications for breadth of attention, memory, and cognitive categorisation. ''Cognition and Emotion, 24''(2), 322–337. https://doi.org/10.1080/02699930903378305

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. ''Frontiers in Psychology, 8'', Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Hasada, R. (1994). ''The semantic aspects of onomatopoeia: focusing on Japanese psychomimes'' [Master's thesis, The Australian National University]. ANU Open Research. https://doi.org/10.25911/5d723cb12c49c 

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. ''British Journal of Educational Psychology, 93''(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Lim, N. (2016). Cultural differences in emotion: differences in emotional arousal level between the East and the West. ''Integrative Medicine Research, 5''(2), 105–109. https://doi.org/10.1016/j.imr.2016.03.004

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. ''The Journal of Positive Psychology'', (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Machizawa, M. G., Lisi, G., Kanayama, N., Mizuochi, R., Makita, K., Sasaoka, T., &amp; Yamawaki, S. (2020). Quantification of anticipation of excitement with a three-axial model of emotion with EEG. ''Journal of Neural Engineering, 17''(3). https://doi.org/10.1088/1741-2552/ab93b4

Oxendine, J. B. (1970). Emotional Arousal and Motor Performance. ''Quest (National Association for Kinesiology in Higher Education), 13''(1), 23–32. https://doi.org/10.1080/00336297.1970.10519673

Piira, O.-P., Huikuri, H. V., &amp; Tulppo, M. P. (2011). Effects of emotional excitement on heart rate and blood pressure dynamics in patients with coronary artery disease. ''Autonomic Neuroscience, 160''(1–2), 107–114. https://doi.org/10.1016/j.autneu.2010.11.011

Posner, J., Russell, J. A., &amp; Peterson, B. S. (2005). The circumplex model of affect: An integrative approach to affective neuroscience, cognitive development, and psychopathology. ''Development and Psychopathology, 17''(3), 715–734. https://doi.org/10.1017/S0954579405050340

Robinson, M. D., &amp; Irvin, R. L. (2022). Out of the shell, into the world: preferences for openness as a substrate of approach motivation and positive affect. ''Motivation and Emotion, 46''(3), 307–318. https://doi.org/10.1007/s11031-022-09934-5

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Schachter, S., &amp; Singer, J. (1962). Cognitive, social, and physiological determinants of emotional state. ''Psychological Review, 69''(5), 379–399. https://doi.org/10.1037/h0046234

Smith, K. E., Woodard, K., &amp; Pollak, S. D. (2025). Arousal May Not Be Anything to Get Excited About. ''Emotion Review, 17''(1), 3–15. https://doi.org/10.1177/17540739241303499

Sohn, J.-H., Kim, H.-E., Sohn, S., Seok, J.-W., Choi, D., &amp; Watanuki, S. (2015). Effect of emotional arousal on inter-temporal decision-making: an fMRI study. ''Journal of Physiological Anthropology, 34''(1), Article 8. https://doi.org/10.1186/s40101-015-0047-5

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. ''Social and Personality Psychology Compass, 2''(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. ''Psychological Review, 35''(5), 351–366. https://doi.org/10.1037/h0071406

Tsai, J. L. (2024). Investigating culture and emotion: From responses to ideals. In M. J. Gelfand, C.-Y. Chiu, &amp; Y.-Y. Hong (Eds.), ''Handbook of advances in culture and psychology'' (pp. 54–117). Oxford University Press.

Tugade, M. M., Shiota, M. N., &amp; Kirby, L. D. (Eds.). (2014). ''Handbook of positive emotions'' (1st ed.). Guilford Press.


}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)
* [https://www.simplypsychology.com/articles/anxiety-reappraisal-strategies Cognitive Reappraisal for Anxiety: Evidence-Based Strategies That Work] (Simply Psychology)

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally characterised to be a positive, high-arousal emotional state associated with preparing an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2023). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014; Russel, 1980). 

Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situation or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring) (Tugade et al., 2014)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal (Gable &amp; Dreisbach, 2021)
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural activation system (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable (Hasada, 1994). Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional image. From this data, the study developed a three-axial model integrating valence, arousal and a new cognitive dimension of expectation/anticipation. Through this study, Macahizawa found that the this added temporal dimension was significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball and hates crowds might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}

=== Physiological responses ===
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) found that after controlling for physical activity, self-reported excitement was associated with increased physiological arousal. This included increased heart rate, alertness and energy with reduced heart rate variability, signalling a heightened sympathetic nervous system (Ketonen et al., 2023). The corresponding associations for anxiety and calmness were not found to be signficant thus possibly signalling excitement as a unique emotional experience despite ununique physiological responses.
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}

=== Psychological processes ===
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought-actions encouraging problem-solving, and affecting exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}

=== Approach motivation and goal pursuit ===
High affective states have been linked to more approach-oriented behaviour, that is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach (2021) suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states can also have goal directed behaviour, however, as excitement is a high positive affect (valence) state and anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}

=== Excitements affect on cognition ===
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

The consequences of positive emotion on cognition may depend partly on motivational intensity and not always translate into greater performance. Excitement may help in focusing in on a task, but an overly narrow focus may make it more difficult to take in necessary information and stimuli; see Table 2.

'''Table 2'''

''Comparison of low-intensity positive affect on cognitive scope versus high (Fredrickson, 2001; Gable &amp; Dreisbach, 2021)''
{| class=&quot;wikitable&quot; style=&quot;margin: auto;&quot;
!
!Low-intensity positive affect
!High-intensity positive affect
|-
|'''Cognitive scope'''
|Broadens attention to access wider range of stimuli and information.
|Narrows attention towards central goal potentially filtering out relevant information.
|-
|'''Potential benefits'''
|Encourages creative exploration, flexible thinking, alternative ideas.
|Focused processing of goal-related information, persistence and performance on tasks with focused attention. 
|-
|'''Potential limitations'''
|Broad focus may cause less action towards specific goal required, or lack intense concentration needed towards target.
|Narrow focus may cause important stimuli to be lost or peripheral information to be overlooked.
|}

Furthermore, according to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., sprinting and football tacking) whereas, fine motor tasks &amp; decision-making were impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.

=== Excitement on behaviour ===

==== Impulsivity and risk taking ====
Unregulated excitement can lead to a sort of behavioural overshooting. Galentino et al. (2017) demonstrates that positive emotional arousal significantly increases preferences for monetary risks by over-valuing rewards over their potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (Sohn et al., 2015; Galentino, Bonini, &amp; Savadori, 2017; Andrade, Odean, &amp; Lin, 2016). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an underestimation of risks and causing impulsive decisions.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Excitement and anxiety share similar high-arousal physiological profiles. A study by Brooks (2014) identified that these similar profiles were difficult to suppress and 90% of participants believed a variation of 'calming down' was the best cognitive strategy under high-pressure tasks. This research demonstrated that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in heart rate. When simply employing this cognitive restrucuture, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

{{RoundBoxTop|theme=3}}'''Scenario application'''
During the finals game, Steve continues to make mistakes and he starts to get anxious. Under this high pressure environment, Steve starts to reframe his mistakes as opprtunities to learn and chances to adjust to his competition. He uses some simple self-statements which he feels helps him connect to his game. His teammates notice his performance improve.{{RoundBoxBottom}}

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Liu et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as energised positive affect. Liu et al. (2026) proposed that pleasant positive affect may stabilise life satisfaction whereas more energised positive affect may be present in individuals with gaps between a current and desired states. These may drive personal growth, agency, and goal adaptation as opposed to baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

Overall, positive affect in general has been shown to increase life satisfaction and relationships over time. As excitement is a positive emotional experience, these can contribute to ones subjective well-being. As this emotional state can make activities feel more engaging and rewarding, so too can this anticipation lead to more engagement and possibly reward. Excitement may not necessarily improve well-being simply because it is a positive emotional state, rather, the emotion may encourage preparation, engagement and goal pursuit which can further contributue to a sense of accomplishment (Liu et al. 2026).

=== Excitement as viewed cross-culturally ===
[[File:Excitement and anticipation at the Reykjavík Children’s Culture Festival 2016 (26145642903).jpg|thumb|'''Figure 4.''' Excitement  may be viewed differently across cultures]]
Tsai (2024) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with some individualistic Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm. This maybe due to an 'ideal affect' that is to say, the desire to assert personal autononmy and influence others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. 

{{anchor|Does excitement help or hinder behaviour?}}

=== Does excitement help or hinder behaviour? ===
With helpful excitement, an individual might move towards a goal by preparing, practising, engaging and performing behaviours that lead to a desired outcome. However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision (Galentino et al., 2017).

Extremely high emotional arousal may become overwhelming, with the consequences of excitement dependent on the context and the individual's ability to regulate their behaviour. Excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion. Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depends on intensity, context and behavioural regulation.
==Conclusion==
Excitement is a positively valenced, high-arousal emotional state associated with anticipation, approach motivation and readiness to act. It can encourage preparation, persistence and engagement with meaningful goals. Although, following in similar physiological traits to other emotions such as anxiety, excitement may differ from other emotions due to its combination of positive valence, high activation/arousal, approach to goals and anticipatory nature (Russell, 1980; Gable &amp; Harmon-Jones, 2010; Macahizawa et al., 2020). Excitement as a state triggers activation of the autonomic nervous system, preparing itself for some kind of action (Oxendine, 1970). Commonm physiological responses include elevated heart rate, alertness, energy and rise of blood pressure (Ketonen et al., 2023). Psychologically, excitement can boost an individual's readiness to act, perceived self-efficacy, and cognitive scope (Brooks, 2014; Fredrickson, 2001).

As a catalyst to engaging with actions towards a certain goal, excitement can effect ones cognition, narrowing or widening its scope (Fredrickson, 2001), and possibly leading to greater impulsive or risk taking behaviours (e.g., Galentino et al., 2017). Excitement can also be a powerful tool in restructuring other emotions, and as a positive emotion, may increase satisfaction across the lifespan (Liu et al., 2016). With its value differing across culture, excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes. Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

TAKE HOME MESSAGE

CHAPTER COMPREHENSION QUIZ

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
==References==
{{Hanging indent|1=

Andrade, E. B., Odean, T., &amp; Lin, S. (2016). Bubbling with Excitement: An Experiment. ''Review of Finance, 20''(2), 447–466. https://doi.org/10.1093/rof/rfv016

Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. ''Journal of Experimental Psychology. General, 143''(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. ''The American Psychologist, 56''(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. ''Current Opinion in Behavioral Sciences, 39'', 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Gable, P., &amp; Harmon-Jones, E. (2010). The motivational dimensional model of affect: Implications for breadth of attention, memory, and cognitive categorisation. ''Cognition and Emotion, 24''(2), 322–337. https://doi.org/10.1080/02699930903378305

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. ''Frontiers in Psychology, 8'', Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Hasada, R. (1994). ''The semantic aspects of onomatopoeia: focusing on Japanese psychomimes'' [Master's thesis, The Australian National University]. ANU Open Research. https://doi.org/10.25911/5d723cb12c49c 

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. ''British Journal of Educational Psychology, 93''(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Lim, N. (2016). Cultural differences in emotion: differences in emotional arousal level between the East and the West. ''Integrative Medicine Research, 5''(2), 105–109. https://doi.org/10.1016/j.imr.2016.03.004

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. ''The Journal of Positive Psychology'', (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Machizawa, M. G., Lisi, G., Kanayama, N., Mizuochi, R., Makita, K., Sasaoka, T., &amp; Yamawaki, S. (2020). Quantification of anticipation of excitement with a three-axial model of emotion with EEG. ''Journal of Neural Engineering, 17''(3). https://doi.org/10.1088/1741-2552/ab93b4

Oxendine, J. B. (1970). Emotional Arousal and Motor Performance. ''Quest (National Association for Kinesiology in Higher Education), 13''(1), 23–32. https://doi.org/10.1080/00336297.1970.10519673

Piira, O.-P., Huikuri, H. V., &amp; Tulppo, M. P. (2011). Effects of emotional excitement on heart rate and blood pressure dynamics in patients with coronary artery disease. ''Autonomic Neuroscience, 160''(1–2), 107–114. https://doi.org/10.1016/j.autneu.2010.11.011

Posner, J., Russell, J. A., &amp; Peterson, B. S. (2005). The circumplex model of affect: An integrative approach to affective neuroscience, cognitive development, and psychopathology. ''Development and Psychopathology, 17''(3), 715–734. https://doi.org/10.1017/S0954579405050340

Robinson, M. D., &amp; Irvin, R. L. (2022). Out of the shell, into the world: preferences for openness as a substrate of approach motivation and positive affect. ''Motivation and Emotion, 46''(3), 307–318. https://doi.org/10.1007/s11031-022-09934-5

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Schachter, S., &amp; Singer, J. (1962). Cognitive, social, and physiological determinants of emotional state. ''Psychological Review, 69''(5), 379–399. https://doi.org/10.1037/h0046234

Smith, K. E., Woodard, K., &amp; Pollak, S. D. (2025). Arousal May Not Be Anything to Get Excited About. ''Emotion Review, 17''(1), 3–15. https://doi.org/10.1177/17540739241303499

Sohn, J.-H., Kim, H.-E., Sohn, S., Seok, J.-W., Choi, D., &amp; Watanuki, S. (2015). Effect of emotional arousal on inter-temporal decision-making: an fMRI study. ''Journal of Physiological Anthropology, 34''(1), Article 8. https://doi.org/10.1186/s40101-015-0047-5

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. ''Social and Personality Psychology Compass, 2''(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. ''Psychological Review, 35''(5), 351–366. https://doi.org/10.1037/h0071406

Tsai, J. L. (2024). Investigating culture and emotion: From responses to ideals. In M. J. Gelfand, C.-Y. Chiu, &amp; Y.-Y. Hong (Eds.), ''Handbook of advances in culture and psychology'' (pp. 54–117). Oxford University Press.

Tugade, M. M., Shiota, M. N., &amp; Kirby, L. D. (Eds.). (2014). ''Handbook of positive emotions'' (1st ed.). Guilford Press.


}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)
* [https://www.simplypsychology.com/articles/anxiety-reappraisal-strategies Cognitive Reappraisal for Anxiety: Evidence-Based Strategies That Work] (Simply Psychology)

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally characterised to be a positive, high-arousal emotional state associated with preparing an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2023). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014; Russel, 1980). 

Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situation or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring) (Tugade et al., 2014)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal (Gable &amp; Dreisbach, 2021)
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural activation system (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable (Hasada, 1994). Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional image. From this data, the study developed a three-axial model integrating valence, arousal and a new cognitive dimension of expectation/anticipation. Through this study, Macahizawa found that the this added temporal dimension was significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball and hates crowds might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}

=== Physiological responses ===
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) found that after controlling for physical activity, self-reported excitement was associated with increased physiological arousal. This included increased heart rate, alertness and energy with reduced heart rate variability, signalling a heightened sympathetic nervous system (Ketonen et al., 2023). The corresponding associations for anxiety and calmness were not found to be signficant thus possibly signalling excitement as a unique emotional experience despite ununique physiological responses.
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}

=== Psychological processes ===
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought-actions encouraging problem-solving, and affecting exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}

=== Approach motivation and goal pursuit ===
High affective states have been linked to more approach-oriented behaviour, that is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach (2021) suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states can also have goal directed behaviour, however, as excitement is a high positive affect (valence) state and anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}

=== Excitements affect on cognition ===
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

The consequences of positive emotion on cognition may depend partly on motivational intensity and not always translate into greater performance. Excitement may help in focusing in on a task, but an overly narrow focus may make it more difficult to take in necessary information and stimuli; see Table 2.

'''Table 2'''

''Comparison of low-intensity positive affect on cognitive scope versus high (Fredrickson, 2001; Gable &amp; Dreisbach, 2021)''
{| class=&quot;wikitable&quot; style=&quot;margin: auto;&quot;
!
!Low-intensity positive affect
!High-intensity positive affect
|-
|'''Cognitive scope'''
|Broadens attention to access wider range of stimuli and information.
|Narrows attention towards central goal potentially filtering out relevant information.
|-
|'''Potential benefits'''
|Encourages creative exploration, flexible thinking, alternative ideas.
|Focused processing of goal-related information, persistence and performance on tasks with focused attention. 
|-
|'''Potential limitations'''
|Broad focus may cause less action towards specific goal required, or lack intense concentration needed towards target.
|Narrow focus may cause important stimuli to be lost or peripheral information to be overlooked.
|}

Furthermore, according to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., sprinting and football tacking) whereas, fine motor tasks &amp; decision-making were impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.

=== Excitement on behaviour ===

==== Impulsivity and risk taking ====
Unregulated excitement can lead to a sort of behavioural overshooting. Galentino et al. (2017) demonstrates that positive emotional arousal significantly increases preferences for monetary risks by over-valuing rewards over their potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (Sohn et al., 2015; Galentino, Bonini, &amp; Savadori, 2017; Andrade, Odean, &amp; Lin, 2016). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an underestimation of risks and causing impulsive decisions.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Excitement and anxiety share similar high-arousal physiological profiles. A study by Brooks (2014) identified that these similar profiles were difficult to suppress and 90% of participants believed a variation of 'calming down' was the best cognitive strategy under high-pressure tasks. This research demonstrated that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in heart rate. When simply employing this cognitive restrucuture, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

{{RoundBoxTop|theme=3}}'''Scenario application'''
During the finals game, Steve continues to make mistakes and he starts to get anxious. Under this high pressure environment, Steve starts to reframe his mistakes as opprtunities to learn and chances to adjust to his competition. He uses some simple self-statements which he feels helps him connect to his game. His teammates notice his performance improve.{{RoundBoxBottom}}

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Liu et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as energised positive affect. Liu et al. (2026) proposed that pleasant positive affect may stabilise life satisfaction whereas more energised positive affect may be present in individuals with gaps between a current and desired states. These may drive personal growth, agency, and goal adaptation as opposed to baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

Overall, positive affect in general has been shown to increase life satisfaction and relationships over time. As excitement is a positive emotional experience, these can contribute to ones subjective well-being. As this emotional state can make activities feel more engaging and rewarding, so too can this anticipation lead to more engagement and possibly reward. Excitement may not necessarily improve well-being simply because it is a positive emotional state, rather, the emotion may encourage preparation, engagement and goal pursuit which can further contributue to a sense of accomplishment (Liu et al. 2026).

=== Excitement as viewed cross-culturally ===
[[File:Excitement and anticipation at the Reykjavík Children’s Culture Festival 2016 (26145642903).jpg|thumb|'''Figure 4.''' Excitement  may be viewed differently across cultures]]
Tsai (2024) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with some individualistic Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm. This maybe due to an 'ideal affect' that is to say, the desire to assert personal autononmy and influence others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. 

{{anchor|Does excitement help or hinder behaviour?}}

=== Does excitement help or hinder behaviour? ===
With helpful excitement, an individual might move towards a goal by preparing, practising, engaging and performing behaviours that lead to a desired outcome. However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision (Galentino et al., 2017).

Extremely high emotional arousal may become overwhelming, with the consequences of excitement dependent on the context and the individual's ability to regulate their behaviour. Excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion. Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depends on intensity, context and behavioural regulation.

{{RoundBoxTop|theme=9}}'''Intervention application'''
To reduce the effects of overwhelm during high emotional arousal, interventions should work in teaching individuals to identify when excitement is too great and cognitive restructure in the form of strategies like 'simple statements' can be used.{{RoundBoxBottom}}

==Conclusion==
Excitement is a positively valenced, high-arousal emotional state associated with anticipation, approach motivation and readiness to act. It can encourage preparation, persistence and engagement with meaningful goals. Although, following in similar physiological traits to other emotions such as anxiety, excitement may differ from other emotions due to its combination of positive valence, high activation/arousal, approach to goals and anticipatory nature (Russell, 1980; Gable &amp; Harmon-Jones, 2010; Macahizawa et al., 2020). Excitement as a state triggers activation of the autonomic nervous system, preparing itself for some kind of action (Oxendine, 1970). Commonm physiological responses include elevated heart rate, alertness, energy and rise of blood pressure (Ketonen et al., 2023). Psychologically, excitement can boost an individual's readiness to act, perceived self-efficacy, and cognitive scope (Brooks, 2014; Fredrickson, 2001).

As a catalyst to engaging with actions towards a certain goal, excitement can effect ones cognition, narrowing or widening its scope (Fredrickson, 2001), and possibly leading to greater impulsive or risk taking behaviours (e.g., Galentino et al., 2017). Excitement can also be a powerful tool in restructuring other emotions, and as a positive emotion, may increase satisfaction across the lifespan (Liu et al., 2016). With its value differing across culture, excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes. Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

TAKE HOME MESSAGE

CHAPTER COMPREHENSION QUIZ

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
==References==
{{Hanging indent|1=

Andrade, E. B., Odean, T., &amp; Lin, S. (2016). Bubbling with Excitement: An Experiment. ''Review of Finance, 20''(2), 447–466. https://doi.org/10.1093/rof/rfv016

Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. ''Journal of Experimental Psychology. General, 143''(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. ''The American Psychologist, 56''(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. ''Current Opinion in Behavioral Sciences, 39'', 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Gable, P., &amp; Harmon-Jones, E. (2010). The motivational dimensional model of affect: Implications for breadth of attention, memory, and cognitive categorisation. ''Cognition and Emotion, 24''(2), 322–337. https://doi.org/10.1080/02699930903378305

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. ''Frontiers in Psychology, 8'', Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Hasada, R. (1994). ''The semantic aspects of onomatopoeia: focusing on Japanese psychomimes'' [Master's thesis, The Australian National University]. ANU Open Research. https://doi.org/10.25911/5d723cb12c49c 

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. ''British Journal of Educational Psychology, 93''(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Lim, N. (2016). Cultural differences in emotion: differences in emotional arousal level between the East and the West. ''Integrative Medicine Research, 5''(2), 105–109. https://doi.org/10.1016/j.imr.2016.03.004

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. ''The Journal of Positive Psychology'', (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Machizawa, M. G., Lisi, G., Kanayama, N., Mizuochi, R., Makita, K., Sasaoka, T., &amp; Yamawaki, S. (2020). Quantification of anticipation of excitement with a three-axial model of emotion with EEG. ''Journal of Neural Engineering, 17''(3). https://doi.org/10.1088/1741-2552/ab93b4

Oxendine, J. B. (1970). Emotional Arousal and Motor Performance. ''Quest (National Association for Kinesiology in Higher Education), 13''(1), 23–32. https://doi.org/10.1080/00336297.1970.10519673

Piira, O.-P., Huikuri, H. V., &amp; Tulppo, M. P. (2011). Effects of emotional excitement on heart rate and blood pressure dynamics in patients with coronary artery disease. ''Autonomic Neuroscience, 160''(1–2), 107–114. https://doi.org/10.1016/j.autneu.2010.11.011

Posner, J., Russell, J. A., &amp; Peterson, B. S. (2005). The circumplex model of affect: An integrative approach to affective neuroscience, cognitive development, and psychopathology. ''Development and Psychopathology, 17''(3), 715–734. https://doi.org/10.1017/S0954579405050340

Robinson, M. D., &amp; Irvin, R. L. (2022). Out of the shell, into the world: preferences for openness as a substrate of approach motivation and positive affect. ''Motivation and Emotion, 46''(3), 307–318. https://doi.org/10.1007/s11031-022-09934-5

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Schachter, S., &amp; Singer, J. (1962). Cognitive, social, and physiological determinants of emotional state. ''Psychological Review, 69''(5), 379–399. https://doi.org/10.1037/h0046234

Smith, K. E., Woodard, K., &amp; Pollak, S. D. (2025). Arousal May Not Be Anything to Get Excited About. ''Emotion Review, 17''(1), 3–15. https://doi.org/10.1177/17540739241303499

Sohn, J.-H., Kim, H.-E., Sohn, S., Seok, J.-W., Choi, D., &amp; Watanuki, S. (2015). Effect of emotional arousal on inter-temporal decision-making: an fMRI study. ''Journal of Physiological Anthropology, 34''(1), Article 8. https://doi.org/10.1186/s40101-015-0047-5

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. ''Social and Personality Psychology Compass, 2''(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. ''Psychological Review, 35''(5), 351–366. https://doi.org/10.1037/h0071406

Tsai, J. L. (2024). Investigating culture and emotion: From responses to ideals. In M. J. Gelfand, C.-Y. Chiu, &amp; Y.-Y. Hong (Eds.), ''Handbook of advances in culture and psychology'' (pp. 54–117). Oxford University Press.

Tugade, M. M., Shiota, M. N., &amp; Kirby, L. D. (Eds.). (2014). ''Handbook of positive emotions'' (1st ed.). Guilford Press.


}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)
* [https://www.simplypsychology.com/articles/anxiety-reappraisal-strategies Cognitive Reappraisal for Anxiety: Evidence-Based Strategies That Work] (Simply Psychology)

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally characterised to be a positive, high-arousal emotional state associated with preparing an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2023). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014; Russel, 1980). 

Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situation or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring) (Tugade et al., 2014)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal (Gable &amp; Dreisbach, 2021)
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural activation system (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable (Hasada, 1994). Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional image. From this data, the study developed a three-axial model integrating valence, arousal and a new cognitive dimension of expectation/anticipation. Through this study, Macahizawa found that the this added temporal dimension was significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball and hates crowds might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}

=== Physiological responses ===
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) found that after controlling for physical activity, self-reported excitement was associated with increased physiological arousal. This included increased heart rate, alertness and energy with reduced heart rate variability, signalling a heightened sympathetic nervous system (Ketonen et al., 2023). The corresponding associations for anxiety and calmness were not found to be signficant thus possibly signalling excitement as a unique emotional experience despite ununique physiological responses.
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}

=== Psychological processes ===
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought-actions encouraging problem-solving, and affecting exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}

=== Approach motivation and goal pursuit ===
High affective states have been linked to more approach-oriented behaviour, that is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach (2021) suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states can also have goal directed behaviour, however, as excitement is a high positive affect (valence) state and anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}

=== Excitements affect on cognition ===
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

The consequences of positive emotion on cognition may depend partly on motivational intensity and not always translate into greater performance. Excitement may help in focusing in on a task, but an overly narrow focus may make it more difficult to take in necessary information and stimuli; see Table 2.

'''Table 2'''

''Comparison of low-intensity positive affect on cognitive scope versus high (Fredrickson, 2001; Gable &amp; Dreisbach, 2021)''
{| class=&quot;wikitable&quot; style=&quot;margin: auto;&quot;
!
!Low-intensity positive affect
!High-intensity positive affect
|-
|'''Cognitive scope'''
|Broadens attention to access wider range of stimuli and information.
|Narrows attention towards central goal potentially filtering out relevant information.
|-
|'''Potential benefits'''
|Encourages creative exploration, flexible thinking, alternative ideas.
|Focused processing of goal-related information, persistence and performance on tasks with focused attention. 
|-
|'''Potential limitations'''
|Broad focus may cause less action towards specific goal required, or lack intense concentration needed towards target.
|Narrow focus may cause important stimuli to be lost or peripheral information to be overlooked.
|}

Furthermore, according to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., sprinting and football tacking) whereas, fine motor tasks &amp; decision-making were impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.

=== Excitement on behaviour ===

==== Impulsivity and risk taking ====
Unregulated excitement can lead to a sort of behavioural overshooting. Galentino et al. (2017) demonstrates that positive emotional arousal significantly increases preferences for monetary risks by over-valuing rewards over their potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (Sohn et al., 2015; Galentino, Bonini, &amp; Savadori, 2017; Andrade, Odean, &amp; Lin, 2016). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an underestimation of risks and causing impulsive decisions.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Excitement and anxiety share similar high-arousal physiological profiles. A study by Brooks (2014) identified that these similar profiles were difficult to suppress and 90% of participants believed a variation of 'calming down' was the best cognitive strategy under high-pressure tasks. This research demonstrated that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in heart rate. When simply employing this cognitive restrucuture, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

{{RoundBoxTop|theme=3}}'''Scenario application'''
During the finals game, Steve continues to make mistakes and he starts to get anxious. Under this high pressure environment, Steve starts to reframe his mistakes as opprtunities to learn and chances to adjust to his competition. He uses some simple self-statements which he feels helps him connect to his game. His teammates notice his performance improve.{{RoundBoxBottom}}

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Liu et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as energised positive affect. Liu et al. (2026) proposed that pleasant positive affect may stabilise life satisfaction whereas more energised positive affect may be present in individuals with gaps between a current and desired states. These may drive personal growth, agency, and goal adaptation as opposed to baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

Overall, positive affect in general has been shown to increase life satisfaction and relationships over time. As excitement is a positive emotional experience, these can contribute to ones subjective well-being. As this emotional state can make activities feel more engaging and rewarding, so too can this anticipation lead to more engagement and possibly reward. Excitement may not necessarily improve well-being simply because it is a positive emotional state, rather, the emotion may encourage preparation, engagement and goal pursuit which can further contributue to a sense of accomplishment (Liu et al. 2026).

=== Excitement as viewed cross-culturally ===
[[File:Excitement and anticipation at the Reykjavík Children’s Culture Festival 2016 (26145642903).jpg|thumb|'''Figure 4.''' Excitement  may be viewed differently across cultures]]
Tsai (2024) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with some individualistic Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm. This maybe due to an 'ideal affect' that is to say, the desire to assert personal autononmy and influence others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. 

{{anchor|Does excitement help or hinder behaviour?}}

=== Does excitement help or hinder behaviour? ===
With helpful excitement, an individual might move towards a goal by preparing, practising, engaging and performing behaviours that lead to a desired outcome. However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision (Galentino et al., 2017).

Extremely high emotional arousal may become overwhelming, with the consequences of excitement dependent on the context and the individual's ability to regulate their behaviour. Excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion. Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depends on intensity, context and behavioural regulation.

{{RoundBoxTop|theme=9}}'''Intervention application'''
To reduce the effects of overwhelm during high emotional arousal, interventions should work in teaching individuals to identify when excitement is too great and cognitive restructure in the form of strategies like 'simple statements' can be used.{{RoundBoxBottom}}

==Conclusion==
Excitement is a positively valenced, high-arousal emotional state associated with anticipation, approach motivation and readiness to act. It can encourage preparation, persistence and engagement with meaningful goals. Although, following in similar physiological traits to other emotions such as anxiety, excitement may differ from other emotions due to its combination of positive valence, high activation/arousal, approach to goals and anticipatory nature (Russell, 1980; Gable &amp; Harmon-Jones, 2010; Macahizawa et al., 2020). Excitement as a state triggers activation of the autonomic nervous system, preparing itself for some kind of action (Oxendine, 1970). Commonm physiological responses include elevated heart rate, alertness, energy and rise of blood pressure (Ketonen et al., 2023). Psychologically, excitement can boost an individual's readiness to act, perceived self-efficacy, and cognitive scope (Brooks, 2014; Fredrickson, 2001).

As a catalyst to engaging with actions towards a certain goal, excitement can effect ones cognition, narrowing or widening its scope (Fredrickson, 2001), and possibly leading to greater impulsive or risk taking behaviours (e.g., Galentino et al., 2017). Excitement can also be a powerful tool in restructuring other emotions, and as a positive emotion, may increase satisfaction across the lifespan (Liu et al., 2016). With its value differing across culture, excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes. Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

{{RoundBoxTop|theme=3}}
'''Take-home message'''

Excitement is a unique emotional state that can be as much of a powerful tool in goal pursuit, action and well-being as it is simply a positive state of being. An event that strikes fear into one, may be exciting for another meaning, ultimately, excitement is shaped by the significance we assign to our experiences. {{RoundBoxBottom}}

CHAPTER COMPREHENSION QUIZ

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
==References==
{{Hanging indent|1=

Andrade, E. B., Odean, T., &amp; Lin, S. (2016). Bubbling with Excitement: An Experiment. ''Review of Finance, 20''(2), 447–466. https://doi.org/10.1093/rof/rfv016

Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. ''Journal of Experimental Psychology. General, 143''(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. ''The American Psychologist, 56''(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. ''Current Opinion in Behavioral Sciences, 39'', 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Gable, P., &amp; Harmon-Jones, E. (2010). The motivational dimensional model of affect: Implications for breadth of attention, memory, and cognitive categorisation. ''Cognition and Emotion, 24''(2), 322–337. https://doi.org/10.1080/02699930903378305

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. ''Frontiers in Psychology, 8'', Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Hasada, R. (1994). ''The semantic aspects of onomatopoeia: focusing on Japanese psychomimes'' [Master's thesis, The Australian National University]. ANU Open Research. https://doi.org/10.25911/5d723cb12c49c 

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. ''British Journal of Educational Psychology, 93''(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Lim, N. (2016). Cultural differences in emotion: differences in emotional arousal level between the East and the West. ''Integrative Medicine Research, 5''(2), 105–109. https://doi.org/10.1016/j.imr.2016.03.004

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. ''The Journal of Positive Psychology'', (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Machizawa, M. G., Lisi, G., Kanayama, N., Mizuochi, R., Makita, K., Sasaoka, T., &amp; Yamawaki, S. (2020). Quantification of anticipation of excitement with a three-axial model of emotion with EEG. ''Journal of Neural Engineering, 17''(3). https://doi.org/10.1088/1741-2552/ab93b4

Oxendine, J. B. (1970). Emotional Arousal and Motor Performance. ''Quest (National Association for Kinesiology in Higher Education), 13''(1), 23–32. https://doi.org/10.1080/00336297.1970.10519673

Piira, O.-P., Huikuri, H. V., &amp; Tulppo, M. P. (2011). Effects of emotional excitement on heart rate and blood pressure dynamics in patients with coronary artery disease. ''Autonomic Neuroscience, 160''(1–2), 107–114. https://doi.org/10.1016/j.autneu.2010.11.011

Posner, J., Russell, J. A., &amp; Peterson, B. S. (2005). The circumplex model of affect: An integrative approach to affective neuroscience, cognitive development, and psychopathology. ''Development and Psychopathology, 17''(3), 715–734. https://doi.org/10.1017/S0954579405050340

Robinson, M. D., &amp; Irvin, R. L. (2022). Out of the shell, into the world: preferences for openness as a substrate of approach motivation and positive affect. ''Motivation and Emotion, 46''(3), 307–318. https://doi.org/10.1007/s11031-022-09934-5

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Schachter, S., &amp; Singer, J. (1962). Cognitive, social, and physiological determinants of emotional state. ''Psychological Review, 69''(5), 379–399. https://doi.org/10.1037/h0046234

Smith, K. E., Woodard, K., &amp; Pollak, S. D. (2025). Arousal May Not Be Anything to Get Excited About. ''Emotion Review, 17''(1), 3–15. https://doi.org/10.1177/17540739241303499

Sohn, J.-H., Kim, H.-E., Sohn, S., Seok, J.-W., Choi, D., &amp; Watanuki, S. (2015). Effect of emotional arousal on inter-temporal decision-making: an fMRI study. ''Journal of Physiological Anthropology, 34''(1), Article 8. https://doi.org/10.1186/s40101-015-0047-5

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. ''Social and Personality Psychology Compass, 2''(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. ''Psychological Review, 35''(5), 351–366. https://doi.org/10.1037/h0071406

Tsai, J. L. (2024). Investigating culture and emotion: From responses to ideals. In M. J. Gelfand, C.-Y. Chiu, &amp; Y.-Y. Hong (Eds.), ''Handbook of advances in culture and psychology'' (pp. 54–117). Oxford University Press.

Tugade, M. M., Shiota, M. N., &amp; Kirby, L. D. (Eds.). (2014). ''Handbook of positive emotions'' (1st ed.). Guilford Press.


}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)
* [https://www.simplypsychology.com/articles/anxiety-reappraisal-strategies Cognitive Reappraisal for Anxiety: Evidence-Based Strategies That Work] (Simply Psychology)

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally characterised to be a positive, high-arousal emotional state associated with preparing an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2023). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014; Russel, 1980). 

Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situation or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring) (Tugade et al., 2014)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal (Gable &amp; Dreisbach, 2021)
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural activation system (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable (Hasada, 1994). Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional image. From this data, the study developed a three-axial model integrating valence, arousal and a new cognitive dimension of expectation/anticipation. Through this study, Macahizawa found that the this added temporal dimension was significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball and hates crowds might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}

=== Physiological responses ===
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) found that after controlling for physical activity, self-reported excitement was associated with increased physiological arousal. This included increased heart rate, alertness and energy with reduced heart rate variability, signalling a heightened sympathetic nervous system (Ketonen et al., 2023). The corresponding associations for anxiety and calmness were not found to be signficant thus possibly signalling excitement as a unique emotional experience despite ununique physiological responses.
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}

=== Psychological processes ===
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought-actions encouraging problem-solving, and affecting exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}

=== Approach motivation and goal pursuit ===
High affective states have been linked to more approach-oriented behaviour, that is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach (2021) suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states can also have goal directed behaviour, however, as excitement is a high positive affect (valence) state and anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}

=== Excitements affect on cognition ===
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

The consequences of positive emotion on cognition may depend partly on motivational intensity and not always translate into greater performance. Excitement may help in focusing in on a task, but an overly narrow focus may make it more difficult to take in necessary information and stimuli; see Table 2.

'''Table 2'''

''Comparison of low-intensity positive affect on cognitive scope versus high (Fredrickson, 2001; Gable &amp; Dreisbach, 2021)''
{| class=&quot;wikitable&quot; style=&quot;margin: auto;&quot;
!
!Low-intensity positive affect
!High-intensity positive affect
|-
|'''Cognitive scope'''
|Broadens attention to access wider range of stimuli and information.
|Narrows attention towards central goal potentially filtering out relevant information.
|-
|'''Potential benefits'''
|Encourages creative exploration, flexible thinking, alternative ideas.
|Focused processing of goal-related information, persistence and performance on tasks with focused attention. 
|-
|'''Potential limitations'''
|Broad focus may cause less action towards specific goal required, or lack intense concentration needed towards target.
|Narrow focus may cause important stimuli to be lost or peripheral information to be overlooked.
|}

Furthermore, according to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., sprinting and football tacking) whereas, fine motor tasks &amp; decision-making were impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.

=== Excitement on behaviour ===

==== Impulsivity and risk taking ====
Unregulated excitement can lead to a sort of behavioural overshooting. Galentino et al. (2017) demonstrates that positive emotional arousal significantly increases preferences for monetary risks by over-valuing rewards over their potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (Sohn et al., 2015; Galentino, Bonini, &amp; Savadori, 2017; Andrade, Odean, &amp; Lin, 2016). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an underestimation of risks and causing impulsive decisions.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Excitement and anxiety share similar high-arousal physiological profiles. A study by Brooks (2014) identified that these similar profiles were difficult to suppress and 90% of participants believed a variation of 'calming down' was the best cognitive strategy under high-pressure tasks. This research demonstrated that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in heart rate. When simply employing this cognitive restrucuture, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

{{RoundBoxTop|theme=3}}'''Scenario application'''
During the finals game, Steve continues to make mistakes and he starts to get anxious. Under this high pressure environment, Steve starts to reframe his mistakes as opprtunities to learn and chances to adjust to his competition. He uses some simple self-statements which he feels helps him connect to his game. His teammates notice his performance improve.{{RoundBoxBottom}}

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Liu et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as energised positive affect. Liu et al. (2026) proposed that pleasant positive affect may stabilise life satisfaction whereas more energised positive affect may be present in individuals with gaps between a current and desired states. These may drive personal growth, agency, and goal adaptation as opposed to baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

Overall, positive affect in general has been shown to increase life satisfaction and relationships over time. As excitement is a positive emotional experience, these can contribute to ones subjective well-being. As this emotional state can make activities feel more engaging and rewarding, so too can this anticipation lead to more engagement and possibly reward. Excitement may not necessarily improve well-being simply because it is a positive emotional state, rather, the emotion may encourage preparation, engagement and goal pursuit which can further contributue to a sense of accomplishment (Liu et al. 2026).

=== Excitement as viewed cross-culturally ===
[[File:Excitement and anticipation at the Reykjavík Children’s Culture Festival 2016 (26145642903).jpg|thumb|'''Figure 4.''' Excitement  may be viewed differently across cultures]]
Tsai (2024) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with some individualistic Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm. This maybe due to an 'ideal affect' that is to say, the desire to assert personal autononmy and influence others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. 

{{anchor|Does excitement help or hinder behaviour?}}

=== Does excitement help or hinder behaviour? ===
With helpful excitement, an individual might move towards a goal by preparing, practising, engaging and performing behaviours that lead to a desired outcome. However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision (Galentino et al., 2017).

Extremely high emotional arousal may become overwhelming, with the consequences of excitement dependent on the context and the individual's ability to regulate their behaviour. Excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion. Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depends on intensity, context and behavioural regulation.

{{RoundBoxTop|theme=9}}'''Intervention application'''
To reduce the effects of overwhelm during high emotional arousal, interventions should work in teaching individuals to identify when excitement is too great and cognitive restructure in the form of strategies like 'simple statements' can be used.{{RoundBoxBottom}}

==Conclusion==
Excitement is a positively valenced, high-arousal emotional state associated with anticipation, approach motivation and readiness to act. It can encourage preparation, persistence and engagement with meaningful goals. Although, following in similar physiological traits to other emotions such as anxiety, excitement may differ from other emotions due to its combination of positive valence, high activation/arousal, approach to goals and anticipatory nature (Russell, 1980; Gable &amp; Harmon-Jones, 2010; Macahizawa et al., 2020). Excitement as a state triggers activation of the autonomic nervous system, preparing itself for some kind of action (Oxendine, 1970). Commonm physiological responses include elevated heart rate, alertness, energy and rise of blood pressure (Ketonen et al., 2023). Psychologically, excitement can boost an individual's readiness to act, perceived self-efficacy, and cognitive scope (Brooks, 2014; Fredrickson, 2001).

As a catalyst to engaging with actions towards a certain goal, excitement can effect ones cognition, narrowing or widening its scope (Fredrickson, 2001), and possibly leading to greater impulsive or risk taking behaviours (e.g., Galentino et al., 2017). Excitement can also be a powerful tool in restructuring other emotions, and as a positive emotion, may increase satisfaction across the lifespan (Liu et al., 2016). With its value differing across culture, excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes. Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

{{RoundBoxTop|theme=3}}
'''Take-home message'''

Excitement is a unique emotional state that can be as much of a powerful tool in goal pursuit, action and well-being as it is simply a positive state of being. An event that strikes fear into one, may be exciting for another, therefore, excitement and emotions as whole come from the unique interplay of our active and passive shaping of the significance we assign to our experiences. {{RoundBoxBottom}}

CHAPTER COMPREHENSION QUIZ

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
==References==
{{Hanging indent|1=

Andrade, E. B., Odean, T., &amp; Lin, S. (2016). Bubbling with Excitement: An Experiment. ''Review of Finance, 20''(2), 447–466. https://doi.org/10.1093/rof/rfv016

Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. ''Journal of Experimental Psychology. General, 143''(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. ''The American Psychologist, 56''(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. ''Current Opinion in Behavioral Sciences, 39'', 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Gable, P., &amp; Harmon-Jones, E. (2010). The motivational dimensional model of affect: Implications for breadth of attention, memory, and cognitive categorisation. ''Cognition and Emotion, 24''(2), 322–337. https://doi.org/10.1080/02699930903378305

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. ''Frontiers in Psychology, 8'', Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Hasada, R. (1994). ''The semantic aspects of onomatopoeia: focusing on Japanese psychomimes'' [Master's thesis, The Australian National University]. ANU Open Research. https://doi.org/10.25911/5d723cb12c49c 

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. ''British Journal of Educational Psychology, 93''(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Lim, N. (2016). Cultural differences in emotion: differences in emotional arousal level between the East and the West. ''Integrative Medicine Research, 5''(2), 105–109. https://doi.org/10.1016/j.imr.2016.03.004

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. ''The Journal of Positive Psychology'', (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Machizawa, M. G., Lisi, G., Kanayama, N., Mizuochi, R., Makita, K., Sasaoka, T., &amp; Yamawaki, S. (2020). Quantification of anticipation of excitement with a three-axial model of emotion with EEG. ''Journal of Neural Engineering, 17''(3). https://doi.org/10.1088/1741-2552/ab93b4

Oxendine, J. B. (1970). Emotional Arousal and Motor Performance. ''Quest (National Association for Kinesiology in Higher Education), 13''(1), 23–32. https://doi.org/10.1080/00336297.1970.10519673

Piira, O.-P., Huikuri, H. V., &amp; Tulppo, M. P. (2011). Effects of emotional excitement on heart rate and blood pressure dynamics in patients with coronary artery disease. ''Autonomic Neuroscience, 160''(1–2), 107–114. https://doi.org/10.1016/j.autneu.2010.11.011

Posner, J., Russell, J. A., &amp; Peterson, B. S. (2005). The circumplex model of affect: An integrative approach to affective neuroscience, cognitive development, and psychopathology. ''Development and Psychopathology, 17''(3), 715–734. https://doi.org/10.1017/S0954579405050340

Robinson, M. D., &amp; Irvin, R. L. (2022). Out of the shell, into the world: preferences for openness as a substrate of approach motivation and positive affect. ''Motivation and Emotion, 46''(3), 307–318. https://doi.org/10.1007/s11031-022-09934-5

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Schachter, S., &amp; Singer, J. (1962). Cognitive, social, and physiological determinants of emotional state. ''Psychological Review, 69''(5), 379–399. https://doi.org/10.1037/h0046234

Smith, K. E., Woodard, K., &amp; Pollak, S. D. (2025). Arousal May Not Be Anything to Get Excited About. ''Emotion Review, 17''(1), 3–15. https://doi.org/10.1177/17540739241303499

Sohn, J.-H., Kim, H.-E., Sohn, S., Seok, J.-W., Choi, D., &amp; Watanuki, S. (2015). Effect of emotional arousal on inter-temporal decision-making: an fMRI study. ''Journal of Physiological Anthropology, 34''(1), Article 8. https://doi.org/10.1186/s40101-015-0047-5

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. ''Social and Personality Psychology Compass, 2''(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. ''Psychological Review, 35''(5), 351–366. https://doi.org/10.1037/h0071406

Tsai, J. L. (2024). Investigating culture and emotion: From responses to ideals. In M. J. Gelfand, C.-Y. Chiu, &amp; Y.-Y. Hong (Eds.), ''Handbook of advances in culture and psychology'' (pp. 54–117). Oxford University Press.

Tugade, M. M., Shiota, M. N., &amp; Kirby, L. D. (Eds.). (2014). ''Handbook of positive emotions'' (1st ed.). Guilford Press.


}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)
* [https://www.simplypsychology.com/articles/anxiety-reappraisal-strategies Cognitive Reappraisal for Anxiety: Evidence-Based Strategies That Work] (Simply Psychology)

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally characterised to be a positive, high-arousal emotional state associated with preparing an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2023). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014; Russel, 1980). 

Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situation or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring) (Tugade et al., 2014)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal (Gable &amp; Dreisbach, 2021)
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural activation system (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable (Hasada, 1994). Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional image. From this data, the study developed a three-axial model integrating valence, arousal and a new cognitive dimension of expectation/anticipation. Through this study, Macahizawa found that the this added temporal dimension was significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball and hates crowds might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}

=== Physiological responses ===
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) found that after controlling for physical activity, self-reported excitement was associated with increased physiological arousal. This included increased heart rate, alertness and energy with reduced heart rate variability, signalling a heightened sympathetic nervous system (Ketonen et al., 2023). The corresponding associations for anxiety and calmness were not found to be signficant thus possibly signalling excitement as a unique emotional experience despite ununique physiological responses.
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}

=== Psychological processes ===
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought-actions encouraging problem-solving, and affecting exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}

=== Approach motivation and goal pursuit ===
High affective states have been linked to more approach-oriented behaviour, that is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach (2021) suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states can also have goal directed behaviour, however, as excitement is a high positive affect (valence) state and anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}

=== Excitements affect on cognition ===
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

The consequences of positive emotion on cognition may depend partly on motivational intensity and not always translate into greater performance. Excitement may help in focusing in on a task, but an overly narrow focus may make it more difficult to take in necessary information and stimuli; see Table 2.

'''Table 2'''

''Comparison of low-intensity positive affect on cognitive scope versus high (Fredrickson, 2001; Gable &amp; Dreisbach, 2021)''
{| class=&quot;wikitable&quot; style=&quot;margin: auto;&quot;
!
!Low-intensity positive affect
!High-intensity positive affect
|-
|'''Cognitive scope'''
|Broadens attention to access wider range of stimuli and information.
|Narrows attention towards central goal potentially filtering out relevant information.
|-
|'''Potential benefits'''
|Encourages creative exploration, flexible thinking, alternative ideas.
|Focused processing of goal-related information, persistence and performance on tasks with focused attention. 
|-
|'''Potential limitations'''
|Broad focus may cause less action towards specific goal required, or lack intense concentration needed towards target.
|Narrow focus may cause important stimuli to be lost or peripheral information to be overlooked.
|}

Furthermore, according to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., sprinting and football tacking) whereas, fine motor tasks &amp; decision-making were impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.

=== Excitement on behaviour ===

==== Impulsivity and risk taking ====
Unregulated excitement can lead to a sort of behavioural overshooting. Galentino et al. (2017) demonstrates that positive emotional arousal significantly increases preferences for monetary risks by over-valuing rewards over their potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (Sohn et al., 2015; Galentino, Bonini, &amp; Savadori, 2017; Andrade, Odean, &amp; Lin, 2016). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an underestimation of risks and causing impulsive decisions.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Excitement and anxiety share similar high-arousal physiological profiles. A study by Brooks (2014) identified that these similar profiles were difficult to suppress and 90% of participants believed a variation of 'calming down' was the best cognitive strategy under high-pressure tasks. This research demonstrated that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in heart rate. When simply employing this cognitive restrucuture, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

{{RoundBoxTop|theme=3}}'''Scenario application'''
During the finals game, Steve continues to make mistakes and he starts to get anxious. Under this high pressure environment, Steve starts to reframe his mistakes as opprtunities to learn and chances to adjust to his competition. He uses some simple self-statements which he feels helps him connect to his game. His teammates notice his performance improve.{{RoundBoxBottom}}

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Liu et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as energised positive affect. Liu et al. (2026) proposed that pleasant positive affect may stabilise life satisfaction whereas more energised positive affect may be present in individuals with gaps between a current and desired states. These may drive personal growth, agency, and goal adaptation as opposed to baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

Overall, positive affect in general has been shown to increase life satisfaction and relationships over time. As excitement is a positive emotional experience, these can contribute to ones subjective well-being. As this emotional state can make activities feel more engaging and rewarding, so too can this anticipation lead to more engagement and possibly reward. Excitement may not necessarily improve well-being simply because it is a positive emotional state, rather, the emotion may encourage preparation, engagement and goal pursuit which can further contributue to a sense of accomplishment (Liu et al. 2026).

=== Excitement as viewed cross-culturally ===
[[File:Excitement and anticipation at the Reykjavík Children’s Culture Festival 2016 (26145642903).jpg|thumb|'''Figure 4.''' Excitement  may be viewed differently across cultures]]
Tsai (2024) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with some individualistic Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm. This maybe due to an 'ideal affect' that is to say, the desire to assert personal autononmy and influence others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. 

{{anchor|Does excitement help or hinder behaviour?}}

=== Does excitement help or hinder behaviour? ===
With helpful excitement, an individual might move towards a goal by preparing, practising, engaging and performing behaviours that lead to a desired outcome. However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision (Galentino et al., 2017).

Extremely high emotional arousal may become overwhelming, with the consequences of excitement dependent on the context and the individual's ability to regulate their behaviour. Excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion. Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depends on intensity, context and behavioural regulation.

{{RoundBoxTop|theme=9}}'''Intervention application'''
To reduce the effects of overwhelm during high emotional arousal, interventions should work in teaching individuals to identify when excitement is too great and cognitive restructure in the form of strategies like 'simple statements' can be used.{{RoundBoxBottom}}

==Conclusion==
Excitement is a positively valenced, high-arousal emotional state associated with anticipation, approach motivation and readiness to act. It can encourage preparation, persistence and engagement with meaningful goals. Although, following in similar physiological traits to other emotions such as anxiety, excitement may differ from other emotions due to its combination of positive valence, high activation/arousal, approach to goals and anticipatory nature (Russell, 1980; Gable &amp; Harmon-Jones, 2010; Macahizawa et al., 2020). Excitement as a state triggers activation of the autonomic nervous system, preparing itself for some kind of action (Oxendine, 1970). Commonm physiological responses include elevated heart rate, alertness, energy and rise of blood pressure (Ketonen et al., 2023). Psychologically, excitement can boost an individual's readiness to act, perceived self-efficacy, and cognitive scope (Brooks, 2014; Fredrickson, 2001).

As a catalyst to engaging with actions towards a certain goal, excitement can effect ones cognition, narrowing or widening its scope (Fredrickson, 2001), and possibly leading to greater impulsive or risk taking behaviours (e.g., Galentino et al., 2017). Excitement can also be a powerful tool in restructuring other emotions, and as a positive emotion, may increase satisfaction across the lifespan (Liu et al., 2016). With its value differing across culture, excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes. Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

{{RoundBoxTop|theme=3}}
'''Take-home message'''

Excitement is a unique emotional state that can be as much of a powerful tool in goal pursuit, action and well-being as it is simply a positive state of being. An event that strikes fear into one, may be exciting for another, therefore, excitement and emotions as whole come from the unique interplay of our active and passive shaping of the significance we assign to our experiences. {{RoundBoxBottom}}

{{RoundBoxTop|theme=11|title=Quiz}}&lt;quiz display=simple&gt;
{'''Chapter quiz:'''
Steve and his team begin to pull away in the final minutes of the game. A smile emerges from his face as he anticipates the messages and coverage he will receive from the crowd and media. His teammate Bob on the otherhand who hates attention begins to feel stressed. According to the chapter, what best explains this situation?
|type=&quot;()&quot;}

+Their individual perceptions and interpretations of the sitatuion influence whether they experience heightened arousal as excitement or stress.
-Everyone experiences excitement the same way.
-Their emotional responses are determined entirely by physiological arousal, rather than how they interpret the situation.
&lt;/quiz&gt;
{{RoundBoxBottom}}

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
==References==
{{Hanging indent|1=

Andrade, E. B., Odean, T., &amp; Lin, S. (2016). Bubbling with Excitement: An Experiment. ''Review of Finance, 20''(2), 447–466. https://doi.org/10.1093/rof/rfv016

Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. ''Journal of Experimental Psychology. General, 143''(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. ''The American Psychologist, 56''(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. ''Current Opinion in Behavioral Sciences, 39'', 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Gable, P., &amp; Harmon-Jones, E. (2010). The motivational dimensional model of affect: Implications for breadth of attention, memory, and cognitive categorisation. ''Cognition and Emotion, 24''(2), 322–337. https://doi.org/10.1080/02699930903378305

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. ''Frontiers in Psychology, 8'', Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Hasada, R. (1994). ''The semantic aspects of onomatopoeia: focusing on Japanese psychomimes'' [Master's thesis, The Australian National University]. ANU Open Research. https://doi.org/10.25911/5d723cb12c49c 

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. ''British Journal of Educational Psychology, 93''(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Lim, N. (2016). Cultural differences in emotion: differences in emotional arousal level between the East and the West. ''Integrative Medicine Research, 5''(2), 105–109. https://doi.org/10.1016/j.imr.2016.03.004

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. ''The Journal of Positive Psychology'', (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Machizawa, M. G., Lisi, G., Kanayama, N., Mizuochi, R., Makita, K., Sasaoka, T., &amp; Yamawaki, S. (2020). Quantification of anticipation of excitement with a three-axial model of emotion with EEG. ''Journal of Neural Engineering, 17''(3). https://doi.org/10.1088/1741-2552/ab93b4

Oxendine, J. B. (1970). Emotional Arousal and Motor Performance. ''Quest (National Association for Kinesiology in Higher Education), 13''(1), 23–32. https://doi.org/10.1080/00336297.1970.10519673

Piira, O.-P., Huikuri, H. V., &amp; Tulppo, M. P. (2011). Effects of emotional excitement on heart rate and blood pressure dynamics in patients with coronary artery disease. ''Autonomic Neuroscience, 160''(1–2), 107–114. https://doi.org/10.1016/j.autneu.2010.11.011

Posner, J., Russell, J. A., &amp; Peterson, B. S. (2005). The circumplex model of affect: An integrative approach to affective neuroscience, cognitive development, and psychopathology. ''Development and Psychopathology, 17''(3), 715–734. https://doi.org/10.1017/S0954579405050340

Robinson, M. D., &amp; Irvin, R. L. (2022). Out of the shell, into the world: preferences for openness as a substrate of approach motivation and positive affect. ''Motivation and Emotion, 46''(3), 307–318. https://doi.org/10.1007/s11031-022-09934-5

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Schachter, S., &amp; Singer, J. (1962). Cognitive, social, and physiological determinants of emotional state. ''Psychological Review, 69''(5), 379–399. https://doi.org/10.1037/h0046234

Smith, K. E., Woodard, K., &amp; Pollak, S. D. (2025). Arousal May Not Be Anything to Get Excited About. ''Emotion Review, 17''(1), 3–15. https://doi.org/10.1177/17540739241303499

Sohn, J.-H., Kim, H.-E., Sohn, S., Seok, J.-W., Choi, D., &amp; Watanuki, S. (2015). Effect of emotional arousal on inter-temporal decision-making: an fMRI study. ''Journal of Physiological Anthropology, 34''(1), Article 8. https://doi.org/10.1186/s40101-015-0047-5

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. ''Social and Personality Psychology Compass, 2''(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. ''Psychological Review, 35''(5), 351–366. https://doi.org/10.1037/h0071406

Tsai, J. L. (2024). Investigating culture and emotion: From responses to ideals. In M. J. Gelfand, C.-Y. Chiu, &amp; Y.-Y. Hong (Eds.), ''Handbook of advances in culture and psychology'' (pp. 54–117). Oxford University Press.

Tugade, M. M., Shiota, M. N., &amp; Kirby, L. D. (Eds.). (2014). ''Handbook of positive emotions'' (1st ed.). Guilford Press.


}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to Turn Anxiety Into Excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of Emotions: Excitement] (The Franklin Institue)
* [https://www.simplypsychology.com/articles/anxiety-reappraisal-strategies Cognitive Reappraisal for Anxiety: Evidence-Based Strategies That Work] (Simply Psychology)

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally characterised to be a positive, high-arousal emotional state associated with preparing an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketnonen et al., 2023). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014; Russel, 1980). 

Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) circumplex model of affect which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situation or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring) (Tugade et al., 2014)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal (Gable &amp; Dreisbach, 2021)
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to drive to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural activation system (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable (Hasada, 1994). Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional image. From this data, the study developed a three-axial model integrating valence, arousal and a new cognitive dimension of expectation/anticipation. Through this study, Macahizawa found that the this added temporal dimension was significant to excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball and hates crowds might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}

=== Physiological responses ===
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) found that after controlling for physical activity, self-reported excitement was associated with increased physiological arousal. This included increased heart rate, alertness and energy with reduced heart rate variability, signalling a heightened sympathetic nervous system (Ketonen et al., 2023). The corresponding associations for anxiety and calmness were not found to be signficant thus possibly signalling excitement as a unique emotional experience despite ununique physiological responses.
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011)
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}

=== Psychological processes ===
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought-actions encouraging problem-solving, and affecting exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}

=== Approach motivation and goal pursuit ===
High affective states have been linked to more approach-oriented behaviour, that is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach (2021) suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states can also have goal directed behaviour, however, as excitement is a high positive affect (valence) state and anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}

=== Excitements affect on cognition ===
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, deemed the cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (2001) describes low-intensity, positive emotions (e.g. contement, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

The consequences of positive emotion on cognition may depend partly on motivational intensity and not always translate into greater performance. Excitement may help in focusing in on a task, but an overly narrow focus may make it more difficult to take in necessary information and stimuli; see Table 2.

'''Table 2'''

''Comparison of low-intensity positive affect on cognitive scope versus high (Fredrickson, 2001; Gable &amp; Dreisbach, 2021)''
{| class=&quot;wikitable&quot; style=&quot;margin: auto;&quot;
!
!Low-intensity positive affect
!High-intensity positive affect
|-
|'''Cognitive scope'''
|Broadens attention to access wider range of stimuli and information.
|Narrows attention towards central goal potentially filtering out relevant information.
|-
|'''Potential benefits'''
|Encourages creative exploration, flexible thinking, alternative ideas.
|Focused processing of goal-related information, persistence and performance on tasks with focused attention. 
|-
|'''Potential limitations'''
|Broad focus may cause less action towards specific goal required, or lack intense concentration needed towards target.
|Narrow focus may cause important stimuli to be lost or peripheral information to be overlooked.
|}

Furthermore, according to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., sprinting and football tacking) whereas, fine motor tasks &amp; decision-making were impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.

=== Excitement on behaviour ===

==== Impulsivity and risk taking ====
Unregulated excitement can lead to a sort of behavioural overshooting. Galentino et al. (2017) demonstrates that positive emotional arousal significantly increases preferences for monetary risks by over-valuing rewards over their potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (Sohn et al., 2015; Galentino, Bonini, &amp; Savadori, 2017; Andrade, Odean, &amp; Lin, 2016). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement, learning and memory.

When helpful, excitement may help an individual towards a goal by preparing, practicing, engaging and performing. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an underestimation of risks and causing impulsive decisions.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Excitement and anxiety share similar high-arousal physiological profiles. A study by Brooks (2014) identified that these similar profiles were difficult to suppress and 90% of participants believed a variation of 'calming down' was the best cognitive strategy under high-pressure tasks. This research demonstrated that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in heart rate. When simply employing this cognitive restrucuture, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

{{RoundBoxTop|theme=3}}'''Scenario application'''
During the finals game, Steve continues to make mistakes and he starts to get anxious. Under this high pressure environment, Steve starts to reframe his mistakes as opprtunities to learn and chances to adjust to his competition. He uses some simple self-statements which he feels helps him connect to his game. His teammates notice his performance improve.{{RoundBoxBottom}}

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Liu et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as energised positive affect. Liu et al. (2026) proposed that pleasant positive affect may stabilise life satisfaction whereas more energised positive affect may be present in individuals with gaps between a current and desired states. These may drive personal growth, agency, and goal adaptation as opposed to baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

Overall, positive affect in general has been shown to increase life satisfaction and relationships over time. As excitement is a positive emotional experience, these can contribute to ones subjective well-being. As this emotional state can make activities feel more engaging and rewarding, so too can this anticipation lead to more engagement and possibly reward. Excitement may not necessarily improve well-being simply because it is a positive emotional state, rather, the emotion may encourage preparation, engagement and goal pursuit which can further contributue to a sense of accomplishment (Liu et al. 2026).

=== Excitement as viewed cross-culturally ===
[[File:Excitement and anticipation at the Reykjavík Children’s Culture Festival 2016 (26145642903).jpg|thumb|'''Figure 4.''' Excitement  may be viewed differently across cultures]]
Tsai (2024) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with some individualistic Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm. This maybe due to an 'ideal affect' that is to say, the desire to assert personal autononmy and influence others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. 

{{anchor|Does excitement help or hinder behaviour?}}

=== Does excitement help or hinder behaviour? ===
With helpful excitement, an individual might move towards a goal by preparing, practising, engaging and performing behaviours that lead to a desired outcome. However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision (Galentino et al., 2017).

Extremely high emotional arousal may become overwhelming, with the consequences of excitement dependent on the context and the individual's ability to regulate their behaviour. Excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion. Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depends on intensity, context and behavioural regulation.

{{RoundBoxTop|theme=9}}'''Intervention application'''
To reduce the effects of overwhelm during high emotional arousal, interventions should work in teaching individuals to identify when excitement is too great and cognitive restructure in the form of strategies like 'simple statements' can be used.{{RoundBoxBottom}}

==Conclusion==
Excitement is a positively valenced, high-arousal emotional state associated with anticipation, approach motivation and readiness to act. It can encourage preparation, persistence and engagement with meaningful goals. Although, following in similar physiological traits to other emotions such as anxiety, excitement may differ from other emotions due to its combination of positive valence, high activation/arousal, approach to goals and anticipatory nature (Russell, 1980; Gable &amp; Harmon-Jones, 2010; Macahizawa et al., 2020). Excitement as a state triggers activation of the autonomic nervous system, preparing itself for some kind of action (Oxendine, 1970). Commonm physiological responses include elevated heart rate, alertness, energy and rise of blood pressure (Ketonen et al., 2023). Psychologically, excitement can boost an individual's readiness to act, perceived self-efficacy, and cognitive scope (Brooks, 2014; Fredrickson, 2001).

As a catalyst to engaging with actions towards a certain goal, excitement can effect ones cognition, narrowing or widening its scope (Fredrickson, 2001), and possibly leading to greater impulsive or risk taking behaviours (e.g., Galentino et al., 2017). Excitement can also be a powerful tool in restructuring other emotions, and as a positive emotion, may increase satisfaction across the lifespan (Liu et al., 2016). With its value differing across culture, excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes. Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

{{RoundBoxTop|theme=3}}
'''Take-home message'''

Excitement is a unique emotional state that can be as much of a powerful tool in goal pursuit, action and well-being as it is simply a positive state of being. An event that strikes fear into one, may be exciting for another, therefore, excitement and emotions as whole come from the unique interplay of our active and passive shaping of the significance we assign to our experiences. {{RoundBoxBottom}}

{{RoundBoxTop|theme=11|title=Quiz}}&lt;quiz display=simple&gt;
{'''Chapter quiz:'''
Steve and his team begin to pull away in the final minutes of the game. A smile emerges from his face as he anticipates the messages and coverage he will receive from the crowd and media. His teammate Bob on the otherhand who hates attention begins to feel stressed. According to the chapter, what best explains this situation?
|type=&quot;()&quot;}

+Their individual perceptions and interpretations of the sitatuion influence whether they experience heightened arousal as excitement or stress.
-Everyone experiences excitement the same way.
-Their emotional responses are determined entirely by physiological arousal, rather than how they interpret the situation.
&lt;/quiz&gt;
{{RoundBoxBottom}}

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
==References==
{{Hanging indent|1=

Andrade, E. B., Odean, T., &amp; Lin, S. (2016). Bubbling with Excitement: An Experiment. ''Review of Finance, 20''(2), 447–466. https://doi.org/10.1093/rof/rfv016

Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. ''Journal of Experimental Psychology. General, 143''(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. ''The American Psychologist, 56''(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. ''Current Opinion in Behavioral Sciences, 39'', 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Gable, P., &amp; Harmon-Jones, E. (2010). The motivational dimensional model of affect: Implications for breadth of attention, memory, and cognitive categorisation. ''Cognition and Emotion, 24''(2), 322–337. https://doi.org/10.1080/02699930903378305

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. ''Frontiers in Psychology, 8'', Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Hasada, R. (1994). ''The semantic aspects of onomatopoeia: focusing on Japanese psychomimes'' [Master's thesis, The Australian National University]. ANU Open Research. https://doi.org/10.25911/5d723cb12c49c 

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. ''British Journal of Educational Psychology, 93''(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Lim, N. (2016). Cultural differences in emotion: differences in emotional arousal level between the East and the West. ''Integrative Medicine Research, 5''(2), 105–109. https://doi.org/10.1016/j.imr.2016.03.004

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. ''The Journal of Positive Psychology'', (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Machizawa, M. G., Lisi, G., Kanayama, N., Mizuochi, R., Makita, K., Sasaoka, T., &amp; Yamawaki, S. (2020). Quantification of anticipation of excitement with a three-axial model of emotion with EEG. ''Journal of Neural Engineering, 17''(3). https://doi.org/10.1088/1741-2552/ab93b4

Oxendine, J. B. (1970). Emotional Arousal and Motor Performance. ''Quest (National Association for Kinesiology in Higher Education), 13''(1), 23–32. https://doi.org/10.1080/00336297.1970.10519673

Piira, O.-P., Huikuri, H. V., &amp; Tulppo, M. P. (2011). Effects of emotional excitement on heart rate and blood pressure dynamics in patients with coronary artery disease. ''Autonomic Neuroscience, 160''(1–2), 107–114. https://doi.org/10.1016/j.autneu.2010.11.011

Posner, J., Russell, J. A., &amp; Peterson, B. S. (2005). The circumplex model of affect: An integrative approach to affective neuroscience, cognitive development, and psychopathology. ''Development and Psychopathology, 17''(3), 715–734. https://doi.org/10.1017/S0954579405050340

Robinson, M. D., &amp; Irvin, R. L. (2022). Out of the shell, into the world: preferences for openness as a substrate of approach motivation and positive affect. ''Motivation and Emotion, 46''(3), 307–318. https://doi.org/10.1007/s11031-022-09934-5

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Schachter, S., &amp; Singer, J. (1962). Cognitive, social, and physiological determinants of emotional state. ''Psychological Review, 69''(5), 379–399. https://doi.org/10.1037/h0046234

Smith, K. E., Woodard, K., &amp; Pollak, S. D. (2025). Arousal May Not Be Anything to Get Excited About. ''Emotion Review, 17''(1), 3–15. https://doi.org/10.1177/17540739241303499

Sohn, J.-H., Kim, H.-E., Sohn, S., Seok, J.-W., Choi, D., &amp; Watanuki, S. (2015). Effect of emotional arousal on inter-temporal decision-making: an fMRI study. ''Journal of Physiological Anthropology, 34''(1), Article 8. https://doi.org/10.1186/s40101-015-0047-5

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. ''Social and Personality Psychology Compass, 2''(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. ''Psychological Review, 35''(5), 351–366. https://doi.org/10.1037/h0071406

Tsai, J. L. (2024). Investigating culture and emotion: From responses to ideals. In M. J. Gelfand, C.-Y. Chiu, &amp; Y.-Y. Hong (Eds.), ''Handbook of advances in culture and psychology'' (pp. 54–117). Oxford University Press.

Tugade, M. M., Shiota, M. N., &amp; Kirby, L. D. (Eds.). (2014). ''Handbook of positive emotions'' (1st ed.). Guilford Press.


}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to turn anxiety into excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of emotions: excitement] (The Franklin Institue)
* [https://www.simplypsychology.com/articles/anxiety-reappraisal-strategies Cognitive reappraisal for anxiety: evidence-based strategies that work] (Simply Psychology)

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__TOC__ 

==Overview== 
{{RoundBoxTop|theme=3}} 

[[File:2022-07-03 Basketball, Männer, European Qualifiers, Deutschland - Polen 1DX 1386 by Stepro.jpg|right|thumb|200px|'''Figure 1'''. Steve is ready and excited to play basketball.]] 

; Consider this scenario 

It's 11:30 p.m. the night before Steve's championship basketball game for the state title. As the undefeated team's captain and leading scorer, he has been preparing his whole life for this moment, and tomorrow, he will get to showcase his skills towards a lifelong dream in front of teammates, coaches, fans, family, and professional basketball team recruiters.  

Instead of feeling nervous, he is suddenly excited.  

His heart beats faster. He feels energetic, alert, and unusually motivated. He starts to imagine himself having a great game. He practises his shooting form in the mirror one more time, sends basketball highlights and tape to his teammates for review and feedback, and even begins planning what he'll do and say if his team wins the game.  

The next morning, he wakes up before his alarm. Steve is still buzzing with anticipation. As he walks onto the court, his attention narrows onto the basket. He feels ready to act (see Figure 1).

But there is a problem.

Steve's excitement becomes so intense that he starts rushing his teams plays too quickly. He manoeuvres through bodies, overlooks an open shot, and finds himself making decisions and passes without thinking them through.  

So, was his excitement helpful or harmful? And why can it motivate us to pursue opportunities while also influencing how we think, behave, and experience well-being?  

{{RoundBoxBottom}}

In Steve's case, excitement primes his body and propels him to prepare for his big game but this also comes with some unanticipated consequences as he begins to rush and miss information.

The following chapter explores excitement as an emotion and how it can influence our behaviours and wellbeing. By examining how and why we get excited, and its physiological and psychological affects, we can better understand  how we perceive and respond to it. This understanding may consciously allows us to reframe and engage with excitement as an active tool to shape our behaviours, experiences, and well-being. 

{{RoundBoxTop|theme=3}}
'''Focus questions'''
* What is excitement as an emotion, and how does it differ from other emotions?
* What are the physiological and psychological processes that underpin excitement? 
* How does excitement influence motivation, cognition, and behaviour?
* How does excitement contribute to, or undermine psychological well-being across individual and cultural contexts? 
{{RoundBoxBottom}}

==Understanding excitement as an emotion==
Excitement is more than the feeling of happiness, it is generally characterised to be a positive, high-arousal emotional state associated with preparing an individual to engage with something anticipated or desired and is linked to things like interest, motivation and even risk-taking (Fredrickson, 2001; Ketonen et al., 2023). It is simultaneously unique from other emotions as it often involves relatively high levels of physiological and psychological activation, but similar, as many of its behaviours, internal feelings and physiological affects can be attributed to other emotional states such as anxiety, or even anger. Excitement is also affected by both the subjective experiences of the emotion and the physiological processes that accompany it as experienced by the individual (Schachter &amp; Singer, 1962, as cited in Brooks, 2014; Russel, 1980). 

Early works by Stratton (1928) identified excitement as a distinct state and a unique emotion characterised by the the intense impulse to be directed towards a specific goal. Stratton noticed that excited individuals often were more organised for a specific task at hand and had greater motor movement and specifically targeted behaviour, proposing that excitement was a purposeful psychophysical state that dictates cognitive and motor responses.

=== The circumplex model of affect ===
One framework to further understand excitement is Russell's (1980) [[Motivation and emotion/Book/2019/Circumplex model of affect|circumplex model of affect]] which places excitement on a set of continuous dimensions:

* [[w:Valence_(psychology)|Valence]], the appraisal of a situation or stimulus as either pleasant (positive) or unpleasant (negaitve).
* [[wikipedia:Arousal|Arousal]], the degree by which a stimulus places the bodys nervous system into physical and mental readiness ranging from a deactived state (e.g. sleepiness) to an activated state (e.g. high alert).

[[File:Valence-Arousal Circumplex.jpg|thumb|'''Figure 2.''' The circumplex model of affect (Russell, 1980). |266x266px]]
Within this model, excitement consistently places in the upper-right quandrant, seen as high-arousal and with a positive valence (see Figure 2).

Across Russell's experiment to investigate emotions, participants interacted with 28 tasks relating to the categorisation of emotions and their word meanings. Russell's model has helped propose the idea that emotions can act as affective states that are systematically interrelated, and not individual. Through the circumplex model of affect, excitement is best able to be understood and characterised compared to other emotions (see Table 1).

;Table 1

''Comparison of Selected Emotions Along Valence and Arousal Dimensions''

{| class=&quot;wikitable&quot;
|+
!Emotion
!Valence
!Arousal/Activation Level
!Primary Motivational Oreintation
|-
|Excitement
|Positive (Pleasant)
|High
|High Apporach (Goal Pursuit) (Gable &amp; Dreisbach, 2021)
|-
|Happiness
|Positve (Pleasant)
|Variable (Moderate to High)
|Moderate Approach (Tugade et al., 2014)
|-
|Contentment
|Positive (Pleasant)
|Low
|Low Approach (Post-Goal Savouring) (Tugade et al., 2014)
|-
|Anxiety
|Negative (Unpleasant)
|High
|High Avoidance/Threat Vigilance (Brooks, 2014)
|-
|Sadness
|Negative (Unpleasant)
|Low
|Low Avoidance/Withdrawal (Gable &amp; Dreisbach, 2021)
|}

=== The motivational dimensional model of affect (MDMA) ===
While the two-dimensional cirumplex model captures valence and arousal, Gable and Harmon-Jones' (2010) [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect (MDMA)]] expands upon this, incorporating motivational intensity, the urge to approach or avoid a stimulus.

MDMA demontrates that excitement is a high-intensity, approach-motivated positive state driven by the [[wikipedia:Gray's_biopsychological_theory_of_personality|Behavioural activation system (BAS)]]. Like excitement, high-intensity pre-goal states prepare organisms for direct action, wehereas low-intensity post-goal states like contentment signal reward and accomplishment (Gable &amp; Dreisbach, 2021).

=== Excitement as an anticipatory emotion ===
The Japanese expression ''waku waku'' (ワクワク) describes a feeling of eager anticipation and excitement and is associated with the expection of something enjoyable (Hasada, 1994). Work by Macahizawa et al. (2020) proposes that excitement is fundamentally an anticipatory emotion driven by the predicting of positive future outcomes under uncertainty. To understand this temporal, future anticipatory dimension of excitement, electroencephalography (EEG) data was recorded from 28 adult participants when tested with different anticipatory tones while predicting an upcoming emotional image. From this data, the study developed a three-axial model integrating valence, arousal and a new cognitive dimension of expectation/anticipation. Through this study, Macahizawa et al., (2020) found that this added temporal dimension was significant to the emotional experience of excitement.

{{RoundBoxTop|theme=3}}
'''Scenario application'''

Steve loves basketball, is skilled at the sport and thrives on competition. His subjective perception of his upcoming final game has a positive valence, high arousal and he is motivated, goal driven and anticpatory, signalling excitement. Steve's girlfriend, who is not so into basketball and hates crowds might have a completely different emotional state if she were put into the same position. One that most likely reflects an unpleasant valence and high arousal making her avoid working towards this reality entirely.
{{RoundBoxBottom}}

==Physiological and psychological processes of excitement==
{{anchor|Physiological responses}}

=== Physiological responses ===
With high arousal, excitement triggers robust [[wikipedia:Autonomic_nervous_system|autonomic nervous sytem]] (ANS) activation, preparing the body for action (Oxendine, 1970).
* A study tracking the biometric markers of 136 high school students compared to their self-report on emotion (i.e. excitement, calm, boredom etc.) found that after controlling for physical activity, self-reported excitement was associated with increased physiological arousal. This included increased heart rate, alertness and energy with reduced heart rate variability, signalling a heightened sympathetic nervous system (Ketonen et al., 2023). The corresponding associations for anxiety and calmness were not found to be signficant thus possibly signalling excitement as a unique emotional experience despite ununique physiological responses i.e., anxiety sharing similar physiological responses to excitement.
* Emotional excitement may also increase blood pressure and/or cause this to spike acutely (Piira et al., 2011).
Physiological arousal isn't inherently positive or negative; its interpretation depends partly on context which may also alter if the individual is perceiving the physiological and psychological changes as excitement or something else (Schachter &amp; Singer, 1962).
[[File:Excitement from Two-Factor Theory.png|thumb|'''Figure 3.''' Physiological and psyhcological changes of excitement altered by the individual's perceived context (Schacter &amp; Singer, 1962)|417x417px]]

{{anchor|Psychological processes}}

=== Psychological processes ===
Psychologically, excitement alters how individuals perceive an upcoming task or event (Brooks, 2014).
*Anticipation and excitement shift cognitive resources toward potential rewards or desirable outcomes, and has been shown to boost self-efficacy and perceived readiness to act in the face of a pre-goal reward expectation (Brooks, 2014).
* Excitement can increase an individual's perceived readiness to act and even alter momentary thought-actions encouraging problem-solving, and affecting an individual's exploration (Fredrickson, 2001).

{{anchor|Anticipatory emotion}}

{{Robelbox|theme=5|width=40%|title=Quiz Question|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt; &lt;quiz display=simple&gt; 
'''What is an example of excitement based on Steve's physiological and psychological changes?'''
|type=&quot;()&quot;} 

- Steve feels calm, his heart rate slows, and he begins to feel sleepy
+ Steve feels ready to take on the world, he feels his heart start to race as he hops out of bed
- Following a bad practice, Steve feels his heart rate and alertness increase, he wants to leave the arena immediately
&lt;/quiz&gt;{{RoundBoxBottom}}

==The influence of excitement on motivation, cognition, and behaviour==
{{anchor|Approach motivation}}

=== Approach motivation and goal pursuit ===
High affective states have been linked to more approach-oriented behaviour, that is to say, motivation to move towards a specific goal. As excitement has a high positive affective state, this emotion has been linked with approach-oriented behaviour with high approach motivation increasing an individual's persistence and goal-directed activation. Research suggests that the emotional state of excitement can influence the willingness to pursue desirable goals. In these instances, excitement may act as a catalyst for approach motivations further reinforcing behavioural activation towards long term goals and increasing persistence. Gable &amp; Dreisbach (2021) suggest that this may be because anticipating a positive outcome can motivate action before the reward is actually obtained and further supports the model of excitement as an anticipatory emotion. From this research, it is important to note that other emotional affective states can also have goal directed behaviour, however, as excitement is a high positive affect (valence) state and anticipatory, it can be posited that excitement compared to some other emotions may be stronger in approach-oriented behaviour.

{{RoundBoxTop|theme=3}}'''Scenario application'''
Steve's excitement leads him to practice and refine his basketball moves and watch tape before the game. An active approach to the challenge rather than not engaging with it or avoiding it completely.

{{RoundBoxBottom}}

{{anchor|Cognitive and behavioural effects}}

=== Excitements affect on cognition ===
Excitement can have affects on cognition, as well as effecting ones ability to take in information and environmental cues, making this broader or narrow, referred to as cognitive scope. Work on positive affect emotions have found that these positively valenced states can alter attentional focus. Fredrickson (2001) describes low-intensity, positive emotions (e.g. contentment, joy, pride) as being able to broaden momentary thought-action repertoires, fostering creative exploration, known as the Broaden-and-build theory.

In contrast, high-intensity approach positive affect such as excitement narrows cognitive scope. Excitement may instead concentrate attention on a central goal stimuli while filtering out peripheral details leading to greater goal performance at the cost of additional detail and exploration (Gable &amp; Dreisbach, 2021).

The consequences of positive emotion on cognition may depend partly on motivational intensity and not always translate into greater performance. Excitement may help in focusing in on a task, but an overly narrow focus may make it more difficult to take in necessary information and stimuli; see Table 2.

'''Table 2'''

''Comparison of low-intensity positive affect on cognitive scope versus high (Fredrickson, 2001; Gable &amp; Dreisbach, 2021)''
{| class=&quot;wikitable&quot; style=&quot;margin: auto;&quot;
!
!Low-intensity positive affect
!High-intensity positive affect
|-
|'''Cognitive scope'''
|Broadens attention to access wider range of stimuli and information.
|Narrows attention towards central goal potentially filtering out relevant information.
|-
|'''Potential benefits'''
|Encourages creative exploration, flexible thinking, alternative ideas.
|Focused processing of goal-related information, persistence and performance on tasks with focused attention. 
|-
|'''Potential limitations'''
|Broad focus may cause less action towards specific goal required, or lack intense concentration needed towards target.
|Narrow focus may cause important stimuli to be lost or peripheral information to be overlooked.
|}

Furthermore, according to Joseph Oxendine's (1968) emotional arousal mode, excitement's effect on motor sports performance follows task-specific requirements. In this research, high excitement improved tasks relying on raw strength, speed, and endurance (e.g., sprinting and football tacking) whereas, fine motor tasks and decision-making were impaired. Activities like basketball free throws and archery that required fine motor precision, steady hand control and complex tactical judgement were negatively affected.

=== Excitement on behaviour ===

==== Impulsivity and risk taking ====
Unregulated excitement can lead to a sort of behavioural overshooting. Galentino et al. (2017) demonstrates that positive emotional arousal significantly increases preferences for monetary risks by over-valuing rewards over their potential losses. This could extend into other behaviours outside of fiscally motivated rewards. Supporting this, Andrede, Odean &amp; Lin (2016) tested 55 experimental asset markets over a number of participants and found that excitement generated significantly larger market bubbles in magnitiude and peak amplitude driving immediate overevaluation across a first round.

While excitement can increase motivion and engagement, this heightened arousal may also influence judgement and behavioural control. Consequently, excitement may encourage productive action in some situations while contributing to impulsive or risky decisions in others (Sohn et al., 2015; Galentino, Bonini, &amp; Savadori, 2017; Andrade, Odean, &amp; Lin, 2016). Storebeck &amp; Clore (2008) also saw high affective arousal impact individuals judgement leading to poorer choices, however, some functions of learning and memory were greater.

When helpful, excitement may aid an individual towards a goal by motivating them to prepare, practice and engage. However, when unhelpful, a person may become excessively excited about an invested reward, with focus and fixation leading to an underestimation of risks and causing impulsive decisions.

== Excitement and its influence on wellbeing ==

=== Cognitively restructuring emotions as excitement ===
Excitement and anxiety share similar high-arousal physiological profiles. A study by Brooks (2014) identified that these similar profiles were difficult to suppress with a majority of of participants believing variations of 'calming down' was the best cognitive strategy to assist when under high-pressure tasks. Instead, this research demonstrated that reframing anxiety via simple self-statements such as &quot;I am excited&quot; or prompts such as &quot;Get excited&quot; shifted participants mindsets from threat to opportunity without requiring an unphysiological drop in responses such as increased heart rate. When simply employing this cognitive restructure, users found increases in activities such as karaoke singing accuracy, public speaking persuasiveness, and math accuracy under pressure.

{{RoundBoxTop|theme=3}}'''Scenario application'''
During the finals game, Steve continues to make mistakes and he starts to get anxious. Under this high pressure environment, Steve starts to reframe his mistakes as opprtunities to learn and chances to adjust to his competition. He uses some simple self-statements which he feels helps him connect to his game. His teammates notice his performance improve.{{RoundBoxBottom}}

=== Excitement across the lifespan ===
Excitement and individuals with the proclivity towards this emotional state may impact them across their lifespan. Liu et al. (2026) evaluated the differential impact on pleasant positive affect (low-arousal/harmony) versus energised positive affect (high-arousal/excitement) on life satisfaction. Using random intercept cross-lagged panel models across a 9-wave longitudinal study, pleasant positive affect exhibited reicprocal associations with life satisfaction that were twice as strong as energised positive affect. Liu et al. (2026) proposed that pleasant positive affect may stabilise life satisfaction whereas more energised positive affect may be present in individuals with gaps between a current and desired states. These may drive personal growth, agency, and goal adaptation as opposed to those with a baseline satisfaction. More research may be required to expand upon this idea, but most individuals may find themselves across both states dictated by life experiences, personal interest and their own perception of ability and performance across tasks.

Overall, positive affect in general has been shown to increase life satisfaction and relationships over time (Liu et al., 2016). As excitement is a positive emotional experience, it too may contribute to ones subjective well-being. By making activities feel more engaging, this anticipation can lead to more engagement and possibly reward. Excitement may not necessarily improve well-being simply because it is a positive emotional state, rather, the emotion may encourage preparation, engagement and goal pursuit which can further contribute to a sense of accomplishment (Liu et al. 2026).

=== Excitement as viewed cross-culturally ===
[[File:Excitement and anticipation at the Reykjavík Children’s Culture Festival 2016 (26145642903).jpg|thumb|'''Figure 4.''' Excitement  may be viewed differently across cultures]]
Tsai (2024) and Lim (2016) highlight that emotional valuation may vary systematically across cultures, with some individualistic Westerm cultures seemingly valuing high arousal positive states, such as excitement and enthusiasm as compared to some Eastern cultures. This may be due to Western cultures individualism,  that is to say, the desire to assert personal autononmy and influence on others. Eastern cultures on the other hand might value low arousal positive states such as calmness, serenity and peacefulness as their ideal affect to promote social harmony so as to better support collectivist values. As excitement is a perception of an event and an individual's own physiological and psychological states, one's own culture and upbringing may begin to give rise to how to react and value this emotional state across a lifespan but also population. 

{{anchor|Does excitement help or hinder behaviour?}}

=== Does excitement help or hinder behaviour? ===
With helpful excitement, an individual might move towards a goal by preparing, practising, engaging and performing behaviours that lead to a desired outcome. However, with unhelpful excitement a person may become excessively excited about an invested reward, this focus and fixation may lead them to underestimate risks and form and impulsive decision (Galentino et al., 2017).

Extremely high emotional arousal may become overwhelming, with the consequences of excitement dependent on the context and the individual's ability to regulate their behaviour. Excitement should not necessarily be conceptualised as beneficial simply because it is a positive emotion. Excitement can support well-being when it facilitates meaningful engagement, motivation and goal pursuit, but its effects depends on intensity, context and behavioural regulation.

{{RoundBoxTop|theme=9}}'''Intervention application'''
To reduce the effects of overwhelm during high emotional arousal, interventions should work in teaching individuals to identify when excitement is too great and use cognitive restructures in the form of strategies like 'simple statements'.{{RoundBoxBottom}}

==Conclusion==
Excitement is a positively valenced, high-arousal emotional state associated with anticipation, approach motivation and readiness to act. It can encourage preparation, persistence and engagement with meaningful goals. Although, following in similar physiological traits to other emotions such as anxiety, excitement may differ from other emotions due to its combination of positive valence, high activation/arousal, approach to goals and anticipatory nature (Russell, 1980; Gable &amp; Harmon-Jones, 2010; Macahizawa et al., 2020). Excitement as a state triggers activation of the autonomic nervous system, preparing itself for some kind of action (Oxendine, 1970). Common physiological responses include elevated heart rate, alertness, energy and rise in blood pressure (Ketonen et al., 2023). Psychologically, excitement can boost an individual's readiness to act, perceived self-efficacy, and cognitive scope (Brooks, 2014; Fredrickson, 2001), while also causing them to underestimate or overevaluate certain aspects of the situation (Galentino, Bonini, &amp; Savadori, 2017; Andrade, Odean, &amp; Lin, 2016).

As a catalyst to engaging with actions towards a certain goal, excitement can effect ones cognition, narrowing or widening its scope (Fredrickson, 2001), and possibly leading to greater impulsive or risk taking behaviours (e.g., Galentino et al., 2017). Excitement can also be a powerful tool in restructuring other emotions, and as a positive emotion, may increase satisfaction across the lifespan (Liu et al., 2016). With its value differing across culture, excitement can support well-being by promoting engagement and pursuit of rewarding experiences, although excessive arousal or poorly regulated excitement may produce less beneficial outcomes. Understanding excitement therefore requires recognising it not simply as a pleasurable feeling, but as an emotion that prepares people to act and can shape how they think, behave and experience their well-being.

{{RoundBoxTop|theme=3}}
'''Take-home message'''

Excitement is a unique emotional state that can be as much of a powerful tool in goal pursuit, action and well-being as it is simply a positive state of being. An event that strikes fear into one, may be exciting for another, therefore, excitement and emotions as whole come from the unique interplay of our active and passive shaping of the significance we assign to our experiences. {{RoundBoxBottom}}

{{RoundBoxTop|theme=11|title=Quiz}}&lt;quiz display=simple&gt;
{'''Chapter quiz:'''
Steve and his team begin to pull away in the final minutes of the game. A smile emerges from his face as he anticipates the messages and coverage he will receive from the crowd and media. On the otherhand, his teammate Bob, hates attention and he begins to feel stressed. According to the chapter, what best explains this situation?
|type=&quot;()&quot;}

+Their individual perceptions and interpretations of the sitatuion influence whether they experience heightened arousal as excitement or stress.
-Everyone experiences excitement the same way.
-Their emotional responses are determined entirely by physiological arousal, rather than how they interpret the situation.
&lt;/quiz&gt;
{{RoundBoxBottom}}

==See also==

* [[w:Affect_(psychology)|Affect (psychology)]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Circumplex model of affect|Circumplex model of affect]] (Book chapter, 2019)
* [[Motivation and emotion/Book/2025/Motivational dimensional model of affect|Motivational dimensional model of affect]] (Book chapter, 2025)
==References==
{{Hanging indent|1=

Andrade, E. B., Odean, T., &amp; Lin, S. (2016). Bubbling with Excitement: An Experiment. ''Review of Finance, 20''(2), 447–466. https://doi.org/10.1093/rof/rfv016

Brooks, A. W. (2014). Get Excited: Reappraising Pre-Performance Anxiety as Excitement. ''Journal of Experimental Psychology. General, 143''(3), 1144–1158. https://doi.org/10.1037/a0035325 

Fredrickson, B. L. (2001). The Role of Positive Emotions in Positive Psychology: The Broaden-and-Build Theory of Positive Emotions. ''The American Psychologist, 56''(3), 218–226. https://doi.org/10.1037/0003-066X.56.3.218

Gable, P. A., &amp; Dreisbach, G. (2021). Approach motivation and positive affect. ''Current Opinion in Behavioral Sciences, 39'', 203–208. https://doi.org/10.1016/j.cobeha.2021.03.030

Gable, P., &amp; Harmon-Jones, E. (2010). The motivational dimensional model of affect: Implications for breadth of attention, memory, and cognitive categorisation. ''Cognition and Emotion, 24''(2), 322–337. https://doi.org/10.1080/02699930903378305

Galentino, A., Bonini, N., &amp; Savadori, L. (2017). Positive Arousal Increases Individuals’ Preferences for Risk. ''Frontiers in Psychology, 8'', Article 2142. https://doi.org/10.3389/fpsyg.2017.02142

Hasada, R. (1994). ''The semantic aspects of onomatopoeia: focusing on Japanese psychomimes'' [Master's thesis, The Australian National University]. ANU Open Research. https://doi.org/10.25911/5d723cb12c49c 

Ketonen, E. E., Salonen, V., Lonka, K., &amp; Salmela‐Aro, K. (2023). Can you feel the excitement? Physiological correlates of students’ self‐reported emotions. ''British Journal of Educational Psychology, 93''(S1), Article 12534. https://doi.org/10.1111/bjep.12534

Lim, N. (2016). Cultural differences in emotion: differences in emotional arousal level between the East and the West. ''Integrative Medicine Research, 5''(2), 105–109. https://doi.org/10.1016/j.imr.2016.03.004

Liu, J., Vittersø, J., Teulings, I. J. E., Nes, R. B., Mayerhofer, L., &amp; Røysamb, E. (2026). Jingle all the way? Pleasant and energized positive affect show differential longitudinal relationships with life satisfaction and personality. ''The Journal of Positive Psychology'', (Latest Articles), 1–13. https://doi.org/10.1080/17439760.2026.2701098

Machizawa, M. G., Lisi, G., Kanayama, N., Mizuochi, R., Makita, K., Sasaoka, T., &amp; Yamawaki, S. (2020). Quantification of anticipation of excitement with a three-axial model of emotion with EEG. ''Journal of Neural Engineering, 17''(3). https://doi.org/10.1088/1741-2552/ab93b4

Oxendine, J. B. (1970). Emotional Arousal and Motor Performance. ''Quest (National Association for Kinesiology in Higher Education), 13''(1), 23–32. https://doi.org/10.1080/00336297.1970.10519673

Piira, O.-P., Huikuri, H. V., &amp; Tulppo, M. P. (2011). Effects of emotional excitement on heart rate and blood pressure dynamics in patients with coronary artery disease. ''Autonomic Neuroscience, 160''(1–2), 107–114. https://doi.org/10.1016/j.autneu.2010.11.011

Posner, J., Russell, J. A., &amp; Peterson, B. S. (2005). The circumplex model of affect: An integrative approach to affective neuroscience, cognitive development, and psychopathology. ''Development and Psychopathology, 17''(3), 715–734. https://doi.org/10.1017/S0954579405050340

Robinson, M. D., &amp; Irvin, R. L. (2022). Out of the shell, into the world: preferences for openness as a substrate of approach motivation and positive affect. ''Motivation and Emotion, 46''(3), 307–318. https://doi.org/10.1007/s11031-022-09934-5

Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714

Schachter, S., &amp; Singer, J. (1962). Cognitive, social, and physiological determinants of emotional state. ''Psychological Review, 69''(5), 379–399. https://doi.org/10.1037/h0046234

Smith, K. E., Woodard, K., &amp; Pollak, S. D. (2025). Arousal May Not Be Anything to Get Excited About. ''Emotion Review, 17''(1), 3–15. https://doi.org/10.1177/17540739241303499

Sohn, J.-H., Kim, H.-E., Sohn, S., Seok, J.-W., Choi, D., &amp; Watanuki, S. (2015). Effect of emotional arousal on inter-temporal decision-making: an fMRI study. ''Journal of Physiological Anthropology, 34''(1), Article 8. https://doi.org/10.1186/s40101-015-0047-5

Storbeck, J., &amp; Clore, G. L. (2008). Affective Arousal as Information: How Affective Arousal Influences Judgments, Learning, and Memory. ''Social and Personality Psychology Compass, 2''(5), 1824–1843. https://doi.org/10.1111/j.1751-9004.2008.00138.x

Stratton, G. M. (1928). The function of emotion as shown particularly in excitement. ''Psychological Review, 35''(5), 351–366. https://doi.org/10.1037/h0071406

Tsai, J. L. (2024). Investigating culture and emotion: From responses to ideals. In M. J. Gelfand, C.-Y. Chiu, &amp; Y.-Y. Hong (Eds.), ''Handbook of advances in culture and psychology'' (pp. 54–117). Oxford University Press.

Tugade, M. M., Shiota, M. N., &amp; Kirby, L. D. (Eds.). (2014). ''Handbook of positive emotions'' (1st ed.). Guilford Press.


}}

==External links==

* [https://www.youtube.com/watch?v=S9tBnXz2B1Q How to turn anxiety into excitement] (SciShow Psych)
* [https://fi.edu/en/blog/science-emotions-excitement?ct=1787858646114 Science of emotions: excitement] (The Franklin Institue)
* [https://www.simplypsychology.com/articles/anxiety-reappraisal-strategies Cognitive reappraisal for anxiety: evidence-based strategies that work] (Simply Psychology)

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__TOC__

==Overview==
{{RoundBoxTop|theme=3}}
[[File:Exhausted smartphone user.JPG|right|thumb|150px|'''Figure 1'''. An emotionally exhausted Aelin at the end of the work day]]

; Scenario

Aelin, a 23-year-old social worker employed at headspace {{ic|Link to the Wikipedia article to help explain what this term means}}, works with approximately 20 {{ic|Explain what sort of}}Imagine you are only 23 years old and are working as a social worker at headspace. You see around 20 clients each week, many of whom have experienced rough living conditions.

During your first six months in this role, you felt highly motivated and excited to help people in need. You are an excellent active listener and can easily remember details about your clients Live’s. You are also good at recognising signs of distress in your client’s body language and adjust yours in order to show warmth and understanding. 

As you progress in your role, you take on more cases that involve complex past traumas. The workload becomes too much for you to get done at work, but you don’t want your clients to miss out, so you take your work home to complete it in the evenings. Your workload increases again and you now start doing work on your weekends as well. After several months of working this way, you start to notice you feel exhausted every morning before you have even started work.
 
You then start to notice you’re responding to people at work differently. Instead of your usual energised active listening response you feel frustrated, empathetic and detached. After work you are too drained to socialise with friends. This begins to worry you. What if you won’t be able to continue working as a social worker?  

{{RoundBoxBottom}}

Aelin is experiencing '''emotional exhaustion''' from a sustained empathic response. 

Due to the nature of Aelin's work, they are constantly engaged in an empathic response. Empathic responses require cognitive and physical resources to sustain. Because Aelin is taking their work home and not resting on weekends, they do not have a chance to rest. It is important for Aelin to recognise what is happening and why. Not actioning the problem has led to empathy fatigue and emotional exhaustion. Emotional exhaustion is one of the key aspects of [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FEmpathy_fatigue_and_emotional_exhaustion&amp;diff=2840411&amp;oldid=2832859 burnout], a long-term condition of existing in a constant state of high stress. 

Psychological science can support Aelin in recognising and mapping the symptoms they are experiencing, understand coping strategies to minimise the current and future effects to improve their wellbeing. Understanding the symptoms will also support their role as a social worker, providing more tools for the people they support on a day-to-day basis.

{{RoundBoxTop|theme=3}}
'''Focus questions'''

* Why do people become emotionally exhausted?
* What is the relationship between empathy fatigue and emotional exhaustion?
* What role does emotional labor play in emotional exhaustion?
* How does understanding emotional labor and empathy fatigue work to reduce the effects of emotional exhaustion?
{{RoundBoxBottom}}

== Emotional Exhaustion ==
General introduction/definition of emotional exhaustion
* Talk about stress and its role in emotional exhaustion
* How would you recognise that someone is emotionally exhausted (symptoms) 
** Emotional exhaustion as a symptom of burnout (De Beer et al., 2024) 
** Introduce theories of emotional exhaustion

=== Conservation of resources stress model   ===

* Psychological stress occurs when individuals lose valued resources (Halbesleben et al., 2014; Hobfoll, 1989)
** Discuss what resources are (e.g. social relationships)
** Discuss how losing resources leads to increased vulnerability to stress
** discuss gain and loss spirals

=== Job Demands-Resources model ===

* Talk about Job demands and job resources (Demerouti et al., 2001)
** Why do we actually feel exhausted after a sustained empathic response?
** Job demands require sustained physical or psychological effort
*** Empathic response can be a job demand
** Job resources support achieving work goals or reduce job demands
* Discuss how the model looks at prolonged job demands depleting energy leading to exhaustion/burnout (Schaufeli, 2017)
* Discuss how the model treats job resources as a mediating factor for reducing the negative effects of job demands 

== Empathy Fatigue ==

* Before understanding empathy fatigue, define what empathy is (what are the theories behind empathy? Why do we have empathy? What theory am I using)
** Individual ability to imagine or understand another person's feelings and/or emotions (Riess, 2017; Shao et al., 2024)

=== What are the types of empathy? ===

* Affective empathy - emotional reaction to someone else's mental state (Shao et al., 2024) 
* Cognitive empathy - understand someone's feelings or emotions (Cui et al., 2022)
* Integrating the two - &quot;affective component is the essence of empathy, and the cognitive component is a process through which that essence comes into being&quot; (Bošnjaković &amp; Radionov, 2018) 
** (Author's note: change quote into paraphrasing)

=== What is compassion fatigue? (theories of compassion fatigue) ===

* Distinction between empathy and compassion fatigue
* Compassion fatigue is closely related to Secondary traumatic stress usually found in healthcare professionals (Figley, 2002)
** Compassion fatigue is to Empathy fatigue as emotional exhaustion is to burnout

* Make it clear that Aelin is experiencing Compassion Fatigue vs Empathy fatigue (they are the same but different)

(Author's note: include an update to the scenario here!)

'''Empathy fatigue questions'''.

Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=simple&gt;
{Surface acting is when the observer actually feels the emotion:
|type=&quot;()&quot;}
- True
+ False

{Compassion fatigue and empathy fatigue are synonymous:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

== Emotional labor as a mediating factor between Empathy fatigue and emotional exhaustion ==
What is emotional labor (Hochschild, 2012)

=== Types of acting ===
* Surface acting
** This is where emotive dissonance comes into play
** Leads to emotional exhaustion

* Deep acting
** People who 'deep act', as in genuinely change the way they feel (match the feelings they have with the feelings that they need to display) often report positive relationships with emotional labor
Discuss the differences in gender norms and expectations in relationships

=== The mediating effect of emotional labor ===
Surface acting does not mediate the effect (high surface acting leads to emotional exhaustion) whereas the inverse is true for deep acting (Wrobel, 2013)

=== Emotional contagion ===
If space/time permits discuss the role of emotional contagion
* Emotional contagion (Panksepp and Lahvis, 2011)
** emotions can spread (expand, combines empathy and acting)
** “the tendency to automatically mimic and synchronize expressions, vocalizations, postures, and movements with those of another person’s and, consequently, to converge emotionally.” (Elaine Hatfield, 1993)

== Strategies for combating Empathy fatigue and emotional fatigue ==

* Talk about emotion regulation (Gross, 1998) and mood regulation strategies as a way to deal with coping (Wrobel, 2013) (Author's note: need more research/references for this section)
* Talk about breaks
** Rest and downtime from not performing emotional labor regenerates
* How do we reduce the amount of emotional labor we're performing (Jeung et al., 2018)
** Communication/boundaries
** Reducing surface acting (allowing ourselves to feel how we actually feel and reduce emotive dissonance)

=== Strategies in the workplace ===
* Discuss types of strategies that are available in the workplace (organisation models)
* SCARF model (Aplin-Houtz, 2025)
** Link back to COR and JDR models e.g. praise could be a job resource vs criticism could be a job demand

==Figures (for reference before final assessment)==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]]

* Use figures to illustrate concepts, add interest, and to serve as examples
* Figures can show photos, diagrams, graphs, video, audio, etc.
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Caption figures (use '''Figure #'''. and explain the relevance of the image to the text)
* Images must be embedded from [[commons:|Wikimedia Commons]]
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Cite each figure at least once in the main text (e.g., see Figure 2)

== Learning features (for reference before final assessment) ==
Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter.

{{anchor|Scenarios}}
;Scenarios
* Scenarios, case studies, or examples describe concepts in action
* Can be real or fictional; if real, provide citations
* Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages)
* Present using [[#Feature boxes|feature boxes]]

{{anchor|Feature box}}
;Feature boxes
* Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect
* Consider using feature boxes for:
** [[#Scenarios|Scenarios]], case studies, or examples
** Focus questions
** Tips
** Quiz questions
** Take-home messages

;Embedded links
* When key words are introduced, use [[Help:Links|interwiki links]] to:
** Wikipedia articles (e.g., &quot;An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]&quot;) or
** Related book chapters (e.g., &quot;If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]&quot;)

{{anchor|Tables}}
;Tables
* Use to tables to organise and summarise information
* Cite each table at least once in the main text (e.g., see Table 1)
* Tables should be captioned
* [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted

'''Table 1''' 

A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., 

The 2 x 2 Johari Window Model Showing Knowing x Self/Other

{| class=&quot;wikitable&quot; style=&quot;margin: auto;
|-
! !! Known to self !! Not known to self
|-
| '''Known to others''' || Open area || Blind spot
|-
| '''Not known to others''' || Hidden area || Unknown
|}

;Quizzes
* Using one or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=simple&gt;
{The purpose of quizzes is to provide an interactive learning feature:
|type=&quot;()&quot;}
+ True
- False

{Long and complex quiz questions are recommended:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

==Conclusion==

* Summarise what empathy fatigue is, and why people become emotionally exhausted (+ the role of emotional labor)
* Summarise the symptoms and how to recognise them in yourself and someone else
* Emphasise and summarise psychological strategies to support someone going through emotional exhaustion
* Summarise ways to prevent emotional exhaustion from happening
* Overall message is: 
*# What is emotional exhaustion
*# how do you recognise it
*# how do you treat it
*# how do you prevent it

* Link back to the focus questions

==See also==
* [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Metacognition_and_emotional_regulation&amp;oldid=2756264 Metacognition and emotional regulation] (Book chapter, 2026) {{ic|Use an internal link style as shown in Tutorial 2}}
* [[wikipedia:Conservation_of_resources_theory|Conservation of resources theory]] (Wikipedia)
* [[wikipedia:Job_demands-resources_model|Job demands-resources model]] (Wikipedia)

==References==
{{Hanging indent|1=

Aplin-Houtz, M. (2025). Unraveling the SCARF: How dimensions of the SCARF model influence the relationship between workplace exclusion and turnover intentions. Journal of Management &amp; Organization, 31(6), 2699–2725. https://doi.org/10.1017/jmo.2025.10026

Bošnjaković, J., &amp; Radionov, T. (2018). Empathy: Concepts, Theories and Neuroscientific Basis. Alcoholism (Zagreb), 54(2), 123–150. https://doi.org/10.20471/de..2018.54.02.04

Cui, F., Huang, X., Jing, Y., Luo, Y., Liu, J., &amp; Gu, R. (2022). How resource sharing resists scarcity: the role of cognitive empathy and its neurobiological mechanisms. Cerebral Cortex (New York, N.Y. 1991), 32(23), 5330–5342. https://doi.org/10.1093/cercor/bhac017

De Beer, L. T., van der Vaart, L., Escaffi-Schwarz, M., De Witte, H., &amp; Schaufeli, W. B. (2024). Maslach Burnout Inventory - General Survey. European Journal of Psychological Assessment : Official Organ of the European Association of Psychological Assessment, 40(5), 360–375. https://doi.org/10.1027/1015-5759/a000797

Demerouti, E., Bakker, A. B., Nachreiner, F., &amp; Schaufeli, W. B. (2001). The Job Demands-Resources Model of Burnout. Journal of Applied Psychology, 86(3), 499–512. https://doi.org/10.1037/0021-9010.86.3.499

Figley, C. R. (2002). Compassion fatigue: Psychotherapists’ chronic lack of self care. Journal of Clinical Psychology, 58(11), 1433–1441. https://doi.org/10.1002/jclp.10090

Grandey, A. A. (2003). When ‘the show must go on’: surface acting and deep acting as determinants of emotional exhaustion and peer-rated service delivery. Academy of Management Journal, 46(1), 86–96. https://doi.org/10.5465/30040678

Gross, J. J. (1998). The emerging field of emotion regulation: An integrative review. Review of General Psychology, 2(3), 271–299. https://doi.org/10.1037/1089-2680.2.3.271

Halbesleben, J. R. B., Neveu, J.-P., Paustian-Underdahl, S. C., &amp; Westman, M. (2014). Getting to the “COR”: Understanding the Role of Resources in Conservation of Resources Theory. Journal of Management, 40(5), 1334–1364. https://doi.org/10.1177/0149206314527130

Hatfield, E., Cacioppo, J. T., &amp; Rapson, R. L. (1993). Emotional Contagion. Current Directions in Psychological Science : A Journal of the American Psychological Society, 2(3), 96–99. https://doi.org/10.1111/1467-8721.ep10770953

Hobfoll, S. E. (1989). Conservation of Resources: A New Attempt at Conceptualizing Stress. The American Psychologist, 44(3), 513–524. https://doi.org/10.1037/0003-066X.44.3.513

Hochschild, A. R. (2012). The managed heart  : commercialization of human feeling (Updated, with a new preface.). University of California Press.

Jeung, D.-Y., Kim, C., &amp; Chang, S.-J. (2018). Emotional Labor and Burnout: A Review of the Literature. Yonsei Medical Journal, 59(2), 187–193. https://doi.org/10.3349/ymj.2018.59.2.187

Lavelle, J. J., Rupp, D. E., Herda, D. N., Pandey, A., &amp; Lauck, J. R. (2021). Customer Injustice and Employee Performance: Roles of Emotional Exhaustion, Surface Acting, and Emotional Demands–Abilities Fit. Journal of Management, 47(3), Article 0149206319869426. https://doi.org/10.1177/0149206319869426

Panksepp, J. B., &amp; Lahvis, G. P. (2011). Rodent empathy and affective neuroscience. Neuroscience and Biobehavioral Reviews, 35(9), 1864–1875. https://doi.org/10.1016/j.neubiorev.2011.05.013

Riess, H. (2017). The Science of Empathy. Journal of Patient Experience, 4(2), 74–77. https://doi.org/10.1177/2374373517699267

Schaufeli, W. B. (2017). Applying the job demands-resources model: a “how to” guide to measuring and tackling work engagement and burnout. Organizational Dynamics, 46(2), 120–132. https://doi.org/10.1016/j.orgdyn.2017.04.008

Shao, M., Li, L., Li, X., Wei, Z., Wang, J., Hong, M., Liu, X., &amp; Meng, J. (2024). The effect of top-down attention on empathy fatigue. Cerebral Cortex (New York, N.Y. 1991), 34(1), Article bhad441. https://doi.org/10.1093/cercor/bhad441

Wharton, A. S. (2009). The Sociology of Emotional Labor. Annual Review of Sociology, 35(1), 147–165. https://doi.org/10.1146/annurev-soc-070308-115944

Wrobel, M. (2013). Can empathy lead to emotional exhaustion in teachers? The mediating role of emotional labor. International Journal of Occupational Medicine and Environmental Health, 26(4), 581–592. https://doi.org/10.2478/s13382-013-0123-1

}}

==External links==
Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Burnout]]
[[Category:Motivation and emotion/Book/Empathy]]</text>
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__TOC__

==Overview==
{{RoundBoxTop|theme=3}}
[[File:Exhausted smartphone user.JPG|right|thumb|150px|'''Figure 1'''. An emotionally exhausted Aelin at the end of the work day]]

; Scenario

Aelin, a 23-year-old social worker employed at headspace {{ic|Link to the Wikipedia article to help explain what this term means}}, works with approximately 20 {{ic|Explain what sort of}}Imagine you are only 23 years old and are working as a social worker at headspace. You see around 20 clients each week, many of whom have experienced rough living conditions.

During your first six months in this role, you felt highly motivated and excited to help people in need. You are an excellent active listener and can easily remember details about your clients Live’s. You are also good at recognising signs of distress in your client’s body language and adjust yours in order to show warmth and understanding. 

As you progress in your role, you take on more cases that involve complex past traumas. The workload becomes too much for you to get done at work, but you don’t want your clients to miss out, so you take your work home to complete it in the evenings. Your workload increases again and you now start doing work on your weekends as well. After several months of working this way, you start to notice you feel exhausted every morning before you have even started work.
 
You then start to notice you’re responding to people at work differently. Instead of your usual energised active listening response you feel frustrated, empathetic and detached. After work you are too drained to socialise with friends. This begins to worry you. What if you won’t be able to continue working as a social worker?  

{{RoundBoxBottom}}

Aelin is experiencing '''emotional exhaustion''' from a sustained empathic response. 

Due to the nature of Aelin's work, they are constantly engaged in an empathic response. Empathic responses require cognitive and physical resources to sustain. Because Aelin is taking their work home and not resting on weekends, they do not have a chance to rest. It is important for Aelin to recognise what is happening and why. Not actioning the problem has led to empathy fatigue and emotional exhaustion. Emotional exhaustion is one of the key aspects of [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FEmpathy_fatigue_and_emotional_exhaustion&amp;diff=2840411&amp;oldid=2832859 burnout], a long-term condition of existing in a constant state of high stress. 

Psychological science can support Aelin in recognising and mapping the symptoms they are experiencing, understand coping strategies to minimise the current and future effects to improve their wellbeing. Understanding the symptoms will also support their role as a social worker, providing more tools for the people they support on a day-to-day basis.

{{RoundBoxTop|theme=3}}
'''Focus questions'''

* Why do people become emotionally exhausted?
* What is the relationship between empathy fatigue and emotional exhaustion?
* What role does emotional labor play in emotional exhaustion?
* How does understanding emotional labor and empathy fatigue work to reduce the effects of emotional exhaustion?
{{RoundBoxBottom}}

== Emotional Exhaustion ==
'''Talk about stress and its role in emotional exhaustion'''

Emotional exhaustion is a major contributing factor in burnout and can be recognised as &quot;''definition''&quot;(De Beer et al., 2024). As a major factor, its symptoms are similar to burnout and stress. '''How would you recognise that someone is emotionally exhausted''' The major symptoms include: &quot;''dot point list of biggest symptoms''&quot; 

There are many theories that attempt to explain why emotional exhaustion occurs. Two of these theories with good evidence are the Conservation of resources stress model (Halbesleben et al., 2014; Hobfoll, 1989) and the Job Demands-Resources model (Demerouti et al., 2001).

=== Conservation of resources stress model   ===

* Psychological stress occurs when individuals lose valued resources (Halbesleben et al., 2014; Hobfoll, 1989)
** Discuss what resources are (e.g. social relationships)
** Discuss how losing resources leads to increased vulnerability to stress
** discuss gain and loss spirals

=== Job Demands-Resources model ===

* Talk about Job demands and job resources (Demerouti et al., 2001)
** Why do we actually feel exhausted after a sustained empathic response?
** Job demands require sustained physical or psychological effort
*** Empathic response can be a job demand
** Job resources support achieving work goals or reduce job demands
* Discuss how the model looks at prolonged job demands depleting energy leading to exhaustion/burnout (Schaufeli, 2017)
* Discuss how the model treats job resources as a mediating factor for reducing the negative effects of job demands 

== Empathy Fatigue ==

* Before understanding empathy fatigue, define what empathy is (what are the theories behind empathy? Why do we have empathy? What theory am I using)
** Individual ability to imagine or understand another person's feelings and/or emotions (Riess, 2017; Shao et al., 2024)

=== What are the types of empathy? ===

* Affective empathy - emotional reaction to someone else's mental state (Shao et al., 2024) 
* Cognitive empathy - understand someone's feelings or emotions (Cui et al., 2022)
* Integrating the two - &quot;affective component is the essence of empathy, and the cognitive component is a process through which that essence comes into being&quot; (Bošnjaković &amp; Radionov, 2018) 
** (Author's note: change quote into paraphrasing)

=== What is compassion fatigue? (theories of compassion fatigue) ===

* Distinction between empathy and compassion fatigue
* Compassion fatigue is closely related to Secondary traumatic stress usually found in healthcare professionals (Figley, 2002)
** Compassion fatigue is to Empathy fatigue as emotional exhaustion is to burnout

* Make it clear that Aelin is experiencing Compassion Fatigue vs Empathy fatigue (they are the same but different)

(Author's note: include an update to the scenario here!)

'''Empathy fatigue questions'''.

Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=simple&gt;
{Surface acting is when the observer actually feels the emotion:
|type=&quot;()&quot;}
- True
+ False

{Compassion fatigue and empathy fatigue are synonymous:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

== Emotional labor as a mediating factor between Empathy fatigue and emotional exhaustion ==
What is emotional labor (Hochschild, 2012)

=== Types of acting ===
* Surface acting
** This is where emotive dissonance comes into play
** Leads to emotional exhaustion (Kenworthy et al., 2014)
** &quot;Should&quot; language - in this situation, this is what I ''should'' feel

* Deep acting
** People who 'deep act', as in genuinely change the way they feel (match the feelings they have with the feelings that they need to display) often report positive relationships with emotional labor
** Actual language - in this situation, this is what I ''actually'' feel
Discuss the differences in gender norms and expectations in relationships

=== The mediating effect of emotional labor ===
Surface acting does not mediate the effect (high surface acting leads to emotional exhaustion) whereas the inverse is true for deep acting (Wrobel, 2013)

=== Emotional contagion ===
If space/time permits discuss the role of emotional contagion
* Emotional contagion (Panksepp and Lahvis, 2011)
** emotions can spread (expand, combines empathy and acting)
** “the tendency to automatically mimic and synchronize expressions, vocalizations, postures, and movements with those of another person’s and, consequently, to converge emotionally.” (Elaine Hatfield, 1993)

== Strategies for combating Empathy fatigue and emotional fatigue ==

* Talk about emotion regulation (Gross, 1998) and mood regulation strategies as a way to deal with coping (Wrobel, 2013) (Author's note: need more research/references for this section)
* Talk about breaks
** Rest and downtime from not performing emotional labor regenerates
* How do we reduce the amount of emotional labor we're performing (Jeung et al., 2018)
** Communication/boundaries
** Reducing surface acting (allowing ourselves to feel how we actually feel and reduce emotive dissonance)

=== Strategies in the workplace ===
* Discuss types of strategies that are available in the workplace (organisation models)
* SCARF model (Aplin-Houtz, 2025)
** Link back to COR and JDR models e.g. praise could be a job resource vs criticism could be a job demand
*Reduce workload to reduce emotional exhaustion, and by extension reduce emotional fatigue.

==Figures (for reference before final assessment)==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]]

* Use figures to illustrate concepts, add interest, and to serve as examples
* Figures can show photos, diagrams, graphs, video, audio, etc.
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Caption figures (use '''Figure #'''. and explain the relevance of the image to the text)
* Images must be embedded from [[commons:|Wikimedia Commons]]
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Cite each figure at least once in the main text (e.g., see Figure 2)

== Learning features (for reference before final assessment) ==
Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter.

{{anchor|Scenarios}}
;Scenarios
* Scenarios, case studies, or examples describe concepts in action
* Can be real or fictional; if real, provide citations
* Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages)
* Present using [[#Feature boxes|feature boxes]]

{{anchor|Feature box}}
;Feature boxes
* Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect
* Consider using feature boxes for:
** [[#Scenarios|Scenarios]], case studies, or examples
** Focus questions
** Tips
** Quiz questions
** Take-home messages

;Embedded links
* When key words are introduced, use [[Help:Links|interwiki links]] to:
** Wikipedia articles (e.g., &quot;An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]&quot;) or
** Related book chapters (e.g., &quot;If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]&quot;)

{{anchor|Tables}}
;Tables
* Use to tables to organise and summarise information
* Cite each table at least once in the main text (e.g., see Table 1)
* Tables should be captioned
* [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted

'''Table 1''' 

A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., 

The 2 x 2 Johari Window Model Showing Knowing x Self/Other

{| class=&quot;wikitable&quot; style=&quot;margin: auto;
|-
! !! Known to self !! Not known to self
|-
| '''Known to others''' || Open area || Blind spot
|-
| '''Not known to others''' || Hidden area || Unknown
|}

;Quizzes
* Using one or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=simple&gt;
{The purpose of quizzes is to provide an interactive learning feature:
|type=&quot;()&quot;}
+ True
- False

{Long and complex quiz questions are recommended:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

==Conclusion==

* Summarise what empathy fatigue is, and why people become emotionally exhausted (+ the role of emotional labor)
* Summarise the symptoms and how to recognise them in yourself and someone else
* Emphasise and summarise psychological strategies to support someone going through emotional exhaustion
* Summarise ways to prevent emotional exhaustion from happening
* Overall message is: 
*# What is emotional exhaustion
*# how do you recognise it
*# how do you treat it
*# how do you prevent it

* Link back to the focus questions

==See also==
* [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Metacognition_and_emotional_regulation&amp;oldid=2756264 Metacognition and emotional regulation] (Book chapter, 2026) {{ic|Use an internal link style as shown in Tutorial 2}}
* [[wikipedia:Conservation_of_resources_theory|Conservation of resources theory]] (Wikipedia)
* [[wikipedia:Job_demands-resources_model|Job demands-resources model]] (Wikipedia)

==References==
{{Hanging indent|1=

Aplin-Houtz, M. (2025). Unraveling the SCARF: How dimensions of the SCARF model influence the relationship between workplace exclusion and turnover intentions. Journal of Management &amp; Organization, 31(6), 2699–2725. https://doi.org/10.1017/jmo.2025.10026

Bošnjaković, J., &amp; Radionov, T. (2018). Empathy: Concepts, Theories and Neuroscientific Basis. Alcoholism (Zagreb), 54(2), 123–150. https://doi.org/10.20471/de..2018.54.02.04

Cui, F., Huang, X., Jing, Y., Luo, Y., Liu, J., &amp; Gu, R. (2022). How resource sharing resists scarcity: the role of cognitive empathy and its neurobiological mechanisms. Cerebral Cortex (New York, N.Y. 1991), 32(23), 5330–5342. https://doi.org/10.1093/cercor/bhac017

De Beer, L. T., van der Vaart, L., Escaffi-Schwarz, M., De Witte, H., &amp; Schaufeli, W. B. (2024). Maslach Burnout Inventory - General Survey. European Journal of Psychological Assessment : Official Organ of the European Association of Psychological Assessment, 40(5), 360–375. https://doi.org/10.1027/1015-5759/a000797

Demerouti, E., Bakker, A. B., Nachreiner, F., &amp; Schaufeli, W. B. (2001). The Job Demands-Resources Model of Burnout. Journal of Applied Psychology, 86(3), 499–512. https://doi.org/10.1037/0021-9010.86.3.499

Figley, C. R. (2002). Compassion fatigue: Psychotherapists’ chronic lack of self care. Journal of Clinical Psychology, 58(11), 1433–1441. https://doi.org/10.1002/jclp.10090

Grandey, A. A. (2003). When ‘the show must go on’: surface acting and deep acting as determinants of emotional exhaustion and peer-rated service delivery. Academy of Management Journal, 46(1), 86–96. https://doi.org/10.5465/30040678

Gross, J. J. (1998). The emerging field of emotion regulation: An integrative review. Review of General Psychology, 2(3), 271–299. https://doi.org/10.1037/1089-2680.2.3.271

Halbesleben, J. R. B., Neveu, J.-P., Paustian-Underdahl, S. C., &amp; Westman, M. (2014). Getting to the “COR”: Understanding the Role of Resources in Conservation of Resources Theory. Journal of Management, 40(5), 1334–1364. https://doi.org/10.1177/0149206314527130

Hatfield, E., Cacioppo, J. T., &amp; Rapson, R. L. (1993). Emotional Contagion. Current Directions in Psychological Science : A Journal of the American Psychological Society, 2(3), 96–99. https://doi.org/10.1111/1467-8721.ep10770953

Hobfoll, S. E. (1989). Conservation of Resources: A New Attempt at Conceptualizing Stress. The American Psychologist, 44(3), 513–524. https://doi.org/10.1037/0003-066X.44.3.513

Hochschild, A. R. (2012). The managed heart  : commercialization of human feeling (Updated, with a new preface.). University of California Press.

Jeung, D.-Y., Kim, C., &amp; Chang, S.-J. (2018). Emotional Labor and Burnout: A Review of the Literature. Yonsei Medical Journal, 59(2), 187–193. https://doi.org/10.3349/ymj.2018.59.2.187

Lavelle, J. J., Rupp, D. E., Herda, D. N., Pandey, A., &amp; Lauck, J. R. (2021). Customer Injustice and Employee Performance: Roles of Emotional Exhaustion, Surface Acting, and Emotional Demands–Abilities Fit. Journal of Management, 47(3), Article 0149206319869426. https://doi.org/10.1177/0149206319869426

Panksepp, J. B., &amp; Lahvis, G. P. (2011). Rodent empathy and affective neuroscience. Neuroscience and Biobehavioral Reviews, 35(9), 1864–1875. https://doi.org/10.1016/j.neubiorev.2011.05.013

Riess, H. (2017). The Science of Empathy. Journal of Patient Experience, 4(2), 74–77. https://doi.org/10.1177/2374373517699267

Schaufeli, W. B. (2017). Applying the job demands-resources model: a “how to” guide to measuring and tackling work engagement and burnout. Organizational Dynamics, 46(2), 120–132. https://doi.org/10.1016/j.orgdyn.2017.04.008

Shao, M., Li, L., Li, X., Wei, Z., Wang, J., Hong, M., Liu, X., &amp; Meng, J. (2024). The effect of top-down attention on empathy fatigue. Cerebral Cortex (New York, N.Y. 1991), 34(1), Article bhad441. https://doi.org/10.1093/cercor/bhad441

Wharton, A. S. (2009). The Sociology of Emotional Labor. Annual Review of Sociology, 35(1), 147–165. https://doi.org/10.1146/annurev-soc-070308-115944

Wrobel, M. (2013). Can empathy lead to emotional exhaustion in teachers? The mediating role of emotional labor. International Journal of Occupational Medicine and Environmental Health, 26(4), 581–592. https://doi.org/10.2478/s13382-013-0123-1

}}

==External links==
Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

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[[Category:Motivation and emotion/Book/Burnout]]
[[Category:Motivation and emotion/Book/Empathy]]</text>
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__TOC__

==Overview==
{{RoundBoxTop|theme=3}}
[[File:Exhausted smartphone user.JPG|right|thumb|150px|'''Figure 1'''. An emotionally exhausted Aelin at the end of the work day]]

; Scenario

Aelin, a 23-year-old social worker employed at headspace {{ic|Link to the Wikipedia article to help explain what this term means}}, works with approximately 20 {{ic|Explain what sort of}}Imagine you are only 23 years old and are working as a social worker at headspace. You see around 20 clients each week, many of whom have experienced rough living conditions.

During your first six months in this role, you felt highly motivated and excited to help people in need. You are an excellent active listener and can easily remember details about your clients Live’s. You are also good at recognising signs of distress in your client’s body language and adjust yours in order to show warmth and understanding. 

As you progress in your role, you take on more cases that involve complex past traumas. The workload becomes too much for you to get done at work, but you don’t want your clients to miss out, so you take your work home to complete it in the evenings. Your workload increases again and you now start doing work on your weekends as well. After several months of working this way, you start to notice you feel exhausted every morning before you have even started work.
 
You then start to notice you’re responding to people at work differently. Instead of your usual energised active listening response you feel frustrated, empathetic and detached. After work you are too drained to socialise with friends. This begins to worry you. What if you won’t be able to continue working as a social worker?  

{{RoundBoxBottom}}

Aelin is experiencing '''emotional exhaustion''' from a sustained empathic response. 

Due to the nature of Aelin's work, they are constantly engaged in an empathic response. Empathic responses require cognitive and physical resources to sustain. Because Aelin is taking their work home and not resting on weekends, they do not have a chance to rest. It is important for Aelin to recognise what is happening and why. Not actioning the problem has led to empathy fatigue and emotional exhaustion. Emotional exhaustion is one of the key aspects of [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FEmpathy_fatigue_and_emotional_exhaustion&amp;diff=2840411&amp;oldid=2832859 burnout], a long-term condition of existing in a constant state of high stress. 

Psychological science can support Aelin in recognising and mapping the symptoms they are experiencing, understand coping strategies to minimise the current and future effects to improve their wellbeing. Understanding the symptoms will also support their role as a social worker, providing more tools for the people they support on a day-to-day basis.

{{RoundBoxTop|theme=3}}
'''Focus questions'''

* Why do people become emotionally exhausted?
* What is the relationship between empathy fatigue and emotional exhaustion?
* What role does emotional labor play in emotional exhaustion?
* How does understanding emotional labor and empathy fatigue work to reduce the effects of emotional exhaustion?
{{RoundBoxBottom}}

== Emotional Exhaustion ==
'''Talk about stress and its role in emotional exhaustion'''

Emotional exhaustion is a major contributing factor in burnout and can be recognised as &quot;''definition''&quot;(De Beer et al., 2024). As a major factor, its symptoms are similar to burnout and stress. '''How would you recognise that someone is emotionally exhausted''' The major symptoms include: &quot;''dot point list of biggest symptoms''&quot; 

There are many theories that attempt to explain why emotional exhaustion occurs. Two of these theories with good evidence are the [[wikipedia:Conservation_of_resources_theory|Conservation of resources stress model]] (Halbesleben et al., 2014; Hobfoll, 1989) and the [[wikipedia:Job_demands-resources_model|Job Demands-Resources model]] (Demerouti et al., 2001).

=== Conservation of resources stress model   ===

* Psychological stress occurs when individuals lose valued resources (Halbesleben et al., 2014; Hobfoll, 1989)
** Discuss what resources are (e.g. social relationships)
** Discuss how losing resources leads to increased vulnerability to stress
** discuss gain and loss spirals

=== Job Demands-Resources model ===

* Talk about Job demands and job resources (Demerouti et al., 2001)
** Why do we actually feel exhausted after a sustained empathic response?
** Job demands require sustained physical or psychological effort
*** Empathic response can be a job demand
** Job resources support achieving work goals or reduce job demands
* Discuss how the model looks at prolonged job demands depleting energy leading to exhaustion/burnout (Schaufeli, 2017)
* Discuss how the model treats job resources as a mediating factor for reducing the negative effects of job demands 

== Empathy Fatigue ==

* Before understanding empathy fatigue, define what empathy is (what are the theories behind empathy? Why do we have empathy? What theory am I using)
** Individual ability to imagine or understand another person's feelings and/or emotions (Riess, 2017; Shao et al., 2024)

=== What are the types of empathy? ===

* Affective empathy - emotional reaction to someone else's mental state (Shao et al., 2024) 
* Cognitive empathy - understand someone's feelings or emotions (Cui et al., 2022)
* Integrating the two - &quot;affective component is the essence of empathy, and the cognitive component is a process through which that essence comes into being&quot; (Bošnjaković &amp; Radionov, 2018) 
** (Author's note: change quote into paraphrasing)

=== What is compassion fatigue? (theories of compassion fatigue) ===

* Distinction between empathy and compassion fatigue
* Compassion fatigue is closely related to Secondary traumatic stress usually found in healthcare professionals (Figley, 2002)
** Compassion fatigue is to Empathy fatigue as emotional exhaustion is to burnout

* Make it clear that Aelin is experiencing Compassion Fatigue vs Empathy fatigue (they are the same but different)

(Author's note: include an update to the scenario here!)

'''Empathy fatigue questions'''.

Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=simple&gt;
{Surface acting is when the observer actually feels the emotion:
|type=&quot;()&quot;}
- True
+ False

{Compassion fatigue and empathy fatigue are synonymous:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

== Emotional labor as a mediating factor between Empathy fatigue and emotional exhaustion ==
What is emotional labor (Hochschild, 2012)

=== Types of acting ===
* Surface acting
** This is where emotive dissonance comes into play
** Leads to emotional exhaustion (Kenworthy et al., 2014)
** &quot;Should&quot; language - in this situation, this is what I ''should'' feel

* Deep acting
** People who 'deep act', as in genuinely change the way they feel (match the feelings they have with the feelings that they need to display) often report positive relationships with emotional labor
** Actual language - in this situation, this is what I ''actually'' feel
Discuss the differences in gender norms and expectations in relationships

=== The mediating effect of emotional labor ===
Surface acting does not mediate the effect (high surface acting leads to emotional exhaustion) whereas the inverse is true for deep acting (Wrobel, 2013)

=== Emotional contagion ===
If space/time permits discuss the role of emotional contagion
* Emotional contagion (Panksepp and Lahvis, 2011)
** emotions can spread (expand, combines empathy and acting)
** “the tendency to automatically mimic and synchronize expressions, vocalizations, postures, and movements with those of another person’s and, consequently, to converge emotionally.” (Elaine Hatfield, 1993)

== Strategies for combating Empathy fatigue and emotional fatigue ==

* Talk about emotion regulation (Gross, 1998) and mood regulation strategies as a way to deal with coping (Wrobel, 2013) (Author's note: need more research/references for this section)
* Talk about breaks
** Rest and downtime from not performing emotional labor regenerates
* How do we reduce the amount of emotional labor we're performing (Jeung et al., 2018)
** Communication/boundaries
** Reducing surface acting (allowing ourselves to feel how we actually feel and reduce emotive dissonance)

=== Strategies in the workplace ===
* Discuss types of strategies that are available in the workplace (organisation models)
* SCARF model (Aplin-Houtz, 2025)
** Link back to COR and JDR models e.g. praise could be a job resource vs criticism could be a job demand
*Reduce workload to reduce emotional exhaustion, and by extension reduce emotional fatigue.

==Figures (for reference before final assessment)==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]]

* Use figures to illustrate concepts, add interest, and to serve as examples
* Figures can show photos, diagrams, graphs, video, audio, etc.
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Caption figures (use '''Figure #'''. and explain the relevance of the image to the text)
* Images must be embedded from [[commons:|Wikimedia Commons]]
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Cite each figure at least once in the main text (e.g., see Figure 2)

== Learning features (for reference before final assessment) ==
Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter.

{{anchor|Scenarios}}
;Scenarios
* Scenarios, case studies, or examples describe concepts in action
* Can be real or fictional; if real, provide citations
* Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages)
* Present using [[#Feature boxes|feature boxes]]

{{anchor|Feature box}}
;Feature boxes
* Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect
* Consider using feature boxes for:
** [[#Scenarios|Scenarios]], case studies, or examples
** Focus questions
** Tips
** Quiz questions
** Take-home messages

;Embedded links
* When key words are introduced, use [[Help:Links|interwiki links]] to:
** Wikipedia articles (e.g., &quot;An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]&quot;) or
** Related book chapters (e.g., &quot;If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]&quot;)

{{anchor|Tables}}
;Tables
* Use to tables to organise and summarise information
* Cite each table at least once in the main text (e.g., see Table 1)
* Tables should be captioned
* [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted

'''Table 1''' 

A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., 

The 2 x 2 Johari Window Model Showing Knowing x Self/Other

{| class=&quot;wikitable&quot; style=&quot;margin: auto;
|-
! !! Known to self !! Not known to self
|-
| '''Known to others''' || Open area || Blind spot
|-
| '''Not known to others''' || Hidden area || Unknown
|}

;Quizzes
* Using one or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=simple&gt;
{The purpose of quizzes is to provide an interactive learning feature:
|type=&quot;()&quot;}
+ True
- False

{Long and complex quiz questions are recommended:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

==Conclusion==

* Summarise what empathy fatigue is, and why people become emotionally exhausted (+ the role of emotional labor)
* Summarise the symptoms and how to recognise them in yourself and someone else
* Emphasise and summarise psychological strategies to support someone going through emotional exhaustion
* Summarise ways to prevent emotional exhaustion from happening
* Overall message is: 
*# What is emotional exhaustion
*# how do you recognise it
*# how do you treat it
*# how do you prevent it

* Link back to the focus questions

==See also==
* [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Metacognition_and_emotional_regulation&amp;oldid=2756264 Metacognition and emotional regulation] (Book chapter, 2026) {{ic|Use an internal link style as shown in Tutorial 2}}
* [[wikipedia:Conservation_of_resources_theory|Conservation of resources theory]] (Wikipedia)
* [[wikipedia:Job_demands-resources_model|Job demands-resources model]] (Wikipedia)

==References==
{{Hanging indent|1=

Aplin-Houtz, M. (2025). Unraveling the SCARF: How dimensions of the SCARF model influence the relationship between workplace exclusion and turnover intentions. Journal of Management &amp; Organization, 31(6), 2699–2725. https://doi.org/10.1017/jmo.2025.10026

Bošnjaković, J., &amp; Radionov, T. (2018). Empathy: Concepts, Theories and Neuroscientific Basis. Alcoholism (Zagreb), 54(2), 123–150. https://doi.org/10.20471/de..2018.54.02.04

Cui, F., Huang, X., Jing, Y., Luo, Y., Liu, J., &amp; Gu, R. (2022). How resource sharing resists scarcity: the role of cognitive empathy and its neurobiological mechanisms. Cerebral Cortex (New York, N.Y. 1991), 32(23), 5330–5342. https://doi.org/10.1093/cercor/bhac017

De Beer, L. T., van der Vaart, L., Escaffi-Schwarz, M., De Witte, H., &amp; Schaufeli, W. B. (2024). Maslach Burnout Inventory - General Survey. European Journal of Psychological Assessment : Official Organ of the European Association of Psychological Assessment, 40(5), 360–375. https://doi.org/10.1027/1015-5759/a000797

Demerouti, E., Bakker, A. B., Nachreiner, F., &amp; Schaufeli, W. B. (2001). The Job Demands-Resources Model of Burnout. Journal of Applied Psychology, 86(3), 499–512. https://doi.org/10.1037/0021-9010.86.3.499

Figley, C. R. (2002). Compassion fatigue: Psychotherapists’ chronic lack of self care. Journal of Clinical Psychology, 58(11), 1433–1441. https://doi.org/10.1002/jclp.10090

Grandey, A. A. (2003). When ‘the show must go on’: surface acting and deep acting as determinants of emotional exhaustion and peer-rated service delivery. Academy of Management Journal, 46(1), 86–96. https://doi.org/10.5465/30040678

Gross, J. J. (1998). The emerging field of emotion regulation: An integrative review. Review of General Psychology, 2(3), 271–299. https://doi.org/10.1037/1089-2680.2.3.271

Halbesleben, J. R. B., Neveu, J.-P., Paustian-Underdahl, S. C., &amp; Westman, M. (2014). Getting to the “COR”: Understanding the Role of Resources in Conservation of Resources Theory. Journal of Management, 40(5), 1334–1364. https://doi.org/10.1177/0149206314527130

Hatfield, E., Cacioppo, J. T., &amp; Rapson, R. L. (1993). Emotional Contagion. Current Directions in Psychological Science : A Journal of the American Psychological Society, 2(3), 96–99. https://doi.org/10.1111/1467-8721.ep10770953

Hobfoll, S. E. (1989). Conservation of Resources: A New Attempt at Conceptualizing Stress. The American Psychologist, 44(3), 513–524. https://doi.org/10.1037/0003-066X.44.3.513

Hochschild, A. R. (2012). The managed heart  : commercialization of human feeling (Updated, with a new preface.). University of California Press.

Jeung, D.-Y., Kim, C., &amp; Chang, S.-J. (2018). Emotional Labor and Burnout: A Review of the Literature. Yonsei Medical Journal, 59(2), 187–193. https://doi.org/10.3349/ymj.2018.59.2.187

Lavelle, J. J., Rupp, D. E., Herda, D. N., Pandey, A., &amp; Lauck, J. R. (2021). Customer Injustice and Employee Performance: Roles of Emotional Exhaustion, Surface Acting, and Emotional Demands–Abilities Fit. Journal of Management, 47(3), Article 0149206319869426. https://doi.org/10.1177/0149206319869426

Panksepp, J. B., &amp; Lahvis, G. P. (2011). Rodent empathy and affective neuroscience. Neuroscience and Biobehavioral Reviews, 35(9), 1864–1875. https://doi.org/10.1016/j.neubiorev.2011.05.013

Riess, H. (2017). The Science of Empathy. Journal of Patient Experience, 4(2), 74–77. https://doi.org/10.1177/2374373517699267

Schaufeli, W. B. (2017). Applying the job demands-resources model: a “how to” guide to measuring and tackling work engagement and burnout. Organizational Dynamics, 46(2), 120–132. https://doi.org/10.1016/j.orgdyn.2017.04.008

Shao, M., Li, L., Li, X., Wei, Z., Wang, J., Hong, M., Liu, X., &amp; Meng, J. (2024). The effect of top-down attention on empathy fatigue. Cerebral Cortex (New York, N.Y. 1991), 34(1), Article bhad441. https://doi.org/10.1093/cercor/bhad441

Wharton, A. S. (2009). The Sociology of Emotional Labor. Annual Review of Sociology, 35(1), 147–165. https://doi.org/10.1146/annurev-soc-070308-115944

Wrobel, M. (2013). Can empathy lead to emotional exhaustion in teachers? The mediating role of emotional labor. International Journal of Occupational Medicine and Environmental Health, 26(4), 581–592. https://doi.org/10.2478/s13382-013-0123-1

}}

==External links==
Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Burnout]]
[[Category:Motivation and emotion/Book/Empathy]]</text>
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        <id>3106785</id>
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__TOC__

==Overview==
{{RoundBoxTop|theme=3}}
[[File:Exhausted smartphone user.JPG|right|thumb|150px|'''Figure 1'''. An emotionally exhausted Aelin at the end of the work day]]

; Scenario

Aelin, a 23-year-old social worker employed at headspace {{ic|Link to the Wikipedia article to help explain what this term means}}, works with approximately 20 {{ic|Explain what sort of}}Imagine you are only 23 years old and are working as a social worker at headspace. You see around 20 clients each week, many of whom have experienced rough living conditions.

During your first six months in this role, you felt highly motivated and excited to help people in need. You are an excellent active listener and can easily remember details about your clients Live’s. You are also good at recognising signs of distress in your client’s body language and adjust yours in order to show warmth and understanding. 

As you progress in your role, you take on more cases that involve complex past traumas. The workload becomes too much for you to get done at work, but you don’t want your clients to miss out, so you take your work home to complete it in the evenings. Your workload increases again and you now start doing work on your weekends as well. After several months of working this way, you start to notice you feel exhausted every morning before you have even started work.
 
You then start to notice you’re responding to people at work differently. Instead of your usual energised active listening response you feel frustrated, empathetic and detached. After work you are too drained to socialise with friends. This begins to worry you. What if you won’t be able to continue working as a social worker?  

{{RoundBoxBottom}}

Aelin is experiencing '''emotional exhaustion''' from a sustained empathic response. 

Due to the nature of Aelin's work, they are constantly engaged in an empathic response. Empathic responses require cognitive and physical resources to sustain. Because Aelin is taking their work home and not resting on weekends, they do not have a chance to rest. It is important for Aelin to recognise what is happening and why. Not actioning the problem has led to empathy fatigue and emotional exhaustion. Emotional exhaustion is one of the key aspects of [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FEmpathy_fatigue_and_emotional_exhaustion&amp;diff=2840411&amp;oldid=2832859 burnout], a long-term condition of existing in a constant state of high stress. 

Psychological science can support Aelin in recognising and mapping the symptoms they are experiencing, understand coping strategies to minimise the current and future effects to improve their wellbeing. Understanding the symptoms will also support their role as a social worker, providing more tools for the people they support on a day-to-day basis.

{{RoundBoxTop|theme=3}}
'''Focus questions'''

* Why do people become emotionally exhausted?
* What is the relationship between empathy fatigue and emotional exhaustion?
* What role does emotional labor play in emotional exhaustion?
* How does understanding emotional labor and empathy fatigue work to reduce the effects of emotional exhaustion?
{{RoundBoxBottom}}

== Emotional Exhaustion ==
'''Talk about stress and its role in emotional exhaustion'''

Emotional exhaustion is the core component of burnout and can be recognised as &quot;''definition''&quot;(De Beer et al., 2024; Seidler et al., 2014). As a major factor, its symptoms are similar to burnout and stress. '''How would you recognise that someone is emotionally exhausted''' The major symptoms include: &quot;''dot point list of biggest symptoms''&quot; 

Someone experiencing these symptoms are at a higher risk of cardiovascular disease, etc. xyz (why bad)

There are many theories that attempt to explain why emotional exhaustion occurs. Two of these theories with good evidence are the [[wikipedia:Conservation_of_resources_theory|Conservation of resources stress model]] (Hobfoll, 1989) and the [[wikipedia:Job_demands-resources_model|Job Demands-Resources model]] (Demerouti et al., 2001).

=== Conservation of resources stress model   ===

* Psychological stress occurs when individuals lose valued resources (Halbesleben et al., 2014; Hobfoll, 1989)
** Discuss what resources are (e.g. social relationships)
** Discuss how losing resources leads to increased vulnerability to stress
** discuss gain and loss spirals

=== Job Demands-Resources model ===

* Talk about Job demands and job resources (Demerouti et al., 2001)
** Why do we actually feel exhausted after a sustained empathic response?
** Job demands require sustained physical or psychological effort
*** Empathic response can be a job demand
** Job resources support achieving work goals or reduce job demands
* Discuss how the model looks at prolonged job demands depleting energy leading to exhaustion/burnout (Schaufeli, 2017)
* Discuss how the model treats job resources as a mediating factor for reducing the negative effects of job demands 

== Empathy Fatigue ==

* Empathy is understood as ... (is there a link to another Wikiversity page? double check)
* Empathy Fatigue is understood as ... . 
* Before understanding empathy fatigue, define what empathy is (what are the theories behind empathy? Why do we have empathy? What theory am I using)
** Individual ability to imagine or understand another person's feelings and/or emotions (Riess, 2017; Shao et al., 2024)

=== What are the types of empathy? ===

* Affective empathy - emotional reaction to someone else's mental state (Shao et al., 2024) 
* Cognitive empathy - understand someone's feelings or emotions (Cui et al., 2022)
* Integrating the two - &quot;affective component is the essence of empathy, and the cognitive component is a process through which that essence comes into being&quot; (Bošnjaković &amp; Radionov, 2018) 
** (Author's note: change quote into paraphrasing)

=== What is compassion fatigue? (theories of compassion fatigue) ===

* Distinction between empathy and compassion fatigue
* Compassion fatigue is closely related to Secondary traumatic stress usually found in healthcare professionals (Figley, 2002)
** Compassion fatigue is to Empathy fatigue as emotional exhaustion is to burnout

* Make it clear that Aelin is experiencing Compassion Fatigue vs Empathy fatigue (they are the same but different)

(Author's note: include an update to the scenario here!)

'''Empathy fatigue questions'''.

Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=simple&gt;
{Surface acting is when the observer actually feels the emotion:
|type=&quot;()&quot;}
- True
+ False

{Compassion fatigue and empathy fatigue are synonymous:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

== Emotional labor as a mediating factor between Empathy fatigue and emotional exhaustion ==
What is emotional labor (Hochschild, 2012)

=== Types of acting ===
* Surface acting
** This is where emotive dissonance comes into play
** Leads to emotional exhaustion (Kenworthy et al., 2014)
** &quot;Should&quot; language - in this situation, this is what I ''should'' feel

* Deep acting
** People who 'deep act', as in genuinely change the way they feel (match the feelings they have with the feelings that they need to display) often report positive relationships with emotional labor
** Actual language - in this situation, this is what I ''actually'' feel
Discuss the differences in gender norms and expectations in relationships

=== The mediating effect of emotional labor ===
Surface acting does not mediate the effect (high surface acting leads to emotional exhaustion) whereas the inverse is true for deep acting (Wrobel, 2013)

=== Emotional contagion ===
If space/time permits discuss the role of emotional contagion
* Emotional contagion (Panksepp and Lahvis, 2011)
** emotions can spread (expand, combines empathy and acting)
** “the tendency to automatically mimic and synchronize expressions, vocalizations, postures, and movements with those of another person’s and, consequently, to converge emotionally.” (Elaine Hatfield, 1993)

== Strategies for combating Empathy fatigue and emotional fatigue ==

* Talk about emotion regulation (Gross, 1998) and mood regulation strategies as a way to deal with coping (Wrobel, 2013) (Author's note: need more research/references for this section)
* Talk about breaks
** Rest and downtime from not performing emotional labor regenerates
* How do we reduce the amount of emotional labor we're performing (Jeung et al., 2018)
** Communication/boundaries
** Reducing surface acting (allowing ourselves to feel how we actually feel and reduce emotive dissonance)

=== Strategies in the workplace ===
* Discuss types of strategies that are available in the workplace (organisation models)
* SCARF model (Aplin-Houtz, 2025)
** Link back to COR and JDR models e.g. praise could be a job resource vs criticism could be a job demand
*Reduce workload to reduce emotional exhaustion, and by extension reduce emotional fatigue.

==Figures (for reference before final assessment)==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]]

* Use figures to illustrate concepts, add interest, and to serve as examples
* Figures can show photos, diagrams, graphs, video, audio, etc.
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Caption figures (use '''Figure #'''. and explain the relevance of the image to the text)
* Images must be embedded from [[commons:|Wikimedia Commons]]
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Cite each figure at least once in the main text (e.g., see Figure 2)

== Learning features (for reference before final assessment) ==
Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter.

{{anchor|Scenarios}}
;Scenarios
* Scenarios, case studies, or examples describe concepts in action
* Can be real or fictional; if real, provide citations
* Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages)
* Present using [[#Feature boxes|feature boxes]]

{{anchor|Feature box}}
;Feature boxes
* Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect
* Consider using feature boxes for:
** [[#Scenarios|Scenarios]], case studies, or examples
** Focus questions
** Tips
** Quiz questions
** Take-home messages

;Embedded links
* When key words are introduced, use [[Help:Links|interwiki links]] to:
** Wikipedia articles (e.g., &quot;An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]&quot;) or
** Related book chapters (e.g., &quot;If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]&quot;)

{{anchor|Tables}}
;Tables
* Use to tables to organise and summarise information
* Cite each table at least once in the main text (e.g., see Table 1)
* Tables should be captioned
* [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted

'''Table 1''' 

A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., 

The 2 x 2 Johari Window Model Showing Knowing x Self/Other

{| class=&quot;wikitable&quot; style=&quot;margin: auto;
|-
! !! Known to self !! Not known to self
|-
| '''Known to others''' || Open area || Blind spot
|-
| '''Not known to others''' || Hidden area || Unknown
|}

;Quizzes
* Using one or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=simple&gt;
{The purpose of quizzes is to provide an interactive learning feature:
|type=&quot;()&quot;}
+ True
- False

{Long and complex quiz questions are recommended:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

==Conclusion==

* Summarise what empathy fatigue is, and why people become emotionally exhausted (+ the role of emotional labor)
* Summarise the symptoms and how to recognise them in yourself and someone else
* Emphasise and summarise psychological strategies to support someone going through emotional exhaustion
* Summarise ways to prevent emotional exhaustion from happening
* Overall message is: 
*# What is emotional exhaustion
*# how do you recognise it
*# how do you treat it
*# how do you prevent it

* Link back to the focus questions

==See also==
* [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Metacognition_and_emotional_regulation&amp;oldid=2756264 Metacognition and emotional regulation] (Book chapter, 2026) {{ic|Use an internal link style as shown in Tutorial 2}}
* [[wikipedia:Conservation_of_resources_theory|Conservation of resources theory]] (Wikipedia)
* [[wikipedia:Job_demands-resources_model|Job demands-resources model]] (Wikipedia)

==References==
{{Hanging indent|1=

Aplin-Houtz, M. (2025). Unraveling the SCARF: How dimensions of the SCARF model influence the relationship between workplace exclusion and turnover intentions. Journal of Management &amp; Organization, 31(6), 2699–2725. https://doi.org/10.1017/jmo.2025.10026

Bošnjaković, J., &amp; Radionov, T. (2018). Empathy: Concepts, Theories and Neuroscientific Basis. Alcoholism (Zagreb), 54(2), 123–150. https://doi.org/10.20471/de..2018.54.02.04

Cui, F., Huang, X., Jing, Y., Luo, Y., Liu, J., &amp; Gu, R. (2022). How resource sharing resists scarcity: the role of cognitive empathy and its neurobiological mechanisms. Cerebral Cortex (New York, N.Y. 1991), 32(23), 5330–5342. https://doi.org/10.1093/cercor/bhac017

De Beer, L. T., van der Vaart, L., Escaffi-Schwarz, M., De Witte, H., &amp; Schaufeli, W. B. (2024). Maslach Burnout Inventory - General Survey. European Journal of Psychological Assessment : Official Organ of the European Association of Psychological Assessment, 40(5), 360–375. https://doi.org/10.1027/1015-5759/a000797

Demerouti, E., Bakker, A. B., Nachreiner, F., &amp; Schaufeli, W. B. (2001). The Job Demands-Resources Model of Burnout. Journal of Applied Psychology, 86(3), 499–512. https://doi.org/10.1037/0021-9010.86.3.499

Figley, C. R. (2002). Compassion fatigue: Psychotherapists’ chronic lack of self care. Journal of Clinical Psychology, 58(11), 1433–1441. https://doi.org/10.1002/jclp.10090

Grandey, A. A. (2003). When ‘the show must go on’: surface acting and deep acting as determinants of emotional exhaustion and peer-rated service delivery. Academy of Management Journal, 46(1), 86–96. https://doi.org/10.5465/30040678

Gross, J. J. (1998). The emerging field of emotion regulation: An integrative review. Review of General Psychology, 2(3), 271–299. https://doi.org/10.1037/1089-2680.2.3.271

Halbesleben, J. R. B., Neveu, J.-P., Paustian-Underdahl, S. C., &amp; Westman, M. (2014). Getting to the “COR”: Understanding the Role of Resources in Conservation of Resources Theory. Journal of Management, 40(5), 1334–1364. https://doi.org/10.1177/0149206314527130

Hatfield, E., Cacioppo, J. T., &amp; Rapson, R. L. (1993). Emotional Contagion. Current Directions in Psychological Science : A Journal of the American Psychological Society, 2(3), 96–99. https://doi.org/10.1111/1467-8721.ep10770953

Hobfoll, S. E. (1989). Conservation of Resources: A New Attempt at Conceptualizing Stress. The American Psychologist, 44(3), 513–524. https://doi.org/10.1037/0003-066X.44.3.513

Hochschild, A. R. (2012). The managed heart  : commercialization of human feeling (Updated, with a new preface.). University of California Press.

Jeung, D.-Y., Kim, C., &amp; Chang, S.-J. (2018). Emotional Labor and Burnout: A Review of the Literature. Yonsei Medical Journal, 59(2), 187–193. https://doi.org/10.3349/ymj.2018.59.2.187

Lavelle, J. J., Rupp, D. E., Herda, D. N., Pandey, A., &amp; Lauck, J. R. (2021). Customer Injustice and Employee Performance: Roles of Emotional Exhaustion, Surface Acting, and Emotional Demands–Abilities Fit. Journal of Management, 47(3), Article 0149206319869426. https://doi.org/10.1177/0149206319869426

Panksepp, J. B., &amp; Lahvis, G. P. (2011). Rodent empathy and affective neuroscience. Neuroscience and Biobehavioral Reviews, 35(9), 1864–1875. https://doi.org/10.1016/j.neubiorev.2011.05.013

Riess, H. (2017). The Science of Empathy. Journal of Patient Experience, 4(2), 74–77. https://doi.org/10.1177/2374373517699267

Schaufeli, W. B. (2017). Applying the job demands-resources model: a “how to” guide to measuring and tackling work engagement and burnout. Organizational Dynamics, 46(2), 120–132. https://doi.org/10.1016/j.orgdyn.2017.04.008

Shao, M., Li, L., Li, X., Wei, Z., Wang, J., Hong, M., Liu, X., &amp; Meng, J. (2024). The effect of top-down attention on empathy fatigue. Cerebral Cortex (New York, N.Y. 1991), 34(1), Article bhad441. https://doi.org/10.1093/cercor/bhad441

Wharton, A. S. (2009). The Sociology of Emotional Labor. Annual Review of Sociology, 35(1), 147–165. https://doi.org/10.1146/annurev-soc-070308-115944

Wrobel, M. (2013). Can empathy lead to emotional exhaustion in teachers? The mediating role of emotional labor. International Journal of Occupational Medicine and Environmental Health, 26(4), 581–592. https://doi.org/10.2478/s13382-013-0123-1

}}

==External links==
Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

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__TOC__

==Overview==
{{RoundBoxTop|theme=3}}&lt;div style=&quot;border: 2px solid #a2a9b1; border-radius: 15px; padding: 12px; background-color: #f8f9fa; width: 150px; float: right; margin: 0.6em 0 10px 10px;&quot;&gt;
[[File:Student rushing to school.png|center|150px]]
&lt;div style=&quot;font-size: 85%; color: #333333; line-height: 1.4; padding-top: 8px; text-align: left;&quot;&gt;
'''Figure 1.''' ''A student rushing to school (AI-Generated).''
&lt;/div&gt;
&lt;/div&gt;
;Picture this

Your alarm rings at 8:30am, just in time to start school at 9:00am. You roll out of bed, get dressed, brush your teeth, and grab a snack before heading out the door to leave for school. The walk to school takes 5 minutes, and by this time, it is 8:50am. With just 5 minutes to spare, you arrive at school and walk into class. You begin to chat with Jane, a fellow classmate and neighbour, who tells you that she arrived at school at 8:00am; well before you were even awake. You sit there while she talks about her morning, thinking “Why can I never make it to school as early as Jane does?”. You and Jane live next door to each other, are in the same grade, and attend the same classes. You are only ever on time when school finishes, leaving right as the final bell rings, while Jane often stays back after class. So, if nothing about your situation is really that different from Jane’s, why is she so much more motivated?

{{RoundBoxBottom}}

=== Parallel lives, different drives ===
[[Motivation]] is widely understood as an intrinsic drive or desire to change a particular aspect of one’s life, whether this be the self or the environment. Through motivation, we can initiate, direct, and sustain our behaviour towards change-related goals (Reeve, 2024). While motivation is often ‘neatly’ defined in literature, it becomes increasingly complex as one considers ''why'' motivation occurs. Particularly, when looking at why individuals or groups who share parallel lives have different drives, motivation becomes further intertwined with an array of psychological phenomena.

For instance, the ‘You vs. Jane’ scenario illustrates that despite environmental similarities, you and Jane have markedly different school routines and motivational levels. This infers that the source of motivation may not lie in the context itself, but rather in the underlying values which drive motivation. However, motivation does not occur in isolation; situations and environments, or ‘situational values’, also communicate what is valued or expected (Strack &amp; Gennerich, 2011). Therefore, we can expect that when personal and situational values align or conflict, this may influence motivation. Thus, in this chapter, we explore several notable psychological theories purported as both solutions and explanations for why value congruence or incongruence occurs

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📍 '''Focus questions'''

* What are personal and situational values?
* How do personal and situational values become aligned or misaligned?
* How does value congruence influence motivation?
* Why does motivation differ between individuals?
* How can understanding value congruence help support motivation?
{{RoundBoxBottom}}

==What are personal and situational values?==
In the realm of motivational science, [[wikipedia:Value_(ethics)|values]] are broadly considered as the relatively enduring beliefs about what is considered important and desirable in guiding goals, behaviour, and decisions (Schwartz, 2012). Values are highly subjective to an individual, making their effect on motivation uniquely idiosyncratic. Therefore, in understanding how values influence motivation, we must first differentiate between the overarching types: personal and situational values.

=== Understanding personal values ===
Many theorists have aimed to compose a set of ‘standard’ values that characterise certain groups, societies, and individuals. Notably, [[wikipedia:Shalom_H._Schwartz|Schwartz]] (2012) devised a Theory of Basic Human Values, in which he identified 10 universal values that are recognised across all cultures. These consist of self-direction, stimulation, hedonism, achievement, power, security, conformity, tradition, benevolence, and universalism (see Table 1). Schwartz emphasises that these values exist on a continuum, which is visualised through a circular structure. However, Kajonius et al. (2015) stipulate that unlike personality traits, values are not genetically heritable. Values are thereby likely to be shaped by environmental and social influences, often referred to as ‘situational values’.

'''Table 1.'''                                                                                                                                                                                                 ''Types of personal values.''
{| class=&quot;wikitable&quot;
|+
! colspan=&quot;2&quot; |Schwartz (2012) proposes 10 basic personal values:
|-
|1. Self-Direction
|Independent thought, action-choosing, creating, and exploring.
|-
|2. Stimulation
|Excitement, novelty, and challenge in life.
|-
|3. Hedonism
|Pleasure of sensuous gratification for onself.
|-
|4. Achievement
|Personal success through demonstration of competence according to social standards and norms. 
|-
|5. Power
|Social status and prestige, control or dominance over people and resources.
|-
|6. Security
|Safety, harmony, and stability of society, of relationships, and of the self.
|-
|7. Conformity
|Restraint of actions, inclinations, and impulses that are likely to upset or harm other as well as violate social expectations or norms.
|-
|8. Tradition
|Respect, commitment, and acceptance of the customs and ideas that one's culture or religion provides.
|-
|9. Benevolence
|Preserving and enhancing the welfare of those with whom one is in frequent personal contact with (i.e., the 'in-group').
|-
|10. Universalism
|Understanding, appreciation, tolerance, and protection for the welfare of all people and for nature.                                              
|}
'''Figure 2.'''                                                                                                                                                                                        ''Schwartz's (2012) theoretical model of relations among value types.''

[[File:Circular structure of values.png|center|frameless|550x550px]]

=== Understanding situational values ===
Just as values vary among individuals, they also vary among situations. Strack and Gennerich (2011) discuss this variation as ‘situational values’; values that become relevant or activated within a specific context. These values are determined by the characteristics, demands, or pressures of a situation, influencing what behaviours are deemed as situation-appropriate. While personal values are considered to be enduring, they can be overridden in situations with strong demands or expectations. For instance, Jane may personally value self-direction, but when she goes to school where conformity is strongly expected, conformity then becomes a situationally-relevant value. In this context, values are transient, eliciting positive or negative [[wikipedia:Affect_(psychology)|affect]] depending on how they align with one’s personal values (Montgomery et al., 2020).

=== From values to goals and behaviour ===
So, how do our personal and situational values translate into goals and behaviour? Schwartz (2012) argues that values are representative of desirable goals, and it is these goals that motivate behaviour and action. Values act as a moral compass of sorts, guiding how we select or evaluate people, actions, policies, and events. This compass is at the forefront of many decisions; what is good or bad, worth engaging in or avoiding, justified or illegitimate? To cope with human existence needs, people develop appropriate goals to communicate with others about their goals, and gain assistance in pursuing these goals. Therefore, an alignment between our personal and situational values is of the utmost importance in driving motivation. A misalignment or conflict between these values can have implications for our initiation, direction, and persistence of goals; aspects that are central to motivation.  

== How do personal and situational values become aligned? ==
In discussing an alignment between personal and situational values, the term ‘value congruence’ becomes increasingly relevant. Value congruence refers to the degree to which an individual’s personal values match with those reflected by their environment or by a particular situation (van Vianen, 2018).

=== Value congruence ===
The compatibility between personal and situational values can be conceptualised through the [[wikipedia:Person–environment_fit|person-environment (P-E) fit]], primarily developed to examine ‘fit’ in the following domains; health and stress, work adjustment, vocational choice, and organisational culture. The P-E fit theory posits that individuals have an inherent drive to fit their environments and to seek environments that align with their own characteristics. van Vianen (2018) argues that value congruence stems from a need to increase consistency among aspects of the self (i.e., attitudes, beliefs) and control over one’s life. Furthermore, fit facilitates an intrinsic need to belong; by having similar values to others in a group, we gain a sense of belonging.

[[File:Person-Organisation Fit Diagram.jpg|600x600px|thumb|'''Figure 3.''' Person-organisation fit model|alt=Figure 3. Person-organisation fit model|center]]

Despite the positive implications of P-E fit (i.e., happiness, life satisfaction), it must be noted that value congruence is highly conditional and does not necessarily guarantee P-E fit. For instance, Jane personally values security, as she regards safety, harmony, and the stability of society and relationships as important (see Table 1). Jane’s school also values security, allowing for congruency between Jane’s personal and situational values. However, a student in Jane’s class constantly teases her for being ‘too uptight’, as she arrives an hour early to school each day. Therefore, this singular aspect of her environment (i.e., the class bully) has misaligned Jane’s P-E fit to some extent.

=== Value incongruence ===
The conditional nature of value congruence introduces the potential for value incongruence, in which personal and situational values do not align. Value incongruence can often be observed in the workplace, where aspects of employees’ personal lives do not align with that of their work environment. van Vianen (2018) suggests that people are attracted to, selected by, and remain in organisations that match their personal attributes. When these attributes do not match, employees may experience reduced job satisfaction and commitment, lowered performance levels, and increased intentions to quit. However, personality, financial aspects, and the economy have been argued to mitigate value incongruence. Thus, value incongruence is not solely determined by a match between personal and situational values, but also by a range of additional factors.

==   How does value congruence influence motivation? ==
One may ask, ‘how does value congruence or incongruence influence motivation?’. In solving this motivation equation, the [[wikipedia:Self-determination_theory|Self-Determination Theory]] (SDT) becomes applicable. With strong ties to humanistic psychology, the SDT is concerned with examining the social conditions in which humans are able or unable to flourish. In particular, people source motivation through the fulfilment of three universal psychological needs; autonomy, competence, and relatedness (Ryan &amp; Deci, 2018). Furthermore, this theory differentiates between autonomous and controlled motivation, the key mechanisms in determining psychological growth, wellbeing, and engagement outcomes (Hagger et al., 2014).

[[File:Self-Determination model.png|center|600px|'''Figure 4.''' Self-determination model.]]

=== Why value congruence supports autonomous motivation ===
So, how does SDT relate to value congruence? Essentially, the better the alignment between personal and situational values, the more likely an individual is to engage in behaviours based on their own willingness. Li et al. (2015) consider this sort of engagement as autonomous motivation, where behaviour is self-determined and consistent with intrinsic values. Following on from the Jane scenario, perhaps Jane ''chooses'' to be early for school each day, as she values self-direction and achievement. Her teachers often praise students that {{g}} effectively manage their time, and by doing so, Jane can fulfil her need for autonomy and competence. Given that autonomous motivation is deeply rooted in intrinsic motivation, Jane’s drive is inherent rather than forced by external pressures (e.g., her peers, teachers).

'''Table 2.'''                                                                                                                                                                                           ''Examples of autonomous vs. controlled motivation.''
{| class=&quot;wikitable&quot;
|+
!Autonomous motivation
!Controlled motivation
|-
|Showing up to class because you want to learn new things.
|Showing up to class because the teacher marks attendence.
|-
|Putting your trash in the bin because you want to protect nature and animals.
|Putting your trash in the bin because others would judge you if they saw you littering
|-
|Attending a pilates session because you care about your physical wellbeing.
|Attending a pilates session just because your friends asked you to go. 
|}

=== Why value-aligned goals are more motivating ===
Goals are central to motivation, that is the initiation, direction, and persistence of pursuing goals. Drawing on Schwartz’s (2012) basic values theory, values are proposed to have an array of underlying motives. From these 10 basic values, four broad motivational dimensions were identified; openness to change, conservation, self-enhancement, and self-transcendence. It is these underlying motives that the Self-Concordance Theory (SCT) is based upon. The SCT asserts that people experience more satisfaction and higher levels of goal accomplishment when their goals are autonomously driven rather than controlled. As was established previously, value congruence is particularly relevant to autonomous motivation. Accordingly, we are more likely to pursue goals that align with our personal values, as they bring a sense of happiness and fulfilment (Downes et al., 2017).

=== When value incongruence is chosen ===
While value congruence is ideal for goal-striving and motivation, an alignment between personal and situational values is not always achievable. Rawolle et al. (2016) attest that motivational problems often stem from incongruence between implicit and explicit motives, goals, or values. Value incongruence can have adverse effects on well-being, identity achievement, life satisfaction, and volitional strength (i.e., reduced autonomous motivation). In this sense, people are not lazy or unmotivated but instead do not find the tasks personally meaningful or stimulating. This often occurs in the workplace, where an individual may choose a role that provides financial security yet does not intrinsically fulfil their needs.

So, why exactly do people choose to remain in environments where they experience value incongruence? In [[wikipedia:Two-factor_theory|Herzberg’s Two-Factor Theory]], an environment can provide certain hygiene factors that make leaving or change undesirable. Hygiene factors are typically work-related such as pay, reward systems, and interpersonal relationships; the latter can be applied to other contexts. Nonetheless, hygiene factors only prevent dissatisfaction, with true motivation and satisfaction arising from intrinsic factors such as value congruence (Jiang et al., 2023). Therefore, when someone stays in an environment that is incongruent with aspects of the self (i.e., values), they become stuck in a ‘limbo’ of sorts where they are not necessarily dissatisfied, but also not motivated. The remedy is often change; a change of environment, a change between personal and situational values, or a change of perspective.

== Why does motivation differ between individuals? ==
Naturally, individuals and groups differ substantially in the relative importance they assign to particular values (Schwartz, 2012). As we age, or values become increasingly stable yet simultaneously responsive to life events and other relevant aspects. Two people can have vastly different motivational reactions to the same situation, on the basis of their assigned value importance (Lake et al., 2025).

=== Individual differences in psychological factors ===
Beyond producing different motivational reactions, personal values are thought of as reliable psychological predictors across a variety of situations (Ponizovskiy et al., 2019). Particularly, our cognitive schemas or ‘mental frameworks’ play a role in strengthening our values over time through repeated value-expressive behaviour (Lake et al., 2025). Within these mental frameworks, value-related attitudes, subjective norms, and perceived behavioural control exist; components of the [[wikipedia:Theory_of_planned_behavior|Theory of Planned Behaviour]].

[[File:Theory of planned behaviour and value congruence model.png|center|600x600px|'''Figure 5.''' Theory of planned behaviour and value congruence: Derived from Ye et al., (2017).]]

In a tourism study of holiday intentions, Ye et al. (2017) found that people whose values aligned strongly with a holiday option had more positive attitudes toward it (e.g., strong openness to change values). Subjective norms toward a holiday option, such as opinions from family or friends, and perceived behavioural control were also related to personal values. Let’s say that Olivia is choosing between a luxury holiday and a volunteering holiday. She strongly values self-enhancement (i.e., achievement, power), which would come with a luxury holiday, yet her parents value benevolence (i.e., helping others). Olivia, therefore, chooses the volunteering holiday option as this better reflects her parents' values, though she changes her mind at the last minute as she doesn’t feel capable of pursuing a volunteer role (i.e., lack of perceived behavioural control). This scenario depicts how a range of psychological differences relate to value congruence, thereby shaping our behaviour and subsequent decisions.

=== Cultural and social differences in values ===
Humans tend to prefer performing familiar tasks or goals that feel ‘safe’ based on their respective experiences and social relationships. Schwartz’s (2012) motivational dimension ‘[[wikipedia:Self-enhancement|self-enhancement]]’ reflects this social influence, in which behaviour is motivated by social standards or norms, even when this behaviour is costly to others. These standards are often influenced by culture, determining how we prioritise or express our values. Konsky et al. (1999) suggest that [[wikipedia:Individualistic_culture|individualistic cultures]] encourage power, achievement, hedonism, stimulation, and self-direction. Conversely, [https://simple.wikipedia.org/wiki/Collectivism collectivist cultures] encourage benevolence, tradition, and conformity, with universalism and security pertaining to both culture types. Thus, individual differences in culture and socialisation can strongly dictate our value congruence, expression, and prioritisation.

== How can understanding value congruence help support motivation? ==
[[File:Value factors of motivation.png|border|right|324x324px]]
One may ask, what actually constitutes a value-aligned environment? 

Through an analysis of relevant literature, we can deduce three key components of value congruent environments; autonomy, meaningfulness, and compatibility.

=== Autonomy ===
Ryan and Deci (2018) assert that humans have an inherent psychological drive to act in a way that is self-endorsed or congruent with one’s values, otherwise known as [[wikipedia:Autonomy|autonomy]]. Essentially, an individual should be able to freely express their personal values despite whatever situational values are present in their environment. Al-Khouja et al. (2020) argue that autonomy-supportive environments help nurture and internalise ethical values, while increasing the likelihood of prosocial behaviours. Likewise, by giving autonomy support to those who they care for, people can experience psychological need satisfaction, intrinsic motivation, efficacy, well-being, improved health, and relationship satisfaction (Reeve, 2024).

=== Meaningfulness ===
Rather than having ownership over your own behaviour through autonomy, meaningfulness involves understanding ''why'' engaging in something matters. Tasks that are otherwise ‘boring’ can become meaningful through various interest-enhancing strategies. This process is referred to as ''[[wikipedia:Internalization_(sociology)|internalisation]]'', in which an individual transforms an environmental rule, behaviour, or value into an internally endorsed one. By doing so, these aspects become engrained into one’s sense of self, making the completion of related-tasks or goals more personally meaningful (Reeve, 2024).

=== Compatibility ===
In line with meaningful work, Hossli et al. (2025) states that one must abide by their personal values when searching for a job. This sort of compatibility is important not only for work satisfaction or engagement, but also for intrinsic motivation. However, identifying your personal values is not always so simple; people are biased towards representations of their ideal self opposed to their current self. Thus, those who want to pursue professional growth must thoroughly understand what they deem important and make career decisions on this basis (Hossli et al., 2025). Nevertheless, compatibility extends beyond the workplace; value compatibility in relationships (whether romantic or platonic) affects relationship satisfaction, quality, and communication (van der Wal et al. 2024). Ultimately, when values are compatible, they are congruent.  

;{{RoundBoxTop|theme=3}}
'''Scenario - Jemma's job''' 
Jemma strongly values universalism, as she strives to care for the environment through sustainable practices. She is offered a job as a climate policy advisor, accepting almost immediately. On her first day, Jemma walks through the foyer and sees a large delivery of boxes, each of which is wrapped thickly in plastic. She feels confused, as this does not align with the values of her new job. {{RoundBoxBottom}}

&lt;quiz display=&quot;simple&quot;&gt;
{Jemma is experiencing:
|type=&quot;()&quot;}
- Value congruence
+ Value incongruence
- Neither; value congruence is complex
&lt;/quiz&gt;

;{{RoundBoxTop|theme=3}}
'''Scenario - Matthew and George''' 

Matthew loves to bake for his friends and family. One day, he decides to bake a cake for his dear friend and roommate George. A couple days after giving George the cake, Matthew finds it in their shared trash can with a single bite taken out of it. Matthew is upset and confronts George, who claimed he didn’t like carrot cake, which is why he threw it away. 
{{RoundBoxBottom}}&lt;quiz display=&quot;simple&quot;&gt;
{Which concept best explains why Matthew is upset?
|type=&quot;()&quot;}
+ Value incongruence
- Individual differences in values
- Situational values
- Value congruence
&lt;/quiz&gt;

==Conclusion==
Taken all together, the congruence or incongruence of personal and situational values creates a motivational experience. With consideration of behaviour, goals, individual differences, and most importantly values, motivation becomes a highly nuanced phenomenon. Take Jane for instance; we discovered that motivational differences lie within the importance placed on certain values. While Jane’s behaviour and routines reflect her value for self-direction and achievement, you may not find these values important. That is why Jane makes it to school early each day, not because she is ‘better’ than you, but because she has different values. The famous quote “comparison is the thief of joy” is widely applicable in this sense. The individual differences that drive our values should be cherished as they define us.

{{RoundBoxTop|theme=3}}
❗'''Remember, our focus was:'''

* What are personal and situational values?
* How do personal and situational values become aligned or misaligned?
* How does value congruence influence motivation?
* Why does motivation differ between individuals?
* How can understanding value congruence help support motivation?
{{RoundBoxBottom}}

In summary, we found that values are enduring beliefs about what is considered important and desirable in guiding goals, behaviour, and decisions. The differentiation between personal and situational values gave rise to value congruence and incongruence, in which these values become aligned or misaligned. With major theoretical underpinnings in the Self-Determination Theory, Self-Concordance Theory, and most notably, Schwartz’s Theory of Basic Human Values, value congruence was established as a key predictor of motivation. Individual differences in values were then implicated as mediators of the value congruence-motivation relationships. Ultimately, it is these aspects that inform the creation of value-aligned environments, in which autonomy, meaningfulness, and compatibility can be fostered to better support motivation.

==See also==

* [[wikipedia:Motivation|Motivation]] (Wikipedia)
* [[Motivation and emotion/Book/2025/Theory of basic human values|Theory of basic human values]] (Book chapter, 2025)
* [[wikipedia:Value_(ethics)|Values (ethics)]] (Wikipedia)

==References==
{{Hanging indent|1=

Al-Khouja, M., Graham, L., Weinstein, N., &amp; Zheng, Y. (2020). How autonomy support and ethical value alignment influences attitudes towards diversity in English police. ''Journal of Moral Education, 49''(3), 365–380. https://doi.org/10.1080/03057240.2019.1697867

Downes, P. E., Kristof-Brown, A. L., Judge, T. A., &amp; Darnold, T. C. (2017). Motivational mechanisms of self-concordance theory: Goal-specific efficacy and person–organization fit. ''Journal of Business and Psychology, 32''(2), 197–215. https://doi.org/10.1007/s10869-016-9444-y

Hagger, M. S., Hardcastle, S. J., Chater, A., Mallett, C., Pal, S., &amp; Chatzisarantis, N. L. D. (2014). Autonomous and controlled motivational regulations for multiple health-related behaviors: Between- and within-participants analyses. ''Health Psychology &amp; Behavioral Medicine, 2''(1), 565–601. https://doi.org/10.1080/21642850.2014.912945

Hossli, N., Natter, M., &amp; Algesheimer, R. (2025). On the importance of congruence between personal and work values – How value incongruence affects job satisfaction: A multiple mediation model. ''International Journal of Wellbeing, 14''(3), 1–18. https://doi.org/10.5502/ijw.v14i3.2905

Jiang, J.-Q., Yao, J., Yu, K.-R., &amp; Li, C.-N. (2023). An empirical study on ‘how to retain rural teachers with emphasis on hygiene or motivation factors’: A case of Western China. ''Frontiers in Psychology, 14'', 1114107. https://doi.org/10.3389/fpsyg.2023.1114107

Kajonius, P. J., Persson, B. N., &amp; Jonason, P. K. (2015). Hedonism, achievement, and power: Universal values that characterize the dark triad. ''Personality and Individual Differences, 77'', 173–178. https://doi.org/10.1016/j.paid.2014.12.055

Konsky, C., Eguchi, M., Blue, J., &amp; Kapoor, S. (1999). Individualist-collectivist values: American, Indian and Japanese cross-cultural study. ''Intercultural Communication Studies, 9''(1), 7. https://www.sciltp.com/journals/ics/articles/1999061006

Lake, J., Bardi, A., Sneddon, J., &amp; Lee, J. A. (2025). A fundamental difference in the nature of personal values and personality traits revealed through different patterns of stability across their distributions. ''Journal of Personality, 93''(4), 830–844. https://doi.org/10.1111/jopy.12979

Li, M., Wang, Z., You, X., &amp; Gao, J. (2015). Value congruence and teachers’ work engagement: The mediating role of autonomous and controlled motivation. ''Personality and Individual Differences, 80'', 113–118. https://doi.org/10.1016/j.paid.2015.02.021

Montgomery, W., Montgomery, H., &amp; Gärling, T. (2020). How situational activation of values evokes positive and negative feelings: Theory and experimental findings. ''Motivation and Emotion, 44''(4), 608–620. https://doi.org/10.1007/s11031-020-09820-y

Ponizovskiy, V., Grigoryan, L., Kühnen, U., &amp; Boehnke, K. (2019). Social construction of the value–behavior relation. ''Frontiers in Psychology, 10'', 934. https://doi.org/10.3389/fpsyg.2019.00934

Rawolle, M., Wallis, M. S. v, Badham, R., &amp; Kehr, H. M. (2016). No fit, no fun: The effect of motive incongruence on job burnout and the mediating role of intrinsic motivation. ''Personality and Individual Differences, 89'', 65–68. https://doi.org/10.1016/j.paid.2015.09.030

Reeve, J. (2024). ''Understanding Motivation and Emotion''. (8th ed.). John Wiley &amp; Sons, Incorporated.

Ryan, R. M., &amp; Deci, E. L. (2018). ''Self-determination theory: Basic psychological needs in motivation, development, and wellness''. The Guildford Press.

Schwartz, S. H. (2012). An overview of the Schwartz theory of basic values. ''Online Readings in Psychology and Culture, 2''(1). https://doi.org/10.9707/2307-0919.1116

Strack, M., &amp; Gennerich, C. (2011). Personal and situational values predict ethical reasoning. ''Europe’s Journal of Psychology, 7''(3), 419. https://doi.org/10.5964/ejop.v7i3.142

van der Wal, R. C., Litzellachner, L. F., Karremans, J. C., Buiter, N., Breukel, J., &amp; Maio, G. R. (2024). Values in romantic relationships. ''Personality &amp; Social Psychology Bulletin, 50''(7), 1066–1079. https://doi.org/10.1177/01461672231156975

van Vianen, A. E. M. (2018). Person-environment fit: A review of its basic tenets. ''Annual Review of Organizational Psychology and Organizational Behavior, 5''(1), 75–101. https://doi.org/10.1146/annurev-orgpsych-032117-104702

Ye, S., Soutar, G. N., Sneddon, J. N., &amp; Lee, J. A. (2017). Personal values and the theory of planned behaviour: A study of values and holiday trade-offs in young adults. ''Tourism Management, 62'', 107–109. https://doi.org/10.1016/j.tourman.2016.12.023

}}

==External links==
* [https://www.melrobbins.com/topic/motivation/ The motivation hub] - (Mel Robbins Podcast, n.d.)
* [https://www.ted.com/talks/anna_marie_dipasquale_align_your_life_with_your_core_values_and_natural_talents Value congruence TED talk] - (DiPasquale, 2019)
* [https://gptw.education.nsw.gov.au/ Everyday values quiz] - (NSW Government, n.d.)

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      <text bytes="17838" sha1="nu0jzazi41ux3njx7jszm5gc88gy0wt" xml:space="preserve">{{title|Subcortical structures and motivational drive:&lt;br&gt;How do subcortical brain regions generate basic motivational impulses and energy?}}
__TOC__

==Overview==
{{RoundBoxTop}}
[[File:Motivation for behavior.png|thumb|'''Figure 1'''. An example of motivational drive in everyday behaviour, illustrating how hunger can influence attention, thoughts and behavior toward obtaining food.]]

'''Imagine this...'''

A person has gone several hours without eating. As their hunger increases, they become increasingly focused on finding food. The sight or smell of food captures their attention, and they feel a strong urge to eat even though they may have other tasks to complete. What causes this motivational drive? {{ic|Explain how this relates to subcortical brain structures}}

{{RoundBoxBottom}}

Motivated behaviour is influenced by both psychological and biological processes. Subcortical structures are brain regions located beneath the cerebral cortex that contribute to processes involved in motivation, emotion, reward and biological regulation. Understanding how these structures function can help explain how internal states and external stimuli influence motivated behaviour.

Psychological and neuroscientific research provides insight into how motivational states arise and how they are translated into behaviour. Rather than being controlled by a single brain region, motivation involves interactions among multiple neural systems. This chapter will examine the role of subcortical structures in motivational drive and consider how these neural processes contribute to motivated behaviour.

{{RoundBoxTop|theme=2}}
'''Focus questions'''

* What are the major subcortical brain regions involved in basic motivational processes?
* How do subcortical brain regions generate basic motivational impulses?
* How do subcortical brain regions interact to regulate motivated behaviour?{{RoundBoxBottom}}

== 1. Major subcortical brain regions involved in motivation ==

==== Key points ====

* Subcortical brain regions form interconnected neural systems that contribute to basic motivational processes, including physiological regulation, reward, emotion and behavioural activation (Berridge, 2012; Haber &amp; Behrens, 2014).
* Rather than motivation being controlled by a single &quot;motivation centre&quot;, different subcortical structures contribute to different components of motivated behaviour and communicate with one another (Haber &amp; Behrens, 2014).
* This section will focus on the '''hypothalamus, amygdala, ventral striatum/nucleus accumbens and midbrain dopaminergic regions''' as key structures involved in motivational processes.

=== 1.1 The hypothalamus and homeostatic motivation ===

==== Key points ====

* The hypothalamus is central to homeostatic regulation and links physiological states with motivated behaviours such as feeding, helping the organism respond to changes in internal conditions (Rossi &amp; Stuber, 2018).
* Changes in physiological states can activate hypothalamic neural circuits that contribute to the generation of motivational states and behaviours directed towards restoring physiological balance (Rossi &amp; Stuber, 2018).
* Research on motivational circuitry demonstrates interactions between the amygdala and other subcortical reward-related systems, supporting its role within broader motivational networks (Berridge, 2009; Haber &amp; Behrens, 2014).

=== 1.2 The amygdala and motivational salience ===

==== Key points ====

* The amygdala contributes to the processing of emotionally significant stimuli, allowing emotionally relevant information to influence motivation and behaviour (Berridge, 2009).
* When stimuli acquire emotional or motivational significance, amygdala-related processes can influence attention, approach and avoidance behaviours (Berridge, 2009).
* Research on motivational circuitry demonstrates interactions between the amygdala and other subcortical reward-related systems, supporting its role within broader motivational networks (Berridge, 2009; Haber &amp; Behrens, 2014).

=== 1.3 The ventral striatum and reward ===

==== Key points ====

* The ventral striatum, including the nucleus accumbens, is associated with reward-related motivation and incentive processes that influence behaviour (Berridge, 2012).
* Reward-related neural activity can increase the motivational value of particular outcomes and promote behaviour directed towards obtaining those outcomes (Berridge, 2012).
* Research on dopamine and reward circuitry indicates that ventral striatal systems contribute to reward seeking, behavioural activation and effortful behaviour (Salamone et al., 2018).

== 2. Generation of basic motivational impulses ==

==== Key points ====

* Motivational impulses can emerge when physiological needs or motivationally significant environmental stimuli activate interconnected neural systems (Berridge, 2012).
* Basic motivational processes involve interactions between internal physiological states, neural signalling and information about potentially rewarding or significant outcomes (Haber &amp; Behrens, 2014).
* This section will examine how homeostatic and reward-related mechanisms contribute to the emergence and direction of motivational impulses.

=== 2.1 Homeostatic signals and motivational states ===

==== Key points ====

* Homeostatic approaches propose that deviations from an optimal physiological state can create motivational states that encourage behaviour aimed at restoring physiological balance.
* Internal signals associated with physiological needs can influence subcortical systems, particularly hypothalamic circuits, to generate motivational responses (Rossi &amp; Stuber, 2018).

* Research on feeding-related neural circuits demonstrates that hypothalamic activity can influence the initiation and regulation of motivated feeding behaviour (Rossi &amp; Stuber, 2018).

=== 2.2 Reward and incentive motivation ===

==== Key points ====

* Reward is not a single process; research distinguishes between &quot;liking&quot;,   and learning, with incentive motivation referring to the process that makes particular outcomes attractive and encourages their pursuit (Berridge et al., 2009).
* Dopamine-related systems contribute to incentive motivation and behavioural activation rather than simply producing pleasurable experiences (Salamone et al., 2018).

* This helps explain how subcortical systems can generate the motivational pull or &quot;energy&quot; that encourages an organism to pursue a desired outcome.

== 3. Physiological needs, motivational energy and behaviour ==

==== Key points ====

* Physiological needs can change both the direction and intensity of motivated behaviour by altering an organism's internal state.
* Hunger provides a useful example of how a physiological need can influence attention, reward processing and behaviour (Opland et al., 2013).

* This section will explore how physiological states can generate motivational energy and influence behavioural priorities.

=== 3.1 Hunger and feeding motivation ===

==== Key points ====

* Hunger can be understood as a motivational state associated with physiological signals indicating a need for energy or nutrients.
* Hypothalamic circuits contribute to feeding motivation, while interactions with reward-related systems influence the attractiveness and pursuit of food (Rossi &amp; Stuber, 2018; Opland et al., 2013).

* Hunger therefore illustrates how a physiological need can be translated by subcortical systems into a motivational impulse and subsequent food-seeking behaviour.

=== 3.2 Motivational energy and effort ===

==== Key points ====

* Motivation involves not only wanting an outcome but also the willingness to expend effort to obtain it (Salamone et al., 2018).
* Dopamine-related systems have been linked to behavioural activation and effort-based responding, suggesting a role in the energetic aspects of motivation (Salamone et al., 2018).
* This research helps explain why motivational states can influence how strongly an individual engages in effortful behaviour to achieve a goal.

== 4. Interactions between subcortical motivational systems ==

==== Key points ==== 
[[File:Subcortical regions 2026.png|thumb|'''Figure 2'''. Major subcortical brain regions involved in motivational drive and their interactions in regulating physiological needs, reward and behavioural activation.]]

* Subcortical structures do not operate independently; motivated behaviour emerges through interactions between systems involved in homeostasis, reward, emotion and behavioural selection (Haber &amp; Behrens, 2014).
* The motivational value of an outcome can change depending on an individual's physiological state, demonstrating interaction between homeostatic and reward systems (Opland et al., 2013).

* Examining these interactions helps explain how an internal need can influence what an individual wants, how strongly they want it and the effort they are willing to invest.

=== 4.1 Homeostatic and reward systems ===

==== Key points ====

* Physiological states can influence the reward value of particular stimuli, meaning that the same outcome may become more or less motivating depending on current needs (Opland et al., 2013).
* Interactions between hypothalamic and mesolimbic systems help connect physiological regulation with reward-related motivation.

* These interactions demonstrate how a physiological need can increase the motivational value of a particular outcome and energise behaviour directed towards it.

=== 4.2 Dopamine and motivational control ===

==== Key points ====

* Dopamine is involved in several aspects of motivation, including incentive motivation, behavioural activation and effort, rather than simply producing pleasure (Berridge, 2012; Salamone et al., 2018).
* Dopaminergic systems interact with the ventral striatum and other neural structures to influence reward-related behaviour.

* These findings help explain how subcortical systems can contribute to the energetic component of motivation by influencing behavioural activation and effort.

=== 4.3 From neural interaction to motivated behaviour ===

==== Key points ====

* Motivated behaviour requires the integration of internal physiological states, reward information and environmental cues.
* Interconnected neural circuits allow motivational information to influence the selection and performance of appropriate behaviours (Haber &amp; Behrens, 2014).

* This provides a network-based explanation for how motivational impulses can develop into coordinated, goal-directed actions.

{{RoundBoxTop|theme=3}}
{| class=&quot;wikitable&quot;
|+Table 1. Subcortical brain systems involved in motivational drive and their contribution to motivated behaviour
!Subcortical system
!Primary motivational role
!How it contributes to motivation
!Example of motivated behaviour
|-
|'''Hypothalamus'''
|Homeostasis and physiological needs
|Detects and responds to changes in internal physiological states and helps generate motivational states related to needs such as hunger.
|Seeking and consuming food when hungry
|-
|'''Amygdala'''
|Emotional and motivational salience
|Processes emotionally significant information and influences the motivational value of environmental stimuli.
|Approaching rewarding stimuli or avoiding threatening stimuli
|-
|'''Ventral striatum / nucleus accumbens'''
|Reward and incentive motivation
|Contributes to the pursuit of rewarding outcomes and the motivational pull of desirable stimuli.
|Seeking food or other rewarding outcomes
|-
|'''Dopaminergic systems'''
|Behavioural activation and effort
|Supports incentive motivation, behavioural activation and willingness to expend effort to obtain desired outcomes.
|Persisting with effort to obtain a desired reward
|-
|'''Interconnected subcortical circuits'''
|Integration of motivational information
|Interactions between homeostatic, emotional and reward systems help translate physiological needs and environmental cues into coordinated motivated behaviour.
|Adjusting behaviour according to current needs and available rewards
|}
{{RoundBoxBottom}}

== 5. Evidence for subcortical motivational systems ==

==== Key points ====

* Research into motivation uses behavioural, neurobiological and neuroscientific approaches to investigate how subcortical structures contribute to motivated behaviour. Evidence from these approaches can help connect physiological states, neural activity and observable behaviour (Berridge, 2012; Haber &amp; Behrens, 2014).
* Neurobiological research has identified interconnected hypothalamic, amygdala, striatal and dopaminergic systems associated with reward, motivation and behavioural activation, while behavioural research demonstrates that motivational states can influence approach behaviour, effort and decisions about which actions to pursue (Berridge, 2012; Salamone et al., 2018).
* Research on feeding provides evidence that physiological states can influence reward processing and motivated behaviour through interactions between homeostatic and reward systems (Opland et al., 2013).
* Findings across these areas suggest that subcortical mechanisms provide an important biological basis for motivation, but they do not fully explain complex human motivated behaviour. Psychological processes such as learning, cognit ion and emotion, together with environmental context, also interact with neural systems to influence behaviour (Haber &amp; Behrens, 2014).

* Overall, the research supports a '''network-based understanding of motivational drive''', in which multiple subcortical systems work together to translate physiological and motivational information into behavioural activation, while broader psychological processes influence how these systems are expressed.

==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==

* [[Motivation and emotion/Book/2026/Hypothalamus and homeostatic motivation|Hypothalamus and homeostatic motivation]] (Book Chapter, 2026)
* [[wikipedia:Motivation|Motivation]] (Wikipedia)

==References==
{{Hanging indent|1=

Berridge, K. C., Robinson, T. E., &amp; Aldridge, J. W. (2009). Dissecting components of reward:‘liking’,‘wanting’, and learning. Current opinion in pharmacology, 9(1), 65-73. 

Berridge, K. C. (2012). From prediction error to incentive salience: mesolimbic computation of reward motivation. European Journal of neuroscience, 35(7), 1124-1143. 

Haber, S. N., &amp; Behrens, T. E. (2014). The neural network underlying incentive-based learning: implications for interpreting circuit disruptions in psychiatric disorders. Neuron, 83(5), 1019-1039.  

Opland, D., Sutton, A., Woodworth, H., Brown, J., Bugescu, R., Garcia, A., Christensen, L., Rhodes, C., Myers Jr, M., &amp; Leinninger, G. (2013). Loss of neurotensin receptor-1 disrupts the control of the mesolimbic dopamine system by leptin and promotes hedonic feeding and obesity. Molecular metabolism, 2(4), 423-434.  

Rossi, M. A., &amp; Stuber, G. D. (2018). Overlapping brain circuits for homeostatic and hedonic feeding. Cell metabolism, 27(1), 42-56.  

Salamone, J. D., Correa, M., Yang, J.-H., Rotolo, R., &amp; Presby, R. (2018). Dopamine, effort-based choice, and behavioral economics: basic and translational research. Frontiers in behavioral neuroscience, 12, 52.

}}

{{tip|Suggestions for this section:
* Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]:
** Use &quot;Edit source&quot;
** &lt;nowiki&gt;{{Hanging indent|1= the full list of references}}&lt;/nowiki&gt;
* Important aspects of APA referencing style
** Author surname, followed by a comma, then the author initials separated by full stops and spaces
** Year of publication in parentheses
** Title of work in lower case (except first letter and proper names), ending in a full-stop
** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop
** doi as a URL which is a working hyperlink (i.e., clickable)
* The most common mistakes include:
** Incorrect capitalisation
** Incorrect italicisation
** dois which aren't clickable as working hyperlinks
** Citing sources that haven't been consulted
}}

==External links==
Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)
* [https://www.ninds.nih.gov/health-information/public-education/brain-basics/brain-basics-know-your-brain Brain basics: Know your brain]
* [https://neuroscience.mssm.edu/nestler/nidappg/brain_reward_pathways.html Brain reward pathways]
* [https://neurosity.co/guides/brain-reward-system-dopamine-motivation Your brain's reward system]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

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      <text bytes="18497" sha1="ldw8cen70i421fdpcfe9sdrn6y3keze" xml:space="preserve">{{title|Subcortical structures and motivational drive:&lt;br&gt;How do subcortical brain regions generate basic motivational impulses and energy?}}
__TOC__

==Overview==
{{RoundBoxTop}}
[[File:Motivation for behavior.png|thumb|'''Figure 1'''. An example of motivational drive in everyday behaviour, illustrating how hunger can influence attention, thoughts and behavior toward obtaining food.]]

'''Imagine this...'''

A person has gone several hours without eating. As their hunger increases, they become increasingly focused on finding food. The sight or smell of food captures their attention, and they feel a strong urge to eat even though they may have other tasks to complete. What causes this motivational drive? {{ic|Explain how this relates to subcortical brain structures}}

{{RoundBoxBottom}}

Motivated behaviour is influenced by both psychological and biological processes. Subcortical structures are brain regions located beneath the cerebral cortex that contribute to motivation, emotion, reward and biological regulation. These structures help the brain integrate internal bodily states with information from the environment, influencing which goals become important and how strongly an individual is motivated to pursue them.

One important explanation of motivational drive is the distinction between reward “wanting” and “liking”. “Wanting” refers to the motivational pull that encourages an individual to pursue a reward, whereas “liking” refers to the pleasure experienced when receiving it. These processes are related but distinct, and dopamine-related neural systems contribute particularly to incentive motivation rather than directly producing pleasure (Berridge et al., 2009; Berridge, 2012; Berridge &amp; Kringelbach, 2015). For example, hunger can increase the motivational pull of food cues, making food more difficult to ignore.

Motivation does not arise from a single brain region. Instead, interconnected subcortical systems contribute to generating motivational impulses, assigning significance to rewards and influencing the intensity and direction of behaviour (Castro et al., 2015; Liu et al., 2011). Understanding these interactions helps explain how basic motivational states influence everyday decisions and actions.{{RoundBoxTop|theme=2}}
'''Focus questions'''

* What are the major subcortical brain regions involved in basic motivational processes?
* How do subcortical brain regions generate basic motivational impulses?
* How do subcortical brain regions interact to regulate motivated behaviour?{{RoundBoxBottom}}

== 1. Major subcortical brain regions involved in motivation ==

==== Key points ====

* Subcortical brain regions form interconnected neural systems that contribute to basic motivational processes, including physiological regulation, reward, emotion and behavioural activation (Berridge, 2012; Haber &amp; Behrens, 2014).
* Rather than motivation being controlled by a single &quot;motivation centre&quot;, different subcortical structures contribute to different components of motivated behaviour and communicate with one another (Haber &amp; Behrens, 2014).
* This section will focus on the '''hypothalamus, amygdala, ventral striatum/nucleus accumbens and midbrain dopaminergic regions''' as key structures involved in motivational processes.

=== 1.1 The hypothalamus and homeostatic motivation ===

==== Key points ====

* The hypothalamus is central to homeostatic regulation and links physiological states with motivated behaviours such as feeding, helping the organism respond to changes in internal conditions (Rossi &amp; Stuber, 2018).
* Changes in physiological states can activate hypothalamic neural circuits that contribute to the generation of motivational states and behaviours directed towards restoring physiological balance (Rossi &amp; Stuber, 2018).
* Research on motivational circuitry demonstrates interactions between the amygdala and other subcortical reward-related systems, supporting its role within broader motivational networks (Berridge, 2009; Haber &amp; Behrens, 2014).

=== 1.2 The amygdala and motivational salience ===

==== Key points ====

* The amygdala contributes to the processing of emotionally significant stimuli, allowing emotionally relevant information to influence motivation and behaviour (Berridge, 2009).
* When stimuli acquire emotional or motivational significance, amygdala-related processes can influence attention, approach and avoidance behaviours (Berridge, 2009).
* Research on motivational circuitry demonstrates interactions between the amygdala and other subcortical reward-related systems, supporting its role within broader motivational networks (Berridge, 2009; Haber &amp; Behrens, 2014).

=== 1.3 The ventral striatum and reward ===

==== Key points ====

* The ventral striatum, including the nucleus accumbens, is associated with reward-related motivation and incentive processes that influence behaviour (Berridge, 2012).
* Reward-related neural activity can increase the motivational value of particular outcomes and promote behaviour directed towards obtaining those outcomes (Berridge, 2012).
* Research on dopamine and reward circuitry indicates that ventral striatal systems contribute to reward seeking, behavioural activation and effortful behaviour (Salamone et al., 2018).

== 2. Generation of basic motivational impulses ==

==== Key points ====

* Motivational impulses can emerge when physiological needs or motivationally significant environmental stimuli activate interconnected neural systems (Berridge, 2012).
* Basic motivational processes involve interactions between internal physiological states, neural signalling and information about potentially rewarding or significant outcomes (Haber &amp; Behrens, 2014).
* This section will examine how homeostatic and reward-related mechanisms contribute to the emergence and direction of motivational impulses.

=== 2.1 Homeostatic signals and motivational states ===

==== Key points ====

* Homeostatic approaches propose that deviations from an optimal physiological state can create motivational states that encourage behaviour aimed at restoring physiological balance.
* Internal signals associated with physiological needs can influence subcortical systems, particularly hypothalamic circuits, to generate motivational responses (Rossi &amp; Stuber, 2018).

* Research on feeding-related neural circuits demonstrates that hypothalamic activity can influence the initiation and regulation of motivated feeding behaviour (Rossi &amp; Stuber, 2018).

=== 2.2 Reward and incentive motivation ===

==== Key points ====

* Reward is not a single process; research distinguishes between &quot;liking&quot;,   and learning, with incentive motivation referring to the process that makes particular outcomes attractive and encourages their pursuit (Berridge et al., 2009).
* Dopamine-related systems contribute to incentive motivation and behavioural activation rather than simply producing pleasurable experiences (Salamone et al., 2018).

* This helps explain how subcortical systems can generate the motivational pull or &quot;energy&quot; that encourages an organism to pursue a desired outcome.

== 3. Physiological needs, motivational energy and behaviour ==

==== Key points ====

* Physiological needs can change both the direction and intensity of motivated behaviour by altering an organism's internal state.
* Hunger provides a useful example of how a physiological need can influence attention, reward processing and behaviour (Opland et al., 2013).

* This section will explore how physiological states can generate motivational energy and influence behavioural priorities.

=== 3.1 Hunger and feeding motivation ===

==== Key points ====

* Hunger can be understood as a motivational state associated with physiological signals indicating a need for energy or nutrients.
* Hypothalamic circuits contribute to feeding motivation, while interactions with reward-related systems influence the attractiveness and pursuit of food (Rossi &amp; Stuber, 2018; Opland et al., 2013).

* Hunger therefore illustrates how a physiological need can be translated by subcortical systems into a motivational impulse and subsequent food-seeking behaviour.

=== 3.2 Motivational energy and effort ===

==== Key points ====

* Motivation involves not only wanting an outcome but also the willingness to expend effort to obtain it (Salamone et al., 2018).
* Dopamine-related systems have been linked to behavioural activation and effort-based responding, suggesting a role in the energetic aspects of motivation (Salamone et al., 2018).
* This research helps explain why motivational states can influence how strongly an individual engages in effortful behaviour to achieve a goal.

== 4. Interactions between subcortical motivational systems ==

==== Key points ==== 
[[File:Subcortical regions 2026.png|thumb|'''Figure 2'''. Major subcortical brain regions involved in motivational drive and their interactions in regulating physiological needs, reward and behavioural activation.]]

* Subcortical structures do not operate independently; motivated behaviour emerges through interactions between systems involved in homeostasis, reward, emotion and behavioural selection (Haber &amp; Behrens, 2014).
* The motivational value of an outcome can change depending on an individual's physiological state, demonstrating interaction between homeostatic and reward systems (Opland et al., 2013).

* Examining these interactions helps explain how an internal need can influence what an individual wants, how strongly they want it and the effort they are willing to invest.

=== 4.1 Homeostatic and reward systems ===

==== Key points ====

* Physiological states can influence the reward value of particular stimuli, meaning that the same outcome may become more or less motivating depending on current needs (Opland et al., 2013).
* Interactions between hypothalamic and mesolimbic systems help connect physiological regulation with reward-related motivation.

* These interactions demonstrate how a physiological need can increase the motivational value of a particular outcome and energise behaviour directed towards it.

=== 4.2 Dopamine and motivational control ===

==== Key points ====

* Dopamine is involved in several aspects of motivation, including incentive motivation, behavioural activation and effort, rather than simply producing pleasure (Berridge, 2012; Salamone et al., 2018).
* Dopaminergic systems interact with the ventral striatum and other neural structures to influence reward-related behaviour.

* These findings help explain how subcortical systems can contribute to the energetic component of motivation by influencing behavioural activation and effort.

=== 4.3 From neural interaction to motivated behaviour ===

==== Key points ====

* Motivated behaviour requires the integration of internal physiological states, reward information and environmental cues.
* Interconnected neural circuits allow motivational information to influence the selection and performance of appropriate behaviours (Haber &amp; Behrens, 2014).

* This provides a network-based explanation for how motivational impulses can develop into coordinated, goal-directed actions.

{{RoundBoxTop|theme=3}}
{| class=&quot;wikitable&quot;
|+Table 1. Subcortical brain systems involved in motivational drive and their contribution to motivated behaviour
!Subcortical system
!Primary motivational role
!How it contributes to motivation
!Example of motivated behaviour
|-
|'''Hypothalamus'''
|Homeostasis and physiological needs
|Detects and responds to changes in internal physiological states and helps generate motivational states related to needs such as hunger.
|Seeking and consuming food when hungry
|-
|'''Amygdala'''
|Emotional and motivational salience
|Processes emotionally significant information and influences the motivational value of environmental stimuli.
|Approaching rewarding stimuli or avoiding threatening stimuli
|-
|'''Ventral striatum / nucleus accumbens'''
|Reward and incentive motivation
|Contributes to the pursuit of rewarding outcomes and the motivational pull of desirable stimuli.
|Seeking food or other rewarding outcomes
|-
|'''Dopaminergic systems'''
|Behavioural activation and effort
|Supports incentive motivation, behavioural activation and willingness to expend effort to obtain desired outcomes.
|Persisting with effort to obtain a desired reward
|-
|'''Interconnected subcortical circuits'''
|Integration of motivational information
|Interactions between homeostatic, emotional and reward systems help translate physiological needs and environmental cues into coordinated motivated behaviour.
|Adjusting behaviour according to current needs and available rewards
|}
{{RoundBoxBottom}}

== 5. Evidence for subcortical motivational systems ==

==== Key points ====

* Research into motivation uses behavioural, neurobiological and neuroscientific approaches to investigate how subcortical structures contribute to motivated behaviour. Evidence from these approaches can help connect physiological states, neural activity and observable behaviour (Berridge, 2012; Haber &amp; Behrens, 2014).
* Neurobiological research has identified interconnected hypothalamic, amygdala, striatal and dopaminergic systems associated with reward, motivation and behavioural activation, while behavioural research demonstrates that motivational states can influence approach behaviour, effort and decisions about which actions to pursue (Berridge, 2012; Salamone et al., 2018).
* Research on feeding provides evidence that physiological states can influence reward processing and motivated behaviour through interactions between homeostatic and reward systems (Opland et al., 2013).
* Findings across these areas suggest that subcortical mechanisms provide an important biological basis for motivation, but they do not fully explain complex human motivated behaviour. Psychological processes such as learning, cognit ion and emotion, together with environmental context, also interact with neural systems to influence behaviour (Haber &amp; Behrens, 2014).

* Overall, the research supports a '''network-based understanding of motivational drive''', in which multiple subcortical systems work together to translate physiological and motivational information into behavioural activation, while broader psychological processes influence how these systems are expressed.

==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==

* [[Motivation and emotion/Book/2026/Hypothalamus and homeostatic motivation|Hypothalamus and homeostatic motivation]] (Book Chapter, 2026)
* [[wikipedia:Motivation|Motivation]] (Wikipedia)

==References==
{{Hanging indent|1=

Berridge, K. C., Robinson, T. E., &amp; Aldridge, J. W. (2009). Dissecting components of reward:‘liking’,‘wanting’, and learning. Current opinion in pharmacology, 9(1), 65-73. 

Berridge, K. C. (2012). From prediction error to incentive salience: mesolimbic computation of reward motivation. European Journal of neuroscience, 35(7), 1124-1143. 

Haber, S. N., &amp; Behrens, T. E. (2014). The neural network underlying incentive-based learning: implications for interpreting circuit disruptions in psychiatric disorders. Neuron, 83(5), 1019-1039.  

Opland, D., Sutton, A., Woodworth, H., Brown, J., Bugescu, R., Garcia, A., Christensen, L., Rhodes, C., Myers Jr, M., &amp; Leinninger, G. (2013). Loss of neurotensin receptor-1 disrupts the control of the mesolimbic dopamine system by leptin and promotes hedonic feeding and obesity. Molecular metabolism, 2(4), 423-434.  

Rossi, M. A., &amp; Stuber, G. D. (2018). Overlapping brain circuits for homeostatic and hedonic feeding. Cell metabolism, 27(1), 42-56.  

Salamone, J. D., Correa, M., Yang, J.-H., Rotolo, R., &amp; Presby, R. (2018). Dopamine, effort-based choice, and behavioral economics: basic and translational research. Frontiers in behavioral neuroscience, 12, 52.

}}

{{tip|Suggestions for this section:
* Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]:
** Use &quot;Edit source&quot;
** &lt;nowiki&gt;{{Hanging indent|1= the full list of references}}&lt;/nowiki&gt;
* Important aspects of APA referencing style
** Author surname, followed by a comma, then the author initials separated by full stops and spaces
** Year of publication in parentheses
** Title of work in lower case (except first letter and proper names), ending in a full-stop
** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop
** doi as a URL which is a working hyperlink (i.e., clickable)
* The most common mistakes include:
** Incorrect capitalisation
** Incorrect italicisation
** dois which aren't clickable as working hyperlinks
** Citing sources that haven't been consulted
}}

==External links==
Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)
* [https://www.ninds.nih.gov/health-information/public-education/brain-basics/brain-basics-know-your-brain Brain basics: Know your brain]
* [https://neuroscience.mssm.edu/nestler/nidappg/brain_reward_pathways.html Brain reward pathways]
* [https://neurosity.co/guides/brain-reward-system-dopamine-motivation Your brain's reward system]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Neuroscience]]</text>
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__TOC__

==Overview==
{{RoundBoxTop}}
[[File:Motivation for behavior.png|thumb|'''Figure 1'''. An example of motivational drive in everyday behaviour, illustrating how hunger can influence attention, thoughts and behavior toward obtaining food.]]

'''Imagine this...'''

A person has gone several hours without eating. As their hunger increases, they become increasingly focused on finding food. The sight or smell of food captures their attention, and they feel a strong urge to eat even though they may have other tasks to complete. What causes this motivational drive? {{ic|Explain how this relates to subcortical brain structures}}

{{RoundBoxBottom}}

Motivated behaviour is influenced by both psychological and biological processes. Subcortical structures are brain regions located beneath the cerebral cortex that contribute to motivation, emotion, reward and biological regulation. These structures help the brain integrate internal bodily states with information from the environment, influencing which goals become important and how strongly an individual is motivated to pursue them.

One important explanation of motivational drive is the distinction between reward “wanting” and “liking”. “Wanting” refers to the motivational pull that encourages an individual to pursue a reward, whereas “liking” refers to the pleasure experienced when receiving it. These processes are related but distinct, and dopamine-related neural systems contribute particularly to incentive motivation rather than directly producing pleasure (Berridge et al., 2009; Berridge, 2012; Berridge &amp; Kringelbach, 2015). For example, hunger can increase the motivational pull of food cues, making food more difficult to ignore.

Motivation does not arise from a single brain region. Instead, interconnected subcortical systems contribute to generating motivational impulses, assigning significance to rewards and influencing the intensity and direction of behaviour (Castro et al., 2015; Liu et al., 2011). Understanding these interactions helps explain how basic motivational states influence everyday decisions and actions.{{RoundBoxTop|theme=2}}
'''Focus questions'''

* What are the major subcortical brain regions involved in basic motivational processes?
* How do subcortical brain regions generate basic motivational impulses?
* How do subcortical brain regions interact to regulate motivated behaviour?{{RoundBoxBottom}}

== Major subcortical brain regions involved in motivation ==

* Subcortical brain regions form interconnected neural systems that contribute to basic motivational processes, including physiological regulation, reward, emotion and behavioural activation (Berridge, 2012; Haber &amp; Behrens, 2014).
* Rather than motivation being controlled by a single &quot;motivation centre&quot;, different subcortical structures contribute to different components of motivated behaviour and communicate with one another (Haber &amp; Behrens, 2014).
* This section will focus on the '''hypothalamus, amygdala, ventral striatum/nucleus accumbens and midbrain dopaminergic regions''' as key structures involved in motivational processes.

=== The hypothalamus and homeostatic motivation ===

* The hypothalamus is central to homeostatic regulation and links physiological states with motivated behaviours such as feeding, helping the organism respond to changes in internal conditions (Rossi &amp; Stuber, 2018).
* Changes in physiological states can activate hypothalamic neural circuits that contribute to the generation of motivational states and behaviours directed towards restoring physiological balance (Rossi &amp; Stuber, 2018).
* Research on motivational circuitry demonstrates interactions between the amygdala and other subcortical reward-related systems, supporting its role within broader motivational networks (Berridge, 2009; Haber &amp; Behrens, 2014).

=== The amygdala and motivational salience ===

* The amygdala contributes to the processing of emotionally significant stimuli, allowing emotionally relevant information to influence motivation and behaviour (Berridge, 2009).
* When stimuli acquire emotional or motivational significance, amygdala-related processes can influence attention, approach and avoidance behaviours (Berridge, 2009).
* Research on motivational circuitry demonstrates interactions between the amygdala and other subcortical reward-related systems, supporting its role within broader motivational networks (Berridge, 2009; Haber &amp; Behrens, 2014).

=== 1.3 The ventral striatum and reward ===

* The ventral striatum, including the nucleus accumbens, is associated with reward-related motivation and incentive processes that influence behaviour (Berridge, 2012).
* Reward-related neural activity can increase the motivational value of particular outcomes and promote behaviour directed towards obtaining those outcomes (Berridge, 2012).
* Research on dopamine and reward circuitry indicates that ventral striatal systems contribute to reward seeking, behavioural activation and effortful behaviour (Salamone et al., 2018).

== 2. Generation of basic motivational impulses ==

==== Key points ====

* Motivational impulses can emerge when physiological needs or motivationally significant environmental stimuli activate interconnected neural systems (Berridge, 2012).
* Basic motivational processes involve interactions between internal physiological states, neural signalling and information about potentially rewarding or significant outcomes (Haber &amp; Behrens, 2014).
* This section will examine how homeostatic and reward-related mechanisms contribute to the emergence and direction of motivational impulses.

=== 2.1 Homeostatic signals and motivational states ===

==== Key points ====

* Homeostatic approaches propose that deviations from an optimal physiological state can create motivational states that encourage behaviour aimed at restoring physiological balance.
* Internal signals associated with physiological needs can influence subcortical systems, particularly hypothalamic circuits, to generate motivational responses (Rossi &amp; Stuber, 2018).

* Research on feeding-related neural circuits demonstrates that hypothalamic activity can influence the initiation and regulation of motivated feeding behaviour (Rossi &amp; Stuber, 2018).

=== 2.2 Reward and incentive motivation ===

==== Key points ====

* Reward is not a single process; research distinguishes between &quot;liking&quot;,   and learning, with incentive motivation referring to the process that makes particular outcomes attractive and encourages their pursuit (Berridge et al., 2009).
* Dopamine-related systems contribute to incentive motivation and behavioural activation rather than simply producing pleasurable experiences (Salamone et al., 2018).

* This helps explain how subcortical systems can generate the motivational pull or &quot;energy&quot; that encourages an organism to pursue a desired outcome.

== 3. Physiological needs, motivational energy and behaviour ==

==== Key points ====

* Physiological needs can change both the direction and intensity of motivated behaviour by altering an organism's internal state.
* Hunger provides a useful example of how a physiological need can influence attention, reward processing and behaviour (Opland et al., 2013).

* This section will explore how physiological states can generate motivational energy and influence behavioural priorities.

=== 3.1 Hunger and feeding motivation ===

==== Key points ====

* Hunger can be understood as a motivational state associated with physiological signals indicating a need for energy or nutrients.
* Hypothalamic circuits contribute to feeding motivation, while interactions with reward-related systems influence the attractiveness and pursuit of food (Rossi &amp; Stuber, 2018; Opland et al., 2013).

* Hunger therefore illustrates how a physiological need can be translated by subcortical systems into a motivational impulse and subsequent food-seeking behaviour.

=== 3.2 Motivational energy and effort ===

==== Key points ====

* Motivation involves not only wanting an outcome but also the willingness to expend effort to obtain it (Salamone et al., 2018).
* Dopamine-related systems have been linked to behavioural activation and effort-based responding, suggesting a role in the energetic aspects of motivation (Salamone et al., 2018).
* This research helps explain why motivational states can influence how strongly an individual engages in effortful behaviour to achieve a goal.

== 4. Interactions between subcortical motivational systems ==

==== Key points ==== 
[[File:Subcortical regions 2026.png|thumb|'''Figure 2'''. Major subcortical brain regions involved in motivational drive and their interactions in regulating physiological needs, reward and behavioural activation.]]

* Subcortical structures do not operate independently; motivated behaviour emerges through interactions between systems involved in homeostasis, reward, emotion and behavioural selection (Haber &amp; Behrens, 2014).
* The motivational value of an outcome can change depending on an individual's physiological state, demonstrating interaction between homeostatic and reward systems (Opland et al., 2013).

* Examining these interactions helps explain how an internal need can influence what an individual wants, how strongly they want it and the effort they are willing to invest.

=== 4.1 Homeostatic and reward systems ===

==== Key points ====

* Physiological states can influence the reward value of particular stimuli, meaning that the same outcome may become more or less motivating depending on current needs (Opland et al., 2013).
* Interactions between hypothalamic and mesolimbic systems help connect physiological regulation with reward-related motivation.

* These interactions demonstrate how a physiological need can increase the motivational value of a particular outcome and energise behaviour directed towards it.

=== 4.2 Dopamine and motivational control ===

==== Key points ====

* Dopamine is involved in several aspects of motivation, including incentive motivation, behavioural activation and effort, rather than simply producing pleasure (Berridge, 2012; Salamone et al., 2018).
* Dopaminergic systems interact with the ventral striatum and other neural structures to influence reward-related behaviour.

* These findings help explain how subcortical systems can contribute to the energetic component of motivation by influencing behavioural activation and effort.

=== 4.3 From neural interaction to motivated behaviour ===

==== Key points ====

* Motivated behaviour requires the integration of internal physiological states, reward information and environmental cues.
* Interconnected neural circuits allow motivational information to influence the selection and performance of appropriate behaviours (Haber &amp; Behrens, 2014).

* This provides a network-based explanation for how motivational impulses can develop into coordinated, goal-directed actions.

{{RoundBoxTop|theme=3}}
{| class=&quot;wikitable&quot;
|+Table 1. Subcortical brain systems involved in motivational drive and their contribution to motivated behaviour
!Subcortical system
!Primary motivational role
!How it contributes to motivation
!Example of motivated behaviour
|-
|'''Hypothalamus'''
|Homeostasis and physiological needs
|Detects and responds to changes in internal physiological states and helps generate motivational states related to needs such as hunger.
|Seeking and consuming food when hungry
|-
|'''Amygdala'''
|Emotional and motivational salience
|Processes emotionally significant information and influences the motivational value of environmental stimuli.
|Approaching rewarding stimuli or avoiding threatening stimuli
|-
|'''Ventral striatum / nucleus accumbens'''
|Reward and incentive motivation
|Contributes to the pursuit of rewarding outcomes and the motivational pull of desirable stimuli.
|Seeking food or other rewarding outcomes
|-
|'''Dopaminergic systems'''
|Behavioural activation and effort
|Supports incentive motivation, behavioural activation and willingness to expend effort to obtain desired outcomes.
|Persisting with effort to obtain a desired reward
|-
|'''Interconnected subcortical circuits'''
|Integration of motivational information
|Interactions between homeostatic, emotional and reward systems help translate physiological needs and environmental cues into coordinated motivated behaviour.
|Adjusting behaviour according to current needs and available rewards
|}
{{RoundBoxBottom}}

== 5. Evidence for subcortical motivational systems ==

==== Key points ====

* Research into motivation uses behavioural, neurobiological and neuroscientific approaches to investigate how subcortical structures contribute to motivated behaviour. Evidence from these approaches can help connect physiological states, neural activity and observable behaviour (Berridge, 2012; Haber &amp; Behrens, 2014).
* Neurobiological research has identified interconnected hypothalamic, amygdala, striatal and dopaminergic systems associated with reward, motivation and behavioural activation, while behavioural research demonstrates that motivational states can influence approach behaviour, effort and decisions about which actions to pursue (Berridge, 2012; Salamone et al., 2018).
* Research on feeding provides evidence that physiological states can influence reward processing and motivated behaviour through interactions between homeostatic and reward systems (Opland et al., 2013).
* Findings across these areas suggest that subcortical mechanisms provide an important biological basis for motivation, but they do not fully explain complex human motivated behaviour. Psychological processes such as learning, cognit ion and emotion, together with environmental context, also interact with neural systems to influence behaviour (Haber &amp; Behrens, 2014).

* Overall, the research supports a '''network-based understanding of motivational drive''', in which multiple subcortical systems work together to translate physiological and motivational information into behavioural activation, while broader psychological processes influence how these systems are expressed.

==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==

* [[Motivation and emotion/Book/2026/Hypothalamus and homeostatic motivation|Hypothalamus and homeostatic motivation]] (Book Chapter, 2026)
* [[wikipedia:Motivation|Motivation]] (Wikipedia)

==References==
{{Hanging indent|1=

Berridge, K. C., Robinson, T. E., &amp; Aldridge, J. W. (2009). Dissecting components of reward:‘liking’,‘wanting’, and learning. Current opinion in pharmacology, 9(1), 65-73. 

Berridge, K. C. (2012). From prediction error to incentive salience: mesolimbic computation of reward motivation. European Journal of neuroscience, 35(7), 1124-1143. 

Haber, S. N., &amp; Behrens, T. E. (2014). The neural network underlying incentive-based learning: implications for interpreting circuit disruptions in psychiatric disorders. Neuron, 83(5), 1019-1039.  

Opland, D., Sutton, A., Woodworth, H., Brown, J., Bugescu, R., Garcia, A., Christensen, L., Rhodes, C., Myers Jr, M., &amp; Leinninger, G. (2013). Loss of neurotensin receptor-1 disrupts the control of the mesolimbic dopamine system by leptin and promotes hedonic feeding and obesity. Molecular metabolism, 2(4), 423-434.  

Rossi, M. A., &amp; Stuber, G. D. (2018). Overlapping brain circuits for homeostatic and hedonic feeding. Cell metabolism, 27(1), 42-56.  

Salamone, J. D., Correa, M., Yang, J.-H., Rotolo, R., &amp; Presby, R. (2018). Dopamine, effort-based choice, and behavioral economics: basic and translational research. Frontiers in behavioral neuroscience, 12, 52.

}}

{{tip|Suggestions for this section:
* Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]:
** Use &quot;Edit source&quot;
** &lt;nowiki&gt;{{Hanging indent|1= the full list of references}}&lt;/nowiki&gt;
* Important aspects of APA referencing style
** Author surname, followed by a comma, then the author initials separated by full stops and spaces
** Year of publication in parentheses
** Title of work in lower case (except first letter and proper names), ending in a full-stop
** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop
** doi as a URL which is a working hyperlink (i.e., clickable)
* The most common mistakes include:
** Incorrect capitalisation
** Incorrect italicisation
** dois which aren't clickable as working hyperlinks
** Citing sources that haven't been consulted
}}

==External links==
Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)
* [https://www.ninds.nih.gov/health-information/public-education/brain-basics/brain-basics-know-your-brain Brain basics: Know your brain]
* [https://neuroscience.mssm.edu/nestler/nidappg/brain_reward_pathways.html Brain reward pathways]
* [https://neurosity.co/guides/brain-reward-system-dopamine-motivation Your brain's reward system]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Neuroscience]]</text>
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__TOC__

==Overview==
{{RoundBoxTop}}
[[File:Motivation for behavior.png|thumb|'''Figure 1'''. An example of motivational drive in everyday behaviour, illustrating how hunger can influence attention, thoughts and behavior toward obtaining food.]]

'''Imagine this...'''

A person has gone several hours without eating. As their hunger increases, they become increasingly focused on finding food. The sight or smell of food captures their attention, and they feel a strong urge to eat even though they may have other tasks to complete. What causes this motivational drive? {{ic|Explain how this relates to subcortical brain structures}}

{{RoundBoxBottom}}

Motivated behaviour is influenced by both psychological and biological processes. Subcortical structures are brain regions located beneath the cerebral cortex that contribute to motivation, emotion, reward and biological regulation. These structures help the brain integrate internal bodily states with information from the environment, influencing which goals become important and how strongly an individual is motivated to pursue them.

One important explanation of motivational drive is the distinction between reward “wanting” and “liking”. “Wanting” refers to the motivational pull that encourages an individual to pursue a reward, whereas “liking” refers to the pleasure experienced when receiving it. These processes are related but distinct, and dopamine-related neural systems contribute particularly to incentive motivation rather than directly producing pleasure (Berridge et al., 2009; Berridge, 2012; Berridge &amp; Kringelbach, 2015). For example, hunger can increase the motivational pull of food cues, making food more difficult to ignore.

Motivation does not arise from a single brain region. Instead, interconnected subcortical systems contribute to generating motivational impulses, assigning significance to rewards and influencing the intensity and direction of behaviour (Castro et al., 2015; Liu et al., 2011). Understanding these interactions helps explain how basic motivational states influence everyday decisions and actions.{{RoundBoxTop|theme=2}}
'''Focus questions'''

* What are the major subcortical brain regions involved in basic motivational processes?
* How do subcortical brain regions generate basic motivational impulses?
* How do subcortical brain regions interact to regulate motivated behaviour?{{RoundBoxBottom}}

== Major subcortical brain regions involved in motivation ==

* Subcortical brain regions form interconnected neural systems that contribute to basic motivational processes, including physiological regulation, reward, emotion and behavioural activation (Berridge, 2012; Haber &amp; Behrens, 2014).
* Rather than motivation being controlled by a single &quot;motivation centre&quot;, different subcortical structures contribute to different components of motivated behaviour and communicate with one another (Haber &amp; Behrens, 2014).
* This section will focus on the '''hypothalamus, amygdala, ventral striatum/nucleus accumbens and midbrain dopaminergic regions''' as key structures involved in motivational processes.

=== The hypothalamus and homeostatic motivation ===

* The hypothalamus is central to homeostatic regulation and links physiological states with motivated behaviours such as feeding, helping the organism respond to changes in internal conditions (Rossi &amp; Stuber, 2018).
* Changes in physiological states can activate hypothalamic neural circuits that contribute to the generation of motivational states and behaviours directed towards restoring physiological balance (Rossi &amp; Stuber, 2018).
* Research on motivational circuitry demonstrates interactions between the amygdala and other subcortical reward-related systems, supporting its role within broader motivational networks (Berridge, 2009; Haber &amp; Behrens, 2014).

=== The amygdala and motivational salience ===

* The amygdala contributes to the processing of emotionally significant stimuli, allowing emotionally relevant information to influence motivation and behaviour (Berridge, 2009).
* When stimuli acquire emotional or motivational significance, amygdala-related processes can influence attention, approach and avoidance behaviours (Berridge, 2009).
* Research on motivational circuitry demonstrates interactions between the amygdala and other subcortical reward-related systems, supporting its role within broader motivational networks (Berridge, 2009; Haber &amp; Behrens, 2014).

=== The ventral striatum and reward ===

* The ventral striatum, including the nucleus accumbens, is associated with reward-related motivation and incentive processes that influence behaviour (Berridge, 2012).
* Reward-related neural activity can increase the motivational value of particular outcomes and promote behaviour directed towards obtaining those outcomes (Berridge, 2012).
* Research on dopamine and reward circuitry indicates that ventral striatal systems contribute to reward seeking, behavioural activation and effortful behaviour (Salamone et al., 2018).

== 2. Generation of basic motivational impulses ==

==== Key points ====

* Motivational impulses can emerge when physiological needs or motivationally significant environmental stimuli activate interconnected neural systems (Berridge, 2012).
* Basic motivational processes involve interactions between internal physiological states, neural signalling and information about potentially rewarding or significant outcomes (Haber &amp; Behrens, 2014).
* This section will examine how homeostatic and reward-related mechanisms contribute to the emergence and direction of motivational impulses.

=== 2.1 Homeostatic signals and motivational states ===

==== Key points ====

* Homeostatic approaches propose that deviations from an optimal physiological state can create motivational states that encourage behaviour aimed at restoring physiological balance.
* Internal signals associated with physiological needs can influence subcortical systems, particularly hypothalamic circuits, to generate motivational responses (Rossi &amp; Stuber, 2018).

* Research on feeding-related neural circuits demonstrates that hypothalamic activity can influence the initiation and regulation of motivated feeding behaviour (Rossi &amp; Stuber, 2018).

=== 2.2 Reward and incentive motivation ===

==== Key points ====

* Reward is not a single process; research distinguishes between &quot;liking&quot;,   and learning, with incentive motivation referring to the process that makes particular outcomes attractive and encourages their pursuit (Berridge et al., 2009).
* Dopamine-related systems contribute to incentive motivation and behavioural activation rather than simply producing pleasurable experiences (Salamone et al., 2018).

* This helps explain how subcortical systems can generate the motivational pull or &quot;energy&quot; that encourages an organism to pursue a desired outcome.

== 3. Physiological needs, motivational energy and behaviour ==

==== Key points ====

* Physiological needs can change both the direction and intensity of motivated behaviour by altering an organism's internal state.
* Hunger provides a useful example of how a physiological need can influence attention, reward processing and behaviour (Opland et al., 2013).

* This section will explore how physiological states can generate motivational energy and influence behavioural priorities.

=== 3.1 Hunger and feeding motivation ===

==== Key points ====

* Hunger can be understood as a motivational state associated with physiological signals indicating a need for energy or nutrients.
* Hypothalamic circuits contribute to feeding motivation, while interactions with reward-related systems influence the attractiveness and pursuit of food (Rossi &amp; Stuber, 2018; Opland et al., 2013).

* Hunger therefore illustrates how a physiological need can be translated by subcortical systems into a motivational impulse and subsequent food-seeking behaviour.

=== 3.2 Motivational energy and effort ===

==== Key points ====

* Motivation involves not only wanting an outcome but also the willingness to expend effort to obtain it (Salamone et al., 2018).
* Dopamine-related systems have been linked to behavioural activation and effort-based responding, suggesting a role in the energetic aspects of motivation (Salamone et al., 2018).
* This research helps explain why motivational states can influence how strongly an individual engages in effortful behaviour to achieve a goal.

== 4. Interactions between subcortical motivational systems ==

==== Key points ==== 
[[File:Subcortical regions 2026.png|thumb|'''Figure 2'''. Major subcortical brain regions involved in motivational drive and their interactions in regulating physiological needs, reward and behavioural activation.]]

* Subcortical structures do not operate independently; motivated behaviour emerges through interactions between systems involved in homeostasis, reward, emotion and behavioural selection (Haber &amp; Behrens, 2014).
* The motivational value of an outcome can change depending on an individual's physiological state, demonstrating interaction between homeostatic and reward systems (Opland et al., 2013).

* Examining these interactions helps explain how an internal need can influence what an individual wants, how strongly they want it and the effort they are willing to invest.

=== 4.1 Homeostatic and reward systems ===

==== Key points ====

* Physiological states can influence the reward value of particular stimuli, meaning that the same outcome may become more or less motivating depending on current needs (Opland et al., 2013).
* Interactions between hypothalamic and mesolimbic systems help connect physiological regulation with reward-related motivation.

* These interactions demonstrate how a physiological need can increase the motivational value of a particular outcome and energise behaviour directed towards it.

=== 4.2 Dopamine and motivational control ===

==== Key points ====

* Dopamine is involved in several aspects of motivation, including incentive motivation, behavioural activation and effort, rather than simply producing pleasure (Berridge, 2012; Salamone et al., 2018).
* Dopaminergic systems interact with the ventral striatum and other neural structures to influence reward-related behaviour.

* These findings help explain how subcortical systems can contribute to the energetic component of motivation by influencing behavioural activation and effort.

=== 4.3 From neural interaction to motivated behaviour ===

==== Key points ====

* Motivated behaviour requires the integration of internal physiological states, reward information and environmental cues.
* Interconnected neural circuits allow motivational information to influence the selection and performance of appropriate behaviours (Haber &amp; Behrens, 2014).

* This provides a network-based explanation for how motivational impulses can develop into coordinated, goal-directed actions.

{{RoundBoxTop|theme=3}}
{| class=&quot;wikitable&quot;
|+Table 1. Subcortical brain systems involved in motivational drive and their contribution to motivated behaviour
!Subcortical system
!Primary motivational role
!How it contributes to motivation
!Example of motivated behaviour
|-
|'''Hypothalamus'''
|Homeostasis and physiological needs
|Detects and responds to changes in internal physiological states and helps generate motivational states related to needs such as hunger.
|Seeking and consuming food when hungry
|-
|'''Amygdala'''
|Emotional and motivational salience
|Processes emotionally significant information and influences the motivational value of environmental stimuli.
|Approaching rewarding stimuli or avoiding threatening stimuli
|-
|'''Ventral striatum / nucleus accumbens'''
|Reward and incentive motivation
|Contributes to the pursuit of rewarding outcomes and the motivational pull of desirable stimuli.
|Seeking food or other rewarding outcomes
|-
|'''Dopaminergic systems'''
|Behavioural activation and effort
|Supports incentive motivation, behavioural activation and willingness to expend effort to obtain desired outcomes.
|Persisting with effort to obtain a desired reward
|-
|'''Interconnected subcortical circuits'''
|Integration of motivational information
|Interactions between homeostatic, emotional and reward systems help translate physiological needs and environmental cues into coordinated motivated behaviour.
|Adjusting behaviour according to current needs and available rewards
|}
{{RoundBoxBottom}}

== 5. Evidence for subcortical motivational systems ==

==== Key points ====

* Research into motivation uses behavioural, neurobiological and neuroscientific approaches to investigate how subcortical structures contribute to motivated behaviour. Evidence from these approaches can help connect physiological states, neural activity and observable behaviour (Berridge, 2012; Haber &amp; Behrens, 2014).
* Neurobiological research has identified interconnected hypothalamic, amygdala, striatal and dopaminergic systems associated with reward, motivation and behavioural activation, while behavioural research demonstrates that motivational states can influence approach behaviour, effort and decisions about which actions to pursue (Berridge, 2012; Salamone et al., 2018).
* Research on feeding provides evidence that physiological states can influence reward processing and motivated behaviour through interactions between homeostatic and reward systems (Opland et al., 2013).
* Findings across these areas suggest that subcortical mechanisms provide an important biological basis for motivation, but they do not fully explain complex human motivated behaviour. Psychological processes such as learning, cognit ion and emotion, together with environmental context, also interact with neural systems to influence behaviour (Haber &amp; Behrens, 2014).

* Overall, the research supports a '''network-based understanding of motivational drive''', in which multiple subcortical systems work together to translate physiological and motivational information into behavioural activation, while broader psychological processes influence how these systems are expressed.

==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==

* [[Motivation and emotion/Book/2026/Hypothalamus and homeostatic motivation|Hypothalamus and homeostatic motivation]] (Book Chapter, 2026)
* [[wikipedia:Motivation|Motivation]] (Wikipedia)

==References==
{{Hanging indent|1=

Berridge, K. C., Robinson, T. E., &amp; Aldridge, J. W. (2009). Dissecting components of reward:‘liking’,‘wanting’, and learning. Current opinion in pharmacology, 9(1), 65-73. 

Berridge, K. C. (2012). From prediction error to incentive salience: mesolimbic computation of reward motivation. European Journal of neuroscience, 35(7), 1124-1143. 

Haber, S. N., &amp; Behrens, T. E. (2014). The neural network underlying incentive-based learning: implications for interpreting circuit disruptions in psychiatric disorders. Neuron, 83(5), 1019-1039.  

Opland, D., Sutton, A., Woodworth, H., Brown, J., Bugescu, R., Garcia, A., Christensen, L., Rhodes, C., Myers Jr, M., &amp; Leinninger, G. (2013). Loss of neurotensin receptor-1 disrupts the control of the mesolimbic dopamine system by leptin and promotes hedonic feeding and obesity. Molecular metabolism, 2(4), 423-434.  

Rossi, M. A., &amp; Stuber, G. D. (2018). Overlapping brain circuits for homeostatic and hedonic feeding. Cell metabolism, 27(1), 42-56.  

Salamone, J. D., Correa, M., Yang, J.-H., Rotolo, R., &amp; Presby, R. (2018). Dopamine, effort-based choice, and behavioral economics: basic and translational research. Frontiers in behavioral neuroscience, 12, 52.

}}

{{tip|Suggestions for this section:
* Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]:
** Use &quot;Edit source&quot;
** &lt;nowiki&gt;{{Hanging indent|1= the full list of references}}&lt;/nowiki&gt;
* Important aspects of APA referencing style
** Author surname, followed by a comma, then the author initials separated by full stops and spaces
** Year of publication in parentheses
** Title of work in lower case (except first letter and proper names), ending in a full-stop
** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop
** doi as a URL which is a working hyperlink (i.e., clickable)
* The most common mistakes include:
** Incorrect capitalisation
** Incorrect italicisation
** dois which aren't clickable as working hyperlinks
** Citing sources that haven't been consulted
}}

==External links==
Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)
* [https://www.ninds.nih.gov/health-information/public-education/brain-basics/brain-basics-know-your-brain Brain basics: Know your brain]
* [https://neuroscience.mssm.edu/nestler/nidappg/brain_reward_pathways.html Brain reward pathways]
* [https://neurosity.co/guides/brain-reward-system-dopamine-motivation Your brain's reward system]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Neuroscience]]</text>
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      <text bytes="20395" sha1="poqzukfeysksfav67fz52u20iz737ng" xml:space="preserve">{{title|Subcortical structures and motivational drive:&lt;br&gt;How do subcortical brain regions generate basic motivational impulses and energy?}}
__TOC__

==Overview==
{{RoundBoxTop}}
[[File:Motivation for behavior.png|thumb|'''Figure 1'''. An example of motivational drive in everyday behaviour, illustrating how hunger can influence attention, thoughts and behavior toward obtaining food.]]

'''Imagine this...'''

Imagine finishing a long day of university classes without having eaten for several hours. Hunger becomes harder to ignore, the smell of food captures your attention, and finding something to eat begins to take priority over other tasks. Even when food is not immediately available, you may feel motivated to search for it. This everyday experience raises an important question: how does the brain turn internal needs and external cues into motivated behaviour?

{{RoundBoxBottom}}

Motivated behaviour is influenced by both psychological and biological processes. Subcortical structures are brain regions located beneath the cerebral cortex that contribute to motivation, emotion, reward and biological regulation. These structures help the brain integrate internal bodily states with information from the environment, influencing which goals become important and how strongly an individual is motivated to pursue them.

One important explanation of motivational drive is the distinction between reward “wanting” and “liking”. “Wanting” refers to the motivational pull that encourages an individual to pursue a reward, whereas “liking” refers to the pleasure experienced when receiving it. These processes are related but distinct, and dopamine-related neural systems contribute particularly to incentive motivation rather than directly producing pleasure (Berridge et al., 2009; Berridge, 2012; Berridge &amp; Kringelbach, 2015). For example, hunger can increase the motivational pull of food cues, making food more difficult to ignore.

Motivation does not arise from a single brain region. Instead, interconnected subcortical systems contribute to generating motivational impulses, assigning significance to rewards and influencing the intensity and direction of behaviour (Castro et al., 2015; Liu et al., 2011). Understanding these interactions helps explain how basic motivational states influence everyday decisions and actions.{{RoundBoxTop|theme=2}}
'''Focus questions'''

* What are the major subcortical brain regions involved in basic motivational processes?
* How do subcortical brain regions generate basic motivational impulses?
* How do subcortical brain regions interact to regulate motivated behaviour?{{RoundBoxBottom}}

== Major subcortical brain regions involved in motivation ==
Motivated behaviour depends on interconnected brain systems rather than a single “motivation centre”. Different subcortical structures contribute to regulating physiological needs, processing significant stimuli and directing behaviour towards rewards. Haber and Behrens (2014) explain that incentive-based behaviour involves networks that evaluate outcomes and connect them with possible actions. The hypothalamus, amygdala and ventral striatum make distinct but overlapping contributions to these processes, including through their interactions with midbrain dopamine pathways.

=== The hypothalamus and homeostatic motivation ===
Homeostatic approaches propose that changes in internal bodily conditions can generate motivational states that encourage behaviour to meet physiological needs. The [[wikipedia:Hypothalamus|hypothalamus]] is central to this process, particularly in regulating feeding and energy balance. Rossi and Stuber (2018) explain that neural circuits involved in homeostatic feeding overlap with reward-related circuits. This suggests that eating is not controlled by hunger alone: the attractiveness and rewarding properties of food can also influence the motivation to eat.

Evidence from primary research illustrates this interaction. Opland et al. (2013) found that disrupting neurotensin receptor-1 in mice altered leptin-related regulation of mesolimbic dopamine function and increased preference for a palatable, high-fat, high-sugar diet. These findings support the view that hypothalamic signalling can influence both physiological regulation and reward-related feeding. However, the study involved a specific genetic manipulation in mice, so its findings cannot establish how strongly the same mechanisms determine everyday eating behaviour in humans.

=== The amygdala and motivational salience ===
The [[wikipedia:Amygdala|amygdala]] contributes to evaluating emotionally and motivationally significant stimuli. In the context of incentive-based learning, stimuli can acquire significance through their association with outcomes, influencing whether behaviour is directed towards or away from them. Haber and Behrens (2014) describe how brain networks connect information about stimuli and outcomes with action selection. The amygdala is therefore better understood as a component of broader motivational networks than as a structure responsible for fear alone.

Human neuroimaging evidence supports this network-based account. Liu et al. (2011), in a meta-analysis of 142 neuroimaging studies, found that the amygdala was more strongly associated with reward outcomes, alongside regions such as the [[wikipedia:Nucleus_accumbens|nucleus accumbens]]. However, the presence of activity in a brain region does not prove that it causes a particular motivational response. The findings identify consistent associations across studies but must be interpreted alongside evidence about neural connections and behavioural effects.

=== The ventral striatum and reward ===
The ventral striatum, including the nucleus accumbens, contributes to reward-related motivation and the pursuit of desirable outcomes. Berridge et al. (2009) distinguish three components of reward: “liking”, the pleasurable impact of an outcome; “wanting”, its motivational pull; and learning, which helps establish associations between cues and outcomes. These processes can interact without being identical. The nucleus accumbens should therefore not be described simply as a pleasure centre, because its activity is also associated with motivational processes that encourage reward seeking.

Midbrain dopamine pathways, particularly projections from the ventral tegmental area, contribute to these reward-related processes. Berridge (2012) explains that incentive salience can change according to an organism’s current physiological state, making a previously learned food cue more compelling during hunger. Research reviewed by Salamone et al. (2018) also links dopamine signalling with effort-based choices, suggesting that dopamine contributes to the willingness to work for rewards rather than merely producing pleasure. However, many findings concerning these mechanisms come from animal experiments, and dopamine’s role depends on the neural circuit and behaviour being studied. Overall, reward motivation is best explained through the interaction of multiple structures and processes rather than the function of one brain region alone.

== 2. Generation of basic motivational impulses ==

==== Key points ====

* Motivational impulses can emerge when physiological needs or motivationally significant environmental stimuli activate interconnected neural systems (Berridge, 2012).
* Basic motivational processes involve interactions between internal physiological states, neural signalling and information about potentially rewarding or significant outcomes (Haber &amp; Behrens, 2014).
* This section will examine how homeostatic and reward-related mechanisms contribute to the emergence and direction of motivational impulses.

=== 2.1 Homeostatic signals and motivational states ===

==== Key points ====

* Homeostatic approaches propose that deviations from an optimal physiological state can create motivational states that encourage behaviour aimed at restoring physiological balance.
* Internal signals associated with physiological needs can influence subcortical systems, particularly hypothalamic circuits, to generate motivational responses (Rossi &amp; Stuber, 2018).

* Research on feeding-related neural circuits demonstrates that hypothalamic activity can influence the initiation and regulation of motivated feeding behaviour (Rossi &amp; Stuber, 2018).

=== 2.2 Reward and incentive motivation ===

==== Key points ====

* Reward is not a single process; research distinguishes between &quot;liking&quot;,   and learning, with incentive motivation referring to the process that makes particular outcomes attractive and encourages their pursuit (Berridge et al., 2009).
* Dopamine-related systems contribute to incentive motivation and behavioural activation rather than simply producing pleasurable experiences (Salamone et al., 2018).

* This helps explain how subcortical systems can generate the motivational pull or &quot;energy&quot; that encourages an organism to pursue a desired outcome.

== 3. Physiological needs, motivational energy and behaviour ==

==== Key points ====

* Physiological needs can change both the direction and intensity of motivated behaviour by altering an organism's internal state.
* Hunger provides a useful example of how a physiological need can influence attention, reward processing and behaviour (Opland et al., 2013).

* This section will explore how physiological states can generate motivational energy and influence behavioural priorities.

=== 3.1 Hunger and feeding motivation ===

==== Key points ====

* Hunger can be understood as a motivational state associated with physiological signals indicating a need for energy or nutrients.
* Hypothalamic circuits contribute to feeding motivation, while interactions with reward-related systems influence the attractiveness and pursuit of food (Rossi &amp; Stuber, 2018; Opland et al., 2013).

* Hunger therefore illustrates how a physiological need can be translated by subcortical systems into a motivational impulse and subsequent food-seeking behaviour.

=== 3.2 Motivational energy and effort ===

==== Key points ====

* Motivation involves not only wanting an outcome but also the willingness to expend effort to obtain it (Salamone et al., 2018).
* Dopamine-related systems have been linked to behavioural activation and effort-based responding, suggesting a role in the energetic aspects of motivation (Salamone et al., 2018).
* This research helps explain why motivational states can influence how strongly an individual engages in effortful behaviour to achieve a goal.

== 4. Interactions between subcortical motivational systems ==

==== Key points ==== 
[[File:Subcortical regions 2026.png|thumb|'''Figure 2'''. Major subcortical brain regions involved in motivational drive and their interactions in regulating physiological needs, reward and behavioural activation.]]

* Subcortical structures do not operate independently; motivated behaviour emerges through interactions between systems involved in homeostasis, reward, emotion and behavioural selection (Haber &amp; Behrens, 2014).
* The motivational value of an outcome can change depending on an individual's physiological state, demonstrating interaction between homeostatic and reward systems (Opland et al., 2013).

* Examining these interactions helps explain how an internal need can influence what an individual wants, how strongly they want it and the effort they are willing to invest.

=== 4.1 Homeostatic and reward systems ===

==== Key points ====

* Physiological states can influence the reward value of particular stimuli, meaning that the same outcome may become more or less motivating depending on current needs (Opland et al., 2013).
* Interactions between hypothalamic and mesolimbic systems help connect physiological regulation with reward-related motivation.

* These interactions demonstrate how a physiological need can increase the motivational value of a particular outcome and energise behaviour directed towards it.

=== 4.2 Dopamine and motivational control ===

==== Key points ====

* Dopamine is involved in several aspects of motivation, including incentive motivation, behavioural activation and effort, rather than simply producing pleasure (Berridge, 2012; Salamone et al., 2018).
* Dopaminergic systems interact with the ventral striatum and other neural structures to influence reward-related behaviour.

* These findings help explain how subcortical systems can contribute to the energetic component of motivation by influencing behavioural activation and effort.

=== 4.3 From neural interaction to motivated behaviour ===

==== Key points ====

* Motivated behaviour requires the integration of internal physiological states, reward information and environmental cues.
* Interconnected neural circuits allow motivational information to influence the selection and performance of appropriate behaviours (Haber &amp; Behrens, 2014).

* This provides a network-based explanation for how motivational impulses can develop into coordinated, goal-directed actions.

{{RoundBoxTop|theme=3}}
{| class=&quot;wikitable&quot;
|+Table 1. Subcortical brain systems involved in motivational drive and their contribution to motivated behaviour
!Subcortical system
!Primary motivational role
!How it contributes to motivation
!Example of motivated behaviour
|-
|'''Hypothalamus'''
|Homeostasis and physiological needs
|Detects and responds to changes in internal physiological states and helps generate motivational states related to needs such as hunger.
|Seeking and consuming food when hungry
|-
|'''Amygdala'''
|Emotional and motivational salience
|Processes emotionally significant information and influences the motivational value of environmental stimuli.
|Approaching rewarding stimuli or avoiding threatening stimuli
|-
|'''Ventral striatum / nucleus accumbens'''
|Reward and incentive motivation
|Contributes to the pursuit of rewarding outcomes and the motivational pull of desirable stimuli.
|Seeking food or other rewarding outcomes
|-
|'''Dopaminergic systems'''
|Behavioural activation and effort
|Supports incentive motivation, behavioural activation and willingness to expend effort to obtain desired outcomes.
|Persisting with effort to obtain a desired reward
|-
|'''Interconnected subcortical circuits'''
|Integration of motivational information
|Interactions between homeostatic, emotional and reward systems help translate physiological needs and environmental cues into coordinated motivated behaviour.
|Adjusting behaviour according to current needs and available rewards
|}
{{RoundBoxBottom}}

== 5. Evidence for subcortical motivational systems ==

==== Key points ====

* Research into motivation uses behavioural, neurobiological and neuroscientific approaches to investigate how subcortical structures contribute to motivated behaviour. Evidence from these approaches can help connect physiological states, neural activity and observable behaviour (Berridge, 2012; Haber &amp; Behrens, 2014).
* Neurobiological research has identified interconnected hypothalamic, amygdala, striatal and dopaminergic systems associated with reward, motivation and behavioural activation, while behavioural research demonstrates that motivational states can influence approach behaviour, effort and decisions about which actions to pursue (Berridge, 2012; Salamone et al., 2018).
* Research on feeding provides evidence that physiological states can influence reward processing and motivated behaviour through interactions between homeostatic and reward systems (Opland et al., 2013).
* Findings across these areas suggest that subcortical mechanisms provide an important biological basis for motivation, but they do not fully explain complex human motivated behaviour. Psychological processes such as learning, cognit ion and emotion, together with environmental context, also interact with neural systems to influence behaviour (Haber &amp; Behrens, 2014).

* Overall, the research supports a '''network-based understanding of motivational drive''', in which multiple subcortical systems work together to translate physiological and motivational information into behavioural activation, while broader psychological processes influence how these systems are expressed.

==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==

* [[Motivation and emotion/Book/2026/Hypothalamus and homeostatic motivation|Hypothalamus and homeostatic motivation]] (Book Chapter, 2026)
* [[wikipedia:Motivation|Motivation]] (Wikipedia)

==References==
{{Hanging indent|1=

Berridge, K. C., Robinson, T. E., &amp; Aldridge, J. W. (2009). Dissecting components of reward:‘liking’,‘wanting’, and learning. Current opinion in pharmacology, 9(1), 65-73. 

Berridge, K. C. (2012). From prediction error to incentive salience: mesolimbic computation of reward motivation. European Journal of neuroscience, 35(7), 1124-1143. 

Haber, S. N., &amp; Behrens, T. E. (2014). The neural network underlying incentive-based learning: implications for interpreting circuit disruptions in psychiatric disorders. Neuron, 83(5), 1019-1039.  

Opland, D., Sutton, A., Woodworth, H., Brown, J., Bugescu, R., Garcia, A., Christensen, L., Rhodes, C., Myers Jr, M., &amp; Leinninger, G. (2013). Loss of neurotensin receptor-1 disrupts the control of the mesolimbic dopamine system by leptin and promotes hedonic feeding and obesity. Molecular metabolism, 2(4), 423-434.  

Rossi, M. A., &amp; Stuber, G. D. (2018). Overlapping brain circuits for homeostatic and hedonic feeding. Cell metabolism, 27(1), 42-56.  

Salamone, J. D., Correa, M., Yang, J.-H., Rotolo, R., &amp; Presby, R. (2018). Dopamine, effort-based choice, and behavioral economics: basic and translational research. Frontiers in behavioral neuroscience, 12, 52.

}}

{{tip|Suggestions for this section:
* Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]:
** Use &quot;Edit source&quot;
** &lt;nowiki&gt;{{Hanging indent|1= the full list of references}}&lt;/nowiki&gt;
* Important aspects of APA referencing style
** Author surname, followed by a comma, then the author initials separated by full stops and spaces
** Year of publication in parentheses
** Title of work in lower case (except first letter and proper names), ending in a full-stop
** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop
** doi as a URL which is a working hyperlink (i.e., clickable)
* The most common mistakes include:
** Incorrect capitalisation
** Incorrect italicisation
** dois which aren't clickable as working hyperlinks
** Citing sources that haven't been consulted
}}

==External links==
Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)
* [https://www.ninds.nih.gov/health-information/public-education/brain-basics/brain-basics-know-your-brain Brain basics: Know your brain]
* [https://neuroscience.mssm.edu/nestler/nidappg/brain_reward_pathways.html Brain reward pathways]
* [https://neurosity.co/guides/brain-reward-system-dopamine-motivation Your brain's reward system]

{{tip|Suggestions for this section:
* Only select links to major external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Neuroscience]]</text>
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      <text bytes="41539" sha1="70gjap704a9htm4h5k005aky02kfwym" xml:space="preserve">{{title|Possible selves and goal pursuit:&lt;br&gt;How do possible selves influence motivation and goal-directed behaviour?}}
__TOC__
==Overview==
{{RoundBoxTop|theme=3}}
[[File:Ueber-die-sammlung-19-jahrhundert-caspar-david-friedrich-wanderer-ueber-dem-nebelmeer.jpg|thumb|right|150px|'''Figure 1'''. The wanderer looks across a sea of fog toward the looming mountains, symbolising the current self and possible self.]]

; Scenario

A university student has started their final year of their bachelor's degree, and the academic standards are higher than previous years. One may imagine their future as exciting: graduating, beginning a meaningful career, becoming financially independent, and becoming the capable and competent person they hope to be. Alternatively, they may imagine their future as unsettling: losing motivation, failing to make use of their opportunities, and becoming someone they once hoped to avoid.

Neither future exists, however, these imagined versions of the self can influence what the student does today – whether they attend lectures and tutorials, persist through difficult assignments and exams, or give up when progress feels slow.
{{RoundBoxBottom}}[https://journals.sagepub.com/doi/10.1037/1089-2680.11.4.348 Possible selves] {{ic|Use either APA style or wiki style, but don't embed external links}} are conceptions of who we may become in the future and involve, to some degree, imagining ourselves as agents within those future situations (Erikson, 2007). They can include versions of ourselves that we hope to become, as well as those we fear becoming. Markus and Nurius (1986) proposed that these future self-representations are motivationally important because they can provide incentives for behaviour and give personal meaning and direction to our goals.

In the opening scenario, the university student can imagine both a desired future of graduating and beginning a meaningful career, and an unwanted future characterised by lost opportunities and lack of direction. Yet imagining either future does not guarantee that the student will study, persist through setbacks, or take advantage of opportunities in the present. This illustrates a central problem in understanding possible selves: how does an imagined future identity become motivation and, ultimately, goal-directed behaviour?

Literature during the 21st century suggests that possible selves are better understood as components of self-regulation through which motivation and behaviour are influenced (Hoyle &amp; Sherrill, 2006; Frazier, Schwartz &amp; Metcalfe, 2021). Research therefore focuses on the conditions under which possible selves provide effective guidance for goal pursuit, including whether they are meaningful, attainable, and connected to realistic behavioural strategies. Examining these processes help to explain why imagined future identities can motivate present goal-directed behaviour in some circumstances, yet remain ineffective in others (Haskins &amp; vanDellen, 2019).

&lt;div style=&quot;background-color: #fbedf2; border: 2px solid #d4779b; border-radius: 12px; padding: 15px 20px;&quot;&gt;
'''Focus questions'''

*What are possible selves, and why can they have motivational significance?
*How do possible selves interact with self-regulatory processes involved in goal pursuit?
*Under what conditions do possible selves facilitate - or fail to facilitate - goal-directed behaviour?
* How can possible selves be used to strengthen motivation and translate future aspirations into present action?
&lt;/div&gt;

== Possible selves ==
=== Definition and theoretical origins ===
The concept of possible selves was introduced by Markus and Nurius (1986) to complement current conceptions of self-knowledge by extending it beyond the present.  They proposed that possible selves represent individuals' ideas of what they might become, what they would like to become, and what they are afraid of becoming, and thus provide a conceptual link between cognition and motivations. More recently, Erikson (2007) emphasised agency, arguing that possible selves involve experiencing oneself, at least to some degree, as an agent within an imagined future situation. This distinguishes a possible self from a simple goal: Wanting to receive a high grade describes a desired outcome, whereas imagining oneself as a capable and successful student places the person within a future identity. Possible selves are therefore closely related to goals, but are distinguished by their explicit connection to who the individual might become. 

Possible selves can take several forms. Hoped-for possible selves represent desirable identities that a person would like to attain. This could include the competent and powerful self, the celebrated and glamorous self, the respected and esteemed self, or the fit self. In contrast, the feared possible selves comprise a similarly compelling set. One's fears and anxieties can become concretely manifest in visions of the lonely self, the undervalued and underpaid self, or the out-of-shape self (Cross &amp; Markus, 1991). Additionally, people may also hold expected possible selves, representing identities they consider realistically likely rather than simply desirable or undesirable. A person might, for example, hope to become an award winning author while expecting to pursue an entirely different career. Markus and Nurius (1986) suggest that much of our significant behavior can be seen primarily as an effort to approach or avoid various possible selves. 

Importantly, people do not construct these future identities in isolation. Content of possible selves is shaped by people's experiences and sociocultural circumstances rather than being a manifestation of the isolated self, as well as by temporal, contextual, developmental factors (Allport, 1937; Frazier &amp; Hooker, 2006). Markus and Nurius (1986) argue that the pool of possible selves available to an individual is influenced by socially salient categories and by the models, images, and examples encountered through media and everyday social experience. Elite sport provides a useful illustration:
&lt;div style=&quot;width: 50%; float: right; background-color: #f0f5f8; border-left: 4px solid #527d99; padding: 2px 15px 2px 15px; margin: 0 0 20px 20px; border-radius: 6px; box-sizing: border-box;&quot;&gt;

'''Case study:''' 

[[File:Eliud Kipchoge in Berlin - 2015 (cropped).jpg|thumb|right|110px|'''Figure 2.''' Eliud Kipchoge (2015).]]

In 2019, Kenyan marathon runner Eliud Kipchoge became the first person to complete a marathon distance in under two hours, demonstrating that a feat long considered beyond human capability was, in fact, achievable. By expanding public perceptions of what was possible, Kipchoge may have helped other elite runners imagine similar achievements as part of their own possible futures. Subsequent athletes to break the two-hour barrier likely absorbed the performance of Eliud Kipchoge within the realm of their own possible selves, giving specific cognitive form to their desire to become exceptional runners. 
&lt;/div&gt;

Importantly, people do not construct these future identities in isolation. Content of possible selves is shaped by people's experiences and sociocultural circumstances rather than being a manifestation of the isolated self, as well as by temporal, contextual, developmental factors (Allport, 1937; Frazier &amp; Hooker, 2006). Markus and Nurius (1986) argue that the pool of possible selves available to an individual is influenced by socially salient categories and by the models, images, and examples encountered through media and everyday social experience. Elite sport provides a useful illustration:

Cross and Markus (1991) similarly found systematic differences in hoped-for and feared possible selves across adulthood, illustrating how possible selves change alongside people's circumstances and developmental priorities. Possible selves therefore reflect an interaction between individual aspirations and the social contexts within which those futures are imagined.


=== Forms and content of possible selves &amp; motivational properties of possible selves ===
Possible selves are particularly relevant to motivational psychology because it allows us to make a more direct connection between motives and actions. Markus and Nurius (1986) proposed that future selves can function as incentives for future behaviour by providing a self-relevant framework that gives meaning, organisation, and direction to our actions. For example, imagining oneself as physically healthy and active in later life may encourage behaviours directed towards that future, while imagining a feared future characterised by poor health may provide motivation to avoid it. Thus, possible selves can transform relatively vague and abstract aspirations or fears into outcomes that are explicitly connected to one's identity. 

Yet not all possible selves are equally motivating. Norman and Aron (2003) found that motivation to attain or avoid an important possible self was significantly predicted by its availability, its accessibility, and the extent to which its attainment or avoidance is perceived as under one's control. Hence, merely possessing a desirable or undesirable future image may be insufficient. A future self that feels vague, remote or outside one's control is unlikely to exert the same motivational influence as one that is psychologically accessible and associated with a sense of agency.

Experimental research also indicates that the way a future self is represented can influence subsequent motivation and behaviour. There is a large body of research that has identified characteristics that render possible selves more or less efficient for prompting behaviour. For instance, it is generally accepted that a possible self has to be salient and easily evoked in order to affect behaviour (Strauss, Griffin, &amp; Parker, 2012; King &amp; Raspin 2004; Norman &amp; Aron, 2003). A recent study by De Place and Brunot (2020) manipulated both the specificity and valence of university students’ imagined possible selves. Across two studies, different combinations of general or specific future success and failure produced differences in attention and academic motivation. Importantly, their results were more complex than simply showing that positive or highly specific future images are always beneficial. Such findings reinforce the idea that the motivational influence of a possible self depends not merely on whether the imagined future is positive or negative, but also on how that future is represented (De Place &amp; Brunot, 2020). 

Possible selves therefore offer a potential source of motivation, but should be understood as a more complex interplay of several different cognitions. Explaining how these future identities translate into sustained goal-directed behavior requires consideration of the processes involved in goal pursuit and self-regulation. 

== Goal pursuit and self-regulation ==
Imagining a meaningful future self may provide direction, but it does not guarantee action. Moving towards a hoped-for possible self or away from a feared one requires people to initiate and sustain behaviour, respond to obstacles, and regulate their progress over time. Goal Pursuit and self-regulation therefore provide the bridge between imagined future identities and present behaviour. 

=== From goals to goal-directed behaviour ===
Goals are internal representations of desired states, which are broadly constructed as outcomes, events, or processes that individuals seek to attain, maintain, or avoid (Austin &amp; Vancouver, 1996). Goal pursuit, in turn, refers to the processes through which individuals work to realise these goals. This is an important distinction because simply holding a strong intention (“I intend to do Z”) does not guarantee goal achievement, and people may fail to deal effectively with self-regulatory problems during goal striving. Take a university student for example, they may strongly value becoming a psychologist while repeatedly postponing study, avoid difficult course work, or fail to seek relevant experience. The desired future provides direction, but it must still be translated into action.

Goal-directed behaviour therefore involves a range of processes after a goal has been formed. Contemporary accounts emphasise that once an individual generates an intent to pursue a given goal, they “cross the rubicon” into several stages that involve planning, effort, persistence, progress, monitoring, and adaptation when difficulties arise (Milyavskaya &amp; Werner, 2018). Importantly, intentions alone are poor predictors of subsequent behaviour; Sheeran and Webb (2016) describe a substantial intention-behaviour gap, whereby people frequently fail to act despite intending to do so which occurs approximately half the time. Goal pursuit must also be sustained over time and adjusted in response to obstacles, competing demands, and changes in goal attainability. One highly efficient means of strengthening the transition from intention to action is through implementation intentions, which specify when, where, or how goal-directed behaviour will occur. They take the format of a cognitive association between a prespecified opportunity for acting and a specific goal-directed behaviour (i.e., “if situation x arises, then I will perform behaviour y”) (Brandstatter &amp; Bernecker, 2022). Several studies have proven implementation intentions to be efficacious, helping individuals to support persistence and improve goal attainment (Belanger-Gravel, 2013; Gollwitzer &amp; Sheeran, 2006). Together, this research demonstrates that motivation towards a desired outcome is only one component of successful goal pursuit. 

This distinction is particularly relevant to possible selves. Envisioning oneself as a competent psychologist may establish a meaningful long-term direction, but that future identity becomes behaviourally consequential only when it is coupled to actions such as completing assignments, developing relevant skills, seeking professional experience, and persisting through tough times. Possible selves may help establish where a person wants to go, while goal-directed behaviour concerns the processes required to move towards that future. 

=== Self-regulation in goal pursuit ===

&lt;div style=&quot;float: right; margin: 0px 0 10px 15px;&quot;&gt;
[[File:Determination on the Everest Expedition.jpg|thumb|right|440px|'''Figure 3.''' Mountaineer ascending Himalayan mountains]]
&lt;/div&gt;

The processes involved in directing and maintaining behaviour towards goals are commonly understood through self-regulation. Frazier et al. (2021) describe self-regulation as a social-cognitive process at the intersection of metacognition, motivation, and behaviour which encompasses how people conceptualise, strive for, and accomplish their goals. Once a goal has been adopted, self-regulation helps translate that desired outcome into an ongoing action by allowing individuals to monitor their progress, adjust their behaviour, and respond to obstacles encountered during goal pursuit. 

One particularly influential account conceptualises self-regulation as a discrepancy-reducing feedback loop (Carver &amp; Scheier, 2002). Within this control-process model, individuals compare their present state against a desired reference point and monitor whether a discrepancy exists between the two. Using the goal as a reference, a person compares their present state to the desired end state (i.e., “am I on track for my goal?”). If a discrepancy is detected, the person acts to reduce this discrepancy, thereby engaging in goal-promoting behaviour (Milyavskaya &amp; Werner, 2018). Self-regulation is therefore an ongoing process of comparison, feedback, and behavioural adjustment rather than a single decision to pursue a goal. 

Possible selves may provide one such future-oriented reference point. By representing who an individual wishes to become or wishes to avoid becoming, they can establish standards against which present behaviour and progress are evaluated. However, merely possessing a future standard does not alone explain how strongly it will influence behaviour. Understanding how possible selves become integrated into self-regulation, and why some guide action more effectively than others, requires closer examination of their role within motivated goal pursuit.

== Possible selves in motivated goal pursuit ==
Personal selves can provide meaningful representation of where an individual wishes to go or what they hope to avoid, while self-regulation provides processes through which these future identities may influence present behaviour. The relationship between the two, however, is not straightforward. Contemporary research suggests that the motivational value of a possible self depends less on the seminal formulation of having positive-valence and more on whether that future identity becomes relevant to the affordances and constraints of their immediate situation, and functions effectively within self-regulatory processes (Oyserman &amp; Horowitz, 2023). Understanding possible selves in goal pursuit therefore requires asking not only ''what future does a person imagine?,'' but also ''how does the imagined future influence what they do now?''

=== Modelling the relationships ===
Markus and Nurius’ (1986) original account proposed that possible selves connect cognition and motivation by giving self-relevant form to people's hopes, fears and aspirations, thereby providing incentives for future behaviour. Subsequent theory has refined this relationship. Rather than treating possible selves as a direct cause of motivation or behaviour, they are better understood as components within broader self-regulatory systems (Hoyle &amp; Sherrill, 2006). In this way, a possible self can provide a behavioural standard or future reference point, while other regulatory processes determine whether and how behaviour is organised around it. Studies demonstrate that embedding possible selves within established models of self-regulation provides some impetus to behaviour and outcome change, as well as meaningful predictions about present behavior, supporting a more process-oriented interpretation of their motivational role (Hoyle &amp; Sherrill, 2006; Oyserman et al., 2004; vanDellen &amp; Hoyle, 2008).

Empirical findings support this process-oriented interpretation. A study by vanDellen and Hoyle (2008) experimentally examined whether hoped-for and feared health-related possible selves could function as behavioural standards within self-regulation. After making these possible selves salient, participants were given opportunities to engage in behaviours that could reduce discrepancies between their current and possible selves. Evidence for discrepancy-reducing behaviour was strongest when feared possible selves were salient and participants possessed sufficient self-regulatory capacity, whereas comparable effects were not found for hope-for possibles selves. These findings suggest that possible selves can guide present behaviour by operating as standard within broader self-regulatory processes rather than directly producing goal attainment (vanDellen &amp; Hoyle, 2008). Likewise, possible selves appear more strongly related to behavioural and academic outcomes when they are linked to strategies and can plausibly function as self-regulatory resources rather than merely positive representations of the future (Oserman et al., 2004). Possible selves therefore do not instantiate goal attainment. Rather, their influence depends on the self-regulatory processes in which they are embedded.

&lt;div style=&quot;float: right; margin: 0px 0 10px 15px;&quot;&gt;
[[File:MAPS model of self-regulation.png|thumb|right|360px|'''Figure 3.''' MAPS model of self-regulation (Frazier et al., 2021).]]
&lt;/div&gt;

The MAPS model of self-regulation provides a more recent framework for understanding these processes. Frazier et al., (2021) propose that goal-directed behaviour emerges from dynamic and synergistic interaction between possible selves, metacognitive knowledge and strategies, and a sense of one's own agency. Possible selves embody representations of desired future outcomes and provide motivational direction; metacognitive knowledge helps people select, monitor and modify strategies for pursuing those outcomes; and agency reflects the extent to which individuals perceive themselves as capable of influencing what happens next. Importantly, these elements continually influence one another. Feedback from goal-directed action can alter perceptions of competence and agency, which in turn can reshape strategies and even beliefs about what future selves remain possible.  

Taken together, these accounts suggest that possible selves influence goal pursuit through an indirect and dynamic manner. Imagining a future self can help to make outcomes personally meaningful and provide a benchmark towards which behaviour can be directed. However, movement towards that future requires individuals to identify reasonable approaches, believe in their agency, monitor progress, and adjust their behaviour in response to feedback. Possible selves may therefore provide the direction and motivational meaning of goal pursuit, while self-regulatory processes provide the means through which that direction is translated into present action.  

Additionally, a future identity must feel relevant to choices in the present. From an identity-based motivation perspective, it requires a ‘shift of focus from what ''future me is–''positive or negative, close or distant, continuous or discontinuous ''with current me–''to what ''future me does''’ (Oyserman &amp; Horowitz, 2023, p. 74)''.'' As illustrated in Figures 4 and 5, future-oriented action is more likely when a possible self feels relevant, difficulties are interpreted as signs of importance rather than impossibility, and the required actions feel consistent with one's identity. This helps explain why the same possible self can strongly guide behaviour in one situation while exerting little influence in another.

&lt;div style=&quot;display: flex; gap: 10px; align-items: stretch;&quot;&gt;

&lt;div style=&quot;width: 50%;&quot;&gt;
[[File:When does a future self influence current action?.png|thumb|center|x300px|'''Figure 4.''' Idenity-based motivation processes linking future selves to behaviour (adapted from Oyserman &amp; Horowitz, 2023).]]
&lt;/div&gt;

&lt;div style=&quot;width: 50%;&quot;&gt;
[[File:How identity-based motivation can orient action toward or away from the future.png|thumb|center|x300px|'''Figure 5.''' Identity-based motivation pathways linking future idenities to action (adapted from Oyserman &amp; Horowitz, 2023).]]
&lt;/div&gt;

&lt;/div&gt;

=== When possible selves facilitate goal pursuit ===
An important condition for possible selves to facilitate goal pursuit is their relationship to plausible strategies for action. Oyserman et al., (2004) distinguish between possible selves that are primarily self-enhancing and those capable of functioning as self-regulators. To investigate this, they examined the extent to which detailed academic possible selves, when linked with strategies, added predictive power. Adolescents whose academic possible selves incorporated strategies for attaining desired futures or avoiding feared ones showed greater classroom participation, spent more time on homework, and achieved better academic outcomes. Indeed, having plausibly self-regulating possible selves is more likely to induce self-improvement behaviour and significantly greater chances of success, compared to possible selves that do not include such self-regulatory guideposts (Hoyle &amp; Sherrill, 2006; Oyserman et al., 2004; Oyserman &amp; James, 2009). 

Whether these strategies influence behaviour also depends on the context in which a possible self is brought to mind. Possible selves differ in accessibility, and identities made salient by the immediate situation are more likely to inform judgment and decision making (Higgins, 1996; Oyserman et al., 2006). Consequently, sustained pursuit requires relevant behavioral strategies to be readily available when the future identity becomes salient. For instance, an academic possible self is in theory more effective when the surrounding environment routinely cues behaviours such as attending lectures, persisting through assignments, seeking assistance, or attending study help. Oyserman et al., (2006) argue that resource-rich contexts are more likely to provide accessible models of success and established pathways towards the ideal futures, whereas resource-limited environments may offer fewer such cues. The motivational effectiveness of a possible self therefore depends partly on whether the social environment makes pathways towards it visible and actionable.  

Possible selves are also more likely to motivate when they feel compatible with important social identities and when difficulties encountered during pursuits are interpreted constructively. Identity-based motivation theory proposes that people are more willing to act in ways that fit the identities on their minds which feel relevant to the affordances and constraints of their immediate situation (Oyserman, 2015). A future identity that appears inconsistent with one's social group, circumstances, or understanding of “people like me” may therefore be less likely to organise behaviour, even when it is personally desirable. Importantly, this does not imply effective motivation requires distancing oneself from existing social identities, rather, future identities become more actionable when they can be experienced as compatible with those identities (Oyserman et al., 2006; Oyserman &amp; Horowitz, 2023).

How people interpret difficulty further shapes this process. Difficulty encountered while pursuing a possible self can be understood as evidence that the future is unattainable, encouraging disengagement, or as a normative indication that an important goal requires effort. Identity-based motivation theory highlights the role of metacognitive experience, particularly the subjective feelings of ease or difficulty associated with pursuing a goal (Oyserman, Bybee, &amp; Terry, 2006). When behaviour feels consistent with one's identity, difficulty may be interpreted as a sign that the goal is important and worth pursuing rather than an impossibility, i.e., “no pain no gain” (Oyserman &amp; Horowitz, 2023). Thus, the motivational consequences of difficulty depend not simply on how hard goal pursuit feels, but on the metacognitive experience of the difficulty and the meaning attributed to that experience.  

Taken together, possible selves are more likely to facilitate goal pursuit when they are connected to realistic strategies, supported and cued by the surrounding context, compatible with salient identities, resilient to experiences of difficulty, and personally meaningful enough to sustain commitment (Haskins &amp; vanDellen, 2019). Their motivational value therefore lies in whether that future can be integrated with the circumstances, interpretations, and actions of the present self. 

=== When possible selves fail to motivate ===
Possible selves can remain self-enhancing rather than self-regulatory, such that possible selves promote positive feelings and maintain a sense of optimism and hope for the future without evoking behavioural strategies required to reach it (Oyserman et al., 2004). For example, a university student may say to themselves ‘I may not be doing well in university this semester but I will succeed next semester’, thereby protecting their self-esteem from the current bad grades, without engaging in any behavioural strategies to improve their academic performance in the following semester. This distinction illustrates why simply valuing or vividly imagining a possible self is insufficient for goal pursuit. 

Importantly, failure to act does not necessarily reflect a lack of ambition, as socioeconomic and social contexts can constrain access to the strategies, role models, and opportunities needed to make a future identity actionable. In low socio-economic contexts, behavioural strategies may be less readily accessible due to fewer role models and resources to guide goal pursuit (Oyserman, Bybee, &amp; Terry, 2006). Furthermore, Oyserman, Johnson, and James (2011) describe part of the problem as “seeing the destination but not the path”; disadvantaged adolescents could hold salient school-focused possible selves while possessing fewer strategies for attaining them. Likewise, difficulty can undermine pursuit when it is interpreted as signaling impossibility rather than importance, particularly when the future identity feels incongruent with one's circumstances or social identities (Oyserman et al., 2006; Oyserman &amp; Horowitz, 2023). Thus, motivational value lies in whether the future self can be translated into plausible, identity-congruent, and contextually supported pathways for behavioral action. 

== Harnessing possible selves for goal pursuit ==

&lt;div style=&quot;float: right; margin: 0px 0 10px 15px;&quot;&gt;
[[File:Ballet, mirror, parquet floor, dance room Fortepan 85036.jpg|thumb|right|420px|'''Figure 6.''' Dancer refining her practice.]]
&lt;/div&gt;

The mechanisms discussed throughout this chapter raise a question: can possible selves be deliberately harnessed to improve goal pursuit? Intervention research provides some evidence that they can. Oyserman et al. (2006) developed a school-based intervention to link academic possible selves with behavioural strategies, a context in which social and personal identities felt congruent, and constructive interpretations of difficulty. Compared with controls, participating adolescents subsequently showed greater academic initiative, improved grades and standardized test scores, fewer absences, and reduced school misbehaviour, with effects sustained over a two-year follow up. More recent research has extended this approach using digital representations of the future self. In a 2026 randomised controlled trial, interventions delivered through smartphone and virtual reality strengthened identification with the future self through visual and interactive experiences, with the virtual reality condition also increasing goal achievement (van Gelder et al., 2026).

However, intervention findings also caution against treating future-self imagery as a simple motivational technique. The same 2026 trial found no improvements in several other outcomes, including academic performance and self-defeating behaviour, suggesting that strengthening future-self identification does not automatically produce broad behavioural change (van Gelder et al., 2026). Additionally, Tettero et al., (2026) conducted a study to investigate how the three components of future self-identification—vividness, connectedness, and valence—were associated with goal achievement over time. It was found that vividness of the future self most consistently predicted subsequent goal achievement, connectedness contributed more modestly, while valence did not predict achievement, which aligns with research that came before it (Kuo et al., 2025). It is believed that the richness of vivid mental images makes the future self more concrete and realistic, reducing the psychological distance between the self and possible self, thus enhancing the perceived relevance of future goals (Bixter et al., 2020; Evans &amp; Wilson, 2014; Hershfield, 2011). These findings reinforce the broader conclusion of this chapter: the motivational value of possible selves lies not simply in imagining a desirable future, but in whether that future becomes sufficiently concrete, relevant, and actionable to influence behaviour.

== Extra sources ==
*Possible selves, self regulation and actual social goal progress (2014)
*Best possible self intervention and academic motivation/commitment (2020)
*Identity-based motivation (2015) 

== Conclusion ==
Possible selves influence motivation and goal-directed behaviour by giving personally meaningful form to the futures people hope to attain or avoid, but their motivational value is neither direct nor certain. Psychological research suggests that they are most effective when they function within broader self-regulatory processes, provide a meaningful future-oriented reference point, and are linked to realistic behavioural strategies, metacognitive monitoring, and a sense of agency. Whether a possible self translates into action further depends on whether it is accessible in the present, compatible with salient social identities, supported by the surrounding context, and resilient to experiences of difficulty. Difficulty can strengthen persistence when interpreted as a normative aspect of pursuing an important goal, but undermine pursuit when it suggests impossibility. Possible selves therefore provide the direction and motivational meaning of goal pursuit, while self-regulatory processes provide the means through which that direction is translated into present action. The practical implication is this: imagining a desirable future is not enough; possible selves become motivationally effective when they are concrete, actionable, and connected to what a person can do now.&lt;div style=&quot;background-color: #fceef3; border: 1px solid #c77b98; border-radius: 10px; padding: 12px 18px; margin: 15px 0;&quot;&gt;

'''Chapter comprehension check'''

&lt;div style=&quot;margin-top: -50px;&quot;&gt;
&lt;quiz display=simple&gt;
{Possible selves are future-oriented representations of who a person might become and can provide motivational direction to present behaviour.
|type=&quot;()&quot;}
+ True
- False

{Possible selves directly produce goal-directed behaviour without relying on broader self-regulatory processes.
|type=&quot;()&quot;}
- True
+ False

{A possible self is more likely to facilitate goal pursuit when it is connected to plausible strategies, relevant to the current context, and compatible with salient identities.
|type=&quot;()&quot;}
+ True
- False

{Interventions strengthen goal pursuit simply by encouraging people to imagine a positive future self.
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;
&lt;/div&gt;
&lt;/div&gt;

==See also==
* [[w:Future self|Future self]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Regulatory focus theory and goal pursuit|Regulatory focus theory and goal pursuits]] (Book chapter, 2019)
* [[w:Goal pursuit|Goal Pursuit]] (Wikipedia)

==References==
{{Hanging indent|1=

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de Place, A.-L., &amp; Brunot, S. (2019). Motivational and behavioral impact of possible selves: When specificity matters. Imagination, Cognition and Personality, 39(4), 329–247. https://doi.org/10.1177/0276236619864275

Erikson, M. G. (2007). The meaning of the future: Toward a more specific definition of possible selves. Review of General Psychology, 11(4), 348–358. https://doi.org/10.1037/1089-2680.11.4.348

Evans, M. B., &amp; Wilson, A. E. (2014). Subjective temporal proximity to future selves moderates the link between exercise intentions and behavior. Sport, Exercise, and Performance Psychology, 3(3), 184–190. https://doi.org/10.1037/spy0000014

Frazier, L. D, &amp; Hooker, K. (2006). APA PsycNet. Apa.Org. https://psycnet.apa.org/record/2006-04587-003

Frazier, L. D., Schwartz, B. L., &amp; Metcalfe, J. (2021). The MAPS model of self-regulation: Integrating metacognition, agency, and possible selves. Metacognition and Learning, 16(2). https://doi.org/10.1007/s11409-020-09255-3 

Gollwitzer, P. M. (1999). Implementation intentions: Strong effects of simple plans. American Psychologist, 54(7), 493–503. https://doi.org/10.1037/0003-066x.54.7.493

Gollwitzer, P. M., &amp; Sheeran, P. (2006). Implementation intentions and goal achievement: A meta‐analysis of effects and processes. Advances in Experimental Social Psychology, 38(1), 69–119. https://doi.org/https://doi.org/10.1016/S0065-2601(06)38002-1

Haskins, L. B., &amp; vanDellen, M. R. (2019). Self‐regulation as relating to one’s ideal possible self. Social and Personality Psychology Compass, 13(10). https://doi.org/10.1111/spc3.12499

Hershfield, H. E. (2011). Future self‐continuity: How conceptions of the future self transform intertemporal choice. Annals of the New York Academy of Sciences, 1235(1), 30–43. https://doi.org/10.1111/j.1749-6632.2011.06201.x

Higgins, E. T. (1996). Ideals, oughts, and regulatory focus: Affect and motivation from distinct pains and pleasures. In The psychology of action: Linking cognition and motivation to behavior. (pp. 91–114). The Guilford Press. https://psycnet.apa.org/record/1996-98326-005

Hoyle, R. H., &amp; Sherrill, M. R. (2006). Future orientation in the self-system: Possible selves, self-regulation, and behavior. Journal of Personality, 74(6), 1673–1696. https://doi.org/10.1111/j.1467-6494.2006.00424.x

King, L. A., &amp; Raspin, C. (2004). Lost and found possible selves, subjective well-being, and ego development in divorced women. Journal of Personality, 72(3), 603–632. https://doi.org/10.1111/j.0022-3506.2004.00274.x

Markus, H., &amp; Nurius, P. (1986). Possible selves. American Psychologist, 41(9), 954–969. https://doi.org/https://doi.org/10.1037/0003-066X.41.9.954

Milyavskaya, M., &amp; Werner, K. M. (2018). Goal pursuit: Current state of affairs and directions for future research. Canadian Psychology/Psychologie Canadienne, 59(2), 163–175. https://doi.org/10.1037/cap0000147

Murru, E. C., &amp; Martin Ginis, K. A. (2010). Imagining the possibilities: The effects of a possible selves intervention on self-regulatory efficacy and exercise behavior. Journal of Sport &amp; Exercise Psychology, 32(4), 537–554. https://doi.org/10.1123/jsep.32.4.537

Norman, C. C., &amp; Aron, A. (2003). Aspects of possible self that predict motivation to achieve or avoid it. Journal of Experimental Social Psychology, 39(5), 500–507. https://doi.org/10.1016/S0022-1031(03)00029-5

Oyserman, D. (2009). Identity‐based motivation: Implications for action‐readiness, procedural‐readiness, and consumer behavior. Journal of Consumer Psychology, 19(3), 250–260. https://doi.org/10.1016/j.jcps.2009.05.008

Oyserman, D. (2015). Pathways to success through identity-based motivation. Oxford University Press. https://psycnet.apa.org/record/2015-16643-000

Oyserman, D., Bybee, D., &amp; Terry, K. (2006). Possible selves and academic outcomes: How and when possible selves impel action. Journal of Personality and Social Psychology, 91(1), 188–204. https://doi.org/10.1037/0022-3514.91.1.188

Oyserman, D., Bybee, D., Terry, K., &amp; Hart-Johnson, T. (2004). Possible selves as roadmaps. Journal of Research in Personality, 38(2), 130–149. https://doi.org/10.1016/s0092-6566(03)00057-6

Oyserman, D., &amp; Horowitz, E. (2023). From possible selves and future selves to current action: An integrated review and identity-based motivation synthesis. In Advances in Motivation Science (pp. 73–147). Elsevier Inc.

Sheeran, P., &amp; Webb, T. L. (2016). The intention-behavior gap. Social and Personality Psychology Compass, 10(9), 503–518. https://doi.org/10.1111/spc3.12265

Strauss, K., Griffin, M. A., &amp; Parker, S. K. (2012). Future work selves: How salient hoped-for identities motivate proactive career behaviors. Journal of Applied Psychology, 97(3), 580–598. https://doi.org/10.1037/a0026423

Tettero, T., Mertens, E. C. A., Siezenga, A. M., &amp; van Gelder, J.-L. (2026). From future vision to current action: The relationship between future self-identification and goal achievement. Personality and Individual Differences, 254, 113645. https://doi.org/10.1016/j.paid.2026.113645

van Gelder, J.-L., Tettero, T., Siezenga, A., &amp; Mertens, E. (2026). Stimulating future-oriented thinking and goal-achievement through the future self using virtual reality and a smartphone app: Randomized controlled trial. Journal of Medical Internet Research, 28, e84420–e84420. https://doi.org/10.2196/84420

vanDellen, M. R., &amp; Hoyle, R. H. (2008). Possible selves as behavioral standards in self-regulation. Self and Identity, 7(3), 295–304. https://doi.org/10.1080/15298860701641108}}

==External links==
* [https://www.hiddenbrain.org/podcast/you-2-0-your-future-is-now/ You 2.0: your future is now] (Hidden Brain)
* [https://www.youtube.com/watch?v=XNbaR54Gpj4&amp;t=177s The psychology of you future self | Dan Gilbert] (Youtube)
* [https://www.psychologytoday.com/au/blog/philosophy-and-therapy/202401/the-philosophy-of-possible-selves Why to start considering your possible selves] (Psychology Today)</text>
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==Overview==
{{RoundBoxTop|theme=3}}
[[File:Ueber-die-sammlung-19-jahrhundert-caspar-david-friedrich-wanderer-ueber-dem-nebelmeer.jpg|thumb|right|150px|'''Figure 1'''. The wanderer looks across a sea of fog toward the looming mountains, symbolising the current self and possible self.]]

; Scenario

A university student has started their final year of their bachelor's degree, and the academic standards are higher than previous years. One may imagine their future as exciting: graduating, beginning a meaningful career, becoming financially independent, and becoming the capable and competent person they hope to be. Alternatively, they may imagine their future as unsettling: losing motivation, failing to make use of their opportunities, and becoming someone they once hoped to avoid.

Neither future exists, however, these imagined versions of the self can influence what the student does today – whether they attend lectures and tutorials, persist through difficult assignments and exams, or give up when progress feels slow.
{{RoundBoxBottom}}[https://journals.sagepub.com/doi/10.1037/1089-2680.11.4.348 Possible selves] {{ic|Use either APA style or wiki style, but don't embed external links}} are conceptions of who we may become in the future and involve, to some degree, imagining ourselves as agents within those future situations (Erikson, 2007). They can include versions of ourselves that we hope to become, as well as those we fear becoming. Markus and Nurius (1986) proposed that these future self-representations are motivationally important because they can provide incentives for behaviour and give personal meaning and direction to our goals.

In the opening scenario, the university student can imagine both a desired future of graduating and beginning a meaningful career, and an unwanted future characterised by lost opportunities and lack of direction. Yet imagining either future does not guarantee that the student will study, persist through setbacks, or take advantage of opportunities in the present. This illustrates a central problem in understanding possible selves: how does an imagined future identity become motivation and, ultimately, goal-directed behaviour?

Literature during the 21st century suggests that possible selves are better understood as components of self-regulation through which motivation and behaviour are influenced (Hoyle &amp; Sherrill, 2006; Frazier, Schwartz &amp; Metcalfe, 2021). Research therefore focuses on the conditions under which possible selves provide effective guidance for goal pursuit, including whether they are meaningful, attainable, and connected to realistic behavioural strategies. Examining these processes help to explain why imagined future identities can motivate present goal-directed behaviour in some circumstances, yet remain ineffective in others (Haskins &amp; vanDellen, 2019).

&lt;div style=&quot;background-color: #fbedf2; border: 2px solid #d4779b; border-radius: 12px; padding: 15px 20px;&quot;&gt;
'''Focus questions'''

*What are possible selves, and why can they have motivational significance?
*How do possible selves interact with self-regulatory processes involved in goal pursuit?
*Under what conditions do possible selves facilitate - or fail to facilitate - goal-directed behaviour?
* How can possible selves be used to strengthen motivation and translate future aspirations into present action?
&lt;/div&gt;

== Possible selves ==
=== Definition and theoretical origins ===
The concept of possible selves was introduced by Markus and Nurius (1986) to complement current conceptions of self-knowledge by extending it beyond the present.  They proposed that possible selves represent individuals' ideas of what they might become, what they would like to become, and what they are afraid of becoming, and thus provide a conceptual link between cognition and motivations. More recently, Erikson (2007) emphasised agency, arguing that possible selves involve experiencing oneself, at least to some degree, as an agent within an imagined future situation. This distinguishes a possible self from a simple goal: Wanting to receive a high grade describes a desired outcome, whereas imagining oneself as a capable and successful student places the person within a future identity. Possible selves are therefore closely related to goals, but are distinguished by their explicit connection to who the individual might become. 

Possible selves can take several forms. Hoped-for possible selves represent desirable identities that a person would like to attain. This could include the competent and powerful self, the celebrated and glamorous self, the respected and esteemed self, or the fit self. In contrast, the feared possible selves comprise a similarly compelling set. One's fears and anxieties can become concretely manifest in visions of the lonely self, the undervalued and underpaid self, or the out-of-shape self (Cross &amp; Markus, 1991). Additionally, people may also hold expected possible selves, representing identities they consider realistically likely rather than simply desirable or undesirable. A person might, for example, hope to become an award winning author while expecting to pursue an entirely different career. Markus and Nurius (1986) suggest that much of our significant behavior can be seen primarily as an effort to approach or avoid various possible selves. 

Importantly, people do not construct these future identities in isolation. Content of possible selves is shaped by people's experiences and sociocultural circumstances rather than being a manifestation of the isolated self, as well as by temporal, contextual, developmental factors (Allport, 1937; Frazier &amp; Hooker, 2006). Markus and Nurius (1986) argue that the pool of possible selves available to an individual is influenced by socially salient categories and by the models, images, and examples encountered through media and everyday social experience. Elite sport provides a useful illustration:
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'''Case study:''' 

[[File:Eliud Kipchoge in Berlin - 2015 (cropped).jpg|thumb|right|110px|'''Figure 2.''' Eliud Kipchoge (2015).]]

In 2019, Kenyan marathon runner Eliud Kipchoge became the first person to complete a marathon distance in under two hours, demonstrating that a feat long considered beyond human capability was, in fact, achievable. By expanding public perceptions of what was possible, Kipchoge may have helped other elite runners imagine similar achievements as part of their own possible futures. Subsequent athletes to break the two-hour barrier likely absorbed the performance of Eliud Kipchoge within the realm of their own possible selves, giving specific cognitive form to their desire to become exceptional runners. 
&lt;/div&gt;

Importantly, people do not construct these future identities in isolation. Content of possible selves is shaped by people's experiences and sociocultural circumstances rather than being a manifestation of the isolated self, as well as by temporal, contextual, developmental factors (Allport, 1937; Frazier &amp; Hooker, 2006). Markus and Nurius (1986) argue that the pool of possible selves available to an individual is influenced by socially salient categories and by the models, images, and examples encountered through media and everyday social experience. Elite sport provides a useful illustration:

Cross and Markus (1991) similarly found systematic differences in hoped-for and feared possible selves across adulthood, illustrating how possible selves change alongside people's circumstances and developmental priorities. Possible selves therefore reflect an interaction between individual aspirations and the social contexts within which those futures are imagined.


=== Forms and content of possible selves &amp; motivational properties of possible selves ===
Possible selves are particularly relevant to motivational psychology because it allows us to make a more direct connection between motives and actions. Markus and Nurius (1986) proposed that future selves can function as incentives for future behaviour by providing a self-relevant framework that gives meaning, organisation, and direction to our actions. For example, imagining oneself as physically healthy and active in later life may encourage behaviours directed towards that future, while imagining a feared future characterised by poor health may provide motivation to avoid it. Thus, possible selves can transform relatively vague and abstract aspirations or fears into outcomes that are explicitly connected to one's identity. 

Yet not all possible selves are equally motivating. Norman and Aron (2003) found that motivation to attain or avoid an important possible self was significantly predicted by its availability, its accessibility, and the extent to which its attainment or avoidance is perceived as under one's control. Hence, merely possessing a desirable or undesirable future image may be insufficient. A future self that feels vague, remote or outside one's control is unlikely to exert the same motivational influence as one that is psychologically accessible and associated with a sense of agency.

Experimental research also indicates that the way a future self is represented can influence subsequent motivation and behaviour. There is a large body of research that has identified characteristics that render possible selves more or less efficient for prompting behaviour. For instance, it is generally accepted that a possible self has to be salient and easily evoked in order to affect behaviour (Strauss, Griffin, &amp; Parker, 2012; King &amp; Raspin 2004; Norman &amp; Aron, 2003). A recent study by De Place and Brunot (2020) manipulated both the specificity and valence of university students’ imagined possible selves. Across two studies, different combinations of general or specific future success and failure produced differences in attention and academic motivation. Importantly, their results were more complex than simply showing that positive or highly specific future images are always beneficial. Such findings reinforce the idea that the motivational influence of a possible self depends not merely on whether the imagined future is positive or negative, but also on how that future is represented (De Place &amp; Brunot, 2020). 

Possible selves therefore offer a potential source of motivation, but should be understood as a more complex interplay of several different cognitions. Explaining how these future identities translate into sustained goal-directed behavior requires consideration of the processes involved in goal pursuit and self-regulation. 

== Goal pursuit and self-regulation ==
Imagining a meaningful future self may provide direction, but it does not guarantee action. Moving towards a hoped-for possible self or away from a feared one requires people to initiate and sustain behaviour, respond to obstacles, and regulate their progress over time. Goal Pursuit and self-regulation therefore provide the bridge between imagined future identities and present behaviour. 

=== From goals to goal-directed behaviour ===
Goals are internal representations of desired states, which are broadly constructed as outcomes, events, or processes that individuals seek to attain, maintain, or avoid (Austin &amp; Vancouver, 1996). Goal pursuit, in turn, refers to the processes through which individuals work to realise these goals. This is an important distinction because simply holding a strong intention (“I intend to do Z”) does not guarantee goal achievement, and people may fail to deal effectively with self-regulatory problems during goal striving. Take a university student for example, they may strongly value becoming a psychologist while repeatedly postponing study, avoid difficult course work, or fail to seek relevant experience. The desired future provides direction, but it must still be translated into action.

Goal-directed behaviour therefore involves a range of processes after a goal has been formed. Contemporary accounts emphasise that once an individual generates an intent to pursue a given goal, they “cross the rubicon” into several stages that involve planning, effort, persistence, progress, monitoring, and adaptation when difficulties arise (Milyavskaya &amp; Werner, 2018). Importantly, intentions alone are poor predictors of subsequent behaviour; Sheeran and Webb (2016) describe a substantial intention-behaviour gap, whereby people frequently fail to act despite intending to do so which occurs approximately half the time. Goal pursuit must also be sustained over time and adjusted in response to obstacles, competing demands, and changes in goal attainability. One highly efficient means of strengthening the transition from intention to action is through implementation intentions, which specify when, where, or how goal-directed behaviour will occur. They take the format of a cognitive association between a prespecified opportunity for acting and a specific goal-directed behaviour (i.e., “if situation x arises, then I will perform behaviour y”) (Brandstatter &amp; Bernecker, 2022). Several studies have proven implementation intentions to be efficacious, helping individuals to support persistence and improve goal attainment (Belanger-Gravel, 2013; Gollwitzer &amp; Sheeran, 2006). Together, this research demonstrates that motivation towards a desired outcome is only one component of successful goal pursuit. 

This distinction is particularly relevant to possible selves. Envisioning oneself as a competent psychologist may establish a meaningful long-term direction, but that future identity becomes behaviourally consequential only when it is coupled to actions such as completing assignments, developing relevant skills, seeking professional experience, and persisting through tough times. Possible selves may help establish where a person wants to go, while goal-directed behaviour concerns the processes required to move towards that future. 

=== Self-regulation in goal pursuit ===

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[[File:Determination on the Everest Expedition.jpg|thumb|right|440px|'''Figure 3.''' Mountaineer ascending Himalayan mountains]]
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The processes involved in directing and maintaining behaviour towards goals are commonly understood through self-regulation. Frazier et al. (2021) describe self-regulation as a social-cognitive process at the intersection of metacognition, motivation, and behaviour which encompasses how people conceptualise, strive for, and accomplish their goals. Once a goal has been adopted, self-regulation helps translate that desired outcome into an ongoing action by allowing individuals to monitor their progress, adjust their behaviour, and respond to obstacles encountered during goal pursuit. 

One particularly influential account conceptualises self-regulation as a discrepancy-reducing feedback loop (Carver &amp; Scheier, 2002). Within this control-process model, individuals compare their present state against a desired reference point and monitor whether a discrepancy exists between the two. Using the goal as a reference, a person compares their present state to the desired end state (i.e., “am I on track for my goal?”). If a discrepancy is detected, the person acts to reduce this discrepancy, thereby engaging in goal-promoting behaviour (Milyavskaya &amp; Werner, 2018). Self-regulation is therefore an ongoing process of comparison, feedback, and behavioural adjustment rather than a single decision to pursue a goal. 

Possible selves may provide one such future-oriented reference point. By representing who an individual wishes to become or wishes to avoid becoming, they can establish standards against which present behaviour and progress are evaluated. However, merely possessing a future standard does not alone explain how strongly it will influence behaviour. Understanding how possible selves become integrated into self-regulation, and why some guide action more effectively than others, requires closer examination of their role within motivated goal pursuit.

== Possible selves in motivated goal pursuit ==
Personal selves can provide meaningful representation of where an individual wishes to go or what they hope to avoid, while self-regulation provides processes through which these future identities may influence present behaviour. The relationship between the two, however, is not straightforward. Contemporary research suggests that the motivational value of a possible self depends less on the seminal formulation of having positive-valence and more on whether that future identity becomes relevant to the affordances and constraints of their immediate situation, and functions effectively within self-regulatory processes (Oyserman &amp; Horowitz, 2023). Understanding possible selves in goal pursuit therefore requires asking not only ''what future does a person imagine?,'' but also ''how does the imagined future influence what they do now?''

=== Modelling the relationships ===
Markus and Nurius’ (1986) original account proposed that possible selves connect cognition and motivation by giving self-relevant form to people's hopes, fears and aspirations, thereby providing incentives for future behaviour. Subsequent theory has refined this relationship. Rather than treating possible selves as a direct cause of motivation or behaviour, they are better understood as components within broader self-regulatory systems (Hoyle &amp; Sherrill, 2006). In this way, a possible self can provide a behavioural standard or future reference point, while other regulatory processes determine whether and how behaviour is organised around it. Studies demonstrate that embedding possible selves within established models of self-regulation provides some impetus to behaviour and outcome change, as well as meaningful predictions about present behavior, supporting a more process-oriented interpretation of their motivational role (Hoyle &amp; Sherrill, 2006; Oyserman et al., 2004; vanDellen &amp; Hoyle, 2008).

Empirical findings support this process-oriented interpretation. A study by vanDellen and Hoyle (2008) experimentally examined whether hoped-for and feared health-related possible selves could function as behavioural standards within self-regulation. After making these possible selves salient, participants were given opportunities to engage in behaviours that could reduce discrepancies between their current and possible selves. Evidence for discrepancy-reducing behaviour was strongest when feared possible selves were salient and participants possessed sufficient self-regulatory capacity, whereas comparable effects were not found for hope-for possibles selves. These findings suggest that possible selves can guide present behaviour by operating as standard within broader self-regulatory processes rather than directly producing goal attainment (vanDellen &amp; Hoyle, 2008). Likewise, possible selves appear more strongly related to behavioural and academic outcomes when they are linked to strategies and can plausibly function as self-regulatory resources rather than merely positive representations of the future (Oserman et al., 2004). Possible selves therefore do not instantiate goal attainment. Rather, their influence depends on the self-regulatory processes in which they are embedded.

&lt;div style=&quot;float: right; margin: 0px 0 10px 15px;&quot;&gt;
[[File:MAPS model of self-regulation.png|thumb|right|360px|'''Figure 4.''' MAPS model of self-regulation (Frazier et al., 2021).]]
&lt;/div&gt;

The MAPS model of self-regulation provides a more recent framework for understanding these processes. Frazier et al., (2021) propose that goal-directed behaviour emerges from dynamic and synergistic interaction between possible selves, metacognitive knowledge and strategies, and a sense of one's own agency. Possible selves embody representations of desired future outcomes and provide motivational direction; metacognitive knowledge helps people select, monitor and modify strategies for pursuing those outcomes; and agency reflects the extent to which individuals perceive themselves as capable of influencing what happens next. Importantly, these elements continually influence one another. Feedback from goal-directed action can alter perceptions of competence and agency, which in turn can reshape strategies and even beliefs about what future selves remain possible.  

Taken together, these accounts suggest that possible selves influence goal pursuit through an indirect and dynamic manner. Imagining a future self can help to make outcomes personally meaningful and provide a benchmark towards which behaviour can be directed. However, movement towards that future requires individuals to identify reasonable approaches, believe in their agency, monitor progress, and adjust their behaviour in response to feedback. Possible selves may therefore provide the direction and motivational meaning of goal pursuit, while self-regulatory processes provide the means through which that direction is translated into present action.  

Additionally, a future identity must feel relevant to choices in the present. From an identity-based motivation perspective, it requires a ‘shift of focus from what ''future me is–''positive or negative, close or distant, continuous or discontinuous ''with current me–''to what ''future me does''’ (Oyserman &amp; Horowitz, 2023, p. 74)''.'' As illustrated in Figures 5 and 6, future-oriented action is more likely when a possible self feels relevant, difficulties are interpreted as signs of importance rather than impossibility, and the required actions feel consistent with one's identity. This helps explain why the same possible self can strongly guide behaviour in one situation while exerting little influence in another.

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&lt;div style=&quot;width: 50%;&quot;&gt;
[[File:When does a future self influence current action?.png|thumb|center|x300px|'''Figure 5.''' Idenity-based motivation processes linking future selves to behaviour (adapted from Oyserman &amp; Horowitz, 2023).]]
&lt;/div&gt;

&lt;div style=&quot;width: 50%;&quot;&gt;
[[File:How identity-based motivation can orient action toward or away from the future.png|thumb|center|x300px|'''Figure 6.''' Identity-based motivation pathways linking future idenities to action (adapted from Oyserman &amp; Horowitz, 2023).]]
&lt;/div&gt;

&lt;/div&gt;

=== When possible selves facilitate goal pursuit ===
An important condition for possible selves to facilitate goal pursuit is their relationship to plausible strategies for action. Oyserman et al., (2004) distinguish between possible selves that are primarily self-enhancing and those capable of functioning as self-regulators. To investigate this, they examined the extent to which detailed academic possible selves, when linked with strategies, added predictive power. Adolescents whose academic possible selves incorporated strategies for attaining desired futures or avoiding feared ones showed greater classroom participation, spent more time on homework, and achieved better academic outcomes. Indeed, having plausibly self-regulating possible selves is more likely to induce self-improvement behaviour and significantly greater chances of success, compared to possible selves that do not include such self-regulatory guideposts (Hoyle &amp; Sherrill, 2006; Oyserman et al., 2004; Oyserman &amp; James, 2009). 

Whether these strategies influence behaviour also depends on the context in which a possible self is brought to mind. Possible selves differ in accessibility, and identities made salient by the immediate situation are more likely to inform judgment and decision making (Higgins, 1996; Oyserman et al., 2006). Consequently, sustained pursuit requires relevant behavioral strategies to be readily available when the future identity becomes salient. For instance, an academic possible self is in theory more effective when the surrounding environment routinely cues behaviours such as attending lectures, persisting through assignments, seeking assistance, or attending study help. Oyserman et al., (2006) argue that resource-rich contexts are more likely to provide accessible models of success and established pathways towards the ideal futures, whereas resource-limited environments may offer fewer such cues. The motivational effectiveness of a possible self therefore depends partly on whether the social environment makes pathways towards it visible and actionable.  

Possible selves are also more likely to motivate when they feel compatible with important social identities and when difficulties encountered during pursuits are interpreted constructively. Identity-based motivation theory proposes that people are more willing to act in ways that fit the identities on their minds which feel relevant to the affordances and constraints of their immediate situation (Oyserman, 2015). A future identity that appears inconsistent with one's social group, circumstances, or understanding of “people like me” may therefore be less likely to organise behaviour, even when it is personally desirable. Importantly, this does not imply effective motivation requires distancing oneself from existing social identities, rather, future identities become more actionable when they can be experienced as compatible with those identities (Oyserman et al., 2006; Oyserman &amp; Horowitz, 2023).

How people interpret difficulty further shapes this process. Difficulty encountered while pursuing a possible self can be understood as evidence that the future is unattainable, encouraging disengagement, or as a normative indication that an important goal requires effort. Identity-based motivation theory highlights the role of metacognitive experience, particularly the subjective feelings of ease or difficulty associated with pursuing a goal (Oyserman, Bybee, &amp; Terry, 2006). When behaviour feels consistent with one's identity, difficulty may be interpreted as a sign that the goal is important and worth pursuing rather than an impossibility, i.e., “no pain no gain” (Oyserman &amp; Horowitz, 2023). Thus, the motivational consequences of difficulty depend not simply on how hard goal pursuit feels, but on the metacognitive experience of the difficulty and the meaning attributed to that experience.  

Taken together, possible selves are more likely to facilitate goal pursuit when they are connected to realistic strategies, supported and cued by the surrounding context, compatible with salient identities, resilient to experiences of difficulty, and personally meaningful enough to sustain commitment (Haskins &amp; vanDellen, 2019). Their motivational value therefore lies in whether that future can be integrated with the circumstances, interpretations, and actions of the present self. 

=== When possible selves fail to motivate ===
Possible selves can remain self-enhancing rather than self-regulatory, such that possible selves promote positive feelings and maintain a sense of optimism and hope for the future without evoking behavioural strategies required to reach it (Oyserman et al., 2004). For example, a university student may say to themselves ‘I may not be doing well in university this semester but I will succeed next semester’, thereby protecting their self-esteem from the current bad grades, without engaging in any behavioural strategies to improve their academic performance in the following semester. This distinction illustrates why simply valuing or vividly imagining a possible self is insufficient for goal pursuit. 

Importantly, failure to act does not necessarily reflect a lack of ambition, as socioeconomic and social contexts can constrain access to the strategies, role models, and opportunities needed to make a future identity actionable. In low socio-economic contexts, behavioural strategies may be less readily accessible due to fewer role models and resources to guide goal pursuit (Oyserman, Bybee, &amp; Terry, 2006). Furthermore, Oyserman, Johnson, and James (2011) describe part of the problem as “seeing the destination but not the path”; disadvantaged adolescents could hold salient school-focused possible selves while possessing fewer strategies for attaining them. Likewise, difficulty can undermine pursuit when it is interpreted as signaling impossibility rather than importance, particularly when the future identity feels incongruent with one's circumstances or social identities (Oyserman et al., 2006; Oyserman &amp; Horowitz, 2023). Thus, motivational value lies in whether the future self can be translated into plausible, identity-congruent, and contextually supported pathways for behavioral action. 

== Harnessing possible selves for goal pursuit ==

&lt;div style=&quot;float: right; margin: 0px 0 10px 15px;&quot;&gt;
[[File:Ballet, mirror, parquet floor, dance room Fortepan 85036.jpg|thumb|right|420px|'''Figure 6.''' Dancer refining her practice.]]
&lt;/div&gt;

The mechanisms discussed throughout this chapter raise a question: can possible selves be deliberately harnessed to improve goal pursuit? Intervention research provides some evidence that they can. Oyserman et al. (2006) developed a school-based intervention to link academic possible selves with behavioural strategies, a context in which social and personal identities felt congruent, and constructive interpretations of difficulty. Compared with controls, participating adolescents subsequently showed greater academic initiative, improved grades and standardized test scores, fewer absences, and reduced school misbehaviour, with effects sustained over a two-year follow up. More recent research has extended this approach using digital representations of the future self. In a 2026 randomised controlled trial, interventions delivered through smartphone and virtual reality strengthened identification with the future self through visual and interactive experiences, with the virtual reality condition also increasing goal achievement (van Gelder et al., 2026).

However, intervention findings also caution against treating future-self imagery as a simple motivational technique. The same 2026 trial found no improvements in several other outcomes, including academic performance and self-defeating behaviour, suggesting that strengthening future-self identification does not automatically produce broad behavioural change (van Gelder et al., 2026). Additionally, Tettero et al., (2026) conducted a study to investigate how the three components of future self-identification—vividness, connectedness, and valence—were associated with goal achievement over time. It was found that vividness of the future self most consistently predicted subsequent goal achievement, connectedness contributed more modestly, while valence did not predict achievement, which aligns with research that came before it (Kuo et al., 2025). It is believed that the richness of vivid mental images makes the future self more concrete and realistic, reducing the psychological distance between the self and possible self, thus enhancing the perceived relevance of future goals (Bixter et al., 2020; Evans &amp; Wilson, 2014; Hershfield, 2011). These findings reinforce the broader conclusion of this chapter: the motivational value of possible selves lies not simply in imagining a desirable future, but in whether that future becomes sufficiently concrete, relevant, and actionable to influence behaviour.

== Extra sources ==
*Possible selves, self regulation and actual social goal progress (2014)
*Best possible self intervention and academic motivation/commitment (2020)
*Identity-based motivation (2015) 

== Conclusion ==
Possible selves influence motivation and goal-directed behaviour by giving personally meaningful form to the futures people hope to attain or avoid, but their motivational value is neither direct nor certain. Psychological research suggests that they are most effective when they function within broader self-regulatory processes, provide a meaningful future-oriented reference point, and are linked to realistic behavioural strategies, metacognitive monitoring, and a sense of agency. Whether a possible self translates into action further depends on whether it is accessible in the present, compatible with salient social identities, supported by the surrounding context, and resilient to experiences of difficulty. Difficulty can strengthen persistence when interpreted as a normative aspect of pursuing an important goal, but undermine pursuit when it suggests impossibility. Possible selves therefore provide the direction and motivational meaning of goal pursuit, while self-regulatory processes provide the means through which that direction is translated into present action. The practical implication is this: imagining a desirable future is not enough; possible selves become motivationally effective when they are concrete, actionable, and connected to what a person can do now.&lt;div style=&quot;background-color: #fceef3; border: 1px solid #c77b98; border-radius: 10px; padding: 12px 18px; margin: 15px 0;&quot;&gt;

'''Chapter comprehension check'''

&lt;div style=&quot;margin-top: -50px;&quot;&gt;
&lt;quiz display=simple&gt;
{Possible selves are future-oriented representations of who a person might become and can provide motivational direction to present behaviour.
|type=&quot;()&quot;}
+ True
- False

{Possible selves directly produce goal-directed behaviour without relying on broader self-regulatory processes.
|type=&quot;()&quot;}
- True
+ False

{A possible self is more likely to facilitate goal pursuit when it is connected to plausible strategies, relevant to the current context, and compatible with salient identities.
|type=&quot;()&quot;}
+ True
- False

{Interventions strengthen goal pursuit simply by encouraging people to imagine a positive future self.
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;
&lt;/div&gt;
&lt;/div&gt;

==See also==
* [[w:Future self|Future self]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Regulatory focus theory and goal pursuit|Regulatory focus theory and goal pursuits]] (Book chapter, 2019)
* [[w:Goal pursuit|Goal Pursuit]] (Wikipedia)

==References==
{{Hanging indent|1=

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Gollwitzer, P. M., &amp; Sheeran, P. (2006). Implementation intentions and goal achievement: A meta‐analysis of effects and processes. Advances in Experimental Social Psychology, 38(1), 69–119. https://doi.org/https://doi.org/10.1016/S0065-2601(06)38002-1

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King, L. A., &amp; Raspin, C. (2004). Lost and found possible selves, subjective well-being, and ego development in divorced women. Journal of Personality, 72(3), 603–632. https://doi.org/10.1111/j.0022-3506.2004.00274.x

Markus, H., &amp; Nurius, P. (1986). Possible selves. American Psychologist, 41(9), 954–969. https://doi.org/https://doi.org/10.1037/0003-066X.41.9.954

Milyavskaya, M., &amp; Werner, K. M. (2018). Goal pursuit: Current state of affairs and directions for future research. Canadian Psychology/Psychologie Canadienne, 59(2), 163–175. https://doi.org/10.1037/cap0000147

Murru, E. C., &amp; Martin Ginis, K. A. (2010). Imagining the possibilities: The effects of a possible selves intervention on self-regulatory efficacy and exercise behavior. Journal of Sport &amp; Exercise Psychology, 32(4), 537–554. https://doi.org/10.1123/jsep.32.4.537

Norman, C. C., &amp; Aron, A. (2003). Aspects of possible self that predict motivation to achieve or avoid it. Journal of Experimental Social Psychology, 39(5), 500–507. https://doi.org/10.1016/S0022-1031(03)00029-5

Oyserman, D. (2009). Identity‐based motivation: Implications for action‐readiness, procedural‐readiness, and consumer behavior. Journal of Consumer Psychology, 19(3), 250–260. https://doi.org/10.1016/j.jcps.2009.05.008

Oyserman, D. (2015). Pathways to success through identity-based motivation. Oxford University Press. https://psycnet.apa.org/record/2015-16643-000

Oyserman, D., Bybee, D., &amp; Terry, K. (2006). Possible selves and academic outcomes: How and when possible selves impel action. Journal of Personality and Social Psychology, 91(1), 188–204. https://doi.org/10.1037/0022-3514.91.1.188

Oyserman, D., Bybee, D., Terry, K., &amp; Hart-Johnson, T. (2004). Possible selves as roadmaps. Journal of Research in Personality, 38(2), 130–149. https://doi.org/10.1016/s0092-6566(03)00057-6

Oyserman, D., &amp; Horowitz, E. (2023). From possible selves and future selves to current action: An integrated review and identity-based motivation synthesis. In Advances in Motivation Science (pp. 73–147). Elsevier Inc.

Sheeran, P., &amp; Webb, T. L. (2016). The intention-behavior gap. Social and Personality Psychology Compass, 10(9), 503–518. https://doi.org/10.1111/spc3.12265

Strauss, K., Griffin, M. A., &amp; Parker, S. K. (2012). Future work selves: How salient hoped-for identities motivate proactive career behaviors. Journal of Applied Psychology, 97(3), 580–598. https://doi.org/10.1037/a0026423

Tettero, T., Mertens, E. C. A., Siezenga, A. M., &amp; van Gelder, J.-L. (2026). From future vision to current action: The relationship between future self-identification and goal achievement. Personality and Individual Differences, 254, 113645. https://doi.org/10.1016/j.paid.2026.113645

van Gelder, J.-L., Tettero, T., Siezenga, A., &amp; Mertens, E. (2026). Stimulating future-oriented thinking and goal-achievement through the future self using virtual reality and a smartphone app: Randomized controlled trial. Journal of Medical Internet Research, 28, e84420–e84420. https://doi.org/10.2196/84420

vanDellen, M. R., &amp; Hoyle, R. H. (2008). Possible selves as behavioral standards in self-regulation. Self and Identity, 7(3), 295–304. https://doi.org/10.1080/15298860701641108}}

==External links==
* [https://www.hiddenbrain.org/podcast/you-2-0-your-future-is-now/ You 2.0: your future is now] (Hidden Brain)
* [https://www.youtube.com/watch?v=XNbaR54Gpj4&amp;t=177s The psychology of you future self | Dan Gilbert] (Youtube)
* [https://www.psychologytoday.com/au/blog/philosophy-and-therapy/202401/the-philosophy-of-possible-selves Why to start considering your possible selves] (Psychology Today)</text>
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__TOC__
==Overview==
{{RoundBoxTop|theme=3}}
[[File:Ueber-die-sammlung-19-jahrhundert-caspar-david-friedrich-wanderer-ueber-dem-nebelmeer.jpg|thumb|right|150px|'''Figure 1'''. The wanderer looks across a sea of fog toward the looming mountains, symbolising the current self and possible self.]]

; Scenario

A university student has started their final year of their bachelor's degree, and the academic standards are higher than previous years. One may imagine their future as exciting: graduating, beginning a meaningful career, becoming financially independent, and becoming the capable and competent person they hope to be. Alternatively, they may imagine their future as unsettling: losing motivation, failing to make use of their opportunities, and becoming someone they once hoped to avoid.

Neither future exists, however, these imagined versions of the self can influence what the student does today – whether they attend lectures and tutorials, persist through difficult assignments and exams, or give up when progress feels slow.
{{RoundBoxBottom}}[https://journals.sagepub.com/doi/10.1037/1089-2680.11.4.348 Possible selves] {{ic|Use either APA style or wiki style, but don't embed external links}} are conceptions of who we may become in the future and involve, to some degree, imagining ourselves as agents within those future situations (Erikson, 2007). They can include versions of ourselves that we hope to become, as well as those we fear becoming. Markus and Nurius (1986) proposed that these future self-representations are motivationally important because they can provide incentives for behaviour and give personal meaning and direction to our goals.

In the opening scenario, the university student can imagine both a desired future of graduating and beginning a meaningful career, and an unwanted future characterised by lost opportunities and lack of direction. Yet imagining either future does not guarantee that the student will study, persist through setbacks, or take advantage of opportunities in the present. This illustrates a central problem in understanding possible selves: how does an imagined future identity become motivation and, ultimately, goal-directed behaviour?

Literature during the 21st century suggests that possible selves are better understood as components of self-regulation through which motivation and behaviour are influenced (Hoyle &amp; Sherrill, 2006; Frazier, Schwartz &amp; Metcalfe, 2021). Research therefore focuses on the conditions under which possible selves provide effective guidance for goal pursuit, including whether they are meaningful, attainable, and connected to realistic behavioural strategies. Examining these processes help to explain why imagined future identities can motivate present goal-directed behaviour in some circumstances, yet remain ineffective in others (Haskins &amp; vanDellen, 2019).

&lt;div style=&quot;background-color: #fbedf2; border: 2px solid #d4779b; border-radius: 12px; padding: 15px 20px;&quot;&gt;
'''Focus questions'''

*What are possible selves, and why can they have motivational significance?
*How do possible selves interact with self-regulatory processes involved in goal pursuit?
*Under what conditions do possible selves facilitate - or fail to facilitate - goal-directed behaviour?
* How can possible selves be used to strengthen motivation and translate future aspirations into present action?
&lt;/div&gt;

== Possible selves ==
=== Definition and theoretical origins ===
The concept of possible selves was introduced by Markus and Nurius (1986) to complement current conceptions of self-knowledge by extending it beyond the present.  They proposed that possible selves represent individuals' ideas of what they might become, what they would like to become, and what they are afraid of becoming, and thus provide a conceptual link between cognition and motivations. More recently, Erikson (2007) emphasised agency, arguing that possible selves involve experiencing oneself, at least to some degree, as an agent within an imagined future situation. This distinguishes a possible self from a simple goal: Wanting to receive a high grade describes a desired outcome, whereas imagining oneself as a capable and successful student places the person within a future identity. Possible selves are therefore closely related to goals, but are distinguished by their explicit connection to who the individual might become. 

Possible selves can take several forms. Hoped-for possible selves represent desirable identities that a person would like to attain. This could include the competent and powerful self, the celebrated and glamorous self, the respected and esteemed self, or the fit self. In contrast, the feared possible selves comprise a similarly compelling set. One's fears and anxieties can become concretely manifest in visions of the lonely self, the undervalued and underpaid self, or the out-of-shape self (Cross &amp; Markus, 1991). Additionally, people may also hold expected possible selves, representing identities they consider realistically likely rather than simply desirable or undesirable. A person might, for example, hope to become an award winning author while expecting to pursue an entirely different career. Markus and Nurius (1986) suggest that much of our significant behavior can be seen primarily as an effort to approach or avoid various possible selves. 

Importantly, people do not construct these future identities in isolation. Content of possible selves is shaped by people's experiences and sociocultural circumstances rather than being a manifestation of the isolated self, as well as by temporal, contextual, developmental factors (Allport, 1937; Frazier &amp; Hooker, 2006). Markus and Nurius (1986) argue that the pool of possible selves available to an individual is influenced by socially salient categories and by the models, images, and examples encountered through media and everyday social experience. Elite sport provides a useful illustration:
&lt;div style=&quot;width: 50%; float: right; background-color: #f0f5f8; border-left: 4px solid #527d99; padding: 2px 15px 2px 15px; margin: 0 0 20px 20px; border-radius: 6px; box-sizing: border-box;&quot;&gt;

'''Case study:''' 

[[File:Eliud Kipchoge in Berlin - 2015 (cropped).jpg|thumb|right|110px|'''Figure 2.''' Eliud Kipchoge (2015).]]

In 2019, Kenyan marathon runner Eliud Kipchoge became the first person to complete a marathon distance in under two hours, demonstrating that a feat long considered beyond human capability was, in fact, achievable. By expanding public perceptions of what was possible, Kipchoge may have helped other elite runners imagine similar achievements as part of their own possible futures. Subsequent athletes to break the two-hour barrier likely absorbed the performance of Eliud Kipchoge within the realm of their own possible selves, giving specific cognitive form to their desire to become exceptional runners. 
&lt;/div&gt;

Importantly, people do not construct these future identities in isolation. Content of possible selves is shaped by people's experiences and sociocultural circumstances rather than being a manifestation of the isolated self, as well as by temporal, contextual, developmental factors (Allport, 1937; Frazier &amp; Hooker, 2006). Markus and Nurius (1986) argue that the pool of possible selves available to an individual is influenced by socially salient categories and by the models, images, and examples encountered through media and everyday social experience. Elite sport provides a useful illustration:

Cross and Markus (1991) similarly found systematic differences in hoped-for and feared possible selves across adulthood, illustrating how possible selves change alongside people's circumstances and developmental priorities. Possible selves therefore reflect an interaction between individual aspirations and the social contexts within which those futures are imagined.


=== Forms and content of possible selves &amp; motivational properties of possible selves ===
Possible selves are particularly relevant to motivational psychology because it allows us to make a more direct connection between motives and actions. Markus and Nurius (1986) proposed that future selves can function as incentives for future behaviour by providing a self-relevant framework that gives meaning, organisation, and direction to our actions. For example, imagining oneself as physically healthy and active in later life may encourage behaviours directed towards that future, while imagining a feared future characterised by poor health may provide motivation to avoid it. Thus, possible selves can transform relatively vague and abstract aspirations or fears into outcomes that are explicitly connected to one's identity. 

Yet not all possible selves are equally motivating. Norman and Aron (2003) found that motivation to attain or avoid an important possible self was significantly predicted by its availability, its accessibility, and the extent to which its attainment or avoidance is perceived as under one's control. Hence, merely possessing a desirable or undesirable future image may be insufficient. A future self that feels vague, remote or outside one's control is unlikely to exert the same motivational influence as one that is psychologically accessible and associated with a sense of agency.

Experimental research also indicates that the way a future self is represented can influence subsequent motivation and behaviour. There is a large body of research that has identified characteristics that render possible selves more or less efficient for prompting behaviour. For instance, it is generally accepted that a possible self has to be salient and easily evoked in order to affect behaviour (Strauss, Griffin, &amp; Parker, 2012; King &amp; Raspin 2004; Norman &amp; Aron, 2003). A recent study by De Place and Brunot (2020) manipulated both the specificity and valence of university students’ imagined possible selves. Across two studies, different combinations of general or specific future success and failure produced differences in attention and academic motivation. Importantly, their results were more complex than simply showing that positive or highly specific future images are always beneficial. Such findings reinforce the idea that the motivational influence of a possible self depends not merely on whether the imagined future is positive or negative, but also on how that future is represented (De Place &amp; Brunot, 2020). 

Possible selves therefore offer a potential source of motivation, but should be understood as a more complex interplay of several different cognitions. Explaining how these future identities translate into sustained goal-directed behavior requires consideration of the processes involved in goal pursuit and self-regulation. 

== Goal pursuit and self-regulation ==
Imagining a meaningful future self may provide direction, but it does not guarantee action. Moving towards a hoped-for possible self or away from a feared one requires people to initiate and sustain behaviour, respond to obstacles, and regulate their progress over time. Goal Pursuit and self-regulation therefore provide the bridge between imagined future identities and present behaviour. 

=== From goals to goal-directed behaviour ===
Goals are internal representations of desired states, which are broadly constructed as outcomes, events, or processes that individuals seek to attain, maintain, or avoid (Austin &amp; Vancouver, 1996). Goal pursuit, in turn, refers to the processes through which individuals work to realise these goals. This is an important distinction because simply holding a strong intention (“I intend to do Z”) does not guarantee goal achievement, and people may fail to deal effectively with self-regulatory problems during goal striving. Take a university student for example, they may strongly value becoming a psychologist while repeatedly postponing study, avoid difficult course work, or fail to seek relevant experience. The desired future provides direction, but it must still be translated into action.

Goal-directed behaviour therefore involves a range of processes after a goal has been formed. Contemporary accounts emphasise that once an individual generates an intent to pursue a given goal, they “cross the rubicon” into several stages that involve planning, effort, persistence, progress, monitoring, and adaptation when difficulties arise (Milyavskaya &amp; Werner, 2018). Importantly, intentions alone are poor predictors of subsequent behaviour; Sheeran and Webb (2016) describe a substantial intention-behaviour gap, whereby people frequently fail to act despite intending to do so which occurs approximately half the time. Goal pursuit must also be sustained over time and adjusted in response to obstacles, competing demands, and changes in goal attainability. One highly efficient means of strengthening the transition from intention to action is through implementation intentions, which specify when, where, or how goal-directed behaviour will occur. They take the format of a cognitive association between a prespecified opportunity for acting and a specific goal-directed behaviour (i.e., “if situation x arises, then I will perform behaviour y”) (Brandstatter &amp; Bernecker, 2022). Several studies have proven implementation intentions to be efficacious, helping individuals to support persistence and improve goal attainment (Belanger-Gravel, 2013; Gollwitzer &amp; Sheeran, 2006). Together, this research demonstrates that motivation towards a desired outcome is only one component of successful goal pursuit. 

This distinction is particularly relevant to possible selves. Envisioning oneself as a competent psychologist may establish a meaningful long-term direction, but that future identity becomes behaviourally consequential only when it is coupled to actions such as completing assignments, developing relevant skills, seeking professional experience, and persisting through tough times. Possible selves may help establish where a person wants to go, while goal-directed behaviour concerns the processes required to move towards that future. 

=== Self-regulation in goal pursuit ===

&lt;div style=&quot;float: right; margin: 0px 0 10px 15px;&quot;&gt;
[[File:Determination on the Everest Expedition.jpg|thumb|right|440px|'''Figure 3.''' Mountaineer ascending Himalayan mountains]]
&lt;/div&gt;

The processes involved in directing and maintaining behaviour towards goals are commonly understood through self-regulation. Frazier et al. (2021) describe self-regulation as a social-cognitive process at the intersection of metacognition, motivation, and behaviour which encompasses how people conceptualise, strive for, and accomplish their goals. Once a goal has been adopted, self-regulation helps translate that desired outcome into an ongoing action by allowing individuals to monitor their progress, adjust their behaviour, and respond to obstacles encountered during goal pursuit. 

One particularly influential account conceptualises self-regulation as a discrepancy-reducing feedback loop (Carver &amp; Scheier, 2002). Within this control-process model, individuals compare their present state against a desired reference point and monitor whether a discrepancy exists between the two. Using the goal as a reference, a person compares their present state to the desired end state (i.e., “am I on track for my goal?”). If a discrepancy is detected, the person acts to reduce this discrepancy, thereby engaging in goal-promoting behaviour (Milyavskaya &amp; Werner, 2018). Self-regulation is therefore an ongoing process of comparison, feedback, and behavioural adjustment rather than a single decision to pursue a goal. 

Possible selves may provide one such future-oriented reference point. By representing who an individual wishes to become or wishes to avoid becoming, they can establish standards against which present behaviour and progress are evaluated. However, merely possessing a future standard does not alone explain how strongly it will influence behaviour. Understanding how possible selves become integrated into self-regulation, and why some guide action more effectively than others, requires closer examination of their role within motivated goal pursuit.

== Possible selves in motivated goal pursuit ==
Personal selves can provide meaningful representation of where an individual wishes to go or what they hope to avoid, while self-regulation provides processes through which these future identities may influence present behaviour. The relationship between the two, however, is not straightforward. Contemporary research suggests that the motivational value of a possible self depends less on the seminal formulation of having positive-valence and more on whether that future identity becomes relevant to the affordances and constraints of their immediate situation, and functions effectively within self-regulatory processes (Oyserman &amp; Horowitz, 2023). Understanding possible selves in goal pursuit therefore requires asking not only ''what future does a person imagine?,'' but also ''how does the imagined future influence what they do now?''

=== Modelling the relationships ===
Markus and Nurius’ (1986) original account proposed that possible selves connect cognition and motivation by giving self-relevant form to people's hopes, fears and aspirations, thereby providing incentives for future behaviour. Subsequent theory has refined this relationship. Rather than treating possible selves as a direct cause of motivation or behaviour, they are better understood as components within broader self-regulatory systems (Hoyle &amp; Sherrill, 2006). In this way, a possible self can provide a behavioural standard or future reference point, while other regulatory processes determine whether and how behaviour is organised around it. Studies demonstrate that embedding possible selves within established models of self-regulation provides some impetus to behaviour and outcome change, as well as meaningful predictions about present behavior, supporting a more process-oriented interpretation of their motivational role (Hoyle &amp; Sherrill, 2006; Oyserman et al., 2004; vanDellen &amp; Hoyle, 2008).

Empirical findings support this process-oriented interpretation. A study by vanDellen and Hoyle (2008) experimentally examined whether hoped-for and feared health-related possible selves could function as behavioural standards within self-regulation. After making these possible selves salient, participants were given opportunities to engage in behaviours that could reduce discrepancies between their current and possible selves. Evidence for discrepancy-reducing behaviour was strongest when feared possible selves were salient and participants possessed sufficient self-regulatory capacity, whereas comparable effects were not found for hope-for possibles selves. These findings suggest that possible selves can guide present behaviour by operating as standard within broader self-regulatory processes rather than directly producing goal attainment (vanDellen &amp; Hoyle, 2008). Likewise, possible selves appear more strongly related to behavioural and academic outcomes when they are linked to strategies and can plausibly function as self-regulatory resources rather than merely positive representations of the future (Oserman et al., 2004). Possible selves therefore do not instantiate goal attainment. Rather, their influence depends on the self-regulatory processes in which they are embedded.

&lt;div style=&quot;float: right; margin: 0px 0 10px 15px;&quot;&gt;
[[File:MAPS model of self-regulation.png|thumb|right|360px|'''Figure 4.''' MAPS model of self-regulation (Frazier et al., 2021).]]
&lt;/div&gt;

The MAPS model of self-regulation provides a more recent framework for understanding these processes. Frazier et al., (2021) propose that goal-directed behaviour emerges from dynamic and synergistic interaction between possible selves, metacognitive knowledge and strategies, and a sense of one's own agency. Possible selves embody representations of desired future outcomes and provide motivational direction; metacognitive knowledge helps people select, monitor and modify strategies for pursuing those outcomes; and agency reflects the extent to which individuals perceive themselves as capable of influencing what happens next. Importantly, these elements continually influence one another. Feedback from goal-directed action can alter perceptions of competence and agency, which in turn can reshape strategies and even beliefs about what future selves remain possible.  

Taken together, these accounts suggest that possible selves influence goal pursuit through an indirect and dynamic manner. Imagining a future self can help to make outcomes personally meaningful and provide a benchmark towards which behaviour can be directed. However, movement towards that future requires individuals to identify reasonable approaches, believe in their agency, monitor progress, and adjust their behaviour in response to feedback. Possible selves may therefore provide the direction and motivational meaning of goal pursuit, while self-regulatory processes provide the means through which that direction is translated into present action.  

Additionally, a future identity must feel relevant to choices in the present. From an identity-based motivation perspective, it requires a ‘shift of focus from what ''future me is–''positive or negative, close or distant, continuous or discontinuous ''with current me–''to what ''future me does''’ (Oyserman &amp; Horowitz, 2023, p. 74)''.'' As illustrated in Figures 5 and 6, future-oriented action is more likely when a possible self feels relevant, difficulties are interpreted as signs of importance rather than impossibility, and the required actions feel consistent with one's identity. This helps explain why the same possible self can strongly guide behaviour in one situation while exerting little influence in another.

&lt;div style=&quot;display: flex; gap: 10px; align-items: stretch;&quot;&gt;

&lt;div style=&quot;width: 50%;&quot;&gt;
[[File:When does a future self influence current action?.png|thumb|center|x300px|'''Figure 5.''' Idenity-based motivation processes linking future selves to behaviour (adapted from Oyserman &amp; Horowitz, 2023).]]
&lt;/div&gt;

&lt;div style=&quot;width: 50%;&quot;&gt;
[[File:How identity-based motivation can orient action toward or away from the future.png|thumb|center|x300px|'''Figure 6.''' Identity-based motivation pathways linking future idenities to action (adapted from Oyserman &amp; Horowitz, 2023).]]
&lt;/div&gt;

&lt;/div&gt;

=== When possible selves facilitate goal pursuit ===
An important condition for possible selves to facilitate goal pursuit is their relationship to plausible strategies for action. Oyserman et al., (2004) distinguish between possible selves that are primarily self-enhancing and those capable of functioning as self-regulators. To investigate this, they examined the extent to which detailed academic possible selves, when linked with strategies, added predictive power. Adolescents whose academic possible selves incorporated strategies for attaining desired futures or avoiding feared ones showed greater classroom participation, spent more time on homework, and achieved better academic outcomes. Indeed, having plausibly self-regulating possible selves is more likely to induce self-improvement behaviour and significantly greater chances of success, compared to possible selves that do not include such self-regulatory guideposts (Hoyle &amp; Sherrill, 2006; Oyserman et al., 2004; Oyserman &amp; James, 2009). 

Whether these strategies influence behaviour also depends on the context in which a possible self is brought to mind. Possible selves differ in accessibility, and identities made salient by the immediate situation are more likely to inform judgment and decision making (Higgins, 1996; Oyserman et al., 2006). Consequently, sustained pursuit requires relevant behavioral strategies to be readily available when the future identity becomes salient. For instance, an academic possible self is in theory more effective when the surrounding environment routinely cues behaviours such as attending lectures, persisting through assignments, seeking assistance, or attending study help. Oyserman et al., (2006) argue that resource-rich contexts are more likely to provide accessible models of success and established pathways towards the ideal futures, whereas resource-limited environments may offer fewer such cues. The motivational effectiveness of a possible self therefore depends partly on whether the social environment makes pathways towards it visible and actionable.  

Possible selves are also more likely to motivate when they feel compatible with important social identities and when difficulties encountered during pursuits are interpreted constructively. Identity-based motivation theory proposes that people are more willing to act in ways that fit the identities on their minds which feel relevant to the affordances and constraints of their immediate situation (Oyserman, 2015). A future identity that appears inconsistent with one's social group, circumstances, or understanding of “people like me” may therefore be less likely to organise behaviour, even when it is personally desirable. Importantly, this does not imply effective motivation requires distancing oneself from existing social identities, rather, future identities become more actionable when they can be experienced as compatible with those identities (Oyserman et al., 2006; Oyserman &amp; Horowitz, 2023).

How people interpret difficulty further shapes this process. Difficulty encountered while pursuing a possible self can be understood as evidence that the future is unattainable, encouraging disengagement, or as a normative indication that an important goal requires effort. Identity-based motivation theory highlights the role of metacognitive experience, particularly the subjective feelings of ease or difficulty associated with pursuing a goal (Oyserman, Bybee, &amp; Terry, 2006). When behaviour feels consistent with one's identity, difficulty may be interpreted as a sign that the goal is important and worth pursuing rather than an impossibility, i.e., “no pain no gain” (Oyserman &amp; Horowitz, 2023). Thus, the motivational consequences of difficulty depend not simply on how hard goal pursuit feels, but on the metacognitive experience of the difficulty and the meaning attributed to that experience.  

Taken together, possible selves are more likely to facilitate goal pursuit when they are connected to realistic strategies, supported and cued by the surrounding context, compatible with salient identities, resilient to experiences of difficulty, and personally meaningful enough to sustain commitment (Haskins &amp; vanDellen, 2019). Their motivational value therefore lies in whether that future can be integrated with the circumstances, interpretations, and actions of the present self. 

=== When possible selves fail to motivate ===
Possible selves can remain self-enhancing rather than self-regulatory, such that possible selves promote positive feelings and maintain a sense of optimism and hope for the future without evoking behavioural strategies required to reach it (Oyserman et al., 2004). For example, a university student may say to themselves ‘I may not be doing well in university this semester but I will succeed next semester’, thereby protecting their self-esteem from the current bad grades, without engaging in any behavioural strategies to improve their academic performance in the following semester. This distinction illustrates why simply valuing or vividly imagining a possible self is insufficient for goal pursuit. 

Importantly, failure to act does not necessarily reflect a lack of ambition, as socioeconomic and social contexts can constrain access to the strategies, role models, and opportunities needed to make a future identity actionable. In low socio-economic contexts, behavioural strategies may be less readily accessible due to fewer role models and resources to guide goal pursuit (Oyserman, Bybee, &amp; Terry, 2006). Furthermore, Oyserman, Johnson, and James (2011) describe part of the problem as “seeing the destination but not the path”; disadvantaged adolescents could hold salient school-focused possible selves while possessing fewer strategies for attaining them. Likewise, difficulty can undermine pursuit when it is interpreted as signaling impossibility rather than importance, particularly when the future identity feels incongruent with one's circumstances or social identities (Oyserman et al., 2006; Oyserman &amp; Horowitz, 2023). Thus, motivational value lies in whether the future self can be translated into plausible, identity-congruent, and contextually supported pathways for behavioral action. 

== Harnessing possible selves for goal pursuit ==

&lt;div style=&quot;float: right; margin: 0px 0 10px 15px;&quot;&gt;
[[File:Ballet, mirror, parquet floor, dance room Fortepan 85036.jpg|thumb|right|420px|'''Figure 7.''' Dancer refining her practice.]]
&lt;/div&gt;

The mechanisms discussed throughout this chapter raise a question: can possible selves be deliberately harnessed to improve goal pursuit? Intervention research provides some evidence that they can. Oyserman et al. (2006) developed a school-based intervention to link academic possible selves with behavioural strategies, a context in which social and personal identities felt congruent, and constructive interpretations of difficulty. Compared with controls, participating adolescents subsequently showed greater academic initiative, improved grades and standardized test scores, fewer absences, and reduced school misbehaviour, with effects sustained over a two-year follow up. More recent research has extended this approach using digital representations of the future self. In a 2026 randomised controlled trial, interventions delivered through smartphone and virtual reality strengthened identification with the future self through visual and interactive experiences, with the virtual reality condition also increasing goal achievement (van Gelder et al., 2026).

However, intervention findings also caution against treating future-self imagery as a simple motivational technique. The same 2026 trial found no improvements in several other outcomes, including academic performance and self-defeating behaviour, suggesting that strengthening future-self identification does not automatically produce broad behavioural change (van Gelder et al., 2026). Additionally, Tettero et al., (2026) conducted a study to investigate how the three components of future self-identification—vividness, connectedness, and valence—were associated with goal achievement over time. It was found that vividness of the future self most consistently predicted subsequent goal achievement, connectedness contributed more modestly, while valence did not predict achievement, which aligns with research that came before it (Kuo et al., 2025). It is believed that the richness of vivid mental images makes the future self more concrete and realistic, reducing the psychological distance between the self and possible self, thus enhancing the perceived relevance of future goals (Bixter et al., 2020; Evans &amp; Wilson, 2014; Hershfield, 2011). These findings reinforce the broader conclusion of this chapter: the motivational value of possible selves lies not simply in imagining a desirable future, but in whether that future becomes sufficiently concrete, relevant, and actionable to influence behaviour.

== Extra sources ==
*Possible selves, self regulation and actual social goal progress (2014)
*Best possible self intervention and academic motivation/commitment (2020)
*Identity-based motivation (2015) 

== Conclusion ==
Possible selves influence motivation and goal-directed behaviour by giving personally meaningful form to the futures people hope to attain or avoid, but their motivational value is neither direct nor certain. Psychological research suggests that they are most effective when they function within broader self-regulatory processes, provide a meaningful future-oriented reference point, and are linked to realistic behavioural strategies, metacognitive monitoring, and a sense of agency. Whether a possible self translates into action further depends on whether it is accessible in the present, compatible with salient social identities, supported by the surrounding context, and resilient to experiences of difficulty. Difficulty can strengthen persistence when interpreted as a normative aspect of pursuing an important goal, but undermine pursuit when it suggests impossibility. Possible selves therefore provide the direction and motivational meaning of goal pursuit, while self-regulatory processes provide the means through which that direction is translated into present action. The practical implication is this: imagining a desirable future is not enough; possible selves become motivationally effective when they are concrete, actionable, and connected to what a person can do now.&lt;div style=&quot;background-color: #fceef3; border: 1px solid #c77b98; border-radius: 10px; padding: 12px 18px; margin: 15px 0;&quot;&gt;

'''Chapter comprehension check'''

&lt;div style=&quot;margin-top: -50px;&quot;&gt;
&lt;quiz display=simple&gt;
{Possible selves are future-oriented representations of who a person might become and can provide motivational direction to present behaviour.
|type=&quot;()&quot;}
+ True
- False

{Possible selves directly produce goal-directed behaviour without relying on broader self-regulatory processes.
|type=&quot;()&quot;}
- True
+ False

{A possible self is more likely to facilitate goal pursuit when it is connected to plausible strategies, relevant to the current context, and compatible with salient identities.
|type=&quot;()&quot;}
+ True
- False

{Interventions strengthen goal pursuit simply by encouraging people to imagine a positive future self.
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;
&lt;/div&gt;
&lt;/div&gt;

==See also==
* [[w:Future self|Future self]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Regulatory focus theory and goal pursuit|Regulatory focus theory and goal pursuits]] (Book chapter, 2019)
* [[w:Goal pursuit|Goal Pursuit]] (Wikipedia)

==References==
{{Hanging indent|1=

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Brandstätter, V., &amp; Bernecker, K. (2022). Persistence and disengagement in personal goal pursuit. Annual Review of Psychology, 73(1), 271–299. https://doi.org/10.1146/annurev-psych-020821-110710

Bélanger-Gravel, A., Godin, G., &amp; Amireault, S. (2011). A meta-analytic review of the effect of implementation intentions on physical activity. Health Psychology Review, 7(1), 23–54. https://doi.org/10.1080/17437199.2011.560095

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Cross, S., &amp; Markus, H. (1991). Possible selves across the life span. Human Development, 34(4), 230–255. https://doi.org/10.1159/000277058

de Place, A.-L., &amp; Brunot, S. (2019). Motivational and behavioral impact of possible selves: When specificity matters. Imagination, Cognition and Personality, 39(4), 329–247. https://doi.org/10.1177/0276236619864275

Erikson, M. G. (2007). The meaning of the future: Toward a more specific definition of possible selves. Review of General Psychology, 11(4), 348–358. https://doi.org/10.1037/1089-2680.11.4.348

Evans, M. B., &amp; Wilson, A. E. (2014). Subjective temporal proximity to future selves moderates the link between exercise intentions and behavior. Sport, Exercise, and Performance Psychology, 3(3), 184–190. https://doi.org/10.1037/spy0000014

Frazier, L. D, &amp; Hooker, K. (2006). APA PsycNet. Apa.Org. https://psycnet.apa.org/record/2006-04587-003

Frazier, L. D., Schwartz, B. L., &amp; Metcalfe, J. (2021). The MAPS model of self-regulation: Integrating metacognition, agency, and possible selves. Metacognition and Learning, 16(2). https://doi.org/10.1007/s11409-020-09255-3 

Gollwitzer, P. M. (1999). Implementation intentions: Strong effects of simple plans. American Psychologist, 54(7), 493–503. https://doi.org/10.1037/0003-066x.54.7.493

Gollwitzer, P. M., &amp; Sheeran, P. (2006). Implementation intentions and goal achievement: A meta‐analysis of effects and processes. Advances in Experimental Social Psychology, 38(1), 69–119. https://doi.org/https://doi.org/10.1016/S0065-2601(06)38002-1

Haskins, L. B., &amp; vanDellen, M. R. (2019). Self‐regulation as relating to one’s ideal possible self. Social and Personality Psychology Compass, 13(10). https://doi.org/10.1111/spc3.12499

Hershfield, H. E. (2011). Future self‐continuity: How conceptions of the future self transform intertemporal choice. Annals of the New York Academy of Sciences, 1235(1), 30–43. https://doi.org/10.1111/j.1749-6632.2011.06201.x

Higgins, E. T. (1996). Ideals, oughts, and regulatory focus: Affect and motivation from distinct pains and pleasures. In The psychology of action: Linking cognition and motivation to behavior. (pp. 91–114). The Guilford Press. https://psycnet.apa.org/record/1996-98326-005

Hoyle, R. H., &amp; Sherrill, M. R. (2006). Future orientation in the self-system: Possible selves, self-regulation, and behavior. Journal of Personality, 74(6), 1673–1696. https://doi.org/10.1111/j.1467-6494.2006.00424.x

King, L. A., &amp; Raspin, C. (2004). Lost and found possible selves, subjective well-being, and ego development in divorced women. Journal of Personality, 72(3), 603–632. https://doi.org/10.1111/j.0022-3506.2004.00274.x

Markus, H., &amp; Nurius, P. (1986). Possible selves. American Psychologist, 41(9), 954–969. https://doi.org/https://doi.org/10.1037/0003-066X.41.9.954

Milyavskaya, M., &amp; Werner, K. M. (2018). Goal pursuit: Current state of affairs and directions for future research. Canadian Psychology/Psychologie Canadienne, 59(2), 163–175. https://doi.org/10.1037/cap0000147

Murru, E. C., &amp; Martin Ginis, K. A. (2010). Imagining the possibilities: The effects of a possible selves intervention on self-regulatory efficacy and exercise behavior. Journal of Sport &amp; Exercise Psychology, 32(4), 537–554. https://doi.org/10.1123/jsep.32.4.537

Norman, C. C., &amp; Aron, A. (2003). Aspects of possible self that predict motivation to achieve or avoid it. Journal of Experimental Social Psychology, 39(5), 500–507. https://doi.org/10.1016/S0022-1031(03)00029-5

Oyserman, D. (2009). Identity‐based motivation: Implications for action‐readiness, procedural‐readiness, and consumer behavior. Journal of Consumer Psychology, 19(3), 250–260. https://doi.org/10.1016/j.jcps.2009.05.008

Oyserman, D. (2015). Pathways to success through identity-based motivation. Oxford University Press. https://psycnet.apa.org/record/2015-16643-000

Oyserman, D., Bybee, D., &amp; Terry, K. (2006). Possible selves and academic outcomes: How and when possible selves impel action. Journal of Personality and Social Psychology, 91(1), 188–204. https://doi.org/10.1037/0022-3514.91.1.188

Oyserman, D., Bybee, D., Terry, K., &amp; Hart-Johnson, T. (2004). Possible selves as roadmaps. Journal of Research in Personality, 38(2), 130–149. https://doi.org/10.1016/s0092-6566(03)00057-6

Oyserman, D., &amp; Horowitz, E. (2023). From possible selves and future selves to current action: An integrated review and identity-based motivation synthesis. In Advances in Motivation Science (pp. 73–147). Elsevier Inc.

Sheeran, P., &amp; Webb, T. L. (2016). The intention-behavior gap. Social and Personality Psychology Compass, 10(9), 503–518. https://doi.org/10.1111/spc3.12265

Strauss, K., Griffin, M. A., &amp; Parker, S. K. (2012). Future work selves: How salient hoped-for identities motivate proactive career behaviors. Journal of Applied Psychology, 97(3), 580–598. https://doi.org/10.1037/a0026423

Tettero, T., Mertens, E. C. A., Siezenga, A. M., &amp; van Gelder, J.-L. (2026). From future vision to current action: The relationship between future self-identification and goal achievement. Personality and Individual Differences, 254, 113645. https://doi.org/10.1016/j.paid.2026.113645

van Gelder, J.-L., Tettero, T., Siezenga, A., &amp; Mertens, E. (2026). Stimulating future-oriented thinking and goal-achievement through the future self using virtual reality and a smartphone app: Randomized controlled trial. Journal of Medical Internet Research, 28, e84420–e84420. https://doi.org/10.2196/84420

vanDellen, M. R., &amp; Hoyle, R. H. (2008). Possible selves as behavioral standards in self-regulation. Self and Identity, 7(3), 295–304. https://doi.org/10.1080/15298860701641108}}

==External links==
* [https://www.hiddenbrain.org/podcast/you-2-0-your-future-is-now/ You 2.0: your future is now] (Hidden Brain)
* [https://www.youtube.com/watch?v=XNbaR54Gpj4&amp;t=177s The psychology of you future self | Dan Gilbert] (Youtube)
* [https://www.psychologytoday.com/au/blog/philosophy-and-therapy/202401/the-philosophy-of-possible-selves Why to start considering your possible selves] (Psychology Today)</text>
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__TOC__
==Overview==
{{RoundBoxTop|theme=3}}
[[File:Ueber-die-sammlung-19-jahrhundert-caspar-david-friedrich-wanderer-ueber-dem-nebelmeer.jpg|thumb|right|150px|'''Figure 1'''. The wanderer looks across a sea of fog toward the looming mountains, symbolising the current self and possible self.]]

; Scenario

A university student has started their final year of their bachelor's degree, and the academic standards are higher than previous years. One may imagine their future as exciting: graduating, beginning a meaningful career, becoming financially independent, and becoming the capable and competent person they hope to be. Alternatively, they may imagine their future as unsettling: losing motivation, failing to make use of their opportunities, and becoming someone they once hoped to avoid.

Neither future exists, however, these imagined versions of the self can influence what the student does today – whether they attend lectures and tutorials, persist through difficult assignments and exams, or give up when progress feels slow.
{{RoundBoxBottom}}
Possible selves are conceptions of who we may become in the future and involve, to some degree, imagining ourselves as agents within those future situations (Erikson, 2007). They can include versions of ourselves that we hope to become, as well as those we fear becoming. Markus and Nurius (1986) proposed that these future self-representations are motivationally important because they can provide incentives for behaviour and give personal meaning and direction to our goals.

In the opening scenario, the university student can imagine both a desired future of graduating and beginning a meaningful career, and an unwanted future characterised by lost opportunities and lack of direction. Yet imagining either future does not guarantee that the student will study, persist through setbacks, or take advantage of opportunities in the present. This illustrates a central problem in understanding possible selves: how does an imagined future identity become motivation and, ultimately, goal-directed behaviour?

Literature during the 21st century suggests that possible selves are better understood as components of self-regulation through which motivation and behaviour are influenced (Hoyle &amp; Sherrill, 2006; Frazier, Schwartz &amp; Metcalfe, 2021). Research therefore focuses on the conditions under which possible selves provide effective guidance for goal pursuit, including whether they are meaningful, attainable, and connected to realistic behavioural strategies. Examining these processes help to explain why imagined future identities can motivate present goal-directed behaviour in some circumstances, yet remain ineffective in others (Haskins &amp; vanDellen, 2019).

&lt;div style=&quot;background-color: #fbedf2; border: 2px solid #d4779b; border-radius: 12px; padding: 15px 20px;&quot;&gt;
'''Focus questions'''

*What are possible selves, and why can they have motivational significance?
*How do possible selves interact with self-regulatory processes involved in goal pursuit?
*Under what conditions do possible selves facilitate - or fail to facilitate - goal-directed behaviour?
* How can possible selves be used to strengthen motivation and translate future aspirations into present action?
&lt;/div&gt;

== Possible selves ==
=== Definition and theoretical origins ===
The concept of possible selves was introduced by Markus and Nurius (1986) to complement current conceptions of self-knowledge by extending it beyond the present.  They proposed that possible selves represent individuals' ideas of what they might become, what they would like to become, and what they are afraid of becoming, and thus provide a conceptual link between cognition and motivations. More recently, Erikson (2007) emphasised agency, arguing that possible selves involve experiencing oneself, at least to some degree, as an agent within an imagined future situation. This distinguishes a possible self from a simple goal: Wanting to receive a high grade describes a desired outcome, whereas imagining oneself as a capable and successful student places the person within a future identity. Possible selves are therefore closely related to goals, but are distinguished by their explicit connection to who the individual might become. 

Possible selves can take several forms. Hoped-for possible selves represent desirable identities that a person would like to attain. This could include the competent and powerful self, the celebrated and glamorous self, the respected and esteemed self, or the fit self. In contrast, the feared possible selves comprise a similarly compelling set. One's fears and anxieties can become concretely manifest in visions of the lonely self, the undervalued and underpaid self, or the out-of-shape self (Cross &amp; Markus, 1991). Additionally, people may also hold expected possible selves, representing identities they consider realistically likely rather than simply desirable or undesirable. A person might, for example, hope to become an award winning author while expecting to pursue an entirely different career. Markus and Nurius (1986) suggest that much of our significant behavior can be seen primarily as an effort to approach or avoid various possible selves. 

Importantly, people do not construct these future identities in isolation. Content of possible selves is shaped by people's experiences and sociocultural circumstances rather than being a manifestation of the isolated self, as well as by temporal, contextual, developmental factors (Allport, 1937; Frazier &amp; Hooker, 2006). Markus and Nurius (1986) argue that the pool of possible selves available to an individual is influenced by socially salient categories and by the models, images, and examples encountered through media and everyday social experience. Elite sport provides a useful illustration:
&lt;div style=&quot;width: 50%; float: right; background-color: #f0f5f8; border-left: 4px solid #527d99; padding: 2px 15px 2px 15px; margin: 0 0 20px 20px; border-radius: 6px; box-sizing: border-box;&quot;&gt;

'''Case study:''' 

[[File:Eliud Kipchoge in Berlin - 2015 (cropped).jpg|thumb|right|110px|'''Figure 2.''' Eliud Kipchoge (2015).]]

In 2019, Kenyan marathon runner Eliud Kipchoge became the first person to complete a marathon distance in under two hours, demonstrating that a feat long considered beyond human capability was, in fact, achievable. By expanding public perceptions of what was possible, Kipchoge may have helped other elite runners imagine similar achievements as part of their own possible futures. Subsequent athletes to break the two-hour barrier likely absorbed the performance of Eliud Kipchoge within the realm of their own possible selves, giving specific cognitive form to their desire to become exceptional runners. 
&lt;/div&gt;

Importantly, people do not construct these future identities in isolation. Content of possible selves is shaped by people's experiences and sociocultural circumstances rather than being a manifestation of the isolated self, as well as by temporal, contextual, developmental factors (Allport, 1937; Frazier &amp; Hooker, 2006). Markus and Nurius (1986) argue that the pool of possible selves available to an individual is influenced by socially salient categories and by the models, images, and examples encountered through media and everyday social experience. Elite sport provides a useful illustration:

Cross and Markus (1991) similarly found systematic differences in hoped-for and feared possible selves across adulthood, illustrating how possible selves change alongside people's circumstances and developmental priorities. Possible selves therefore reflect an interaction between individual aspirations and the social contexts within which those futures are imagined.


=== Forms and content of possible selves &amp; motivational properties of possible selves ===
Possible selves are particularly relevant to motivational psychology because it allows us to make a more direct connection between motives and actions. Markus and Nurius (1986) proposed that future selves can function as incentives for future behaviour by providing a self-relevant framework that gives meaning, organisation, and direction to our actions. For example, imagining oneself as physically healthy and active in later life may encourage behaviours directed towards that future, while imagining a feared future characterised by poor health may provide motivation to avoid it. Thus, possible selves can transform relatively vague and abstract aspirations or fears into outcomes that are explicitly connected to one's identity. 

Yet not all possible selves are equally motivating. Norman and Aron (2003) found that motivation to attain or avoid an important possible self was significantly predicted by its availability, its accessibility, and the extent to which its attainment or avoidance is perceived as under one's control. Hence, merely possessing a desirable or undesirable future image may be insufficient. A future self that feels vague, remote or outside one's control is unlikely to exert the same motivational influence as one that is psychologically accessible and associated with a sense of agency.

Experimental research also indicates that the way a future self is represented can influence subsequent motivation and behaviour. There is a large body of research that has identified characteristics that render possible selves more or less efficient for prompting behaviour. For instance, it is generally accepted that a possible self has to be salient and easily evoked in order to affect behaviour (Strauss, Griffin, &amp; Parker, 2012; King &amp; Raspin 2004; Norman &amp; Aron, 2003). A recent study by De Place and Brunot (2020) manipulated both the specificity and valence of university students’ imagined possible selves. Across two studies, different combinations of general or specific future success and failure produced differences in attention and academic motivation. Importantly, their results were more complex than simply showing that positive or highly specific future images are always beneficial. Such findings reinforce the idea that the motivational influence of a possible self depends not merely on whether the imagined future is positive or negative, but also on how that future is represented (De Place &amp; Brunot, 2020). 

Possible selves therefore offer a potential source of motivation, but should be understood as a more complex interplay of several different cognitions. Explaining how these future identities translate into sustained goal-directed behavior requires consideration of the processes involved in goal pursuit and self-regulation. 

== Goal pursuit and self-regulation ==
Imagining a meaningful future self may provide direction, but it does not guarantee action. Moving towards a hoped-for possible self or away from a feared one requires people to initiate and sustain behaviour, respond to obstacles, and regulate their progress over time. Goal Pursuit and self-regulation therefore provide the bridge between imagined future identities and present behaviour. 

=== From goals to goal-directed behaviour ===
Goals are internal representations of desired states, which are broadly constructed as outcomes, events, or processes that individuals seek to attain, maintain, or avoid (Austin &amp; Vancouver, 1996). Goal pursuit, in turn, refers to the processes through which individuals work to realise these goals. This is an important distinction because simply holding a strong intention (“I intend to do Z”) does not guarantee goal achievement, and people may fail to deal effectively with self-regulatory problems during goal striving. Take a university student for example, they may strongly value becoming a psychologist while repeatedly postponing study, avoid difficult course work, or fail to seek relevant experience. The desired future provides direction, but it must still be translated into action.

Goal-directed behaviour therefore involves a range of processes after a goal has been formed. Contemporary accounts emphasise that once an individual generates an intent to pursue a given goal, they “cross the rubicon” into several stages that involve planning, effort, persistence, progress, monitoring, and adaptation when difficulties arise (Milyavskaya &amp; Werner, 2018). Importantly, intentions alone are poor predictors of subsequent behaviour; Sheeran and Webb (2016) describe a substantial intention-behaviour gap, whereby people frequently fail to act despite intending to do so which occurs approximately half the time. Goal pursuit must also be sustained over time and adjusted in response to obstacles, competing demands, and changes in goal attainability. One highly efficient means of strengthening the transition from intention to action is through implementation intentions, which specify when, where, or how goal-directed behaviour will occur. They take the format of a cognitive association between a prespecified opportunity for acting and a specific goal-directed behaviour (i.e., “if situation x arises, then I will perform behaviour y”) (Brandstatter &amp; Bernecker, 2022). Several studies have proven implementation intentions to be efficacious, helping individuals to support persistence and improve goal attainment (Belanger-Gravel, 2013; Gollwitzer &amp; Sheeran, 2006). Together, this research demonstrates that motivation towards a desired outcome is only one component of successful goal pursuit. 

This distinction is particularly relevant to possible selves. Envisioning oneself as a competent psychologist may establish a meaningful long-term direction, but that future identity becomes behaviourally consequential only when it is coupled to actions such as completing assignments, developing relevant skills, seeking professional experience, and persisting through tough times. Possible selves may help establish where a person wants to go, while goal-directed behaviour concerns the processes required to move towards that future. 

=== Self-regulation in goal pursuit ===

&lt;div style=&quot;float: right; margin: 0px 0 10px 15px;&quot;&gt;
[[File:Determination on the Everest Expedition.jpg|thumb|right|440px|'''Figure 3.''' Mountaineer ascending Himalayan mountains]]
&lt;/div&gt;

The processes involved in directing and maintaining behaviour towards goals are commonly understood through self-regulation. Frazier et al. (2021) describe self-regulation as a social-cognitive process at the intersection of metacognition, motivation, and behaviour which encompasses how people conceptualise, strive for, and accomplish their goals. Once a goal has been adopted, self-regulation helps translate that desired outcome into an ongoing action by allowing individuals to monitor their progress, adjust their behaviour, and respond to obstacles encountered during goal pursuit. 

One particularly influential account conceptualises self-regulation as a discrepancy-reducing feedback loop (Carver &amp; Scheier, 2002). Within this control-process model, individuals compare their present state against a desired reference point and monitor whether a discrepancy exists between the two. Using the goal as a reference, a person compares their present state to the desired end state (i.e., “am I on track for my goal?”). If a discrepancy is detected, the person acts to reduce this discrepancy, thereby engaging in goal-promoting behaviour (Milyavskaya &amp; Werner, 2018). Self-regulation is therefore an ongoing process of comparison, feedback, and behavioural adjustment rather than a single decision to pursue a goal. 

Possible selves may provide one such future-oriented reference point. By representing who an individual wishes to become or wishes to avoid becoming, they can establish standards against which present behaviour and progress are evaluated. However, merely possessing a future standard does not alone explain how strongly it will influence behaviour. Understanding how possible selves become integrated into self-regulation, and why some guide action more effectively than others, requires closer examination of their role within motivated goal pursuit.

== Possible selves in motivated goal pursuit ==
Personal selves can provide meaningful representation of where an individual wishes to go or what they hope to avoid, while self-regulation provides processes through which these future identities may influence present behaviour. The relationship between the two, however, is not straightforward. Contemporary research suggests that the motivational value of a possible self depends less on the seminal formulation of having positive-valence and more on whether that future identity becomes relevant to the affordances and constraints of their immediate situation, and functions effectively within self-regulatory processes (Oyserman &amp; Horowitz, 2023). Understanding possible selves in goal pursuit therefore requires asking not only ''what future does a person imagine?,'' but also ''how does the imagined future influence what they do now?''

=== Modelling the relationships ===
Markus and Nurius’ (1986) original account proposed that possible selves connect cognition and motivation by giving self-relevant form to people's hopes, fears and aspirations, thereby providing incentives for future behaviour. Subsequent theory has refined this relationship. Rather than treating possible selves as a direct cause of motivation or behaviour, they are better understood as components within broader self-regulatory systems (Hoyle &amp; Sherrill, 2006). In this way, a possible self can provide a behavioural standard or future reference point, while other regulatory processes determine whether and how behaviour is organised around it. Studies demonstrate that embedding possible selves within established models of self-regulation provides some impetus to behaviour and outcome change, as well as meaningful predictions about present behavior, supporting a more process-oriented interpretation of their motivational role (Hoyle &amp; Sherrill, 2006; Oyserman et al., 2004; vanDellen &amp; Hoyle, 2008).

Empirical findings support this process-oriented interpretation. A study by vanDellen and Hoyle (2008) experimentally examined whether hoped-for and feared health-related possible selves could function as behavioural standards within self-regulation. After making these possible selves salient, participants were given opportunities to engage in behaviours that could reduce discrepancies between their current and possible selves. Evidence for discrepancy-reducing behaviour was strongest when feared possible selves were salient and participants possessed sufficient self-regulatory capacity, whereas comparable effects were not found for hope-for possibles selves. These findings suggest that possible selves can guide present behaviour by operating as standard within broader self-regulatory processes rather than directly producing goal attainment (vanDellen &amp; Hoyle, 2008). Likewise, possible selves appear more strongly related to behavioural and academic outcomes when they are linked to strategies and can plausibly function as self-regulatory resources rather than merely positive representations of the future (Oserman et al., 2004). Possible selves therefore do not instantiate goal attainment. Rather, their influence depends on the self-regulatory processes in which they are embedded.

&lt;div style=&quot;float: right; margin: 0px 0 10px 15px;&quot;&gt;
[[File:MAPS model of self-regulation.png|thumb|right|360px|'''Figure 4.''' MAPS model of self-regulation (Frazier et al., 2021).]]
&lt;/div&gt;

The MAPS model of self-regulation provides a more recent framework for understanding these processes. Frazier et al., (2021) propose that goal-directed behaviour emerges from dynamic and synergistic interaction between possible selves, metacognitive knowledge and strategies, and a sense of one's own agency. Possible selves embody representations of desired future outcomes and provide motivational direction; metacognitive knowledge helps people select, monitor and modify strategies for pursuing those outcomes; and agency reflects the extent to which individuals perceive themselves as capable of influencing what happens next. Importantly, these elements continually influence one another. Feedback from goal-directed action can alter perceptions of competence and agency, which in turn can reshape strategies and even beliefs about what future selves remain possible.  

Taken together, these accounts suggest that possible selves influence goal pursuit through an indirect and dynamic manner. Imagining a future self can help to make outcomes personally meaningful and provide a benchmark towards which behaviour can be directed. However, movement towards that future requires individuals to identify reasonable approaches, believe in their agency, monitor progress, and adjust their behaviour in response to feedback. Possible selves may therefore provide the direction and motivational meaning of goal pursuit, while self-regulatory processes provide the means through which that direction is translated into present action.  

Additionally, a future identity must feel relevant to choices in the present. From an identity-based motivation perspective, it requires a ‘shift of focus from what ''future me is–''positive or negative, close or distant, continuous or discontinuous ''with current me–''to what ''future me does''’ (Oyserman &amp; Horowitz, 2023, p. 74)''.'' As illustrated in Figures 5 and 6, future-oriented action is more likely when a possible self feels relevant, difficulties are interpreted as signs of importance rather than impossibility, and the required actions feel consistent with one's identity. This helps explain why the same possible self can strongly guide behaviour in one situation while exerting little influence in another.

&lt;div style=&quot;display: flex; gap: 10px; align-items: stretch;&quot;&gt;

&lt;div style=&quot;width: 50%;&quot;&gt;
[[File:When does a future self influence current action?.png|thumb|center|x300px|'''Figure 5.''' Idenity-based motivation processes linking future selves to behaviour (adapted from Oyserman &amp; Horowitz, 2023).]]
&lt;/div&gt;

&lt;div style=&quot;width: 50%;&quot;&gt;
[[File:How identity-based motivation can orient action toward or away from the future.png|thumb|center|x300px|'''Figure 6.''' Identity-based motivation pathways linking future idenities to action (adapted from Oyserman &amp; Horowitz, 2023).]]
&lt;/div&gt;

&lt;/div&gt;

=== When possible selves facilitate goal pursuit ===
An important condition for possible selves to facilitate goal pursuit is their relationship to plausible strategies for action. Oyserman et al., (2004) distinguish between possible selves that are primarily self-enhancing and those capable of functioning as self-regulators. To investigate this, they examined the extent to which detailed academic possible selves, when linked with strategies, added predictive power. Adolescents whose academic possible selves incorporated strategies for attaining desired futures or avoiding feared ones showed greater classroom participation, spent more time on homework, and achieved better academic outcomes. Indeed, having plausibly self-regulating possible selves is more likely to induce self-improvement behaviour and significantly greater chances of success, compared to possible selves that do not include such self-regulatory guideposts (Hoyle &amp; Sherrill, 2006; Oyserman et al., 2004; Oyserman &amp; James, 2009). 

Whether these strategies influence behaviour also depends on the context in which a possible self is brought to mind. Possible selves differ in accessibility, and identities made salient by the immediate situation are more likely to inform judgment and decision making (Higgins, 1996; Oyserman et al., 2006). Consequently, sustained pursuit requires relevant behavioral strategies to be readily available when the future identity becomes salient. For instance, an academic possible self is in theory more effective when the surrounding environment routinely cues behaviours such as attending lectures, persisting through assignments, seeking assistance, or attending study help. Oyserman et al., (2006) argue that resource-rich contexts are more likely to provide accessible models of success and established pathways towards the ideal futures, whereas resource-limited environments may offer fewer such cues. The motivational effectiveness of a possible self therefore depends partly on whether the social environment makes pathways towards it visible and actionable.  

Possible selves are also more likely to motivate when they feel compatible with important social identities and when difficulties encountered during pursuits are interpreted constructively. Identity-based motivation theory proposes that people are more willing to act in ways that fit the identities on their minds which feel relevant to the affordances and constraints of their immediate situation (Oyserman, 2015). A future identity that appears inconsistent with one's social group, circumstances, or understanding of “people like me” may therefore be less likely to organise behaviour, even when it is personally desirable. Importantly, this does not imply effective motivation requires distancing oneself from existing social identities, rather, future identities become more actionable when they can be experienced as compatible with those identities (Oyserman et al., 2006; Oyserman &amp; Horowitz, 2023).

How people interpret difficulty further shapes this process. Difficulty encountered while pursuing a possible self can be understood as evidence that the future is unattainable, encouraging disengagement, or as a normative indication that an important goal requires effort. Identity-based motivation theory highlights the role of metacognitive experience, particularly the subjective feelings of ease or difficulty associated with pursuing a goal (Oyserman, Bybee, &amp; Terry, 2006). When behaviour feels consistent with one's identity, difficulty may be interpreted as a sign that the goal is important and worth pursuing rather than an impossibility, i.e., “no pain no gain” (Oyserman &amp; Horowitz, 2023). Thus, the motivational consequences of difficulty depend not simply on how hard goal pursuit feels, but on the metacognitive experience of the difficulty and the meaning attributed to that experience.  

Taken together, possible selves are more likely to facilitate goal pursuit when they are connected to realistic strategies, supported and cued by the surrounding context, compatible with salient identities, resilient to experiences of difficulty, and personally meaningful enough to sustain commitment (Haskins &amp; vanDellen, 2019). Their motivational value therefore lies in whether that future can be integrated with the circumstances, interpretations, and actions of the present self. 

=== When possible selves fail to motivate ===
Possible selves can remain self-enhancing rather than self-regulatory, such that possible selves promote positive feelings and maintain a sense of optimism and hope for the future without evoking behavioural strategies required to reach it (Oyserman et al., 2004). For example, a university student may say to themselves ‘I may not be doing well in university this semester but I will succeed next semester’, thereby protecting their self-esteem from the current bad grades, without engaging in any behavioural strategies to improve their academic performance in the following semester. This distinction illustrates why simply valuing or vividly imagining a possible self is insufficient for goal pursuit. 

Importantly, failure to act does not necessarily reflect a lack of ambition, as socioeconomic and social contexts can constrain access to the strategies, role models, and opportunities needed to make a future identity actionable. In low socio-economic contexts, behavioural strategies may be less readily accessible due to fewer role models and resources to guide goal pursuit (Oyserman, Bybee, &amp; Terry, 2006). Furthermore, Oyserman, Johnson, and James (2011) describe part of the problem as “seeing the destination but not the path”; disadvantaged adolescents could hold salient school-focused possible selves while possessing fewer strategies for attaining them. Likewise, difficulty can undermine pursuit when it is interpreted as signaling impossibility rather than importance, particularly when the future identity feels incongruent with one's circumstances or social identities (Oyserman et al., 2006; Oyserman &amp; Horowitz, 2023). Thus, motivational value lies in whether the future self can be translated into plausible, identity-congruent, and contextually supported pathways for behavioral action. 

== Harnessing possible selves for goal pursuit ==

&lt;div style=&quot;float: right; margin: 0px 0 10px 15px;&quot;&gt;
[[File:Ballet, mirror, parquet floor, dance room Fortepan 85036.jpg|thumb|right|420px|'''Figure 7.''' Dancer refining her practice.]]
&lt;/div&gt;

The mechanisms discussed throughout this chapter raise a question: can possible selves be deliberately harnessed to improve goal pursuit? Intervention research provides some evidence that they can. Oyserman et al. (2006) developed a school-based intervention to link academic possible selves with behavioural strategies, a context in which social and personal identities felt congruent, and constructive interpretations of difficulty. Compared with controls, participating adolescents subsequently showed greater academic initiative, improved grades and standardized test scores, fewer absences, and reduced school misbehaviour, with effects sustained over a two-year follow up. More recent research has extended this approach using digital representations of the future self. In a 2026 randomised controlled trial, interventions delivered through smartphone and virtual reality strengthened identification with the future self through visual and interactive experiences, with the virtual reality condition also increasing goal achievement (van Gelder et al., 2026).

However, intervention findings also caution against treating future-self imagery as a simple motivational technique. The same 2026 trial found no improvements in several other outcomes, including academic performance and self-defeating behaviour, suggesting that strengthening future-self identification does not automatically produce broad behavioural change (van Gelder et al., 2026). Additionally, Tettero et al., (2026) conducted a study to investigate how the three components of future self-identification—vividness, connectedness, and valence—were associated with goal achievement over time. It was found that vividness of the future self most consistently predicted subsequent goal achievement, connectedness contributed more modestly, while valence did not predict achievement, which aligns with research that came before it (Kuo et al., 2025). It is believed that the richness of vivid mental images makes the future self more concrete and realistic, reducing the psychological distance between the self and possible self, thus enhancing the perceived relevance of future goals (Bixter et al., 2020; Evans &amp; Wilson, 2014; Hershfield, 2011). These findings reinforce the broader conclusion of this chapter: the motivational value of possible selves lies not simply in imagining a desirable future, but in whether that future becomes sufficiently concrete, relevant, and actionable to influence behaviour.

== Extra sources ==
*Possible selves, self regulation and actual social goal progress (2014)
*Best possible self intervention and academic motivation/commitment (2020)
*Identity-based motivation (2015) 

== Conclusion ==
Possible selves influence motivation and goal-directed behaviour by giving personally meaningful form to the futures people hope to attain or avoid, but their motivational value is neither direct nor certain. Psychological research suggests that they are most effective when they function within broader self-regulatory processes, provide a meaningful future-oriented reference point, and are linked to realistic behavioural strategies, metacognitive monitoring, and a sense of agency. Whether a possible self translates into action further depends on whether it is accessible in the present, compatible with salient social identities, supported by the surrounding context, and resilient to experiences of difficulty. Difficulty can strengthen persistence when interpreted as a normative aspect of pursuing an important goal, but undermine pursuit when it suggests impossibility. Possible selves therefore provide the direction and motivational meaning of goal pursuit, while self-regulatory processes provide the means through which that direction is translated into present action. The practical implication is this: imagining a desirable future is not enough; possible selves become motivationally effective when they are concrete, actionable, and connected to what a person can do now.&lt;div style=&quot;background-color: #fceef3; border: 1px solid #c77b98; border-radius: 10px; padding: 12px 18px; margin: 15px 0;&quot;&gt;

'''Chapter comprehension check'''

&lt;div style=&quot;margin-top: -50px;&quot;&gt;
&lt;quiz display=simple&gt;
{Possible selves are future-oriented representations of who a person might become and can provide motivational direction to present behaviour.
|type=&quot;()&quot;}
+ True
- False

{Possible selves directly produce goal-directed behaviour without relying on broader self-regulatory processes.
|type=&quot;()&quot;}
- True
+ False

{A possible self is more likely to facilitate goal pursuit when it is connected to plausible strategies, relevant to the current context, and compatible with salient identities.
|type=&quot;()&quot;}
+ True
- False

{Interventions strengthen goal pursuit simply by encouraging people to imagine a positive future self.
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;
&lt;/div&gt;
&lt;/div&gt;

==See also==
* [[w:Future self|Future self]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Regulatory focus theory and goal pursuit|Regulatory focus theory and goal pursuits]] (Book chapter, 2019)
* [[w:Goal pursuit|Goal Pursuit]] (Wikipedia)

==References==
{{Hanging indent|1=

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King, L. A., &amp; Raspin, C. (2004). Lost and found possible selves, subjective well-being, and ego development in divorced women. Journal of Personality, 72(3), 603–632. https://doi.org/10.1111/j.0022-3506.2004.00274.x

Markus, H., &amp; Nurius, P. (1986). Possible selves. American Psychologist, 41(9), 954–969. https://doi.org/https://doi.org/10.1037/0003-066X.41.9.954

Milyavskaya, M., &amp; Werner, K. M. (2018). Goal pursuit: Current state of affairs and directions for future research. Canadian Psychology/Psychologie Canadienne, 59(2), 163–175. https://doi.org/10.1037/cap0000147

Murru, E. C., &amp; Martin Ginis, K. A. (2010). Imagining the possibilities: The effects of a possible selves intervention on self-regulatory efficacy and exercise behavior. Journal of Sport &amp; Exercise Psychology, 32(4), 537–554. https://doi.org/10.1123/jsep.32.4.537

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Oyserman, D. (2009). Identity‐based motivation: Implications for action‐readiness, procedural‐readiness, and consumer behavior. Journal of Consumer Psychology, 19(3), 250–260. https://doi.org/10.1016/j.jcps.2009.05.008

Oyserman, D. (2015). Pathways to success through identity-based motivation. Oxford University Press. https://psycnet.apa.org/record/2015-16643-000

Oyserman, D., Bybee, D., &amp; Terry, K. (2006). Possible selves and academic outcomes: How and when possible selves impel action. Journal of Personality and Social Psychology, 91(1), 188–204. https://doi.org/10.1037/0022-3514.91.1.188

Oyserman, D., Bybee, D., Terry, K., &amp; Hart-Johnson, T. (2004). Possible selves as roadmaps. Journal of Research in Personality, 38(2), 130–149. https://doi.org/10.1016/s0092-6566(03)00057-6

Oyserman, D., &amp; Horowitz, E. (2023). From possible selves and future selves to current action: An integrated review and identity-based motivation synthesis. In Advances in Motivation Science (pp. 73–147). Elsevier Inc.

Sheeran, P., &amp; Webb, T. L. (2016). The intention-behavior gap. Social and Personality Psychology Compass, 10(9), 503–518. https://doi.org/10.1111/spc3.12265

Strauss, K., Griffin, M. A., &amp; Parker, S. K. (2012). Future work selves: How salient hoped-for identities motivate proactive career behaviors. Journal of Applied Psychology, 97(3), 580–598. https://doi.org/10.1037/a0026423

Tettero, T., Mertens, E. C. A., Siezenga, A. M., &amp; van Gelder, J.-L. (2026). From future vision to current action: The relationship between future self-identification and goal achievement. Personality and Individual Differences, 254, 113645. https://doi.org/10.1016/j.paid.2026.113645

van Gelder, J.-L., Tettero, T., Siezenga, A., &amp; Mertens, E. (2026). Stimulating future-oriented thinking and goal-achievement through the future self using virtual reality and a smartphone app: Randomized controlled trial. Journal of Medical Internet Research, 28, e84420–e84420. https://doi.org/10.2196/84420

vanDellen, M. R., &amp; Hoyle, R. H. (2008). Possible selves as behavioral standards in self-regulation. Self and Identity, 7(3), 295–304. https://doi.org/10.1080/15298860701641108}}

==External links==
* [https://www.hiddenbrain.org/podcast/you-2-0-your-future-is-now/ You 2.0: your future is now] (Hidden Brain)
* [https://www.youtube.com/watch?v=XNbaR54Gpj4&amp;t=177s The psychology of you future self | Dan Gilbert] (Youtube)
* [https://www.psychologytoday.com/au/blog/philosophy-and-therapy/202401/the-philosophy-of-possible-selves Why to start considering your possible selves] (Psychology Today)</text>
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__TOC__
==Overview==
{{RoundBoxTop|theme=3}}
[[File:Ueber-die-sammlung-19-jahrhundert-caspar-david-friedrich-wanderer-ueber-dem-nebelmeer.jpg|thumb|right|150px|'''Figure 1'''. The wanderer looks across a sea of fog toward the looming mountains, symbolising the current self and possible self.]]

; Scenario

A university student has started their final year of their bachelor's degree, and the academic standards are higher than previous years. One may imagine their future as exciting: graduating, beginning a meaningful career, becoming financially independent, and becoming the capable and competent person they hope to be. Alternatively, they may imagine their future as unsettling: losing motivation, failing to make use of their opportunities, and becoming someone they once hoped to avoid.

Neither future exists, however, these imagined versions of the self can influence what the student does today – whether they attend lectures and tutorials, persist through difficult assignments and exams, or give up when progress feels slow.
{{RoundBoxBottom}}
Possible selves are conceptions of who we may become in the future and involve, to some degree, imagining ourselves as agents within those future situations (Erikson, 2007). They can include versions of ourselves that we hope to become, as well as those we fear becoming. Markus and Nurius (1986) proposed that these future self-representations are motivationally important because they can provide incentives for behaviour and give personal meaning and direction to our goals.

In the opening scenario, the university student can imagine both a desired future of graduating and beginning a meaningful career, and an unwanted future characterised by lost opportunities and lack of direction. Yet imagining either future does not guarantee that the student will study, persist through setbacks, or take advantage of opportunities in the present. This illustrates a central problem in understanding possible selves: how does an imagined future identity become motivation and, ultimately, goal-directed behaviour?

Literature during the 21st century suggests that possible selves are better understood as components of self-regulation through which motivation and behaviour are influenced (Hoyle &amp; Sherrill, 2006; Frazier, Schwartz &amp; Metcalfe, 2021). Research therefore focuses on the conditions under which possible selves provide effective guidance for goal pursuit, including whether they are meaningful, attainable, and connected to realistic behavioural strategies. Examining these processes help to explain why imagined future identities can motivate present goal-directed behaviour in some circumstances, yet remain ineffective in others (Haskins &amp; vanDellen, 2019).

&lt;div style=&quot;background-color: #fbedf2; border: 2px solid #d4779b; border-radius: 12px; padding: 15px 20px;&quot;&gt;
'''Focus questions'''

*What are possible selves, and why can they have motivational significance?
*How do possible selves interact with self-regulatory processes involved in goal pursuit?
*Under what conditions do possible selves facilitate - or fail to facilitate - goal-directed behaviour?
* How can possible selves be used to strengthen motivation and translate future aspirations into present action?
&lt;/div&gt;

== Possible selves ==
=== Definition and theoretical origins ===
The concept of possible selves was introduced by Markus and Nurius (1986) to complement current conceptions of self-knowledge by extending it beyond the present.  They proposed that possible selves represent individuals' ideas of what they might become, what they would like to become, and what they are afraid of becoming, and thus provide a conceptual link between cognition and motivations. More recently, Erikson (2007) emphasised agency, arguing that possible selves involve experiencing oneself, at least to some degree, as an agent within an imagined future situation. This distinguishes a possible self from a simple goal: Wanting to receive a high grade describes a desired outcome, whereas imagining oneself as a capable and successful student places the person within a future identity. Possible selves are therefore closely related to goals, but are distinguished by their explicit connection to who the individual might become. 

Possible selves can take several forms. Hoped-for possible selves represent desirable identities that a person would like to attain. This could include the competent and powerful self, the celebrated and glamorous self, the respected and esteemed self, or the fit self. In contrast, the feared possible selves comprise a similarly compelling set. One's fears and anxieties can become concretely manifest in visions of the lonely self, the undervalued and underpaid self, or the out-of-shape self (Cross &amp; Markus, 1991). Additionally, people may also hold expected possible selves, representing identities they consider realistically likely rather than simply desirable or undesirable. A person might, for example, hope to become an award winning author while expecting to pursue an entirely different career. Markus and Nurius (1986) suggest that much of our significant behavior can be seen primarily as an effort to approach or avoid various possible selves. 

Importantly, people do not construct these future identities in isolation. Content of possible selves is shaped by people's experiences and sociocultural circumstances rather than being a manifestation of the isolated self, as well as by temporal, contextual, developmental factors (Allport, 1937; Frazier &amp; Hooker, 2006). Markus and Nurius (1986) argue that the pool of possible selves available to an individual is influenced by socially salient categories and by the models, images, and examples encountered through media and everyday social experience. Elite sport provides a useful illustration:
&lt;div style=&quot;width: 50%; float: right; background-color: #f0f5f8; border-left: 4px solid #527d99; padding: 2px 15px 2px 15px; margin: 0 0 20px 20px; border-radius: 6px; box-sizing: border-box;&quot;&gt;

'''Case study:''' 

[[File:Eliud Kipchoge in Berlin - 2015 (cropped).jpg|thumb|right|110px|'''Figure 2.''' Eliud Kipchoge (2015).]]

In 2019, Kenyan marathon runner Eliud Kipchoge became the first person to complete a marathon distance in under two hours, demonstrating that a feat long considered beyond human capability was, in fact, achievable. By expanding public perceptions of what was possible, Kipchoge may have helped other elite runners imagine similar achievements as part of their own possible futures. Subsequent athletes to break the two-hour barrier likely absorbed the performance of Eliud Kipchoge within the realm of their own possible selves, giving specific cognitive form to their desire to become exceptional runners. 
&lt;/div&gt;

Importantly, people do not construct these future identities in isolation. Content of possible selves is shaped by people's experiences and sociocultural circumstances rather than being a manifestation of the isolated self, as well as by temporal, contextual, developmental factors (Allport, 1937; Frazier &amp; Hooker, 2006). Markus and Nurius (1986) argue that the pool of possible selves available to an individual is influenced by socially salient categories and by the models, images, and examples encountered through media and everyday social experience. Elite sport provides a useful illustration:

Cross and Markus (1991) similarly found systematic differences in hoped-for and feared possible selves across adulthood, illustrating how possible selves change alongside people's circumstances and developmental priorities. Possible selves therefore reflect an interaction between individual aspirations and the social contexts within which those futures are imagined.


=== Forms and content of possible selves &amp; motivational properties of possible selves ===
Possible selves are particularly relevant to motivational psychology because it allows us to make a more direct connection between motives and actions. Markus and Nurius (1986) proposed that future selves can function as incentives for future behaviour by providing a self-relevant framework that gives meaning, organisation, and direction to our actions. For example, imagining oneself as physically healthy and active in later life may encourage behaviours directed towards that future, while imagining a feared future characterised by poor health may provide motivation to avoid it. Thus, possible selves can transform relatively vague and abstract aspirations or fears into outcomes that are explicitly connected to one's identity. 

Yet not all possible selves are equally motivating. Norman and Aron (2003) found that motivation to attain or avoid an important possible self was significantly predicted by its availability, its accessibility, and the extent to which its attainment or avoidance is perceived as under one's control. Hence, merely possessing a desirable or undesirable future image may be insufficient. A future self that feels vague, remote or outside one's control is unlikely to exert the same motivational influence as one that is psychologically accessible and associated with a sense of agency.

Experimental research also indicates that the way a future self is represented can influence subsequent motivation and behaviour. There is a large body of research that has identified characteristics that render possible selves more or less efficient for prompting behaviour. For instance, it is generally accepted that a possible self has to be salient and easily evoked in order to affect behaviour (Strauss, Griffin, &amp; Parker, 2012; King &amp; Raspin 2004; Norman &amp; Aron, 2003). A recent study by De Place and Brunot (2020) manipulated both the specificity and [[w:Valence (psychology)|valence]] of university students’ imagined possible selves. Across two studies, different combinations of general or specific future success and failure produced differences in attention and academic motivation. Importantly, their results were more complex than simply showing that positive or highly specific future images are always beneficial. Such findings reinforce the idea that the motivational influence of a possible self depends not merely on whether the imagined future is positive or negative, but also on how that future is represented (De Place &amp; Brunot, 2020). 

Possible selves therefore offer a potential source of motivation, but should be understood as a more complex interplay of several different cognitions. Explaining how these future identities translate into sustained goal-directed behavior requires consideration of the processes involved in goal pursuit and self-regulation.

== Goal pursuit and self-regulation ==
Imagining a meaningful future self may provide direction, but it does not guarantee action. Moving towards a hoped-for possible self or away from a feared one requires people to initiate and sustain behaviour, respond to obstacles, and regulate their progress over time. Goal Pursuit and self-regulation therefore provide the bridge between imagined future identities and present behaviour. 

=== From goals to goal-directed behaviour ===
Goals are internal representations of desired states, which are broadly constructed as outcomes, events, or processes that individuals seek to attain, maintain, or avoid (Austin &amp; Vancouver, 1996). Goal pursuit, in turn, refers to the processes through which individuals work to realise these goals. This is an important distinction because simply holding a strong intention (“I intend to do Z”) does not guarantee goal achievement, and people may fail to deal effectively with self-regulatory problems during goal striving. Take a university student for example, they may strongly value becoming a psychologist while repeatedly postponing study, avoid difficult course work, or fail to seek relevant experience. The desired future provides direction, but it must still be translated into action.

Goal-directed behaviour therefore involves a range of processes after a goal has been formed. Contemporary accounts emphasise that once an individual generates an intent to pursue a given goal, they “cross the rubicon” into several stages that involve planning, effort, persistence, progress, monitoring, and adaptation when difficulties arise (Milyavskaya &amp; Werner, 2018). Importantly, intentions alone are poor predictors of subsequent behaviour; Sheeran and Webb (2016) describe a substantial intention-behaviour gap, whereby people frequently fail to act despite intending to do so which occurs approximately half the time. Goal pursuit must also be sustained over time and adjusted in response to obstacles, competing demands, and changes in goal attainability. One highly efficient means of strengthening the transition from intention to action is through implementation intentions, which specify when, where, or how goal-directed behaviour will occur. They take the format of a cognitive association between a prespecified opportunity for acting and a specific goal-directed behaviour (i.e., “if situation x arises, then I will perform behaviour y”) (Brandstatter &amp; Bernecker, 2022). Several studies have proven implementation intentions to be efficacious, helping individuals to support persistence and improve goal attainment (Belanger-Gravel, 2013; Gollwitzer &amp; Sheeran, 2006). Together, this research demonstrates that motivation towards a desired outcome is only one component of successful goal pursuit. 

This distinction is particularly relevant to possible selves. Envisioning oneself as a competent psychologist may establish a meaningful long-term direction, but that future identity becomes behaviourally consequential only when it is coupled to actions such as completing assignments, developing relevant skills, seeking professional experience, and persisting through tough times. Possible selves may help establish where a person wants to go, while goal-directed behaviour concerns the processes required to move towards that future. 

=== Self-regulation in goal pursuit ===

&lt;div style=&quot;float: right; margin: 0px 0 10px 15px;&quot;&gt;
[[File:Determination on the Everest Expedition.jpg|thumb|right|440px|'''Figure 3.''' Mountaineer ascending Himalayan mountains]]
&lt;/div&gt;

The processes involved in directing and maintaining behaviour towards goals are commonly understood through self-regulation. Frazier et al. (2021) describe self-regulation as a social-cognitive process at the intersection of metacognition, motivation, and behaviour which encompasses how people conceptualise, strive for, and accomplish their goals. Once a goal has been adopted, self-regulation helps translate that desired outcome into an ongoing action by allowing individuals to monitor their progress, adjust their behaviour, and respond to obstacles encountered during goal pursuit. 

One particularly influential account conceptualises self-regulation as a discrepancy-reducing feedback loop (Carver &amp; Scheier, 2002). Within this control-process model, individuals compare their present state against a desired reference point and monitor whether a discrepancy exists between the two. Using the goal as a reference, a person compares their present state to the desired end state (i.e., “am I on track for my goal?”). If a discrepancy is detected, the person acts to reduce this discrepancy, thereby engaging in goal-promoting behaviour (Milyavskaya &amp; Werner, 2018). Self-regulation is therefore an ongoing process of comparison, feedback, and behavioural adjustment rather than a single decision to pursue a goal. 

Possible selves may provide one such future-oriented reference point. By representing who an individual wishes to become or wishes to avoid becoming, they can establish standards against which present behaviour and progress are evaluated. However, merely possessing a future standard does not alone explain how strongly it will influence behaviour. Understanding how possible selves become integrated into self-regulation, and why some guide action more effectively than others, requires closer examination of their role within motivated goal pursuit.

== Possible selves in motivated goal pursuit ==
Personal selves can provide meaningful representation of where an individual wishes to go or what they hope to avoid, while self-regulation provides processes through which these future identities may influence present behaviour. The relationship between the two, however, is not straightforward. Contemporary research suggests that the motivational value of a possible self depends less on the seminal formulation of having positive-valence and more on whether that future identity becomes relevant to the affordances and constraints of their immediate situation, and functions effectively within self-regulatory processes (Oyserman &amp; Horowitz, 2023). Understanding possible selves in goal pursuit therefore requires asking not only ''what future does a person imagine?,'' but also ''how does the imagined future influence what they do now?''

=== Modelling the relationships ===
Markus and Nurius’ (1986) original account proposed that possible selves connect cognition and motivation by giving self-relevant form to people's hopes, fears and aspirations, thereby providing incentives for future behaviour. Subsequent theory has refined this relationship. Rather than treating possible selves as a direct cause of motivation or behaviour, they are better understood as components within broader self-regulatory systems (Hoyle &amp; Sherrill, 2006). In this way, a possible self can provide a behavioural standard or future reference point, while other regulatory processes determine whether and how behaviour is organised around it. Studies demonstrate that embedding possible selves within established models of self-regulation provides some impetus to behaviour and outcome change, as well as meaningful predictions about present behavior, supporting a more process-oriented interpretation of their motivational role (Hoyle &amp; Sherrill, 2006; Oyserman et al., 2004; vanDellen &amp; Hoyle, 2008).

Empirical findings support this process-oriented interpretation. A study by vanDellen and Hoyle (2008) experimentally examined whether hoped-for and feared health-related possible selves could function as behavioural standards within self-regulation. After making these possible selves salient, participants were given opportunities to engage in behaviours that could reduce discrepancies between their current and possible selves. Evidence for discrepancy-reducing behaviour was strongest when feared possible selves were salient and participants possessed sufficient self-regulatory capacity, whereas comparable effects were not found for hope-for possibles selves. These findings suggest that possible selves can guide present behaviour by operating as standard within broader self-regulatory processes rather than directly producing goal attainment (vanDellen &amp; Hoyle, 2008). Likewise, possible selves appear more strongly related to behavioural and academic outcomes when they are linked to strategies and can plausibly function as self-regulatory resources rather than merely positive representations of the future (Oserman et al., 2004). Possible selves therefore do not instantiate goal attainment. Rather, their influence depends on the self-regulatory processes in which they are embedded.

&lt;div style=&quot;float: right; margin: 0px 0 10px 15px;&quot;&gt;
[[File:MAPS model of self-regulation.png|thumb|right|360px|'''Figure 4.''' MAPS model of self-regulation (Frazier et al., 2021).]]
&lt;/div&gt;

The MAPS model of self-regulation provides a more recent framework for understanding these processes. Frazier et al., (2021) propose that goal-directed behaviour emerges from dynamic and synergistic interaction between possible selves, metacognitive knowledge and strategies, and a sense of one's own agency. Possible selves embody representations of desired future outcomes and provide motivational direction; metacognitive knowledge helps people select, monitor and modify strategies for pursuing those outcomes; and agency reflects the extent to which individuals perceive themselves as capable of influencing what happens next. Importantly, these elements continually influence one another. Feedback from goal-directed action can alter perceptions of competence and agency, which in turn can reshape strategies and even beliefs about what future selves remain possible.  

Taken together, these accounts suggest that possible selves influence goal pursuit through an indirect and dynamic manner. Imagining a future self can help to make outcomes personally meaningful and provide a benchmark towards which behaviour can be directed. However, movement towards that future requires individuals to identify reasonable approaches, believe in their agency, monitor progress, and adjust their behaviour in response to feedback. Possible selves may therefore provide the direction and motivational meaning of goal pursuit, while self-regulatory processes provide the means through which that direction is translated into present action.  

Additionally, a future identity must feel relevant to choices in the present. From an identity-based motivation perspective, it requires a ‘shift of focus from what ''future me is–''positive or negative, close or distant, continuous or discontinuous ''with current me–''to what ''future me does''’ (Oyserman &amp; Horowitz, 2023, p. 74)''.'' As illustrated in Figures 5 and 6, future-oriented action is more likely when a possible self feels relevant, difficulties are interpreted as signs of importance rather than impossibility, and the required actions feel consistent with one's identity. This helps explain why the same possible self can strongly guide behaviour in one situation while exerting little influence in another.

&lt;div style=&quot;display: flex; gap: 10px; align-items: stretch;&quot;&gt;

&lt;div style=&quot;width: 50%;&quot;&gt;
[[File:When does a future self influence current action?.png|thumb|center|x300px|'''Figure 5.''' Idenity-based motivation processes linking future selves to behaviour (adapted from Oyserman &amp; Horowitz, 2023).]]
&lt;/div&gt;

&lt;div style=&quot;width: 50%;&quot;&gt;
[[File:How identity-based motivation can orient action toward or away from the future.png|thumb|center|x300px|'''Figure 6.''' Identity-based motivation pathways linking future idenities to action (adapted from Oyserman &amp; Horowitz, 2023).]]
&lt;/div&gt;

&lt;/div&gt;

=== When possible selves facilitate goal pursuit ===
An important condition for possible selves to facilitate goal pursuit is their relationship to plausible strategies for action. Oyserman et al., (2004) distinguish between possible selves that are primarily self-enhancing and those capable of functioning as self-regulators. To investigate this, they examined the extent to which detailed academic possible selves, when linked with strategies, added predictive power. Adolescents whose academic possible selves incorporated strategies for attaining desired futures or avoiding feared ones showed greater classroom participation, spent more time on homework, and achieved better academic outcomes. Indeed, having plausibly self-regulating possible selves is more likely to induce self-improvement behaviour and significantly greater chances of success, compared to possible selves that do not include such self-regulatory guideposts (Hoyle &amp; Sherrill, 2006; Oyserman et al., 2004; Oyserman &amp; James, 2009). 

Whether these strategies influence behaviour also depends on the context in which a possible self is brought to mind. Possible selves differ in accessibility, and identities made salient by the immediate situation are more likely to inform judgment and decision making (Higgins, 1996; Oyserman et al., 2006). Consequently, sustained pursuit requires relevant behavioral strategies to be readily available when the future identity becomes salient. For instance, an academic possible self is in theory more effective when the surrounding environment routinely cues behaviours such as attending lectures, persisting through assignments, seeking assistance, or attending study help. Oyserman et al., (2006) argue that resource-rich contexts are more likely to provide accessible models of success and established pathways towards the ideal futures, whereas resource-limited environments may offer fewer such cues. The motivational effectiveness of a possible self therefore depends partly on whether the social environment makes pathways towards it visible and actionable.  

Possible selves are also more likely to motivate when they feel compatible with important social identities and when difficulties encountered during pursuits are interpreted constructively. Identity-based motivation theory proposes that people are more willing to act in ways that fit the identities on their minds which feel relevant to the affordances and constraints of their immediate situation (Oyserman, 2015). A future identity that appears inconsistent with one's social group, circumstances, or understanding of “people like me” may therefore be less likely to organise behaviour, even when it is personally desirable. Importantly, this does not imply effective motivation requires distancing oneself from existing social identities, rather, future identities become more actionable when they can be experienced as compatible with those identities (Oyserman et al., 2006; Oyserman &amp; Horowitz, 2023).

How people interpret difficulty further shapes this process. Difficulty encountered while pursuing a possible self can be understood as evidence that the future is unattainable, encouraging disengagement, or as a normative indication that an important goal requires effort. Identity-based motivation theory highlights the role of metacognitive experience, particularly the subjective feelings of ease or difficulty associated with pursuing a goal (Oyserman, Bybee, &amp; Terry, 2006). When behaviour feels consistent with one's identity, difficulty may be interpreted as a sign that the goal is important and worth pursuing rather than an impossibility, i.e., “no pain no gain” (Oyserman &amp; Horowitz, 2023). Thus, the motivational consequences of difficulty depend not simply on how hard goal pursuit feels, but on the metacognitive experience of the difficulty and the meaning attributed to that experience.  

Taken together, possible selves are more likely to facilitate goal pursuit when they are connected to realistic strategies, supported and cued by the surrounding context, compatible with salient identities, resilient to experiences of difficulty, and personally meaningful enough to sustain commitment (Haskins &amp; vanDellen, 2019). Their motivational value therefore lies in whether that future can be integrated with the circumstances, interpretations, and actions of the present self. 

=== When possible selves fail to motivate ===
Possible selves can remain self-enhancing rather than self-regulatory, such that possible selves promote positive feelings and maintain a sense of optimism and hope for the future without evoking behavioural strategies required to reach it (Oyserman et al., 2004). For example, a university student may say to themselves ‘I may not be doing well in university this semester but I will succeed next semester’, thereby protecting their self-esteem from the current bad grades, without engaging in any behavioural strategies to improve their academic performance in the following semester. This distinction illustrates why simply valuing or vividly imagining a possible self is insufficient for goal pursuit. 

Importantly, failure to act does not necessarily reflect a lack of ambition, as socioeconomic and social contexts can constrain access to the strategies, role models, and opportunities needed to make a future identity actionable. In low socio-economic contexts, behavioural strategies may be less readily accessible due to fewer role models and resources to guide goal pursuit (Oyserman, Bybee, &amp; Terry, 2006). Furthermore, Oyserman, Johnson, and James (2011) describe part of the problem as “seeing the destination but not the path”; disadvantaged adolescents could hold salient school-focused possible selves while possessing fewer strategies for attaining them. Likewise, difficulty can undermine pursuit when it is interpreted as signaling impossibility rather than importance, particularly when the future identity feels incongruent with one's circumstances or social identities (Oyserman et al., 2006; Oyserman &amp; Horowitz, 2023). Thus, motivational value lies in whether the future self can be translated into plausible, identity-congruent, and contextually supported pathways for behavioral action. 

== Harnessing possible selves for goal pursuit ==

&lt;div style=&quot;float: right; margin: 0px 0 10px 15px;&quot;&gt;
[[File:Ballet, mirror, parquet floor, dance room Fortepan 85036.jpg|thumb|right|420px|'''Figure 7.''' Dancer refining her practice.]]
&lt;/div&gt;

The mechanisms discussed throughout this chapter raise a question: can possible selves be deliberately harnessed to improve goal pursuit? Intervention research provides some evidence that they can. Oyserman et al. (2006) developed a school-based intervention to link academic possible selves with behavioural strategies, a context in which social and personal identities felt congruent, and constructive interpretations of difficulty. Compared with controls, participating adolescents subsequently showed greater academic initiative, improved grades and standardized test scores, fewer absences, and reduced school misbehaviour, with effects sustained over a two-year follow up. More recent research has extended this approach using digital representations of the future self. In a 2026 randomised controlled trial, interventions delivered through smartphone and virtual reality strengthened identification with the future self through visual and interactive experiences, with the virtual reality condition also increasing goal achievement (van Gelder et al., 2026).

However, intervention findings also caution against treating future-self imagery as a simple motivational technique. The same 2026 trial found no improvements in several other outcomes, including academic performance and self-defeating behaviour, suggesting that strengthening future-self identification does not automatically produce broad behavioural change (van Gelder et al., 2026). Additionally, Tettero et al., (2026) conducted a study to investigate how the three components of future self-identification—vividness, connectedness, and valence—were associated with goal achievement over time. It was found that vividness of the future self most consistently predicted subsequent goal achievement, connectedness contributed more modestly, while valence did not predict achievement, which aligns with research that came before it (Kuo et al., 2025). It is believed that the richness of vivid mental images makes the future self more concrete and realistic, reducing the psychological distance between the self and possible self, thus enhancing the perceived relevance of future goals (Bixter et al., 2020; Evans &amp; Wilson, 2014; Hershfield, 2011). These findings reinforce the broader conclusion of this chapter: the motivational value of possible selves lies not simply in imagining a desirable future, but in whether that future becomes sufficiently concrete, relevant, and actionable to influence behaviour.

== Extra sources ==
*Possible selves, self regulation and actual social goal progress (2014)
*Best possible self intervention and academic motivation/commitment (2020)
*Identity-based motivation (2015) 

== Conclusion ==
Possible selves influence motivation and goal-directed behaviour by giving personally meaningful form to the futures people hope to attain or avoid, but their motivational value is neither direct nor certain. Psychological research suggests that they are most effective when they function within broader self-regulatory processes, provide a meaningful future-oriented reference point, and are linked to realistic behavioural strategies, metacognitive monitoring, and a sense of agency. Whether a possible self translates into action further depends on whether it is accessible in the present, compatible with salient social identities, supported by the surrounding context, and resilient to experiences of difficulty. Difficulty can strengthen persistence when interpreted as a normative aspect of pursuing an important goal, but undermine pursuit when it suggests impossibility. Possible selves therefore provide the direction and motivational meaning of goal pursuit, while self-regulatory processes provide the means through which that direction is translated into present action. The practical implication is this: imagining a desirable future is not enough; possible selves become motivationally effective when they are concrete, actionable, and connected to what a person can do now.&lt;div style=&quot;background-color: #fceef3; border: 1px solid #c77b98; border-radius: 10px; padding: 12px 18px; margin: 15px 0;&quot;&gt;

'''Chapter comprehension check'''

&lt;div style=&quot;margin-top: -50px;&quot;&gt;
&lt;quiz display=simple&gt;
{Possible selves are future-oriented representations of who a person might become and can provide motivational direction to present behaviour.
|type=&quot;()&quot;}
+ True
- False

{Possible selves directly produce goal-directed behaviour without relying on broader self-regulatory processes.
|type=&quot;()&quot;}
- True
+ False

{A possible self is more likely to facilitate goal pursuit when it is connected to plausible strategies, relevant to the current context, and compatible with salient identities.
|type=&quot;()&quot;}
+ True
- False

{Interventions strengthen goal pursuit simply by encouraging people to imagine a positive future self.
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;
&lt;/div&gt;
&lt;/div&gt;

==See also==
* [[w:Future self|Future self]] (Wikipedia)
* [[Motivation and emotion/Book/2019/Regulatory focus theory and goal pursuit|Regulatory focus theory and goal pursuits]] (Book chapter, 2019)
* [[w:Goal pursuit|Goal Pursuit]] (Wikipedia)

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{{Hanging indent|1=

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==External links==
* [https://www.hiddenbrain.org/podcast/you-2-0-your-future-is-now/ You 2.0: your future is now] (Hidden Brain)
* [https://www.youtube.com/watch?v=XNbaR54Gpj4&amp;t=177s The psychology of you future self | Dan Gilbert] (Youtube)
* [https://www.psychologytoday.com/au/blog/philosophy-and-therapy/202401/the-philosophy-of-possible-selves Why to start considering your possible selves] (Psychology Today)</text>
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      <text bytes="2010" sha1="853dslums1dkyiqjf6aiv9dyrsxk15x" xml:space="preserve">== About me ==

My name is Jack Eager, I am a third year student at the [https://www.canberra.edu.au/?utm_source=google&amp;utm_medium=search&amp;utm_campaign=Always+On+Domestic+Search+2026&amp;utm_term=exact+match&amp;utm_content=study+at+uc&amp;ef_id=CjwKCAjwqJXUBhBNEiwA8BgG7gVrDcfqsFkI_krMN939VcOSlFRigCDj6-XAx5pB-s2FxjkFsBm65BoC0iQQAvD_BwE:G:s&amp;s_kwcid=AL!10441!3!793469273490!e!!g!!university%20of%20canberra!20950742786!163508319248&amp;gad_source=1&amp;gad_campaignid=20950742786&amp;gbraid=0AAAAADQmSqsV8IGOJfVzdTEgkOgcwiLLA&amp;gclid=CjwKCAjwqJXUBhBNEiwA8BgG7gVrDcfqsFkI_krMN939VcOSlFRigCDj6-XAx5pB-s2FxjkFsBm65BoC0iQQAvD_BwE University of Canberra] studying a Bachelor of Science in Psychology / Bachelor of Arts (specialising in Global Studies).

I am contributing to Wikiversity as part of the [[Motivation and emotion]] course. My book chapter will explore the relationship between possible selves and goal pursuit, with the aim of answering the question: how do possible selves influence motivation and goal directed behaviour?

== Book chapter ==

[[Motivation and emotion/Book/2026/Possible selves and goal pursuit]]

[https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Possible_selves_and_goal_pursuit&amp;oldid=2841145 Generative AI statement]

== Social contributions ==

# [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FRomantic_jealousy&amp;diff=2823578&amp;oldid=2823239 Fixed a title]
#[[Talk:Motivation and emotion/Book/2026/Exercise gamification motivation|Made a suggestion about literature in overview]]
#[https://uclearn.canberra.edu.au/courses/20143/discussion_topics/456345 Shared about how I motivate myself]
# [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Youth_environmental_activism_motivation&amp;oldid=2841167| Recommendation/comment and further research suggestion]
#[https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Apocalyptic_fear&amp;oldid=2841258| Referencing adjustment suggestion]</text>
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      <text bytes="2130" sha1="2ckw4q6gvkc1t70tsh6zpzsjlacqnyn" xml:space="preserve">== About me ==

My name is Jack Eager, I am a third year student at the [https://www.canberra.edu.au/?utm_source=google&amp;utm_medium=search&amp;utm_campaign=Always+On+Domestic+Search+2026&amp;utm_term=exact+match&amp;utm_content=study+at+uc&amp;ef_id=CjwKCAjwqJXUBhBNEiwA8BgG7gVrDcfqsFkI_krMN939VcOSlFRigCDj6-XAx5pB-s2FxjkFsBm65BoC0iQQAvD_BwE:G:s&amp;s_kwcid=AL!10441!3!793469273490!e!!g!!university%20of%20canberra!20950742786!163508319248&amp;gad_source=1&amp;gad_campaignid=20950742786&amp;gbraid=0AAAAADQmSqsV8IGOJfVzdTEgkOgcwiLLA&amp;gclid=CjwKCAjwqJXUBhBNEiwA8BgG7gVrDcfqsFkI_krMN939VcOSlFRigCDj6-XAx5pB-s2FxjkFsBm65BoC0iQQAvD_BwE University of Canberra] studying a Bachelor of Science in Psychology / Bachelor of Arts (specialising in Global Studies).

I am contributing to Wikiversity as part of the [[Motivation and emotion]] course. My book chapter will explore the relationship between possible selves and goal pursuit, with the aim of answering the question: how do possible selves influence motivation and goal directed behaviour?

== Book chapter ==

[[Motivation and emotion/Book/2026/Possible selves and goal pursuit]]

[https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Possible_selves_and_goal_pursuit&amp;oldid=2841145 Generative AI statement]

== Social contributions ==

# [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FRomantic_jealousy&amp;diff=2823578&amp;oldid=2823239 Fixed a title]
#[[Talk:Motivation and emotion/Book/2026/Exercise gamification motivation|Made a suggestion about literature in overview]]
#[https://uclearn.canberra.edu.au/courses/20143/discussion_topics/456345 Shared about how I motivate myself]
# [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Youth_environmental_activism_motivation&amp;oldid=2841167| Recommendation/comment and further research suggestion]
#[https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Apocalyptic_fear&amp;oldid=2841258| Referencing adjustment suggestion]
#[https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Jack4234&amp;ilshowall=1| Added to wikimedia commons]
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      <text bytes="2755" sha1="h9uqhl54qfx1i8ba7o1g9q3mp45c26n" xml:space="preserve">== About me ==

My name is Jack Eager, I am a third year student at the [https://www.canberra.edu.au/?utm_source=google&amp;utm_medium=search&amp;utm_campaign=Always+On+Domestic+Search+2026&amp;utm_term=exact+match&amp;utm_content=study+at+uc&amp;ef_id=CjwKCAjwqJXUBhBNEiwA8BgG7gVrDcfqsFkI_krMN939VcOSlFRigCDj6-XAx5pB-s2FxjkFsBm65BoC0iQQAvD_BwE:G:s&amp;s_kwcid=AL!10441!3!793469273490!e!!g!!university%20of%20canberra!20950742786!163508319248&amp;gad_source=1&amp;gad_campaignid=20950742786&amp;gbraid=0AAAAADQmSqsV8IGOJfVzdTEgkOgcwiLLA&amp;gclid=CjwKCAjwqJXUBhBNEiwA8BgG7gVrDcfqsFkI_krMN939VcOSlFRigCDj6-XAx5pB-s2FxjkFsBm65BoC0iQQAvD_BwE University of Canberra] studying a Bachelor of Science in Psychology / Bachelor of Arts (specialising in Global Studies).

I am contributing to Wikiversity as part of the [[Motivation and emotion]] course. My book chapter will explore the relationship between possible selves and goal pursuit, with the aim of answering the question: how do possible selves influence motivation and goal directed behaviour?

== Book chapter ==

[[Motivation and emotion/Book/2026/Possible selves and goal pursuit]]

[https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Possible_selves_and_goal_pursuit&amp;oldid=2841145 Generative AI statement]

== Social contributions ==

# [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FRomantic_jealousy&amp;diff=2823578&amp;oldid=2823239 Fixed a title]
#[[Talk:Motivation and emotion/Book/2026/Exercise gamification motivation|Made a suggestion about literature in overview]]
#[https://uclearn.canberra.edu.au/courses/20143/discussion_topics/456345 Shared about how I motivate myself]
# [https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Youth_environmental_activism_motivation&amp;oldid=2841167| Recommendation/comment and further research suggestion]
#[https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Apocalyptic_fear&amp;oldid=2841258| Referencing adjustment suggestion]
#[https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Jack4234&amp;ilshowall=1| Added to wikimedia commons]
#[https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2026/Creative_inspiration_and_effort&amp;oldid=2841372| Topic development feedback and article suggestions]
#[https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Types_of_impulsivity&amp;oldid=2841374| Internal link embedded]
#[https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Trust_rebuilding_after_trauma&amp;oldid=2841376| Internal link embedded]
#[https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Breathing_exercises_and_relaxation&amp;oldid=2841377| Internal link embedded]</text>
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      <text bytes="27612" sha1="dhc7puh7o9tr78zez7dfddsjn9czq59" xml:space="preserve">{{title|Attachment styles and relatedness motivation:&lt;br&gt;How do attachment styles shape the need for relatedness?}}
__TOC__
==Overview==
{{RoundBoxTop|theme=3}}

[[File:People and stands at the Museum Reserve, Orientation Week MS-5342 012 002.jpg|thumb|'''Figure 1'''. People and stands at the Museum Reserve, Orientation Week]]


Harry and Caitlin have both recently moved to a new neighbourhood and are adjusting to their new community. 

Harry makes an effort to meet people by attending local social events. He enjoys feeling included, but when plans are made without him or a message goes unanswered, he wonders whether people actually like him. After spending time with his new neighbours, he replays conversations and worries about whether he said or did something wrong.

Caitlin also enjoys meeting her neighbours and likes being included in group activities. She chats easily with people at events but often turns down invitations to spend more time together. When conversations turn more personal or neighbours begin trying to get to know her better, she changes the subject, leaves early, and may decide to avoid the next event. Although she enjoys being part of the neighbourhood, she finds keeping some distance more comfortable. 

Harry and Caitlin both appear to value connection and belonging, yet their need for relatedness seems to be experienced and expressed in very different ways
{{RoundBoxBottom}}
Relatedness, the need to feel connected, cared for, and significant to others (Van den Broeck et al., 2016), is considered a basic psychological need within [[wikipedia:Self-determination_theory|self-determination theory]]. Satisfaction of relatedness is associated with positive psychological functioning, whereas frustration of relatedness is associated poorer psychological functioning (Chen et al., 2015) '''(more detail?)''', highlighting the importance of understanding the factors that support or interfere with relatedness satisfaction.  However, despite relatedness being proposed as a universal psychological need, individuals differ in how they seek connection and experience relatedness satisfaction. 

One factor that may explain these differences is attachment style. Attachment theory proposes that experiences with attachment figures during infancy contribute to expectations about the availability and responsiveness of others, which influences how attachment-related needs are regulated and expressed. In adulthood, secure, anxious-preoccupied, dismissive-avoidant, and fearful-avoidant attachment styles are associated with different patterns of seeking and responding to connection and support. 

'''(link to chapter aims)'''

This chapter investigates whether adult attachment styles shape how relatedness is experienced, expressed, pursued, and satisfied or influence the need for relatedness itself. Additionally, it considers whether experiences of relatedness satisfaction or frustration may contribute to changes in attachment style over time.
{{RoundBoxTop|theme=1}}
;Focus questions [[File:Crystal Clear app ktip.svg|left|20px|]]
* How do different attachment styles influence the way the need for relatedness is experienced and expressed?
* How might experiences of relatedness satisfaction or frustration shape attachment over time?

{{RoundBoxBottom}}

==Self-determination theory and relatedness==
[[wikipedia:Self-determination_theory|Self-determination theory]] (SDT) is an approach to human motivation that seeks to explain the conditions that support or undermine motivation and psychological wellbeing.

A central proposition of SDT is the that individuals have inherent tendencies towards psychological growth, mastery, and connection with others (Ryan &amp; Deci, 2002). 

Within SDT [[wikipedia:Self-determination_theory#:~:text=Summary%20of%20the%20SDT%20mini%2Dtheories|six mini-theories]] address different aspects of motivation and psychological functioning. Of particular relevance to this chapter is the Basic Psychological Needs Theory (BPNT), which proposes that individuals must satisfy three [[wikipedia:Self-determination_theory#:~:text=%5B18%5D-,Basic%20psychological%20needs,-edit|basic psychological needs]], autonomy, competence, and relatedness, for healthy psychological growth and wellbeing ('''Source'''). Satisfaction of these needs is not only important for, psychological growth, effective functioning, and wellbeing, but has been linked to more intrinsic forms of motivation (Deci &amp; Ryan, 2000; Ryan &amp; Deci, 2020) ('''additional source for need satisfaction + intrinsic motivation?''')

=== Need satisfaction and frustration ===
Within BPNT, psychological needs can either be satisfied or frustrated depending on the extent to which a person's environment supports or obstructs those needs. 

Need satisfaction occurs when our environments allow for experiences where the psychological need can be fulfilled. It is considered psychologically nourishing and supports motivation, psychological growth, effective functioning, and wellbeing (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013) ('''studies for this, i.e. impacts of need satisfaction''')

In contrast, need frustration occurs when a psychological need is actively obstructed or undermined (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013). ('''more empirical evidence, impacts of need frustration''')

Importantly, need frustration is not simply the absence of need satisfaction. A person may experience low need satisfaction because they have fewer opportunities to fulfill a need, whereas need frustration involves an environment that actively thwarts or undermines a need. 

===Relatedness===
Relatedness refers to the need to feel connected to others, including both the need to care for others and to feel cared for, valued, and significant to others (Van den Broeck et al., 2016). 

('''More info?''')

==== Relatedness satisfaction and frustration ====
Relatedness satisfaction involves experiencing genuine connection and closeness to others, and a sense of belonging, whereas relatedness frustration involves experiences of rejection, exclusion, disconnection, or loneliness (Chen et al., 2015). 

('''More info/end of section?''')

{{RoundBoxTop|theme=3}}A few weeks later, Harry and Caitlin are invited to a neighbourhood barbecue. 

Harry spends the afternoon talking with several neighbours and is included in plans for another get-together the following weekend. He leaves feeling welcomed and like he is beginning to belong in the community. However, later that week he notices that several neighbours have organised another gathering without inviting him. 

During the barbecue, Caitlin enjoys chatting with people. When one neighbour later invites her over for coffee, she politely declines and does not suggest another time. Although no one has rejected or excluded her. 

Harry’s experience at the barbecue illustrates relatedness satisfaction because he feels welcomed, included, and valued by others, giving him a sense of connection and belonging. When he is later deliberately left out of plans, this may represent relatedness frustration, because the opportunity for connection is undermined through exclusion.

Caitlin’s experience is different. By repeatedly declining invitations and keeping some distance, she may have fewer opportunities to experience meaningful connection, resulting in relatively low relatedness satisfaction. However, because others are still inviting and including her, her need for relatedness is not necessarily being actively thwarted.{{RoundBoxBottom}}

==Attachment theory and styles==
* [[wikipedia:Attachment_theory|Attachment theory]] ''(Issues with wikipage, still include?)'' was first developed by British psychoanalyst John Bowlby, who sought to understand the anxiety and distress infants experience when separated from their primary caregivers
* Bowlby observed that infants use attachment behaviours (e.g. crying, clinging, following) to prevent separation from, or re-establish proximity to, their caregivers (Bowlby, 1958). He proposed that these behaviours form part of an attachment behavioural system, an innate psychobiological mechanism that motivates individuals to seek and maintain closeness to a primary caregiver or attachment figure for safety and protection as infants who were able to maintain proximity to an attachment figure (someone who provides support, protection, and care) would be more likely to survive to reproductive age (Bowlby, 1982)
* Although Bowlby considered the attachment system to be universal, he recognised that infants could differ in how attachment was experienced and expressed. He theorised that early attachment experiences with caregivers contribute to internal working models (mental representations of expectations of whether attachment figures are available and responsive, and whether the self is worthy of care and support). These models are thought to guide how infants respond to situations that activate their attachment system (i.e. distress, separation) (Bretherton &amp; Munholland, 2008; Collins &amp; Allard, 2004; Sherman et al., 2015)
* Mary Ainsworth extended Bowlby's work by examining how individual differences in attachment were expressed in infant's behaviour. She developed the [[wikipedia:Strange_situation|Strange Situation procedure]], which involved observing infants during brief separations from and reunions with their caregivers, focusing primarily on exploration, separation and reunion responses, and reactions to a stranger (Ainsworth et al., 1978). 
* The procedure identified three organised attachment patterns—'''secure, anxious-ambivalent/resistant, and avoidant'''—with '''disorganised-disoriented attachment''' later identified by Main and Solomon (1986) to describe infant behaviours that did not fit comfortably within Ainsworth’s original classifications.

===Secure attachment===
Securely attached infants use their caregiver as a secure base, exploring their environment independently while seeking proximity and comfort from caregiver when needed (Vaughn &amp; Waters, 1990).
* Developmental Factors/Caregiver response (Benoit, 2004)
** associated with caregiving that is usually available and responds appropriately (generally sensitive, responsive, and consistent) when the infant signals distress or a need for support
** Internal Working Model (Sherman et al., 2015)
*** Repeated experiences of having needs responded to positively may lead the infant to expect that the caregiver will be available and responsive when support is required.
*** The infant can therefore express distress and seek proximity without needing to excessively intensify or suppress attachment behaviour.

===Anxious-ambivalent attachment===

* Typical behaviour (Benoit, 2004)
** May remain highly attentive to the caregiver rather than exploring freely.
** Can become easily distressed by separation or uncertainty about the caregiver's availability, seeking frequent proximity, attention, or reassurance.
** Can have difficulty settling even when comfort is offered.
** May appear clingy while also showing frustration, anger, or resistance toward the caregiver.
* Developmental Factors/Caregiver response (Benoit, 2004)
** Associated with caregiving that may be inconsistent or unpredictable.
** The caregiver may sometimes respond to distress but may be unavailable or less responsive at other times.
** Internal working model (Sherman et al., 2015)
*** Availability of caregiver is experienced as uncertain or unpredictable.
*** Expectation that support cannot be consistently available develops, causing infant to become particularly attentive to the caregiver’s availability and intensify attachment signals in an attempt to obtain a response '''(maximising or hyperactivating attachment strategy)''' ''(cant find interwiki source, is external okay?)''

===Anxious-avoidant attachment===

* Typical behaviour (Benoit, 2004)
** May appear unusually independent and spend more time focused on objects, activities, or exploration than on the caregiver
** May show relatively little outward distress when hurt, upset, or separated despite still experiencing physiological or emotional distress
** Is less likely to openly seek comfort or reassurance from the caregiver, may turn away, ignore, or minimise contact even when distressed
** Tends to suppress or minimise visible attachment signals
* Developmental Factors/Caregiver response (Benoit, 2004)
** Associated with caregiving that may be relatively unresponsive, rejecting, or uncomfortable with expressions of distress and bids for comfort.
*** Internal working model (Sherman et al., 2015)
**** infant may have developed an expectation that attempts to obtain comfort or support are unlikely to be met with a responsive reaction.
**** As a result, attachment signals may be minimised or suppressed ('''deactivating or minimising attachment strategy)'''. ''(cant find interwiki source, is external okay?)''

===Disorganised-disoriented attachment===

* Disorganised-disoriented attachment was introduced later by Main and Solomon (1986).
* The classification emerged from observations of infant behaviours that did not fit comfortably within Ainsworth’s original secure, resistant, and avoidant classifications.
* Typical behaviour (Granqvist et al., 2017)
** Behaviour toward the caregiver may be inconsistent or difficult to predict, can show unusual combinations of proximity-seeking and withdrawal.
** May have difficulty developing a consistent strategy for obtaining comfort when distressed.
** Behaviour can become particularly confused or disorganised during situations involving fear, stress, or uncertainty
* Developmental Factors/Caregiver response (Benoit, 2004)
** Has been associated with caregiving that is frightening, frightened, highly disrupted, or unpredictable.
** It is also found at higher rates in some contexts involving significant adversity (Zeanah et al., 1997)
*** Internal working model (Sherman et al., 2015)
**** more difficult to explain through one coherent internal working model because the infant does not appear to have a consistent strategy for obtaining safety.
**** One proposed explanation is that the caregiver may simultaneously represent a potential source of safety and a source of fear or uncertainty, creating conflict between approaching the caregiver for protection and moving away from them.

{{RoundBoxTop|theme=2}}


;Knowledge check [[File:Quiz.png|left|20px|]]
&lt;quiz display=simple&gt;
{Disorganised-disoriented attachment is characterised by a breakdown or lack of a coherent strategy for responding to attachment-related distress.
|type=&quot;()&quot;}
+ TRUE.
|| Yes. Disorganised-disoriented attachment involves a disruption or lack of a consistent organised strategy when the attachment system is activated.
- FALSE.
|| Not quite. Unlike secure, anxious-ambivalent, and avoidant attachment, disorganised-disoriented attachment is characterised by contradictory or disoriented behaviour rather than a consistent organised strategy.

{How do internal working models help explain differences between infant attachment patterns?
|type=&quot;()&quot;}
- They determine how strongly an infant is biologically attached to their caregiver.
|| Internal working models do not determine whether an infant '''has''' an attachment to their caregiver. Instead, they shape expectations about whether caregivers will be available and responsive, which can influence how the infant seeks comfort and responds when the attachment system is activated.
+ They shape expectations about whether caregivers will be available and responsive when support is needed.
|| Yes. Internal working models develop through attachment experiences and shape expectations about whether attachment figures will be available and responsive.
- They determine how much distress every infant experiences during separation.
|| Internal working models can influence how infants respond when distressed, but they do not simply determine how much separation distress an infant experiences.
&lt;/quiz&gt;

{{RoundBoxBottom}}

===Adult attachment theory===
* Attachment theory was later extended beyond infancy to explain how attachment may continue into adulthood

* Hazan and Shaver (1987) were among the first researchers to apply Bowlby and Ainsworth’s attachment framework to adults.
** They proposed that the same attachment behavioural system underlying infant attachment could continue to operate in adulthood, and that internal working models developed through earlier attachment experiences may continue to shape attachment-related expectations and behaviour.
** Their early adult attachment model adapted Ainsworth’s three infant attachment classifications (secure, avoidant, and anxious/ambivalent) for use in adulthood.
** Bartholomew (1990), and Bartholomew and Horowitz (1991) later refined adult attachment by proposing that attachment in adulthood could be understood through two underlying dimensions:
*** Model of self: Reflects a person's sense of self-worth and whether they feel worthy of love and support. (Bartholomew, 1990)
*** Model of others: Reflects whether a person expects others to be available, trustworthy, and supportive (Bartholomew, 1990)

* Combining positive and negative models of the self and others produced four adult attachment styles, Secure, Anxious-preoccupied, Dismissive-avoidant, Fearful-avoidant. '''[https://pmc.ncbi.nlm.nih.gov/articles/PMC8198184/?utm_source=chatgpt.com#B17-ijerph-18-05770:~:text=1.3.2.%20Four%2DFactor%20Model%20of%20Adult%20Attachment%20(Bartholomew%2C%201990) To expand on each one in final book chapter] [https://psychiatryonline.org/doi/10.1176/foc.8.1.foc127?utm_source=chatgpt.com another source]'''

* Although Bartholomew's model describes four attachment styles, contemporary adult attachment research often assess attachment along the continuous dimensions of attachment anxiety and attachment avoidance
** attachment anxiety: the degree to which individuals worry about being underappreciated or abandoned by their romantic partners   (Simpson &amp; Steven Rholes, 2017).
** attachment avoidance: the degree to which individuals are comfortable with closeness and emotional intimacy in relationships (Simpson &amp; Steven Rholes, 2017).
*Brennan et al. (1998) indentified these two dimensions through factor analysis drawn from existing adult attachment measures. A hierarchical cluster analysis also revealed how they corresponded to Bartholomew's four-factor model: 
**Secure: low attachment anxiety and avoidance
**Anxious-preoccupied: high attachment anxiety and low avoidance
**Dismissive-avoidant: low attachment anxiety and high attachment avoidance
**Fearful-avoidant: high attachment anxiety and avoidance
* '''Adult attachment styles are thought to reflect the continuation and development of infant internal working models, although attachment is not considered completely fixed and may change across time and experience (Bartholomew, 1990; Bartholomew &amp; Horowitz, 1991)'''
* '''Adult attachment is therefore generally conceptualised as differences in the way individuals regulate attachment-related needs and respond when the attachment system is activated, rather than as four separate personality types (Bartholomew, 1990; Bartholomew &amp; Horowitz, 1991)'''

==Attachment styles and the need for relatedness==

* Self-determination theory proposes that relatedness is a universal psychological need, suggesting that all individuals have a need to feel connected, valued, and that they belong.
* However, attachment styles may influence how this need is experienced, expressed, pursued, or satisfied.
* An important focus of this section will therefore be whether attachment styles actually influence the strength of the need for relatedness itself, or whether they primarily affect the way individuals respond to and regulate that need.
* The section will also consider whether differences in attachment style are associated with relatedness need satisfaction or frustration, rather than simply differences in how much relatedness people need.
* Finally, the chapter will examine whether the relationship may work in both directions, with repeated experiences of relatedness satisfaction or frustration potentially contributing to changes in attachment over time.

{{RoundBoxTop|theme=4}}
Information to be added for book chapter: Research evidence examining attachment anxiety/avoidance, relatedness motivation, basic psychological need satisfaction/frustration, and possible reciprocal effects between attachment and relatedness.
{{RoundBoxBottom}}

==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
* [[wikipedia:Attachment_in_adults|Attachment in adults]] (Wikipedia)
* [[wikipedia:Self-determination_theory|Self-determination theory]] (Wikipedia)

==References==
{{Hanging indent|1=

Ainsworth, M. D. S., Blehar, M. C., Waters, E., &amp; Wall, S. (1978). ''Patterns of attachment: A psychological study of the strange situation''. Lawrence Erlbaum. 

Bartholomew, K. (1990). Avoidance of Intimacy: An Attachment Perspective. ''Journal of Social and Personal Relationships'', 7(2), 147–178. https://doi.org/10.1177/0265407590072001 

Bartholomew, K., &amp; Horowitz, L. (1991). Attachment Styles Among Young Adults: A Test of a Four-Category Model. ''Journal of Personality and Social Psychology'', 61, 226–244. https://doi.org/10.1037/0022-3514.61.2.226 

Benoit, D. (2004). Infant-parent attachment: Definition, types, antecedents, measurement and outcome. ''Paediatrics &amp; Child Health'', 9(8), 541–545. https://doi.org/10.1093/pch/9.8.541 

Bowlby, J. (1958). The nature of the child's tie to his mother. ''Int J Psychoanal'', 39(5), 350–373. 

Bowlby, J. (1982). Attachment and loss: Retrospect and prospect. American ''Journal of Orthopsychiatry'', 52(4), 664–678. https://doi.org/10.1111/j.1939-0025.1982.tb01456.x 

Bretherton, I., &amp; Munholland, K. A. (2008). Internal working models in attachment relationships: Elaborating a central construct in attachment theory. In ''Handbook of attachment: Theory, research, and clinical applications'', 2nd ed. (pp. 102–127). The Guilford Press. 

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. ''Motivation and Emotion'', 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1 

Collins, N. L., &amp; Allard, L. M. (2003). Cognitive Representations of Attachment: The Content and Function of Working Models. In Garth J. O. Fletcher &amp; M. S. Clark (Eds.), ''Blackwell Handbook of Social Psychology: Interpersonal Processes'' (pp. 60–85). Blackwell Publishing. https://doi.org/https://doi.org/10.1002/9780470998557.ch3 

Deci, E. L., &amp; Ryan, R. M. (2000). The &quot;What&quot; and &quot;Why&quot; of Goal Pursuits: Human Needs and the Self-Determination of Behavior. ''Psychological Inquiry'', 11(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 

Duschinsky, R. (2018). Disorganization, fear and attachment: working towards clarification. ''Infant Ment Health J'', 39(1), 17–29. https://doi.org/10.1002/imhj.21689 

Granqvist, P., Sroufe, L. A., Dozier, M., Hesse, E., Steele, M., van Ijzendoorn, M., Solomon, J., Schuengel, C., Fearon, P., Bakermans-Kranenburg, M., Steele, H., Cassidy, J., Carlson, E., Madigan, S., Jacobvitz, D., Foster, S., Behrens, K., Rifkin-Graboi, A., Gribneau, N.,…Duschinsky, R. (2017). Disorganized attachment in infancy: a review of the phenomenon and its implications for clinicians and policy-makers. ''Attachment &amp; Human Development'', 19(6), 534–558. https://doi.org/10.1080/14616734.2017.1354040 

Hazan, C., &amp; Shaver, P. (1987). Romantic love conceptualized as an attachment process. ''J Pers Soc Psychol'', 52(3), 511–524. https://doi.org/10.1037//0022-351

Main, M., &amp; Solomon, J. (1986). Discovery of An Insecure Disorganized Disoriented Attachment Pattern. In T. B. Brazelton &amp; M. W. Yogman (Eds.), ''Affective development in infancy'' (pp. 95–124). Ablex Publishing. 

Perasso, G. (2023). Strange Situation Procedure (SSP). In T. K. Shackelford (Ed.), ''Encyclopedia of Sexual Psychology and Behavior''. Springer, Cham. https://doi.org/https://doi.org/10.1007/978-3-031-08956-5_128-1 

Ryan, R. M., &amp; Deci, E. L. (2002). Overview of self-determination theory: An organismic-dialectical perspective. In ''Handbook of self-determination research''. (pp. 3–33). University of Rochester Press. 

Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology'', 61, 101860. https://doi.org/https://doi.org/10.1016/j.cedpsych.2020.101860 

Sherman, L. J., Rice, K., &amp; Cassidy, J. (2015). Infant capacities related to building internal working models of attachment figures: A theoretical and empirical review. ''Developmental Review'', 37, 109–141. https://doi.org/https://doi.org/10.1016/j.dr.2015.06.001 

Sroufe, L. A. (1988). The role of infant-caregiver attachment in development. In ''Clinical implications of attachment''. (pp. 18–38). Lawrence Erlbaum Associates, Inc. 

Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A Review of Self-Determination Theory’s Basic Psychological Needs at Work. ''Journal of Management'', 42(5), 1195-1229. https://doi.org/10.1177/0149206316632058 

Vansteenkiste, M., &amp; Ryan, R. (2013). On Psychological Growth and Vulnerability: Basic Psychological Need Satisfaction and Need Frustration as a Unifying Principle. ''Journal of Psychotherapy Integration'', 23, 263–280. https://doi.org/10.1037/a0032359 

Vaughn, B. E., &amp; Waters, E. (1990). Attachment Behavior at Home and in the Laboratory: Q-Sort Observations and Strange Situation Classifications of One-Year-Olds. ''Child Development'', 61(6), 1965–1973. https://doi.org/10.2307/1130850 

Zeanah, C. H., Berlin, L. J., &amp; Boris, N. W. (2011). Practitioner review: clinical applications of attachment theory and research for infants and young children. ''J Child Psychol Psychiatry'', 52(8), 819–833. https://doi.org/10.1111/j.1469-7610.2011.02399.x 

Zeanah, C. H., Boris, N. W., &amp; Larrieu, J. A. (1997). Infant Development and Developmental Risk: A Review of the Past 10 Years. ''Journal of the American Academy of Child &amp; Adolescent Psychiatry'', 36(2), 165–178. https://doi.org/https://doi.org/10.1097/00004583-199702000-00007 

}}

==External links==
* [https://www.attachmentproject.com/attachment-theory/john-bowlby/ Bowlby and attachment theory: insights and legacy] (attachmentproject.com)
* [https://www.simplypsychology.org/self-determination-theory.html Self-determination theory of motivation] (simplypsychology.org)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Relationships/Attachment]]
[[Category:Motivation and emotion/Book/Needs/Psychological/Relatedness]]</text>
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__TOC__
==Overview==
{{RoundBoxTop|theme=3}}

[[File:People and stands at the Museum Reserve, Orientation Week MS-5342 012 002.jpg|thumb|'''Figure 1'''. People and stands at the Museum Reserve, Orientation Week]]


Harry and Caitlin have both recently moved to a new neighbourhood and are adjusting to their new community. 

Harry makes an effort to meet people by attending local social events. He enjoys feeling included, but when plans are made without him or a message goes unanswered, he wonders whether people actually like him. After spending time with his new neighbours, he replays conversations and worries about whether he said or did something wrong.

Caitlin also enjoys meeting her neighbours and likes being included in group activities. She chats easily with people at events but often turns down invitations to spend more time together. When conversations turn more personal or neighbours begin trying to get to know her better, she changes the subject, leaves early, and may decide to avoid the next event. Although she enjoys being part of the neighbourhood, she finds keeping some distance more comfortable. 

Harry and Caitlin both appear to value connection and belonging, yet their need for relatedness seems to be experienced and expressed in very different ways
{{RoundBoxBottom}}
Relatedness, the need to feel connected, cared for, and significant to others (Van den Broeck et al., 2016), is considered a basic psychological need within [[wikipedia:Self-determination_theory|self-determination theory]]. Satisfaction of relatedness is associated with positive psychological functioning, whereas frustration of relatedness is associated poorer psychological functioning (Chen et al., 2015) '''(more detail?)''', highlighting the importance of understanding the factors that support or interfere with relatedness satisfaction.  However, despite relatedness being proposed as a universal psychological need, individuals differ in how they seek connection and experience relatedness satisfaction. 

One factor that may explain these differences is attachment style. Attachment theory proposes that experiences with attachment figures during infancy contribute to expectations about the availability and responsiveness of others, which influences how attachment-related needs are regulated and expressed. In adulthood, secure, anxious-preoccupied, dismissive-avoidant, and fearful-avoidant attachment styles are associated with different patterns of seeking and responding to connection and support. 

'''(link to chapter aims)'''

This chapter investigates whether adult attachment styles shape how relatedness is experienced, expressed, pursued, and satisfied or influence the need for relatedness itself. Additionally, it considers whether experiences of relatedness satisfaction or frustration may contribute to changes in attachment style over time.
{{RoundBoxTop|theme=1}}
;Focus questions [[File:Crystal Clear app ktip.svg|left|20px|]]
* How do different attachment styles influence the way the need for relatedness is experienced and expressed?
* How might experiences of relatedness satisfaction or frustration shape attachment over time?

{{RoundBoxBottom}}

==Self-determination theory and relatedness==
[[wikipedia:Self-determination_theory|Self-determination theory]] (SDT) is an approach to human motivation that seeks to explain the conditions that support or undermine motivation and psychological wellbeing.

A central proposition of SDT is the that individuals have inherent tendencies towards psychological growth, mastery, and connection with others (Ryan &amp; Deci, 2002). 

Within SDT [[wikipedia:Self-determination_theory#:~:text=Summary%20of%20the%20SDT%20mini%2Dtheories|six mini-theories]] address different aspects of motivation and psychological functioning. Of particular relevance to this chapter is the Basic Psychological Needs Theory (BPNT), which proposes that individuals must satisfy three [[wikipedia:Self-determination_theory#:~:text=%5B18%5D-,Basic%20psychological%20needs,-edit|basic psychological needs]], autonomy, competence, and relatedness, for healthy psychological growth and wellbeing ('''Source'''). Satisfaction of these needs is not only important for, psychological growth, effective functioning, and wellbeing, but has been linked to more intrinsic forms of motivation (Deci &amp; Ryan, 2000; Ryan &amp; Deci, 2020) ('''additional source for need satisfaction + intrinsic motivation?''')

=== Need satisfaction and frustration ===
Within BPNT, psychological needs can either be satisfied or frustrated depending on the extent to which a person's environment supports or obstructs those needs. 

Need satisfaction occurs when our environments allow for experiences where the psychological need can be fulfilled. It is considered psychologically nourishing and supports motivation, psychological growth, effective functioning, and wellbeing (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013) ('''studies for this, i.e. impacts of need satisfaction''')

In contrast, need frustration occurs when a psychological need is actively obstructed or undermined (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013). ('''more empirical evidence, impacts of need frustration''')

Importantly, need frustration is not simply the absence of need satisfaction. A person may experience low need satisfaction because they have fewer opportunities to fulfill a need, whereas need frustration involves an environment that actively thwarts or undermines a need. 

===Relatedness===
Relatedness refers to the need to feel connected to others, including both the need to care for others and to feel cared for, valued, and significant to others (Van den Broeck et al., 2016). 

('''More info?''')

==== Relatedness satisfaction and frustration ====
Relatedness satisfaction involves experiencing genuine connection and closeness to others, and a sense of belonging, whereas relatedness frustration involves experiences of rejection, exclusion, disconnection, or loneliness (Chen et al., 2015). 

('''More info/end of section?''')

{{RoundBoxTop|theme=3}}
[[File:Case Icon.png|left|20px|]] A few weeks later, Harry and Caitlin are invited to a neighbourhood barbecue. 

Harry spends the afternoon talking with several neighbours and is included in plans for another get-together the following weekend. He leaves feeling welcomed and like he is beginning to belong in the community. However, later that week he notices that several neighbours have organised another gathering without inviting him. 

During the barbecue, Caitlin enjoys chatting with people. When one neighbour later invites her over for coffee, she politely declines and does not suggest another time. Although no one has rejected or excluded her. 

Harry’s experience at the barbecue illustrates relatedness satisfaction because he feels welcomed, included, and valued by others, giving him a sense of connection and belonging. When he is later deliberately left out of plans, this may represent relatedness frustration, because the opportunity for connection is undermined through exclusion.

Caitlin’s experience is different. By repeatedly declining invitations and keeping some distance, she may have fewer opportunities to experience meaningful connection, resulting in relatively low relatedness satisfaction. However, because others are still inviting and including her, her need for relatedness is not necessarily being actively thwarted.{{RoundBoxBottom}}

==Attachment theory and styles==
* [[wikipedia:Attachment_theory|Attachment theory]] ''(Issues with wikipage, still include?)'' was first developed by British psychoanalyst John Bowlby, who sought to understand the anxiety and distress infants experience when separated from their primary caregivers
* Bowlby observed that infants use attachment behaviours (e.g. crying, clinging, following) to prevent separation from, or re-establish proximity to, their caregivers (Bowlby, 1958). He proposed that these behaviours form part of an attachment behavioural system, an innate psychobiological mechanism that motivates individuals to seek and maintain closeness to a primary caregiver or attachment figure for safety and protection as infants who were able to maintain proximity to an attachment figure (someone who provides support, protection, and care) would be more likely to survive to reproductive age (Bowlby, 1982)
* Although Bowlby considered the attachment system to be universal, he recognised that infants could differ in how attachment was experienced and expressed. He theorised that early attachment experiences with caregivers contribute to internal working models (mental representations of expectations of whether attachment figures are available and responsive, and whether the self is worthy of care and support). These models are thought to guide how infants respond to situations that activate their attachment system (i.e. distress, separation) (Bretherton &amp; Munholland, 2008; Collins &amp; Allard, 2004; Sherman et al., 2015)
* Mary Ainsworth extended Bowlby's work by examining how individual differences in attachment were expressed in infant's behaviour. She developed the [[wikipedia:Strange_situation|Strange Situation procedure]], which involved observing infants during brief separations from and reunions with their caregivers, focusing primarily on exploration, separation and reunion responses, and reactions to a stranger (Ainsworth et al., 1978). 
* The procedure identified three organised attachment patterns—'''secure, anxious-ambivalent/resistant, and avoidant'''—with '''disorganised-disoriented attachment''' later identified by Main and Solomon (1986) to describe infant behaviours that did not fit comfortably within Ainsworth’s original classifications.

===Secure attachment===
Securely attached infants use their caregiver as a secure base, exploring their environment independently while seeking proximity and comfort from caregiver when needed (Vaughn &amp; Waters, 1990).
* Developmental Factors/Caregiver response (Benoit, 2004)
** associated with caregiving that is usually available and responds appropriately (generally sensitive, responsive, and consistent) when the infant signals distress or a need for support
** Internal Working Model (Sherman et al., 2015)
*** Repeated experiences of having needs responded to positively may lead the infant to expect that the caregiver will be available and responsive when support is required.
*** The infant can therefore express distress and seek proximity without needing to excessively intensify or suppress attachment behaviour.

===Anxious-ambivalent attachment===

* Typical behaviour (Benoit, 2004)
** May remain highly attentive to the caregiver rather than exploring freely.
** Can become easily distressed by separation or uncertainty about the caregiver's availability, seeking frequent proximity, attention, or reassurance.
** Can have difficulty settling even when comfort is offered.
** May appear clingy while also showing frustration, anger, or resistance toward the caregiver.
* Developmental Factors/Caregiver response (Benoit, 2004)
** Associated with caregiving that may be inconsistent or unpredictable.
** The caregiver may sometimes respond to distress but may be unavailable or less responsive at other times.
** Internal working model (Sherman et al., 2015)
*** Availability of caregiver is experienced as uncertain or unpredictable.
*** Expectation that support cannot be consistently available develops, causing infant to become particularly attentive to the caregiver’s availability and intensify attachment signals in an attempt to obtain a response '''(maximising or hyperactivating attachment strategy)''' ''(cant find interwiki source, is external okay?)''

===Anxious-avoidant attachment===

* Typical behaviour (Benoit, 2004)
** May appear unusually independent and spend more time focused on objects, activities, or exploration than on the caregiver
** May show relatively little outward distress when hurt, upset, or separated despite still experiencing physiological or emotional distress
** Is less likely to openly seek comfort or reassurance from the caregiver, may turn away, ignore, or minimise contact even when distressed
** Tends to suppress or minimise visible attachment signals
* Developmental Factors/Caregiver response (Benoit, 2004)
** Associated with caregiving that may be relatively unresponsive, rejecting, or uncomfortable with expressions of distress and bids for comfort.
*** Internal working model (Sherman et al., 2015)
**** infant may have developed an expectation that attempts to obtain comfort or support are unlikely to be met with a responsive reaction.
**** As a result, attachment signals may be minimised or suppressed ('''deactivating or minimising attachment strategy)'''. ''(cant find interwiki source, is external okay?)''

===Disorganised-disoriented attachment===

* Disorganised-disoriented attachment was introduced later by Main and Solomon (1986).
* The classification emerged from observations of infant behaviours that did not fit comfortably within Ainsworth’s original secure, resistant, and avoidant classifications.
* Typical behaviour (Granqvist et al., 2017)
** Behaviour toward the caregiver may be inconsistent or difficult to predict, can show unusual combinations of proximity-seeking and withdrawal.
** May have difficulty developing a consistent strategy for obtaining comfort when distressed.
** Behaviour can become particularly confused or disorganised during situations involving fear, stress, or uncertainty
* Developmental Factors/Caregiver response (Benoit, 2004)
** Has been associated with caregiving that is frightening, frightened, highly disrupted, or unpredictable.
** It is also found at higher rates in some contexts involving significant adversity (Zeanah et al., 1997)
*** Internal working model (Sherman et al., 2015)
**** more difficult to explain through one coherent internal working model because the infant does not appear to have a consistent strategy for obtaining safety.
**** One proposed explanation is that the caregiver may simultaneously represent a potential source of safety and a source of fear or uncertainty, creating conflict between approaching the caregiver for protection and moving away from them.

{{RoundBoxTop|theme=2}}


;Knowledge check [[File:Quiz.png|left|20px|]]
&lt;quiz display=simple&gt;
{Disorganised-disoriented attachment is characterised by a breakdown or lack of a coherent strategy for responding to attachment-related distress.
|type=&quot;()&quot;}
+ TRUE.
|| Yes. Disorganised-disoriented attachment involves a disruption or lack of a consistent organised strategy when the attachment system is activated.
- FALSE.
|| Not quite. Unlike secure, anxious-ambivalent, and avoidant attachment, disorganised-disoriented attachment is characterised by contradictory or disoriented behaviour rather than a consistent organised strategy.

{How do internal working models help explain differences between infant attachment patterns?
|type=&quot;()&quot;}
- They determine how strongly an infant is biologically attached to their caregiver.
|| Internal working models do not determine whether an infant '''has''' an attachment to their caregiver. Instead, they shape expectations about whether caregivers will be available and responsive, which can influence how the infant seeks comfort and responds when the attachment system is activated.
+ They shape expectations about whether caregivers will be available and responsive when support is needed.
|| Yes. Internal working models develop through attachment experiences and shape expectations about whether attachment figures will be available and responsive.
- They determine how much distress every infant experiences during separation.
|| Internal working models can influence how infants respond when distressed, but they do not simply determine how much separation distress an infant experiences.
&lt;/quiz&gt;

{{RoundBoxBottom}}

===Adult attachment theory===
* Attachment theory was later extended beyond infancy to explain how attachment may continue into adulthood

* Hazan and Shaver (1987) were among the first researchers to apply Bowlby and Ainsworth’s attachment framework to adults.
** They proposed that the same attachment behavioural system underlying infant attachment could continue to operate in adulthood, and that internal working models developed through earlier attachment experiences may continue to shape attachment-related expectations and behaviour.
** Their early adult attachment model adapted Ainsworth’s three infant attachment classifications (secure, avoidant, and anxious/ambivalent) for use in adulthood.
** Bartholomew (1990), and Bartholomew and Horowitz (1991) later refined adult attachment by proposing that attachment in adulthood could be understood through two underlying dimensions:
*** Model of self: Reflects a person's sense of self-worth and whether they feel worthy of love and support. (Bartholomew, 1990)
*** Model of others: Reflects whether a person expects others to be available, trustworthy, and supportive (Bartholomew, 1990)

* Combining positive and negative models of the self and others produced four adult attachment styles, Secure, Anxious-preoccupied, Dismissive-avoidant, Fearful-avoidant. '''[https://pmc.ncbi.nlm.nih.gov/articles/PMC8198184/?utm_source=chatgpt.com#B17-ijerph-18-05770:~:text=1.3.2.%20Four%2DFactor%20Model%20of%20Adult%20Attachment%20(Bartholomew%2C%201990) To expand on each one in final book chapter] [https://psychiatryonline.org/doi/10.1176/foc.8.1.foc127?utm_source=chatgpt.com another source]'''

* Although Bartholomew's model describes four attachment styles, contemporary adult attachment research often assess attachment along the continuous dimensions of attachment anxiety and attachment avoidance
** attachment anxiety: the degree to which individuals worry about being underappreciated or abandoned by their romantic partners   (Simpson &amp; Steven Rholes, 2017).
** attachment avoidance: the degree to which individuals are comfortable with closeness and emotional intimacy in relationships (Simpson &amp; Steven Rholes, 2017).
*Brennan et al. (1998) indentified these two dimensions through factor analysis drawn from existing adult attachment measures. A hierarchical cluster analysis also revealed how they corresponded to Bartholomew's four-factor model: 
**Secure: low attachment anxiety and avoidance
**Anxious-preoccupied: high attachment anxiety and low avoidance
**Dismissive-avoidant: low attachment anxiety and high attachment avoidance
**Fearful-avoidant: high attachment anxiety and avoidance
* '''Adult attachment styles are thought to reflect the continuation and development of infant internal working models, although attachment is not considered completely fixed and may change across time and experience (Bartholomew, 1990; Bartholomew &amp; Horowitz, 1991)'''
* '''Adult attachment is therefore generally conceptualised as differences in the way individuals regulate attachment-related needs and respond when the attachment system is activated, rather than as four separate personality types (Bartholomew, 1990; Bartholomew &amp; Horowitz, 1991)'''

==Attachment styles and the need for relatedness==

* Self-determination theory proposes that relatedness is a universal psychological need, suggesting that all individuals have a need to feel connected, valued, and that they belong.
* However, attachment styles may influence how this need is experienced, expressed, pursued, or satisfied.
* An important focus of this section will therefore be whether attachment styles actually influence the strength of the need for relatedness itself, or whether they primarily affect the way individuals respond to and regulate that need.
* The section will also consider whether differences in attachment style are associated with relatedness need satisfaction or frustration, rather than simply differences in how much relatedness people need.
* Finally, the chapter will examine whether the relationship may work in both directions, with repeated experiences of relatedness satisfaction or frustration potentially contributing to changes in attachment over time.

{{RoundBoxTop|theme=4}}
Information to be added for book chapter: Research evidence examining attachment anxiety/avoidance, relatedness motivation, basic psychological need satisfaction/frustration, and possible reciprocal effects between attachment and relatedness.
{{RoundBoxBottom}}

==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
* [[wikipedia:Attachment_in_adults|Attachment in adults]] (Wikipedia)
* [[wikipedia:Self-determination_theory|Self-determination theory]] (Wikipedia)

==References==
{{Hanging indent|1=

Ainsworth, M. D. S., Blehar, M. C., Waters, E., &amp; Wall, S. (1978). ''Patterns of attachment: A psychological study of the strange situation''. Lawrence Erlbaum. 

Bartholomew, K. (1990). Avoidance of Intimacy: An Attachment Perspective. ''Journal of Social and Personal Relationships'', 7(2), 147–178. https://doi.org/10.1177/0265407590072001 

Bartholomew, K., &amp; Horowitz, L. (1991). Attachment Styles Among Young Adults: A Test of a Four-Category Model. ''Journal of Personality and Social Psychology'', 61, 226–244. https://doi.org/10.1037/0022-3514.61.2.226 

Benoit, D. (2004). Infant-parent attachment: Definition, types, antecedents, measurement and outcome. ''Paediatrics &amp; Child Health'', 9(8), 541–545. https://doi.org/10.1093/pch/9.8.541 

Bowlby, J. (1958). The nature of the child's tie to his mother. ''Int J Psychoanal'', 39(5), 350–373. 

Bowlby, J. (1982). Attachment and loss: Retrospect and prospect. American ''Journal of Orthopsychiatry'', 52(4), 664–678. https://doi.org/10.1111/j.1939-0025.1982.tb01456.x 

Bretherton, I., &amp; Munholland, K. A. (2008). Internal working models in attachment relationships: Elaborating a central construct in attachment theory. In ''Handbook of attachment: Theory, research, and clinical applications'', 2nd ed. (pp. 102–127). The Guilford Press. 

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. ''Motivation and Emotion'', 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1 

Collins, N. L., &amp; Allard, L. M. (2003). Cognitive Representations of Attachment: The Content and Function of Working Models. In Garth J. O. Fletcher &amp; M. S. Clark (Eds.), ''Blackwell Handbook of Social Psychology: Interpersonal Processes'' (pp. 60–85). Blackwell Publishing. https://doi.org/https://doi.org/10.1002/9780470998557.ch3 

Deci, E. L., &amp; Ryan, R. M. (2000). The &quot;What&quot; and &quot;Why&quot; of Goal Pursuits: Human Needs and the Self-Determination of Behavior. ''Psychological Inquiry'', 11(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 

Duschinsky, R. (2018). Disorganization, fear and attachment: working towards clarification. ''Infant Ment Health J'', 39(1), 17–29. https://doi.org/10.1002/imhj.21689 

Granqvist, P., Sroufe, L. A., Dozier, M., Hesse, E., Steele, M., van Ijzendoorn, M., Solomon, J., Schuengel, C., Fearon, P., Bakermans-Kranenburg, M., Steele, H., Cassidy, J., Carlson, E., Madigan, S., Jacobvitz, D., Foster, S., Behrens, K., Rifkin-Graboi, A., Gribneau, N.,…Duschinsky, R. (2017). Disorganized attachment in infancy: a review of the phenomenon and its implications for clinicians and policy-makers. ''Attachment &amp; Human Development'', 19(6), 534–558. https://doi.org/10.1080/14616734.2017.1354040 

Hazan, C., &amp; Shaver, P. (1987). Romantic love conceptualized as an attachment process. ''J Pers Soc Psychol'', 52(3), 511–524. https://doi.org/10.1037//0022-351

Main, M., &amp; Solomon, J. (1986). Discovery of An Insecure Disorganized Disoriented Attachment Pattern. In T. B. Brazelton &amp; M. W. Yogman (Eds.), ''Affective development in infancy'' (pp. 95–124). Ablex Publishing. 

Perasso, G. (2023). Strange Situation Procedure (SSP). In T. K. Shackelford (Ed.), ''Encyclopedia of Sexual Psychology and Behavior''. Springer, Cham. https://doi.org/https://doi.org/10.1007/978-3-031-08956-5_128-1 

Ryan, R. M., &amp; Deci, E. L. (2002). Overview of self-determination theory: An organismic-dialectical perspective. In ''Handbook of self-determination research''. (pp. 3–33). University of Rochester Press. 

Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology'', 61, 101860. https://doi.org/https://doi.org/10.1016/j.cedpsych.2020.101860 

Sherman, L. J., Rice, K., &amp; Cassidy, J. (2015). Infant capacities related to building internal working models of attachment figures: A theoretical and empirical review. ''Developmental Review'', 37, 109–141. https://doi.org/https://doi.org/10.1016/j.dr.2015.06.001 

Sroufe, L. A. (1988). The role of infant-caregiver attachment in development. In ''Clinical implications of attachment''. (pp. 18–38). Lawrence Erlbaum Associates, Inc. 

Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A Review of Self-Determination Theory’s Basic Psychological Needs at Work. ''Journal of Management'', 42(5), 1195-1229. https://doi.org/10.1177/0149206316632058 

Vansteenkiste, M., &amp; Ryan, R. (2013). On Psychological Growth and Vulnerability: Basic Psychological Need Satisfaction and Need Frustration as a Unifying Principle. ''Journal of Psychotherapy Integration'', 23, 263–280. https://doi.org/10.1037/a0032359 

Vaughn, B. E., &amp; Waters, E. (1990). Attachment Behavior at Home and in the Laboratory: Q-Sort Observations and Strange Situation Classifications of One-Year-Olds. ''Child Development'', 61(6), 1965–1973. https://doi.org/10.2307/1130850 

Zeanah, C. H., Berlin, L. J., &amp; Boris, N. W. (2011). Practitioner review: clinical applications of attachment theory and research for infants and young children. ''J Child Psychol Psychiatry'', 52(8), 819–833. https://doi.org/10.1111/j.1469-7610.2011.02399.x 

Zeanah, C. H., Boris, N. W., &amp; Larrieu, J. A. (1997). Infant Development and Developmental Risk: A Review of the Past 10 Years. ''Journal of the American Academy of Child &amp; Adolescent Psychiatry'', 36(2), 165–178. https://doi.org/https://doi.org/10.1097/00004583-199702000-00007 

}}

==External links==
* [https://www.attachmentproject.com/attachment-theory/john-bowlby/ Bowlby and attachment theory: insights and legacy] (attachmentproject.com)
* [https://www.simplypsychology.org/self-determination-theory.html Self-determination theory of motivation] (simplypsychology.org)

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__TOC__
==Overview==
{{RoundBoxTop|theme=3}}

[[File:People and stands at the Museum Reserve, Orientation Week MS-5342 012 002.jpg|thumb|'''Figure 1'''. People and stands at the Museum Reserve, Orientation Week]]


Harry and Caitlin have both recently moved to a new neighbourhood and are adjusting to their new community. 

Harry makes an effort to meet people by attending local social events. He enjoys feeling included, but when plans are made without him or a message goes unanswered, he wonders whether people actually like him. After spending time with his new neighbours, he replays conversations and worries about whether he said or did something wrong.

Caitlin also enjoys meeting her neighbours and likes being included in group activities. She chats easily with people at events but often turns down invitations to spend more time together. When conversations turn more personal or neighbours begin trying to get to know her better, she changes the subject, leaves early, and may decide to avoid the next event. Although she enjoys being part of the neighbourhood, she finds keeping some distance more comfortable. 

Harry and Caitlin both appear to value connection and belonging, yet their need for relatedness seems to be experienced and expressed in very different ways
{{RoundBoxBottom}}
Relatedness, the need to feel connected, cared for, and significant to others (Van den Broeck et al., 2016), is considered a basic psychological need within [[wikipedia:Self-determination_theory|self-determination theory]]. Satisfaction of relatedness is associated with positive psychological functioning, whereas frustration of relatedness is associated poorer psychological functioning (Chen et al., 2015) '''(more detail?)''', highlighting the importance of understanding the factors that support or interfere with relatedness satisfaction.  However, despite relatedness being proposed as a universal psychological need, individuals differ in how they seek connection and experience relatedness satisfaction. 

One factor that may explain these differences is attachment style. Attachment theory proposes that experiences with attachment figures during infancy contribute to expectations about the availability and responsiveness of others, which influences how attachment-related needs are regulated and expressed. In adulthood, secure, anxious-preoccupied, dismissive-avoidant, and fearful-avoidant attachment styles are associated with different patterns of seeking and responding to connection and support. 

'''(link to chapter aims)'''

This chapter investigates whether adult attachment styles shape how relatedness is experienced, expressed, pursued, and satisfied or influence the need for relatedness itself. Additionally, it considers whether experiences of relatedness satisfaction or frustration may contribute to changes in attachment style over time.
{{RoundBoxTop|theme=1}}
;Focus questions [[File:Crystal Clear app ktip.svg|left|20px|]]
* How do different attachment styles influence the way the need for relatedness is experienced and expressed?
* How might experiences of relatedness satisfaction or frustration shape attachment over time?

{{RoundBoxBottom}}

==Self-determination theory and relatedness==
[[wikipedia:Self-determination_theory|Self-determination theory]] (SDT) is an approach to human motivation that seeks to explain the conditions that support or undermine motivation and psychological wellbeing.

A central proposition of SDT is the that individuals have inherent tendencies towards psychological growth, mastery, and connection with others (Ryan &amp; Deci, 2002). 

Within SDT [[wikipedia:Self-determination_theory#:~:text=Summary%20of%20the%20SDT%20mini%2Dtheories|six mini-theories]] address different aspects of motivation and psychological functioning. Of particular relevance to this chapter is the Basic Psychological Needs Theory (BPNT), which proposes that individuals must satisfy three [[wikipedia:Self-determination_theory#:~:text=%5B18%5D-,Basic%20psychological%20needs,-edit|basic psychological needs]], autonomy, competence, and relatedness, for healthy psychological growth and wellbeing ('''Source'''). Satisfaction of these needs is not only important for, psychological growth, effective functioning, and wellbeing, but has been linked to more intrinsic forms of motivation (Deci &amp; Ryan, 2000; Ryan &amp; Deci, 2020) ('''additional source for need satisfaction + intrinsic motivation?''')

=== Need satisfaction and frustration ===
Within BPNT, psychological needs can either be satisfied or frustrated depending on the extent to which a person's environment supports or obstructs those needs. 

Need satisfaction occurs when our environments allow for experiences where the psychological need can be fulfilled. It is considered psychologically nourishing and supports motivation, psychological growth, effective functioning, and wellbeing (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013) ('''studies for this, i.e. impacts of need satisfaction''')

In contrast, need frustration occurs when a psychological need is actively obstructed or undermined (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013). ('''more empirical evidence, impacts of need frustration''')

Importantly, need frustration is not simply the absence of need satisfaction. A person may experience low need satisfaction because they have fewer opportunities to fulfill a need, whereas need frustration involves an environment that actively thwarts or undermines a need. 

===Relatedness===
Relatedness refers to the need to feel connected to others, including both the need to care for others and to feel cared for, valued, and significant to others (Van den Broeck et al., 2016). 

('''More info?''')

==== Relatedness satisfaction and frustration ====
Relatedness satisfaction involves experiencing genuine connection and closeness to others, and a sense of belonging, whereas relatedness frustration involves experiences of rejection, exclusion, disconnection, or loneliness (Chen et al., 2015). 

('''More info/end of section?''')

{{RoundBoxTop|theme=3}}
[[File:Case Icon.png|left|20px|]] A few weeks later, Harry and Caitlin are invited to a neighbourhood barbecue. 

Harry spends the afternoon talking with several neighbours and is included in plans for another get-together the following weekend. He leaves feeling welcomed and like he is beginning to belong in the community. However, later that week he notices that several neighbours have organised another gathering without inviting him. 

During the barbecue, Caitlin enjoys chatting with people. When one neighbour later invites her over for coffee, she politely declines and does not suggest another time. Although no one has rejected or excluded her. 

Harry’s experience at the barbecue illustrates relatedness satisfaction because he feels welcomed, included, and valued by others, giving him a sense of connection and belonging. When he is later deliberately left out of plans, this may represent relatedness frustration, because the opportunity for connection is undermined through exclusion.

Caitlin’s experience is different. By repeatedly declining invitations and keeping some distance, she may have fewer opportunities to experience meaningful connection, resulting in relatively low relatedness satisfaction. However, because others are still inviting and including her, her need for relatedness is not necessarily being actively thwarted.{{RoundBoxBottom}}

==Attachment theory and styles==
[[wikipedia:Attachment_theory|Attachment theory]] ''('''Issues with wikipage, still include?''')'' was first developed by John Bowlby to explain the anxiety and distress infants experience when separated from their caregivers ('''source'''). Bowlby observed that infants use attachment behaviours, such as crying, clinging, following, to prevent separation or re-establish proximity to their caregivers (Bowlby, 1958). ''He proposed that these behaviours form part of an attachment behavioural system (ABS), an innate psychobiological mechanism that motivates infants to seek and maintain closeness to an attachment figure, reasoning the system is evolutionary based as infants that stayed close to caregivers would be more likely to survive to reproductive age (Bowlby, 1982). '''sentence too long'''''

Although Bowlby considered the ABS to be universal, he recognised that infants could differ in how attachment was experienced and expressed. He theorised that early experiences with caregivers contribute to internal working models, mental representations of expectations of whether attachment figures are available and responsive, and whether the self is worthy of care and support. These expectations are thought to guide an infants response to situations that activate their ABS, including whether the infant seeks support, intensifies attachment behaviours, or minimises them (Bretherton &amp; Munholland, 2008; Collins &amp; Allard, 2004; Sherman et al., 2015). 

[[wikipedia:Mary_Ainsworth|Mary Ainsworth]] extended Bowlby's work by examining how individual differences in attachment were expressed in infant's behaviour through the [[wikipedia:Strange_situation|Strange Situation procedure]]. The procedure involved observing infants during brief separations and reunions with a caregiver, focusing primarily on exploration, separation and reunion responses, and reactions to a stranger (Ainsworth et al., 1978). Through this, Ainsworth identified three infant attachment patterns, Secure, Anxious-ambivalent/, and Anxious-avoidant—with disorganised-disoriented attachment later identified by Main and Solomon (1986) to describe infant behaviours that did not fit comfortably within Ainsworth’s original classifications (See Table 1.)

Table 1.

''Infant Attachment Patterns, Associated Caregiving Experiences, and Attachment Strategies''
{| class=&quot;wikitable&quot;
|+
!Infant attachment style
!Typical attachment response
!Associated caregiving experiences
!Internal working model
|-
|Secure attachment
|Securely attached infants use their caregiver as a secure base, exploring their environment independently while seeking proximity and comfort from caregiver when needed
|associated with caregiving that is usually available and responds appropriately (generally sensitive, responsive, and consistent) when the infant signals distress or a need for support
|Repeated experiences of having needs responded to positively may lead the infant to expect that the caregiver will be available and responsive when support is required.

The infant can therefore express distress and seek proximity without needing to excessively intensify or suppress attachment behaviour.
|-
|Anxious-ambivalent attachment
|
*May remain highly attentive to the caregiver rather than exploring freely.
* Can become easily distressed by separation or uncertainty about the caregiver's availability, seeking frequent proximity, attention, or reassurance.
* Can have difficulty settling even when comfort is offered.
* May appear clingy while also showing frustration, anger, or resistance toward the caregiver.
|
*Associated with caregiving that may be inconsistent or unpredictable.
* The caregiver may sometimes respond to distress but may be unavailable or less responsive at other times.
* Internal working model (Sherman et al., 2015)
|
***Availability of caregiver is experienced as uncertain or unpredictable.
*** Expectation that support cannot be consistently available develops, causing infant to become particularly attentive to the caregiver’s availability and intensify attachment signals in an attempt to obtain a response '''(maximising or hyperactivating attachment strategy)''' ''(cant find interwiki source, is external okay?)''
|-
|Anxious-avoidant attachment
|
*May appear unusually independent and spend more time focused on objects, activities, or exploration than on the caregiver
* May show relatively little outward distress when hurt, upset, or separated despite still experiencing physiological or emotional distress
* Is less likely to openly seek comfort or reassurance from the caregiver, may turn away, ignore, or minimise contact even when distressed
* Tends to suppress or minimise visible attachment signals
|Associated with caregiving that may be relatively unresponsive, rejecting, or uncomfortable with expressions of distress and bids for comfort.
|
****infant may have developed an expectation that attempts to obtain comfort or support are unlikely to be met with a responsive reaction.
**** As a result, attachment signals may be minimised or suppressed ('''deactivating or minimising attachment strategy)'''. ''(cant find interwiki source, is external okay?)''
|-
|Disorganised-disoriented attachment
|
*Behaviour toward the caregiver may be inconsistent or difficult to predict, can show unusual combinations of proximity-seeking and withdrawal.
* May have difficulty developing a consistent strategy for obtaining comfort when distressed.
|
*Has been associated with caregiving that is frightening, frightened, highly disrupted, or unpredictable.
* It is also found at higher rates in some contexts involving significant adversity (Zeanah et al., 1997)
|
*more difficult to explain through one coherent internal working model because the infant does not appear to have a consistent strategy for obtaining safety.
* One proposed explanation is that the caregiver may simultaneously represent a potential source of safety and a source of fear or uncertainty, creating conflict between approaching the caregiver for protection and moving away from them.
|}
''Note''. Caregiving experiences are associated with, rather than solely determining, attachment patterns. Adapted from Benoit (2004), Granqvist et al. (2017), Main and Solomon (1986), Sherman et al. (2015), Vaughn and Waters (1990), and (Zeanah et al. (1997). {{RoundBoxTop|theme=2}}


;Knowledge check [[File:Quiz.png|left|20px|]]
&lt;quiz display=simple&gt;
{Disorganised-disoriented attachment is characterised by a breakdown or lack of a coherent strategy for responding to attachment-related distress.
|type=&quot;()&quot;}
+ TRUE.
|| Yes. Disorganised-disoriented attachment involves a disruption or lack of a consistent organised strategy when the attachment system is activated.
- FALSE.
|| Not quite. Unlike secure, anxious-ambivalent, and avoidant attachment, disorganised-disoriented attachment is characterised by contradictory or disoriented behaviour rather than a consistent organised strategy.

{How do internal working models help explain differences between infant attachment patterns?
|type=&quot;()&quot;}
- They determine how strongly an infant is biologically attached to their caregiver.
|| Internal working models do not determine whether an infant '''has''' an attachment to their caregiver. Instead, they shape expectations about whether caregivers will be available and responsive, which can influence how the infant seeks comfort and responds when the attachment system is activated.
+ They shape expectations about whether caregivers will be available and responsive when support is needed.
|| Yes. Internal working models develop through attachment experiences and shape expectations about whether attachment figures will be available and responsive.
- They determine how much distress every infant experiences during separation.
|| Internal working models can influence how infants respond when distressed, but they do not simply determine how much separation distress an infant experiences.
&lt;/quiz&gt;

{{RoundBoxBottom}}

===Adult attachment theory===
Attachment theory was later extended beyond infancy to explain how attachment may continue into adulthood. Hazan and Shaver (1987) were among the first to construct a self-report measure of adult attachment patterns, though this was in the context of romantic relationships. Their measure was based on the idea that individual differences in the ways adults engage in romantic relationships echo Ainsworth's classifications.

Bartholomew (1990), and Bartholomew and Horowitz (1991) later created a four-factor moled of adult attachment, proposing that attachment in adulthood could be understood through two underlying dimensions:
* Model of self: Reflects a person's sense of self-worth and whether they feel worthy of love and support. (Bartholomew, 1990)
* Model of others: Reflects whether a person expects others to be available, trustworthy, and supportive (Bartholomew, 1990)
Combining positive and negative models of the self and others produced four adult attachment styles, Secure, Anxious-preoccupied, Dismissive-avoidant, Fearful-avoidant.  '''[https://pmc.ncbi.nlm.nih.gov/articles/PMC8198184/?utm_source=chatgpt.com#B17-ijerph-18-05770:~:text=1.3.2.%20Four%2DFactor%20Model%20of%20Adult%20Attachment%20(Bartholomew%2C%201990) To expand on each one in final book chapter] [https://psychiatryonline.org/doi/10.1176/foc.8.1.foc127?utm_source=chatgpt.com another source]'''

==== Attachment anxiety and avoidance ====
Although Bartholomew's model describes four attachment styles, contemporary adult attachment research often assess attachment along the continuous dimensions of attachment anxiety and attachment avoidance
* attachment anxiety: the degree to which individuals worry about being underappreciated or abandoned by their romantic partners   (Simpson &amp; Steven Rholes, 2017).
* attachment avoidance: the degree to which individuals are comfortable with closeness and emotional intimacy in relationships (Simpson &amp; Steven Rholes, 2017).
Using factor and hierarchical cluster analyses, Brennan et al. (1998) identified attachment anxiety and avoidance as two underlying dimensions of adult attachment and demonstrated that different combination of these dimensions broadly correspond to Bartholomew and Horowitz's four attachment styles (see Figure 2.).
*Secure: low attachment anxiety and avoidance
*Anxious-preoccupied: high attachment anxiety and low avoidance
*Dismissive-avoidant: low attachment anxiety and high attachment avoidance
*Fearful-avoidant: high attachment anxiety and avoidance ('''Could this be a figure or table?''')
[[File:Four Adult Attachment Styles Based on Models of Self and Others and Attachment Anxiety and Avoidance.svg|alt=|thumb|475x475px|'''''Figure 2'''.'' Diagram of Bartholomew’s four adult attachment styles based on models of self and others, and their correspondence with attachment anxiety and attachment avoidance.                                                                                      ''Note''. Adapted from Alareqe et al. (2021)and Morse et al. (2012).]]
Because contemporary research commonly measures attachment along the continuous dimensions of attachment anxiety and avoidance, this chapter draws on evidence from both dimensional and categorical approaches when examining attachment and relatedness. Where studies report findings for attachment anxiety and avoidance, these findings are interpreted in relation to the attachment styles they are most consistent with based on their established dimensional profiles. However, these interpretations should be used cautiously, as dimensional findings do not directly demonstrate effects for categorical attachment styles.

==Attachment styles and the need for relatedness==

* Self-determination theory proposes that relatedness is a universal psychological need, suggesting that all individuals have a need to feel connected, valued, and that they belong.
* However, attachment styles may influence how this need is experienced, expressed, pursued, or satisfied.
* An important focus of this section will therefore be whether attachment styles actually influence the strength of the need for relatedness itself, or whether they primarily affect the way individuals respond to and regulate that need.
* The section will also consider whether differences in attachment style are associated with relatedness need satisfaction or frustration, rather than simply differences in how much relatedness people need.
* Finally, the chapter will examine whether the relationship may work in both directions, with repeated experiences of relatedness satisfaction or frustration potentially contributing to changes in attachment over time.

{{RoundBoxTop|theme=4}}
Information to be added for book chapter: Research evidence examining attachment anxiety/avoidance, relatedness motivation, basic psychological need satisfaction/frustration, and possible reciprocal effects between attachment and relatedness.
{{RoundBoxBottom}}

==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
* [[wikipedia:Attachment_in_adults|Attachment in adults]] (Wikipedia)
* [[wikipedia:Self-determination_theory|Self-determination theory]] (Wikipedia)

==References==
{{Hanging indent|1=

Ainsworth, M. D. S., Blehar, M. C., Waters, E., &amp; Wall, S. (1978). ''Patterns of attachment: A psychological study of the strange situation''. Lawrence Erlbaum. 

Bartholomew, K. (1990). Avoidance of Intimacy: An Attachment Perspective. ''Journal of Social and Personal Relationships'', 7(2), 147–178. https://doi.org/10.1177/0265407590072001 

Bartholomew, K., &amp; Horowitz, L. (1991). Attachment Styles Among Young Adults: A Test of a Four-Category Model. ''Journal of Personality and Social Psychology'', 61, 226–244. https://doi.org/10.1037/0022-3514.61.2.226 

Benoit, D. (2004). Infant-parent attachment: Definition, types, antecedents, measurement and outcome. ''Paediatrics &amp; Child Health'', 9(8), 541–545. https://doi.org/10.1093/pch/9.8.541 

Bowlby, J. (1958). The nature of the child's tie to his mother. ''Int J Psychoanal'', 39(5), 350–373. 

Bowlby, J. (1982). Attachment and loss: Retrospect and prospect. American ''Journal of Orthopsychiatry'', 52(4), 664–678. https://doi.org/10.1111/j.1939-0025.1982.tb01456.x 

Bretherton, I., &amp; Munholland, K. A. (2008). Internal working models in attachment relationships: Elaborating a central construct in attachment theory. In ''Handbook of attachment: Theory, research, and clinical applications'', 2nd ed. (pp. 102–127). The Guilford Press. 

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. ''Motivation and Emotion'', 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1 

Collins, N. L., &amp; Allard, L. M. (2003). Cognitive Representations of Attachment: The Content and Function of Working Models. In Garth J. O. Fletcher &amp; M. S. Clark (Eds.), ''Blackwell Handbook of Social Psychology: Interpersonal Processes'' (pp. 60–85). Blackwell Publishing. https://doi.org/https://doi.org/10.1002/9780470998557.ch3 

Deci, E. L., &amp; Ryan, R. M. (2000). The &quot;What&quot; and &quot;Why&quot; of Goal Pursuits: Human Needs and the Self-Determination of Behavior. ''Psychological Inquiry'', 11(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 

Duschinsky, R. (2018). Disorganization, fear and attachment: working towards clarification. ''Infant Ment Health J'', 39(1), 17–29. https://doi.org/10.1002/imhj.21689 

Granqvist, P., Sroufe, L. A., Dozier, M., Hesse, E., Steele, M., van Ijzendoorn, M., Solomon, J., Schuengel, C., Fearon, P., Bakermans-Kranenburg, M., Steele, H., Cassidy, J., Carlson, E., Madigan, S., Jacobvitz, D., Foster, S., Behrens, K., Rifkin-Graboi, A., Gribneau, N.,…Duschinsky, R. (2017). Disorganized attachment in infancy: a review of the phenomenon and its implications for clinicians and policy-makers. ''Attachment &amp; Human Development'', 19(6), 534–558. https://doi.org/10.1080/14616734.2017.1354040 

Hazan, C., &amp; Shaver, P. (1987). Romantic love conceptualized as an attachment process. ''J Pers Soc Psychol'', 52(3), 511–524. https://doi.org/10.1037//0022-351

Main, M., &amp; Solomon, J. (1986). Discovery of An Insecure Disorganized Disoriented Attachment Pattern. In T. B. Brazelton &amp; M. W. Yogman (Eds.), ''Affective development in infancy'' (pp. 95–124). Ablex Publishing. 

Perasso, G. (2023). Strange Situation Procedure (SSP). In T. K. Shackelford (Ed.), ''Encyclopedia of Sexual Psychology and Behavior''. Springer, Cham. https://doi.org/https://doi.org/10.1007/978-3-031-08956-5_128-1 

Ryan, R. M., &amp; Deci, E. L. (2002). Overview of self-determination theory: An organismic-dialectical perspective. In ''Handbook of self-determination research''. (pp. 3–33). University of Rochester Press. 

Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology'', 61, 101860. https://doi.org/https://doi.org/10.1016/j.cedpsych.2020.101860 

Sherman, L. J., Rice, K., &amp; Cassidy, J. (2015). Infant capacities related to building internal working models of attachment figures: A theoretical and empirical review. ''Developmental Review'', 37, 109–141. https://doi.org/https://doi.org/10.1016/j.dr.2015.06.001 

Sroufe, L. A. (1988). The role of infant-caregiver attachment in development. In ''Clinical implications of attachment''. (pp. 18–38). Lawrence Erlbaum Associates, Inc. 

Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A Review of Self-Determination Theory’s Basic Psychological Needs at Work. ''Journal of Management'', 42(5), 1195-1229. https://doi.org/10.1177/0149206316632058 

Vansteenkiste, M., &amp; Ryan, R. (2013). On Psychological Growth and Vulnerability: Basic Psychological Need Satisfaction and Need Frustration as a Unifying Principle. ''Journal of Psychotherapy Integration'', 23, 263–280. https://doi.org/10.1037/a0032359 

Vaughn, B. E., &amp; Waters, E. (1990). Attachment Behavior at Home and in the Laboratory: Q-Sort Observations and Strange Situation Classifications of One-Year-Olds. ''Child Development'', 61(6), 1965–1973. https://doi.org/10.2307/1130850 

Zeanah, C. H., Berlin, L. J., &amp; Boris, N. W. (2011). Practitioner review: clinical applications of attachment theory and research for infants and young children. ''J Child Psychol Psychiatry'', 52(8), 819–833. https://doi.org/10.1111/j.1469-7610.2011.02399.x 

Zeanah, C. H., Boris, N. W., &amp; Larrieu, J. A. (1997). Infant Development and Developmental Risk: A Review of the Past 10 Years. ''Journal of the American Academy of Child &amp; Adolescent Psychiatry'', 36(2), 165–178. https://doi.org/https://doi.org/10.1097/00004583-199702000-00007 

}}

==External links==
* [https://www.attachmentproject.com/attachment-theory/john-bowlby/ Bowlby and attachment theory: insights and legacy] (attachmentproject.com)
* [https://www.simplypsychology.org/self-determination-theory.html Self-determination theory of motivation] (simplypsychology.org)

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__TOC__
==Overview==
{{RoundBoxTop|theme=3}}

[[File:People and stands at the Museum Reserve, Orientation Week MS-5342 012 002.jpg|thumb|'''Figure 1'''. People and stands at the Museum Reserve, Orientation Week]]


Harry and Caitlin have both recently moved to a new neighbourhood and are adjusting to their new community. 

Harry makes an effort to meet people by attending local social events. He enjoys feeling included, but when plans are made without him or a message goes unanswered, he wonders whether people actually like him. After spending time with his new neighbours, he replays conversations and worries about whether he said or did something wrong.

Caitlin also enjoys meeting her neighbours and likes being included in group activities. She chats easily with people at events but often turns down invitations to spend more time together. When conversations turn more personal or neighbours begin trying to get to know her better, she changes the subject, leaves early, and may decide to avoid the next event. Although she enjoys being part of the neighbourhood, she finds keeping some distance more comfortable. 

Harry and Caitlin both appear to value connection and belonging, yet their need for relatedness seems to be experienced and expressed in very different ways
{{RoundBoxBottom}}
Relatedness, the need to feel connected, cared for, and significant to others (Van den Broeck et al., 2016), is considered a basic psychological need within [[wikipedia:Self-determination_theory|self-determination theory]]. Satisfaction of relatedness is associated with positive psychological functioning, whereas frustration of relatedness is associated poorer psychological functioning (Chen et al., 2015) '''(more detail?)''', highlighting the importance of understanding the factors that support or interfere with relatedness satisfaction.  However, despite relatedness being proposed as a universal psychological need, individuals differ in how they seek connection and experience relatedness satisfaction. 

One factor that may explain these differences is attachment style. Attachment theory proposes that experiences with attachment figures during infancy contribute to expectations about the availability and responsiveness of others, which influences how attachment-related needs are regulated and expressed. In adulthood, secure, anxious-preoccupied, dismissive-avoidant, and fearful-avoidant attachment styles are associated with different patterns of seeking and responding to connection and support. 

'''(link to chapter aims)'''

This chapter investigates whether adult attachment styles shape how relatedness is experienced, expressed, pursued, and satisfied or influence the need for relatedness itself. Additionally, it considers whether experiences of relatedness satisfaction or frustration may contribute to changes in attachment style over time.
{{RoundBoxTop|theme=1}}
;Focus questions [[File:Crystal Clear app ktip.svg|left|20px|]]
* How do different attachment styles influence the way the need for relatedness is experienced and expressed?
* How might experiences of relatedness satisfaction or frustration shape attachment over time?

{{RoundBoxBottom}}

==Self-determination theory and relatedness==
[[wikipedia:Self-determination_theory|Self-determination theory]] (SDT) is an approach to human motivation that seeks to explain the conditions that support or undermine motivation and psychological wellbeing.

A central proposition of SDT is the that individuals have inherent tendencies towards psychological growth, mastery, and connection with others (Ryan &amp; Deci, 2002). 

Within SDT [[wikipedia:Self-determination_theory#:~:text=Summary%20of%20the%20SDT%20mini%2Dtheories|six mini-theories]] address different aspects of motivation and psychological functioning. Of particular relevance to this chapter is the Basic Psychological Needs Theory (BPNT), which proposes that individuals must satisfy three [[wikipedia:Self-determination_theory#:~:text=%5B18%5D-,Basic%20psychological%20needs,-edit|basic psychological needs]], autonomy, competence, and relatedness, for healthy psychological growth and wellbeing ('''Source'''). Satisfaction of these needs is not only important for, psychological growth, effective functioning, and wellbeing, but has been linked to more intrinsic forms of motivation (Deci &amp; Ryan, 2000; Ryan &amp; Deci, 2020) ('''additional source for need satisfaction + intrinsic motivation?''')

=== Need satisfaction and frustration ===
Within BPNT, psychological needs can either be satisfied or frustrated depending on the extent to which a person's environment supports or obstructs those needs. 

Need satisfaction occurs when our environments allow for experiences where the psychological need can be fulfilled. It is considered psychologically nourishing and supports motivation, psychological growth, effective functioning, and wellbeing (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013) ('''studies for this, i.e. impacts of need satisfaction''')

In contrast, need frustration occurs when a psychological need is actively obstructed or undermined (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013). ('''more empirical evidence, impacts of need frustration''')

Importantly, need frustration is not simply the absence of need satisfaction. A person may experience low need satisfaction because they have fewer opportunities to fulfill a need, whereas need frustration involves an environment that actively thwarts or undermines a need. 

===Relatedness===
Relatedness refers to the need to feel connected to others, including both the need to care for others and to feel cared for, valued, and significant to others (Van den Broeck et al., 2016). 

('''More info?''')

==== Relatedness satisfaction and frustration ====
Relatedness satisfaction involves experiencing genuine connection and closeness to others, and a sense of belonging, whereas relatedness frustration involves experiences of rejection, exclusion, disconnection, or loneliness (Chen et al., 2015). 

('''More info/end of section?''')

{{RoundBoxTop|theme=3}}
[[File:Case Icon.png|left|20px|]] A few weeks later, Harry and Caitlin are invited to a neighbourhood barbecue. 

Harry spends the afternoon talking with several neighbours and is included in plans for another get-together the following weekend. He leaves feeling welcomed and like he is beginning to belong in the community. However, later that week he notices that several neighbours have organised another gathering without inviting him. 

During the barbecue, Caitlin enjoys chatting with people. When one neighbour later invites her over for coffee, she politely declines and does not suggest another time. Although no one has rejected or excluded her. 

Harry’s experience at the barbecue illustrates relatedness satisfaction because he feels welcomed, included, and valued by others, giving him a sense of connection and belonging. When he is later deliberately left out of plans, this may represent relatedness frustration, because the opportunity for connection is undermined through exclusion.

Caitlin’s experience is different. By repeatedly declining invitations and keeping some distance, she may have fewer opportunities to experience meaningful connection, resulting in relatively low relatedness satisfaction. However, because others are still inviting and including her, her need for relatedness is not necessarily being actively thwarted.{{RoundBoxBottom}}

==Attachment theory and styles==
[[wikipedia:Attachment_theory|Attachment theory]] ''('''Issues with wikipage, still include?''')'' was first developed by John Bowlby to explain the anxiety and distress infants experience when separated from their caregivers ('''source'''). Bowlby observed that infants use attachment behaviours, such as crying, clinging, following, to prevent separation or re-establish proximity to their caregivers (Bowlby, 1958). ''He proposed that these behaviours form part of an attachment behavioural system (ABS), an innate psychobiological mechanism that motivates infants to seek and maintain closeness to an attachment figure, reasoning the system is evolutionary based as infants that stayed close to caregivers would be more likely to survive to reproductive age (Bowlby, 1982). '''sentence too long'''''

Although Bowlby considered the ABS to be universal, he recognised that infants could differ in how attachment was experienced and expressed. He theorised that early experiences with caregivers contribute to internal working models, mental representations of expectations of whether attachment figures are available and responsive, and whether the self is worthy of care and support. These expectations are thought to guide an infants response to situations that activate their ABS, including whether the infant seeks support, intensifies attachment behaviours, or minimises them (Bretherton &amp; Munholland, 2008; Collins &amp; Allard, 2004; Sherman et al., 2015). 

[[wikipedia:Mary_Ainsworth|Mary Ainsworth]] extended Bowlby's work by examining how individual differences in attachment were expressed in infant's behaviour through the [[wikipedia:Strange_situation|Strange Situation procedure]]. The procedure involved observing infants during brief separations and reunions with a caregiver, focusing primarily on exploration, separation and reunion responses, and reactions to a stranger (Ainsworth et al., 1978). Through this, Ainsworth identified three infant attachment patterns, Secure, Anxious-ambivalent/, and Anxious-avoidant—with disorganised-disoriented attachment later identified by Main and Solomon (1986) to describe infant behaviours that did not fit comfortably within Ainsworth’s original classifications (See Table 1.)

Table 1.

''Infant Attachment Patterns, Associated Caregiving Experiences, and Attachment Strategies''
{| class=&quot;wikitable&quot;
|+
!Infant attachment style
!Typical attachment response
!Associated caregiving experiences
!Internal working model
|-
|Secure attachment
|Securely attached infants use their caregiver as a secure base, exploring their environment independently while seeking proximity and comfort from caregiver when needed
|associated with caregiving that is usually available and responds appropriately (generally sensitive, responsive, and consistent) when the infant signals distress or a need for support
|Repeated experiences of having needs responded to positively may lead the infant to expect that the caregiver will be available and responsive when support is required.

The infant can therefore express distress and seek proximity without needing to excessively intensify or suppress attachment behaviour.
|-
|Anxious-ambivalent attachment
|
*May remain highly attentive to the caregiver rather than exploring freely.
* Can become easily distressed by separation or uncertainty about the caregiver's availability, seeking frequent proximity, attention, or reassurance.
* Can have difficulty settling even when comfort is offered.
* May appear clingy while also showing frustration, anger, or resistance toward the caregiver.
|
*Associated with caregiving that may be inconsistent or unpredictable.
* The caregiver may sometimes respond to distress but may be unavailable or less responsive at other times.
* Internal working model (Sherman et al., 2015)
|
***Availability of caregiver is experienced as uncertain or unpredictable.
*** Expectation that support cannot be consistently available develops, causing infant to become particularly attentive to the caregiver’s availability and intensify attachment signals in an attempt to obtain a response '''(maximising or hyperactivating attachment strategy)''' ''(cant find interwiki source, is external okay?)''
|-
|Anxious-avoidant attachment
|
*May appear unusually independent and spend more time focused on objects, activities, or exploration than on the caregiver
* May show relatively little outward distress when hurt, upset, or separated despite still experiencing physiological or emotional distress
* Is less likely to openly seek comfort or reassurance from the caregiver, may turn away, ignore, or minimise contact even when distressed
* Tends to suppress or minimise visible attachment signals
|Associated with caregiving that may be relatively unresponsive, rejecting, or uncomfortable with expressions of distress and bids for comfort.
|
****infant may have developed an expectation that attempts to obtain comfort or support are unlikely to be met with a responsive reaction.
**** As a result, attachment signals may be minimised or suppressed ('''deactivating or minimising attachment strategy)'''. ''(cant find interwiki source, is external okay?)''
|-
|Disorganised-disoriented attachment
|
*Behaviour toward the caregiver may be inconsistent or difficult to predict, can show unusual combinations of proximity-seeking and withdrawal.
* May have difficulty developing a consistent strategy for obtaining comfort when distressed.
|
*Has been associated with caregiving that is frightening, frightened, highly disrupted, or unpredictable.
* It is also found at higher rates in some contexts involving significant adversity (Zeanah et al., 1997)
|
*more difficult to explain through one coherent internal working model because the infant does not appear to have a consistent strategy for obtaining safety.
* One proposed explanation is that the caregiver may simultaneously represent a potential source of safety and a source of fear or uncertainty, creating conflict between approaching the caregiver for protection and moving away from them.
|}
''Note''. Caregiving experiences are associated with, rather than solely determining, attachment patterns. Adapted from Benoit (2004), Granqvist et al. (2017), Main and Solomon (1986), Sherman et al. (2015), Vaughn and Waters (1990), and (Zeanah et al. (1997). {{RoundBoxTop|theme=2}}


;Knowledge check [[File:Quiz.png|left|20px|]]
&lt;quiz display=simple&gt;
{Disorganised-disoriented attachment is characterised by a breakdown or lack of a coherent strategy for responding to attachment-related distress.
|type=&quot;()&quot;}
+ TRUE.
|| Yes. Disorganised-disoriented attachment involves a disruption or lack of a consistent organised strategy when the attachment system is activated.
- FALSE.
|| Not quite. Unlike secure, anxious-ambivalent, and avoidant attachment, disorganised-disoriented attachment is characterised by contradictory or disoriented behaviour rather than a consistent organised strategy.

{How do internal working models help explain differences between infant attachment patterns?
|type=&quot;()&quot;}
- They determine how strongly an infant is biologically attached to their caregiver.
|| Internal working models do not determine whether an infant '''has''' an attachment to their caregiver. Instead, they shape expectations about whether caregivers will be available and responsive, which can influence how the infant seeks comfort and responds when the attachment system is activated.
+ They shape expectations about whether caregivers will be available and responsive when support is needed.
|| Yes. Internal working models develop through attachment experiences and shape expectations about whether attachment figures will be available and responsive.
- They determine how much distress every infant experiences during separation.
|| Internal working models can influence how infants respond when distressed, but they do not simply determine how much separation distress an infant experiences.
&lt;/quiz&gt;

{{RoundBoxBottom}}

===Adult attachment theory===
Attachment theory was later extended beyond infancy to explain how attachment may continue into adulthood. Hazan and Shaver (1987) were among the first to construct a self-report measure of adult attachment patterns, though this was in the context of romantic relationships. Their measure was based on the idea that individual differences in the ways adults engage in romantic relationships echo Ainsworth's classifications.

Bartholomew (1990), and Bartholomew and Horowitz (1991) later created a four-factor moled of adult attachment, proposing that attachment in adulthood could be understood through two underlying dimensions:
* Model of self: Reflects a person's sense of self-worth and whether they feel worthy of love and support. (Bartholomew, 1990)
* Model of others: Reflects whether a person expects others to be available, trustworthy, and supportive (Bartholomew, 1990)
Combining positive and negative models of the self and others produced four adult attachment styles, Secure, Anxious-preoccupied, Dismissive-avoidant, Fearful-avoidant.  '''[https://pmc.ncbi.nlm.nih.gov/articles/PMC8198184/?utm_source=chatgpt.com#B17-ijerph-18-05770:~:text=1.3.2.%20Four%2DFactor%20Model%20of%20Adult%20Attachment%20(Bartholomew%2C%201990) To expand on each one in final book chapter] [https://psychiatryonline.org/doi/10.1176/foc.8.1.foc127?utm_source=chatgpt.com another source]'''

==== Attachment anxiety and avoidance ====
Although Bartholomew's model describes four attachment styles, contemporary adult attachment research often assess attachment along the continuous dimensions of attachment anxiety and attachment avoidance
* attachment anxiety: the degree to which individuals worry about being underappreciated or abandoned by their romantic partners   (Simpson &amp; Steven Rholes, 2017).
* attachment avoidance: the degree to which individuals are comfortable with closeness and emotional intimacy in relationships (Simpson &amp; Steven Rholes, 2017).[[File:Four Adult Attachment Styles Based on Models of Self and Others and Attachment Anxiety and Avoidance.svg|thumb|465x465px|'''''Figure 2'''.'' Diagram of Bartholomew’s four adult attachment styles based on models of self and others, and their correspondence with attachment anxiety and attachment avoidance.                                                                                      ''Note''. Adapted from Alareqe et al. (2021)and Morse et al. (2012).]]
Using factor and hierarchical cluster analyses, Brennan et al. (1998) identified attachment anxiety and avoidance as two underlying dimensions of adult attachment and demonstrated that different combination of these dimensions broadly correspond to Bartholomew and Horowitz's four attachment styles (see Figure 2.).

Because contemporary research commonly measures attachment along the continuous dimensions of attachment anxiety and avoidance, this chapter draws on evidence from both dimensional and categorical approaches when examining attachment and relatedness. Where studies report findings for attachment anxiety and avoidance, these findings are interpreted in relation to the attachment styles they are most consistent with based on their established dimensional profiles. However, these interpretations should be used cautiously, as dimensional findings do not directly demonstrate effects for categorical attachment styles.

==Attachment styles and the need for relatedness==

* Self-determination theory proposes that relatedness is a universal psychological need, suggesting that all individuals have a need to feel connected, valued, and that they belong.
* However, attachment styles may influence how this need is experienced, expressed, pursued, or satisfied.
* An important focus of this section will therefore be whether attachment styles actually influence the strength of the need for relatedness itself, or whether they primarily affect the way individuals respond to and regulate that need.
* The section will also consider whether differences in attachment style are associated with relatedness need satisfaction or frustration, rather than simply differences in how much relatedness people need.
* Finally, the chapter will examine whether the relationship may work in both directions, with repeated experiences of relatedness satisfaction or frustration potentially contributing to changes in attachment over time.

{{RoundBoxTop|theme=4}}
Information to be added for book chapter: Research evidence examining attachment anxiety/avoidance, relatedness motivation, basic psychological need satisfaction/frustration, and possible reciprocal effects between attachment and relatedness.
{{RoundBoxBottom}}

==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
* [[wikipedia:Attachment_in_adults|Attachment in adults]] (Wikipedia)
* [[wikipedia:Self-determination_theory|Self-determination theory]] (Wikipedia)

==References==
{{Hanging indent|1=

Ainsworth, M. D. S., Blehar, M. C., Waters, E., &amp; Wall, S. (1978). ''Patterns of attachment: A psychological study of the strange situation''. Lawrence Erlbaum. 

Bartholomew, K. (1990). Avoidance of Intimacy: An Attachment Perspective. ''Journal of Social and Personal Relationships'', 7(2), 147–178. https://doi.org/10.1177/0265407590072001 

Bartholomew, K., &amp; Horowitz, L. (1991). Attachment Styles Among Young Adults: A Test of a Four-Category Model. ''Journal of Personality and Social Psychology'', 61, 226–244. https://doi.org/10.1037/0022-3514.61.2.226 

Benoit, D. (2004). Infant-parent attachment: Definition, types, antecedents, measurement and outcome. ''Paediatrics &amp; Child Health'', 9(8), 541–545. https://doi.org/10.1093/pch/9.8.541 

Bowlby, J. (1958). The nature of the child's tie to his mother. ''Int J Psychoanal'', 39(5), 350–373. 

Bowlby, J. (1982). Attachment and loss: Retrospect and prospect. American ''Journal of Orthopsychiatry'', 52(4), 664–678. https://doi.org/10.1111/j.1939-0025.1982.tb01456.x 

Bretherton, I., &amp; Munholland, K. A. (2008). Internal working models in attachment relationships: Elaborating a central construct in attachment theory. In ''Handbook of attachment: Theory, research, and clinical applications'', 2nd ed. (pp. 102–127). The Guilford Press. 

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. ''Motivation and Emotion'', 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1 

Collins, N. L., &amp; Allard, L. M. (2003). Cognitive Representations of Attachment: The Content and Function of Working Models. In Garth J. O. Fletcher &amp; M. S. Clark (Eds.), ''Blackwell Handbook of Social Psychology: Interpersonal Processes'' (pp. 60–85). Blackwell Publishing. https://doi.org/https://doi.org/10.1002/9780470998557.ch3 

Deci, E. L., &amp; Ryan, R. M. (2000). The &quot;What&quot; and &quot;Why&quot; of Goal Pursuits: Human Needs and the Self-Determination of Behavior. ''Psychological Inquiry'', 11(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 

Duschinsky, R. (2018). Disorganization, fear and attachment: working towards clarification. ''Infant Ment Health J'', 39(1), 17–29. https://doi.org/10.1002/imhj.21689 

Granqvist, P., Sroufe, L. A., Dozier, M., Hesse, E., Steele, M., van Ijzendoorn, M., Solomon, J., Schuengel, C., Fearon, P., Bakermans-Kranenburg, M., Steele, H., Cassidy, J., Carlson, E., Madigan, S., Jacobvitz, D., Foster, S., Behrens, K., Rifkin-Graboi, A., Gribneau, N.,…Duschinsky, R. (2017). Disorganized attachment in infancy: a review of the phenomenon and its implications for clinicians and policy-makers. ''Attachment &amp; Human Development'', 19(6), 534–558. https://doi.org/10.1080/14616734.2017.1354040 

Hazan, C., &amp; Shaver, P. (1987). Romantic love conceptualized as an attachment process. ''J Pers Soc Psychol'', 52(3), 511–524. https://doi.org/10.1037//0022-351

Main, M., &amp; Solomon, J. (1986). Discovery of An Insecure Disorganized Disoriented Attachment Pattern. In T. B. Brazelton &amp; M. W. Yogman (Eds.), ''Affective development in infancy'' (pp. 95–124). Ablex Publishing. 

Perasso, G. (2023). Strange Situation Procedure (SSP). In T. K. Shackelford (Ed.), ''Encyclopedia of Sexual Psychology and Behavior''. Springer, Cham. https://doi.org/https://doi.org/10.1007/978-3-031-08956-5_128-1 

Ryan, R. M., &amp; Deci, E. L. (2002). Overview of self-determination theory: An organismic-dialectical perspective. In ''Handbook of self-determination research''. (pp. 3–33). University of Rochester Press. 

Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology'', 61, 101860. https://doi.org/https://doi.org/10.1016/j.cedpsych.2020.101860 

Sherman, L. J., Rice, K., &amp; Cassidy, J. (2015). Infant capacities related to building internal working models of attachment figures: A theoretical and empirical review. ''Developmental Review'', 37, 109–141. https://doi.org/https://doi.org/10.1016/j.dr.2015.06.001 

Sroufe, L. A. (1988). The role of infant-caregiver attachment in development. In ''Clinical implications of attachment''. (pp. 18–38). Lawrence Erlbaum Associates, Inc. 

Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A Review of Self-Determination Theory’s Basic Psychological Needs at Work. ''Journal of Management'', 42(5), 1195-1229. https://doi.org/10.1177/0149206316632058 

Vansteenkiste, M., &amp; Ryan, R. (2013). On Psychological Growth and Vulnerability: Basic Psychological Need Satisfaction and Need Frustration as a Unifying Principle. ''Journal of Psychotherapy Integration'', 23, 263–280. https://doi.org/10.1037/a0032359 

Vaughn, B. E., &amp; Waters, E. (1990). Attachment Behavior at Home and in the Laboratory: Q-Sort Observations and Strange Situation Classifications of One-Year-Olds. ''Child Development'', 61(6), 1965–1973. https://doi.org/10.2307/1130850 

Zeanah, C. H., Berlin, L. J., &amp; Boris, N. W. (2011). Practitioner review: clinical applications of attachment theory and research for infants and young children. ''J Child Psychol Psychiatry'', 52(8), 819–833. https://doi.org/10.1111/j.1469-7610.2011.02399.x 

Zeanah, C. H., Boris, N. W., &amp; Larrieu, J. A. (1997). Infant Development and Developmental Risk: A Review of the Past 10 Years. ''Journal of the American Academy of Child &amp; Adolescent Psychiatry'', 36(2), 165–178. https://doi.org/https://doi.org/10.1097/00004583-199702000-00007 

}}

==External links==
* [https://www.attachmentproject.com/attachment-theory/john-bowlby/ Bowlby and attachment theory: insights and legacy] (attachmentproject.com)
* [https://www.simplypsychology.org/self-determination-theory.html Self-determination theory of motivation] (simplypsychology.org)

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[[Category:Motivation and emotion/Book/Relationships/Attachment]]
[[Category:Motivation and emotion/Book/Needs/Psychological/Relatedness]]</text>
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__TOC__
==Overview==
{{RoundBoxTop|theme=3}}

[[File:People and stands at the Museum Reserve, Orientation Week MS-5342 012 002.jpg|thumb|'''Figure 1'''. People and stands at the Museum Reserve, Orientation Week]]


Harry and Caitlin have both recently moved to a new neighbourhood and are adjusting to their new community. 

Harry makes an effort to meet people by attending local social events. He enjoys feeling included, but when plans are made without him or a message goes unanswered, he wonders whether people actually like him. After spending time with his new neighbours, he replays conversations and worries about whether he said or did something wrong.

Caitlin also enjoys meeting her neighbours and likes being included in group activities. She chats easily with people at events but often turns down invitations to spend more time together. When conversations turn more personal or neighbours begin trying to get to know her better, she changes the subject, leaves early, and may decide to avoid the next event. Although she enjoys being part of the neighbourhood, she finds keeping some distance more comfortable. 

Harry and Caitlin both appear to value connection and belonging, yet their need for relatedness seems to be experienced and expressed in very different ways
{{RoundBoxBottom}}
Relatedness, the need to feel connected, cared for, and significant to others (Van den Broeck et al., 2016), is considered a basic psychological need within [[wikipedia:Self-determination_theory|self-determination theory]]. Satisfaction of relatedness is associated with positive psychological functioning, whereas frustration of relatedness is associated poorer psychological functioning (Chen et al., 2015) '''(more detail?)''', highlighting the importance of understanding the factors that support or interfere with relatedness satisfaction.  However, despite relatedness being proposed as a universal psychological need, individuals differ in how they seek connection and experience relatedness satisfaction. 

One factor that may explain these differences is attachment style. Attachment theory proposes that experiences with attachment figures during infancy contribute to expectations about the availability and responsiveness of others, which influences how attachment-related needs are regulated and expressed. In adulthood, secure, anxious-preoccupied, dismissive-avoidant, and fearful-avoidant attachment styles are associated with different patterns of seeking and responding to connection and support. 

'''(link to chapter aims)'''

This chapter investigates whether adult attachment styles shape how relatedness is experienced, expressed, pursued, and satisfied or influence the need for relatedness itself. Additionally, it considers whether experiences of relatedness satisfaction or frustration may contribute to changes in attachment style over time.
{{RoundBoxTop|theme=1}}
;Focus questions [[File:Crystal Clear app ktip.svg|left|20px|]]
* How do different attachment styles influence the way the need for relatedness is experienced and expressed?
* How might experiences of relatedness satisfaction or frustration shape attachment over time?

{{RoundBoxBottom}}

==Self-determination theory and relatedness==
[[wikipedia:Self-determination_theory|Self-determination theory]] (SDT) is an approach to human motivation that seeks to explain the conditions that support or undermine motivation and psychological wellbeing.

A central proposition of SDT is the that individuals have inherent tendencies towards psychological growth, mastery, and connection with others (Ryan &amp; Deci, 2002). 

Within SDT [[wikipedia:Self-determination_theory#:~:text=Summary%20of%20the%20SDT%20mini%2Dtheories|six mini-theories]] address different aspects of motivation and psychological functioning. Of particular relevance to this chapter is the Basic Psychological Needs Theory (BPNT), which proposes that individuals must satisfy three [[wikipedia:Self-determination_theory#:~:text=%5B18%5D-,Basic%20psychological%20needs,-edit|basic psychological needs]], autonomy, competence, and relatedness, for healthy psychological growth and wellbeing ('''Source'''). Satisfaction of these needs is not only important for, psychological growth, effective functioning, and wellbeing, but has been linked to more intrinsic forms of motivation (Deci &amp; Ryan, 2000; Ryan &amp; Deci, 2020) ('''additional source for need satisfaction + intrinsic motivation?''')

=== Need satisfaction and frustration ===
Within BPNT, psychological needs can either be satisfied or frustrated depending on the extent to which a person's environment supports or obstructs those needs. 

Need satisfaction occurs when our environments allow for experiences where the psychological need can be fulfilled. It is considered psychologically nourishing and supports motivation, psychological growth, effective functioning, and wellbeing (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013) ('''studies for this, i.e. impacts of need satisfaction''')

In contrast, need frustration occurs when a psychological need is actively obstructed or undermined (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013). ('''more empirical evidence, impacts of need frustration''')

Importantly, need frustration is not simply the absence of need satisfaction. A person may experience low need satisfaction because they have fewer opportunities to fulfill a need, whereas need frustration involves an environment that actively thwarts or undermines a need. 

===Relatedness===
Relatedness refers to the need to feel connected to others, including both the need to care for others and to feel cared for, valued, and significant to others (Van den Broeck et al., 2016). 

('''More info?''')

==== Relatedness satisfaction and frustration ====
Relatedness satisfaction involves experiencing genuine connection and closeness to others, and a sense of belonging, whereas relatedness frustration involves experiences of rejection, exclusion, disconnection, or loneliness (Chen et al., 2015). 

('''More info/end of section?''')

{{RoundBoxTop|theme=3}}
[[File:Case Icon.png|left|20px|]] A few weeks later, Harry and Caitlin are invited to a neighbourhood barbecue. 

Harry spends the afternoon talking with several neighbours and is included in plans for another get-together the following weekend. He leaves feeling welcomed and like he is beginning to belong in the community. However, later that week he notices that several neighbours have organised another gathering without inviting him. 

During the barbecue, Caitlin enjoys chatting with people. When one neighbour later invites her over for coffee, she politely declines and does not suggest another time. Although no one has rejected or excluded her. 

Harry’s experience at the barbecue illustrates relatedness satisfaction because he feels welcomed, included, and valued by others, giving him a sense of connection and belonging. When he is later deliberately left out of plans, this may represent relatedness frustration, because the opportunity for connection is undermined through exclusion.

Caitlin’s experience is different. By repeatedly declining invitations and keeping some distance, she may have fewer opportunities to experience meaningful connection, resulting in relatively low relatedness satisfaction. However, because others are still inviting and including her, her need for relatedness is not necessarily being actively thwarted.{{RoundBoxBottom}}

==Attachment theory and styles==
[[wikipedia:Attachment_theory|Attachment theory]] ''('''Issues with wikipage, still include?''')'' was first developed by John Bowlby to explain the anxiety and distress infants experience when separated from their caregivers ('''source'''). Bowlby observed that infants use attachment behaviours, such as crying, clinging, following, to prevent separation or re-establish proximity to their caregivers (Bowlby, 1958). ''He proposed that these behaviours form part of an attachment behavioural system (ABS), an innate psychobiological mechanism that motivates infants to seek and maintain closeness to an attachment figure, reasoning the system is evolutionary based as infants that stayed close to caregivers would be more likely to survive to reproductive age (Bowlby, 1982). '''sentence too long'''''

Although Bowlby considered the ABS to be universal, he recognised that infants could differ in how attachment was experienced and expressed. He theorised that early experiences with caregivers contribute to internal working models, mental representations of expectations of whether attachment figures are available and responsive, and whether the self is worthy of care and support. These expectations are thought to guide an infants response to situations that activate their ABS, including whether the infant seeks support, intensifies attachment behaviours, or minimises them (Bretherton &amp; Munholland, 2008; Collins &amp; Allard, 2004; Sherman et al., 2015). 

[[wikipedia:Mary_Ainsworth|Mary Ainsworth]] extended Bowlby's work by examining how individual differences in attachment were expressed in infant's behaviour through the [[wikipedia:Strange_situation|Strange Situation procedure]]. The procedure involved observing infants during brief separations and reunions with a caregiver, focusing primarily on exploration, separation and reunion responses, and reactions to a stranger (Ainsworth et al., 1978). Through this, Ainsworth identified three infant attachment patterns, Secure, Anxious-ambivalent/, and Anxious-avoidant—with disorganised-disoriented attachment later identified by Main and Solomon (1986) to describe infant behaviours that did not fit comfortably within Ainsworth’s original classifications (See Table 1.)

Table 1.

''Infant Attachment Patterns, Associated Caregiving Experiences, and Attachment Strategies''
{| class=&quot;wikitable&quot;
|+
!Infant attachment style
!Typical attachment response
!Associated caregiving experiences
!Internal working model
|-
|Secure attachment
|Securely attached infants use their caregiver as a secure base, exploring their environment independently while seeking proximity and comfort from caregiver when needed
|associated with caregiving that is usually available and responds appropriately (generally sensitive, responsive, and consistent) when the infant signals distress or a need for support
|Repeated experiences of having needs responded to positively may lead the infant to expect that the caregiver will be available and responsive when support is required.

The infant can therefore express distress and seek proximity without needing to excessively intensify or suppress attachment behaviour.
|-
|Anxious-ambivalent attachment
|
*May remain highly attentive to the caregiver rather than exploring freely.
* Can become easily distressed by separation or uncertainty about the caregiver's availability, seeking frequent proximity, attention, or reassurance.
* Can have difficulty settling even when comfort is offered.
* May appear clingy while also showing frustration, anger, or resistance toward the caregiver.
|
*Associated with caregiving that may be inconsistent or unpredictable.
* The caregiver may sometimes respond to distress but may be unavailable or less responsive at other times.
* Internal working model (Sherman et al., 2015)
|
***Availability of caregiver is experienced as uncertain or unpredictable.
*** Expectation that support cannot be consistently available develops, causing infant to become particularly attentive to the caregiver’s availability and intensify attachment signals in an attempt to obtain a response '''(maximising or hyperactivating attachment strategy)''' ''(cant find interwiki source, is external okay?)''
|-
|Anxious-avoidant attachment
|
*May appear unusually independent and spend more time focused on objects, activities, or exploration than on the caregiver
* May show relatively little outward distress when hurt, upset, or separated despite still experiencing physiological or emotional distress
* Is less likely to openly seek comfort or reassurance from the caregiver, may turn away, ignore, or minimise contact even when distressed
* Tends to suppress or minimise visible attachment signals
|Associated with caregiving that may be relatively unresponsive, rejecting, or uncomfortable with expressions of distress and bids for comfort.
|
****infant may have developed an expectation that attempts to obtain comfort or support are unlikely to be met with a responsive reaction.
**** As a result, attachment signals may be minimised or suppressed ('''deactivating or minimising attachment strategy)'''. ''(cant find interwiki source, is external okay?)''
|-
|Disorganised-disoriented attachment
|
*Behaviour toward the caregiver may be inconsistent or difficult to predict, can show unusual combinations of proximity-seeking and withdrawal.
* May have difficulty developing a consistent strategy for obtaining comfort when distressed.
|
*Has been associated with caregiving that is frightening, frightened, highly disrupted, or unpredictable.
* It is also found at higher rates in some contexts involving significant adversity (Zeanah et al., 1997)
|
*more difficult to explain through one coherent internal working model because the infant does not appear to have a consistent strategy for obtaining safety.
* One proposed explanation is that the caregiver may simultaneously represent a potential source of safety and a source of fear or uncertainty, creating conflict between approaching the caregiver for protection and moving away from them.
|}
{{RoundBoxTop|theme=2}}
;Knowledge check [[File:Quiz.png|left|20px|]]
&lt;quiz display=simple&gt;
{How do internal working models help explain differences between infant attachment patterns?
|type=&quot;()&quot;}
- They determine how strongly an infant is biologically attached to their caregiver.
|| Internal working models do not determine whether an infant '''has''' an attachment to their caregiver. Instead, they shape expectations about whether caregivers will be available and responsive, which can influence how the infant seeks comfort and responds when the attachment system is activated.
+ They shape expectations about whether caregivers will be available and responsive when support is needed.
|| Yes. Internal working models develop through attachment experiences and shape expectations about whether attachment figures will be available and responsive.
- They determine how much distress every infant experiences during separation.
|| Internal working models can influence how infants respond when distressed, but they do not simply determine how much separation distress an infant experiences.
&lt;/quiz&gt;

{{RoundBoxBottom}}

===Adult attachment theory===
Attachment theory was later extended beyond infancy to explain how attachment may continue into adulthood. Hazan and Shaver (1987) were among the first to construct a self-report measure of adult attachment patterns, though this was in the context of romantic relationships. Their measure was based on the idea that individual differences in the ways adults engage in romantic relationships echo Ainsworth's classifications.

Bartholomew (1990), and Bartholomew and Horowitz (1991) later created a four-factor moled of adult attachment, proposing that attachment in adulthood could be understood through two underlying dimensions:
* Model of self: Reflects a person's sense of self-worth and whether they feel worthy of love and support. (Bartholomew, 1990)
* Model of others: Reflects whether a person expects others to be available, trustworthy, and supportive (Bartholomew, 1990)
Combining positive and negative models of the self and others produced four adult attachment styles, Secure, Anxious-preoccupied, Dismissive-avoidant, Fearful-avoidant.  '''[https://pmc.ncbi.nlm.nih.gov/articles/PMC8198184/?utm_source=chatgpt.com#B17-ijerph-18-05770:~:text=1.3.2.%20Four%2DFactor%20Model%20of%20Adult%20Attachment%20(Bartholomew%2C%201990) To expand on each one in final book chapter] [https://psychiatryonline.org/doi/10.1176/foc.8.1.foc127?utm_source=chatgpt.com another source]'''

==== Attachment anxiety and avoidance ====
Although Bartholomew's model describes four attachment styles, contemporary adult attachment research often assess attachment along the continuous dimensions of attachment anxiety and attachment avoidance
* Attachment anxiety: the degree to which individuals worry about being underappreciated or abandoned by their romantic partners   (Simpson &amp; Steven Rholes, 2017).
* Attachment avoidance: the degree to which individuals are comfortable with closeness and emotional intimacy in relationships (Simpson &amp; Steven Rholes, 2017).[[File:Four Adult Attachment Styles Based on Models of Self and Others and Attachment Anxiety and Avoidance.svg|thumb|465x465px|'''''Figure 2'''.'' Diagram of Bartholomew’s four adult attachment styles based on models of self and others, and their correspondence with attachment anxiety and attachment avoidance.                                                                                      ''Note''. Adapted from Alareqe et al. (2021), Bartholomew (1990), Bartholomew and Horowitz (1991), and Morse et al. (2012).]]
Using factor and hierarchical cluster analyses, Brennan et al. (1998) identified attachment anxiety and avoidance as two underlying dimensions of adult attachment and demonstrated that different combination of these dimensions broadly correspond to Bartholomew and Horowitz's four attachment styles (see Figure 2.).

Because contemporary research commonly measures attachment along the continuous dimensions of attachment anxiety and avoidance, this chapter draws on evidence from both dimensional and categorical approaches when examining attachment and relatedness. Where studies report findings for attachment anxiety and avoidance, these findings are interpreted in relation to the attachment styles they are most consistent with based on their established dimensional profiles. However, these interpretations should be used cautiously, as dimensional findings do not directly demonstrate effects for categorical attachment styles.

{{RoundBoxTop|theme=2}}
;Knowledge check [[File:Quiz.png|left|20px|]]
&lt;quiz display=simple&gt;
{Adult attachment is completely determined by experiences in infancy.
|type=&quot;()&quot;}
+ TRUE.
|| Not quite. Early attachment experiences may contribute to the development of internal working models, but attachment is not considered permanently fixed and may change across later experiences and relationships.
- FALSE.
|| Correct. Early attachment experiences may influence internal working models and later attachment patterns, but adult attachment is not completely determined by infancy and may change across time and experience.
&lt;/quiz&gt;

{{RoundBoxBottom}}

==Attachment styles and the need for relatedness==

* Self-determination theory proposes that relatedness is a universal psychological need, suggesting that all individuals have a need to feel connected, valued, and that they belong.
* However, attachment styles may influence how this need is experienced, expressed, pursued, or satisfied.
* An important focus of this section will therefore be whether attachment styles actually influence the strength of the need for relatedness itself, or whether they primarily affect the way individuals respond to and regulate that need.
* The section will also consider whether differences in attachment style are associated with relatedness need satisfaction or frustration, rather than simply differences in how much relatedness people need.
* Finally, the chapter will examine whether the relationship may work in both directions, with repeated experiences of relatedness satisfaction or frustration potentially contributing to changes in attachment over time.

{{RoundBoxTop|theme=4}}
Information to be added for book chapter: Research evidence examining attachment anxiety/avoidance, relatedness motivation, basic psychological need satisfaction/frustration, and possible reciprocal effects between attachment and relatedness.
{{RoundBoxBottom}}

==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
* [[wikipedia:Attachment_in_adults|Attachment in adults]] (Wikipedia)
* [[wikipedia:Self-determination_theory|Self-determination theory]] (Wikipedia)

==References==
{{Hanging indent|1=

Ainsworth, M. D. S., Blehar, M. C., Waters, E., &amp; Wall, S. (1978). ''Patterns of attachment: A psychological study of the strange situation''. Lawrence Erlbaum. 

Bartholomew, K. (1990). Avoidance of Intimacy: An Attachment Perspective. ''Journal of Social and Personal Relationships'', 7(2), 147–178. https://doi.org/10.1177/0265407590072001 

Bartholomew, K., &amp; Horowitz, L. (1991). Attachment Styles Among Young Adults: A Test of a Four-Category Model. ''Journal of Personality and Social Psychology'', 61, 226–244. https://doi.org/10.1037/0022-3514.61.2.226 

Benoit, D. (2004). Infant-parent attachment: Definition, types, antecedents, measurement and outcome. ''Paediatrics &amp; Child Health'', 9(8), 541–545. https://doi.org/10.1093/pch/9.8.541 

Bowlby, J. (1958). The nature of the child's tie to his mother. ''Int J Psychoanal'', 39(5), 350–373. 

Bowlby, J. (1982). Attachment and loss: Retrospect and prospect. American ''Journal of Orthopsychiatry'', 52(4), 664–678. https://doi.org/10.1111/j.1939-0025.1982.tb01456.x 

Bretherton, I., &amp; Munholland, K. A. (2008). Internal working models in attachment relationships: Elaborating a central construct in attachment theory. In ''Handbook of attachment: Theory, research, and clinical applications'', 2nd ed. (pp. 102–127). The Guilford Press. 

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. ''Motivation and Emotion'', 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1 

Collins, N. L., &amp; Allard, L. M. (2003). Cognitive Representations of Attachment: The Content and Function of Working Models. In Garth J. O. Fletcher &amp; M. S. Clark (Eds.), ''Blackwell Handbook of Social Psychology: Interpersonal Processes'' (pp. 60–85). Blackwell Publishing. https://doi.org/https://doi.org/10.1002/9780470998557.ch3 

Deci, E. L., &amp; Ryan, R. M. (2000). The &quot;What&quot; and &quot;Why&quot; of Goal Pursuits: Human Needs and the Self-Determination of Behavior. ''Psychological Inquiry'', 11(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 

Duschinsky, R. (2018). Disorganization, fear and attachment: working towards clarification. ''Infant Ment Health J'', 39(1), 17–29. https://doi.org/10.1002/imhj.21689 

Granqvist, P., Sroufe, L. A., Dozier, M., Hesse, E., Steele, M., van Ijzendoorn, M., Solomon, J., Schuengel, C., Fearon, P., Bakermans-Kranenburg, M., Steele, H., Cassidy, J., Carlson, E., Madigan, S., Jacobvitz, D., Foster, S., Behrens, K., Rifkin-Graboi, A., Gribneau, N.,…Duschinsky, R. (2017). Disorganized attachment in infancy: a review of the phenomenon and its implications for clinicians and policy-makers. ''Attachment &amp; Human Development'', 19(6), 534–558. https://doi.org/10.1080/14616734.2017.1354040 

Hazan, C., &amp; Shaver, P. (1987). Romantic love conceptualized as an attachment process. ''J Pers Soc Psychol'', 52(3), 511–524. https://doi.org/10.1037//0022-351

Main, M., &amp; Solomon, J. (1986). Discovery of An Insecure Disorganized Disoriented Attachment Pattern. In T. B. Brazelton &amp; M. W. Yogman (Eds.), ''Affective development in infancy'' (pp. 95–124). Ablex Publishing. 

Perasso, G. (2023). Strange Situation Procedure (SSP). In T. K. Shackelford (Ed.), ''Encyclopedia of Sexual Psychology and Behavior''. Springer, Cham. https://doi.org/https://doi.org/10.1007/978-3-031-08956-5_128-1 

Ryan, R. M., &amp; Deci, E. L. (2002). Overview of self-determination theory: An organismic-dialectical perspective. In ''Handbook of self-determination research''. (pp. 3–33). University of Rochester Press. 

Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology'', 61, 101860. https://doi.org/https://doi.org/10.1016/j.cedpsych.2020.101860 

Sherman, L. J., Rice, K., &amp; Cassidy, J. (2015). Infant capacities related to building internal working models of attachment figures: A theoretical and empirical review. ''Developmental Review'', 37, 109–141. https://doi.org/https://doi.org/10.1016/j.dr.2015.06.001 

Sroufe, L. A. (1988). The role of infant-caregiver attachment in development. In ''Clinical implications of attachment''. (pp. 18–38). Lawrence Erlbaum Associates, Inc. 

Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A Review of Self-Determination Theory’s Basic Psychological Needs at Work. ''Journal of Management'', 42(5), 1195-1229. https://doi.org/10.1177/0149206316632058 

Vansteenkiste, M., &amp; Ryan, R. (2013). On Psychological Growth and Vulnerability: Basic Psychological Need Satisfaction and Need Frustration as a Unifying Principle. ''Journal of Psychotherapy Integration'', 23, 263–280. https://doi.org/10.1037/a0032359 

Vaughn, B. E., &amp; Waters, E. (1990). Attachment Behavior at Home and in the Laboratory: Q-Sort Observations and Strange Situation Classifications of One-Year-Olds. ''Child Development'', 61(6), 1965–1973. https://doi.org/10.2307/1130850 

Zeanah, C. H., Berlin, L. J., &amp; Boris, N. W. (2011). Practitioner review: clinical applications of attachment theory and research for infants and young children. ''J Child Psychol Psychiatry'', 52(8), 819–833. https://doi.org/10.1111/j.1469-7610.2011.02399.x 

Zeanah, C. H., Boris, N. W., &amp; Larrieu, J. A. (1997). Infant Development and Developmental Risk: A Review of the Past 10 Years. ''Journal of the American Academy of Child &amp; Adolescent Psychiatry'', 36(2), 165–178. https://doi.org/https://doi.org/10.1097/00004583-199702000-00007 

}}

==External links==
* [https://www.attachmentproject.com/attachment-theory/john-bowlby/ Bowlby and attachment theory: insights and legacy] (attachmentproject.com)
* [https://www.simplypsychology.org/self-determination-theory.html Self-determination theory of motivation] (simplypsychology.org)

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[[Category:Motivation and emotion/Book/Needs/Psychological/Relatedness]]</text>
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__TOC__
==Overview==
{{RoundBoxTop|theme=3}}

[[File:People and stands at the Museum Reserve, Orientation Week MS-5342 012 002.jpg|thumb|'''Figure 1'''. People and stands at the Museum Reserve, Orientation Week]]


Harry and Caitlin have both recently moved to a new neighbourhood and are adjusting to their new community. 

Harry makes an effort to meet people by attending local social events. He enjoys feeling included, but when plans are made without him or a message goes unanswered, he wonders whether people actually like him. After spending time with his new neighbours, he replays conversations and worries about whether he said or did something wrong.

Caitlin also enjoys meeting her neighbours and likes being included in group activities. She chats easily with people at events but often turns down invitations to spend more time together. When conversations turn more personal or neighbours begin trying to get to know her better, she changes the subject, leaves early, and may decide to avoid the next event. Although she enjoys being part of the neighbourhood, she finds keeping some distance more comfortable. 

Harry and Caitlin both appear to value connection and belonging, yet their need for relatedness seems to be experienced and expressed in very different ways
{{RoundBoxBottom}}
Relatedness, the need to feel connected, cared for, and significant to others (Van den Broeck et al., 2016), is considered a basic psychological need within [[wikipedia:Self-determination_theory|self-determination theory]]. Satisfaction of relatedness is associated with positive psychological functioning, whereas frustration of relatedness is associated poorer psychological functioning (Chen et al., 2015) '''(more detail?)''', highlighting the importance of understanding the factors that support or interfere with relatedness satisfaction.  However, despite relatedness being proposed as a universal psychological need, individuals differ in how they seek connection and experience relatedness satisfaction. 

One factor that may explain these differences is attachment style. Attachment theory proposes that experiences with attachment figures during infancy contribute to expectations about the availability and responsiveness of others, which influences how attachment-related needs are regulated and expressed. In adulthood, secure, anxious-preoccupied, dismissive-avoidant, and fearful-avoidant attachment styles are associated with different patterns of seeking and responding to connection and support. 

'''(link to chapter aims)'''

This chapter investigates whether adult attachment styles shape how relatedness is experienced, expressed, pursued, and satisfied or influence the need for relatedness itself. Additionally, it considers whether experiences of relatedness satisfaction or frustration may contribute to changes in attachment style over time.
{{RoundBoxTop|theme=1}}
;Focus questions [[File:Crystal Clear app ktip.svg|left|20px|]]
* How do different attachment styles influence the way the need for relatedness is experienced and expressed?
* How might experiences of relatedness satisfaction or frustration shape attachment over time?

{{RoundBoxBottom}}

==Self-determination theory and relatedness==
[[wikipedia:Self-determination_theory|Self-determination theory]] (SDT) is an approach to human motivation that seeks to explain the conditions that support or undermine motivation and psychological wellbeing.

A central proposition of SDT is the that individuals have inherent tendencies towards psychological growth, mastery, and connection with others (Ryan &amp; Deci, 2002). 

Within SDT [[wikipedia:Self-determination_theory#:~:text=Summary%20of%20the%20SDT%20mini%2Dtheories|six mini-theories]] address different aspects of motivation and psychological functioning. Of particular relevance to this chapter is the Basic Psychological Needs Theory (BPNT), which proposes that individuals must satisfy three [[wikipedia:Self-determination_theory#:~:text=%5B18%5D-,Basic%20psychological%20needs,-edit|basic psychological needs]], autonomy, competence, and relatedness, for healthy psychological growth and wellbeing ('''Source'''). Satisfaction of these needs is not only important for, psychological growth, effective functioning, and wellbeing, but has been linked to more intrinsic forms of motivation (Deci &amp; Ryan, 2000; Ryan &amp; Deci, 2020) ('''additional source for need satisfaction + intrinsic motivation?''')

=== Need satisfaction and frustration ===
Within BPNT, psychological needs can either be satisfied or frustrated depending on the extent to which a person's environment supports or obstructs those needs. 

Need satisfaction occurs when our environments allow for experiences where the psychological need can be fulfilled. It is considered psychologically nourishing and supports motivation, psychological growth, effective functioning, and wellbeing (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013) ('''studies for this, i.e. impacts of need satisfaction''')

In contrast, need frustration occurs when a psychological need is actively obstructed or undermined (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013). ('''more empirical evidence, impacts of need frustration''')

Importantly, need frustration is not simply the absence of need satisfaction. A person may experience low need satisfaction because they have fewer opportunities to fulfill a need, whereas need frustration involves an environment that actively thwarts or undermines a need. 

===Relatedness===
Relatedness refers to the need to feel connected to others, including both the need to care for others and to feel cared for, valued, and significant to others (Van den Broeck et al., 2016). 

('''More info?''')

==== Relatedness satisfaction and frustration ====
Relatedness satisfaction involves experiencing genuine connection and closeness to others, and a sense of belonging, whereas relatedness frustration involves experiences of rejection, exclusion, disconnection, or loneliness (Chen et al., 2015). 

('''More info/end of section?''')

{{RoundBoxTop|theme=3}}
[[File:Case Icon.png|left|20px|]] A few weeks later, Harry and Caitlin are invited to a neighbourhood barbecue. 

Harry spends the afternoon talking with several neighbours and is included in plans for another get-together the following weekend. He leaves feeling welcomed and like he is beginning to belong in the community. However, later that week he notices that several neighbours have organised another gathering without inviting him. 

During the barbecue, Caitlin enjoys chatting with people. When one neighbour later invites her over for coffee, she politely declines and does not suggest another time. Although no one has rejected or excluded her. 

Harry’s experience at the barbecue illustrates relatedness satisfaction because he feels welcomed, included, and valued by others, giving him a sense of connection and belonging. When he is later deliberately left out of plans, this may represent relatedness frustration, because the opportunity for connection is undermined through exclusion.

Caitlin’s experience is different. By repeatedly declining invitations and keeping some distance, she may have fewer opportunities to experience meaningful connection, resulting in relatively low relatedness satisfaction. However, because others are still inviting and including her, her need for relatedness is not necessarily being actively thwarted.{{RoundBoxBottom}}

==Attachment theory and styles==
[[wikipedia:Attachment_theory|Attachment theory]] ''('''Issues with wikipage, still include?''')'' was first developed by John Bowlby to explain the anxiety and distress infants experience when separated from their caregivers ('''source'''). Bowlby observed that infants use attachment behaviours, such as crying, clinging, following, to prevent separation or re-establish proximity to their caregivers (Bowlby, 1958). ''He proposed that these behaviours form part of an attachment behavioural system (ABS), an innate psychobiological mechanism that motivates infants to seek and maintain closeness to an attachment figure, reasoning the system is evolutionary based as infants that stayed close to caregivers would be more likely to survive to reproductive age (Bowlby, 1982). '''sentence too long'''''

Although Bowlby considered the ABS to be universal, he recognised that infants could differ in how attachment was experienced and expressed. He theorised that early experiences with caregivers contribute to internal working models, mental representations of expectations of whether attachment figures are available and responsive, and whether the self is worthy of care and support. These expectations are thought to guide an infants response to situations that activate their ABS, including whether the infant seeks support, intensifies attachment behaviours, or minimises them (Bretherton &amp; Munholland, 2008; Collins &amp; Allard, 2004; Sherman et al., 2015). 

[[wikipedia:Mary_Ainsworth|Mary Ainsworth]] extended Bowlby's work by examining how individual differences in attachment were expressed in infant's behaviour through the [[wikipedia:Strange_situation|Strange Situation procedure]]. The procedure involved observing infants during brief separations and reunions with a caregiver, focusing primarily on exploration, separation and reunion responses, and reactions to a stranger (Ainsworth et al., 1978). Through this, Ainsworth identified three infant attachment patterns, Secure, Anxious-ambivalent/, and Anxious-avoidant—with disorganised-disoriented attachment later identified by Main and Solomon (1986) to describe infant behaviours that did not fit comfortably within Ainsworth’s original classifications (See Table 1.)

Table 1.

''Infant Attachment Patterns, Associated Caregiving Experiences, and Attachment Strategies''
{| class=&quot;wikitable&quot;
|+
!Infant attachment style
!Typical attachment response
!Associated caregiving experiences
!Internal working model
|-
|Secure attachment
|Uses caregiver as a secure base, exploring environment independently while seeking proximity and comfort when distressed. 
|Associated with caregiving that is generally sensitive, responsive, and consistent. 
|Expects caregiver will be available and responsive when support is required. Attachment needs can therefore expressed distress without intensifying or suppressing attachment behaviour.
|-
|Anxious-ambivalent attachment
|Remains highly attentive to  caregiver availability while exploring. May become easily distressed by separation and seeks frequent proximity, attention, or reassurance, while sometimes difficult to soothe. 
|Associated with caregiving that may be inconsistent or unpredictable.
|


Expects caregiver to be inconsistent, causing infant to become attentive to caregiver’s availability and intensify attachment signals in an attempt to obtain a response. 
|-
|Anxious-avoidant attachment
|May appear unusually independent and spend more time focused on objects, activities, or exploration than on caregiver. Less likely to openly seek comfort or reassurance from the caregiver. 
|Associated with caregiving that may be relatively unresponsive, rejecting, or uncomfortable with expressions of distress. 
|Expects attempts to obtain comfort or support as unlikely to be met with a responsive reaction. Causes infant to minimise or suppress attachment signals.
|-
|Disorganised-disoriented attachment
|Displays contradictory, confused, or disoriented attachment behaviour and may alternate between proximity-seeking and avoidance without a consistent strategy.
|Associated with caregiving that is frightening, frightened, highly disrupted, or unpredictable.Has been found at higher rates in some contexts involving significant adversity. 
|Difficult to explain through one coherent internal working model as infant does not appear to have a consistent strategy for obtaining comfort.

One proposed explanation is that  caregiver may simultaneously represent a source of safety and a source of fear or uncertainty, creating conflict between approaching the caregiver for protection and moving away from them.
|}
''Note.'' Caregiving experiences are associated with, rather than solely determining, infant attachment patterns. Adapted from (Ainsworth et al., 1978), Benoit (2004), Main and Solomon (1986), Sherman et al. (2015), Granqvist et al. (2017), Vaughn and Waters (1990), and Zeanah et al. (1997).{{RoundBoxTop|theme=2}}
;Knowledge check [[File:Quiz.png|left|20px|]]
&lt;quiz display=simple&gt;
{How do internal working models help explain differences between infant attachment patterns?
|type=&quot;()&quot;}
- They determine how strongly an infant is biologically attached to their caregiver.
|| Internal working models do not determine whether an infant '''has''' an attachment to their caregiver. Instead, they shape expectations about whether caregivers will be available and responsive, which can influence how the infant seeks comfort and responds when the attachment system is activated.
+ They shape expectations about whether caregivers will be available and responsive when support is needed.
|| Yes. Internal working models develop through attachment experiences and shape expectations about whether attachment figures will be available and responsive.
- They determine how much distress every infant experiences during separation.
|| Internal working models can influence how infants respond when distressed, but they do not simply determine how much separation distress an infant experiences.
&lt;/quiz&gt;

{{RoundBoxBottom}}

===Adult attachment theory===
Attachment theory was later extended beyond infancy to explain how attachment may continue into adulthood. Hazan and Shaver (1987) were among the first to construct a self-report measure of adult attachment patterns, though this was in the context of romantic relationships. Their measure was based on the idea that individual differences in the ways adults engage in romantic relationships echo Ainsworth's classifications.

Bartholomew (1990), and Bartholomew and Horowitz (1991) later created a four-factor moled of adult attachment, proposing that attachment in adulthood could be understood through two underlying dimensions:
* Model of self: Reflects a person's sense of self-worth and whether they feel worthy of love and support. (Bartholomew, 1990)
* Model of others: Reflects whether a person expects others to be available, trustworthy, and supportive (Bartholomew, 1990)
Combining positive and negative models of the self and others produced four adult attachment styles, Secure, Anxious-preoccupied, Dismissive-avoidant, Fearful-avoidant.  '''[https://pmc.ncbi.nlm.nih.gov/articles/PMC8198184/?utm_source=chatgpt.com#B17-ijerph-18-05770:~:text=1.3.2.%20Four%2DFactor%20Model%20of%20Adult%20Attachment%20(Bartholomew%2C%201990) To expand on each one in final book chapter] [https://psychiatryonline.org/doi/10.1176/foc.8.1.foc127?utm_source=chatgpt.com another source]'''

==== Attachment anxiety and avoidance ====
Although Bartholomew's model describes four attachment styles, contemporary adult attachment research often assess attachment along the continuous dimensions of attachment anxiety and attachment avoidance
* Attachment anxiety: the degree to which individuals worry about being underappreciated or abandoned by their romantic partners   (Simpson &amp; Steven Rholes, 2017).
* Attachment avoidance: the degree to which individuals are comfortable with closeness and emotional intimacy in relationships (Simpson &amp; Steven Rholes, 2017).[[File:Four Adult Attachment Styles Based on Models of Self and Others and Attachment Anxiety and Avoidance.svg|thumb|465x465px|'''''Figure 2'''.'' Diagram of Bartholomew’s four adult attachment styles based on models of self and others, and their correspondence with attachment anxiety and attachment avoidance.                                                                                      ''Note''. Adapted from Alareqe et al. (2021), Bartholomew (1990), Bartholomew and Horowitz (1991), and Morse et al. (2012).]]
Using factor and hierarchical cluster analyses, Brennan et al. (1998) identified attachment anxiety and avoidance as two underlying dimensions of adult attachment and demonstrated that different combination of these dimensions broadly correspond to Bartholomew and Horowitz's four attachment styles (see Figure 2.).

Because contemporary research commonly measures attachment along the continuous dimensions of attachment anxiety and avoidance, this chapter draws on evidence from both dimensional and categorical approaches when examining attachment and relatedness. Where studies report findings for attachment anxiety and avoidance, these findings are interpreted in relation to the attachment styles they are most consistent with based on their established dimensional profiles. However, these interpretations should be used cautiously, as dimensional findings do not directly demonstrate effects for categorical attachment styles.

{{RoundBoxTop|theme=3}}
[[File:Case Icon.png|left|20px|]] continue case study{{RoundBoxBottom}}

{{RoundBoxTop|theme=2}}
;Knowledge check [[File:Quiz.png|left|20px|]]
&lt;quiz display=simple&gt;
{Adult attachment is completely determined by experiences in infancy.
|type=&quot;()&quot;}
+ TRUE.
|| Not quite. Early attachment experiences may contribute to the development of internal working models, but attachment is not considered permanently fixed and may change across later experiences and relationships.
- FALSE.
|| Correct. Early attachment experiences may influence internal working models and later attachment patterns, but adult attachment is not completely determined by infancy and may change across time and experience.
&lt;/quiz&gt;

{{RoundBoxBottom}}

==Attachment styles and the need for relatedness==

* Self-determination theory proposes that relatedness is a universal psychological need, suggesting that all individuals have a need to feel connected, valued, and that they belong.
* However, attachment styles may influence how this need is experienced, expressed, pursued, or satisfied.
* An important focus of this section will therefore be whether attachment styles actually influence the strength of the need for relatedness itself, or whether they primarily affect the way individuals respond to and regulate that need.
* The section will also consider whether differences in attachment style are associated with relatedness need satisfaction or frustration, rather than simply differences in how much relatedness people need.
* Finally, the chapter will examine whether the relationship may work in both directions, with repeated experiences of relatedness satisfaction or frustration potentially contributing to changes in attachment over time.

{{RoundBoxTop|theme=4}}
Information to be added for book chapter: Research evidence examining attachment anxiety/avoidance, relatedness motivation, basic psychological need satisfaction/frustration, and possible reciprocal effects between attachment and relatedness.
{{RoundBoxBottom}}

==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
* [[wikipedia:Attachment_in_adults|Attachment in adults]] (Wikipedia)
* [[wikipedia:Self-determination_theory|Self-determination theory]] (Wikipedia)

==References==
{{Hanging indent|1=

Ainsworth, M. D. S., Blehar, M. C., Waters, E., &amp; Wall, S. (1978). ''Patterns of attachment: A psychological study of the strange situation''. Lawrence Erlbaum. 

Bartholomew, K. (1990). Avoidance of Intimacy: An Attachment Perspective. ''Journal of Social and Personal Relationships'', 7(2), 147–178. https://doi.org/10.1177/0265407590072001 

Bartholomew, K., &amp; Horowitz, L. (1991). Attachment Styles Among Young Adults: A Test of a Four-Category Model. ''Journal of Personality and Social Psychology'', 61, 226–244. https://doi.org/10.1037/0022-3514.61.2.226 

Benoit, D. (2004). Infant-parent attachment: Definition, types, antecedents, measurement and outcome. ''Paediatrics &amp; Child Health'', 9(8), 541–545. https://doi.org/10.1093/pch/9.8.541 

Bowlby, J. (1958). The nature of the child's tie to his mother. ''Int J Psychoanal'', 39(5), 350–373. 

Bowlby, J. (1982). Attachment and loss: Retrospect and prospect. American ''Journal of Orthopsychiatry'', 52(4), 664–678. https://doi.org/10.1111/j.1939-0025.1982.tb01456.x 

Bretherton, I., &amp; Munholland, K. A. (2008). Internal working models in attachment relationships: Elaborating a central construct in attachment theory. In ''Handbook of attachment: Theory, research, and clinical applications'', 2nd ed. (pp. 102–127). The Guilford Press. 

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. ''Motivation and Emotion'', 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1 

Collins, N. L., &amp; Allard, L. M. (2003). Cognitive Representations of Attachment: The Content and Function of Working Models. In Garth J. O. Fletcher &amp; M. S. Clark (Eds.), ''Blackwell Handbook of Social Psychology: Interpersonal Processes'' (pp. 60–85). Blackwell Publishing. https://doi.org/https://doi.org/10.1002/9780470998557.ch3 

Deci, E. L., &amp; Ryan, R. M. (2000). The &quot;What&quot; and &quot;Why&quot; of Goal Pursuits: Human Needs and the Self-Determination of Behavior. ''Psychological Inquiry'', 11(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 

Duschinsky, R. (2018). Disorganization, fear and attachment: working towards clarification. ''Infant Ment Health J'', 39(1), 17–29. https://doi.org/10.1002/imhj.21689 

Granqvist, P., Sroufe, L. A., Dozier, M., Hesse, E., Steele, M., van Ijzendoorn, M., Solomon, J., Schuengel, C., Fearon, P., Bakermans-Kranenburg, M., Steele, H., Cassidy, J., Carlson, E., Madigan, S., Jacobvitz, D., Foster, S., Behrens, K., Rifkin-Graboi, A., Gribneau, N.,…Duschinsky, R. (2017). Disorganized attachment in infancy: a review of the phenomenon and its implications for clinicians and policy-makers. ''Attachment &amp; Human Development'', 19(6), 534–558. https://doi.org/10.1080/14616734.2017.1354040 

Hazan, C., &amp; Shaver, P. (1987). Romantic love conceptualized as an attachment process. ''J Pers Soc Psychol'', 52(3), 511–524. https://doi.org/10.1037//0022-351

Main, M., &amp; Solomon, J. (1986). Discovery of An Insecure Disorganized Disoriented Attachment Pattern. In T. B. Brazelton &amp; M. W. Yogman (Eds.), ''Affective development in infancy'' (pp. 95–124). Ablex Publishing. 

Perasso, G. (2023). Strange Situation Procedure (SSP). In T. K. Shackelford (Ed.), ''Encyclopedia of Sexual Psychology and Behavior''. Springer, Cham. https://doi.org/https://doi.org/10.1007/978-3-031-08956-5_128-1 

Ryan, R. M., &amp; Deci, E. L. (2002). Overview of self-determination theory: An organismic-dialectical perspective. In ''Handbook of self-determination research''. (pp. 3–33). University of Rochester Press. 

Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology'', 61, 101860. https://doi.org/https://doi.org/10.1016/j.cedpsych.2020.101860 

Sherman, L. J., Rice, K., &amp; Cassidy, J. (2015). Infant capacities related to building internal working models of attachment figures: A theoretical and empirical review. ''Developmental Review'', 37, 109–141. https://doi.org/https://doi.org/10.1016/j.dr.2015.06.001 

Sroufe, L. A. (1988). The role of infant-caregiver attachment in development. In ''Clinical implications of attachment''. (pp. 18–38). Lawrence Erlbaum Associates, Inc. 

Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A Review of Self-Determination Theory’s Basic Psychological Needs at Work. ''Journal of Management'', 42(5), 1195-1229. https://doi.org/10.1177/0149206316632058 

Vansteenkiste, M., &amp; Ryan, R. (2013). On Psychological Growth and Vulnerability: Basic Psychological Need Satisfaction and Need Frustration as a Unifying Principle. ''Journal of Psychotherapy Integration'', 23, 263–280. https://doi.org/10.1037/a0032359 

Vaughn, B. E., &amp; Waters, E. (1990). Attachment Behavior at Home and in the Laboratory: Q-Sort Observations and Strange Situation Classifications of One-Year-Olds. ''Child Development'', 61(6), 1965–1973. https://doi.org/10.2307/1130850 

Zeanah, C. H., Berlin, L. J., &amp; Boris, N. W. (2011). Practitioner review: clinical applications of attachment theory and research for infants and young children. ''J Child Psychol Psychiatry'', 52(8), 819–833. https://doi.org/10.1111/j.1469-7610.2011.02399.x 

Zeanah, C. H., Boris, N. W., &amp; Larrieu, J. A. (1997). Infant Development and Developmental Risk: A Review of the Past 10 Years. ''Journal of the American Academy of Child &amp; Adolescent Psychiatry'', 36(2), 165–178. https://doi.org/https://doi.org/10.1097/00004583-199702000-00007 

}}

==External links==
* [https://www.attachmentproject.com/attachment-theory/john-bowlby/ Bowlby and attachment theory: insights and legacy] (attachmentproject.com)
* [https://www.simplypsychology.org/self-determination-theory.html Self-determination theory of motivation] (simplypsychology.org)

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[[Category:Motivation and emotion/Book/Relationships/Attachment]]
[[Category:Motivation and emotion/Book/Needs/Psychological/Relatedness]]</text>
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__TOC__
==Overview==
{{RoundBoxTop|theme=3}}

[[File:People and stands at the Museum Reserve, Orientation Week MS-5342 012 002.jpg|thumb|'''Figure 1'''. People and stands at the Museum Reserve, Orientation Week]]


Harry and Caitlin have both recently moved to a new neighbourhood and are adjusting to their new community. 

Harry makes an effort to meet people by attending local social events. He enjoys feeling included, but when plans are made without him or a message goes unanswered, he wonders whether people actually like him. After spending time with his new neighbours, he replays conversations and worries about whether he said or did something wrong.

Caitlin also enjoys meeting her neighbours and likes being included in group activities. She chats easily with people at events but often turns down invitations to spend more time together. When conversations turn more personal or neighbours begin trying to get to know her better, she changes the subject, leaves early, and may decide to avoid the next event. Although she enjoys being part of the neighbourhood, she finds keeping some distance more comfortable. 

Harry and Caitlin both appear to value connection and belonging, yet their need for relatedness seems to be experienced and expressed in very different ways
{{RoundBoxBottom}}
Relatedness, the need to feel connected, cared for, and significant to others (Van den Broeck et al., 2016), is considered a basic psychological need within [[wikipedia:Self-determination_theory|self-determination theory]]. Satisfaction of relatedness is associated with positive psychological functioning, whereas frustration of relatedness is associated poorer psychological functioning (Chen et al., 2015) '''(more detail?)''', highlighting the importance of understanding the factors that support or interfere with relatedness satisfaction.  However, despite relatedness being proposed as a universal psychological need, individuals differ in how they seek connection and experience relatedness satisfaction. 

One factor that may explain these differences is attachment style. Attachment theory proposes that experiences with attachment figures during infancy contribute to expectations about the availability and responsiveness of others, which influences how attachment-related needs are regulated and expressed. In adulthood, secure, anxious-preoccupied, dismissive-avoidant, and fearful-avoidant attachment styles are associated with different patterns of seeking and responding to connection and support. 

'''(link to chapter aims)'''

This chapter investigates whether adult attachment styles shape how relatedness is experienced, expressed, pursued, and satisfied or influence the need for relatedness itself. Additionally, it considers whether experiences of relatedness satisfaction or frustration may contribute to changes in attachment style over time.
{{RoundBoxTop|theme=1}}
;Focus questions [[File:Crystal Clear app ktip.svg|left|20px|]]
* How do different attachment styles influence the way the need for relatedness is experienced and expressed?
* How might experiences of relatedness satisfaction or frustration shape attachment over time?

{{RoundBoxBottom}}

==Self-determination theory and relatedness==
[[wikipedia:Self-determination_theory|Self-determination theory]] (SDT) is an approach to human motivation that seeks to explain the conditions that support or undermine motivation and psychological wellbeing.

A central proposition of SDT is the that individuals have inherent tendencies towards psychological growth, mastery, and connection with others (Ryan &amp; Deci, 2002). 

Within SDT [[wikipedia:Self-determination_theory#:~:text=Summary%20of%20the%20SDT%20mini%2Dtheories|six mini-theories]] address different aspects of motivation and psychological functioning. Of particular relevance to this chapter is the Basic Psychological Needs Theory (BPNT), which proposes that individuals must satisfy three [[wikipedia:Self-determination_theory#:~:text=%5B18%5D-,Basic%20psychological%20needs,-edit|basic psychological needs]], autonomy, competence, and relatedness, for healthy psychological growth and wellbeing ('''Source'''). Satisfaction of these needs is not only important for, psychological growth, effective functioning, and wellbeing, but has been linked to more intrinsic forms of motivation (Deci &amp; Ryan, 2000; Ryan &amp; Deci, 2020) ('''additional source for need satisfaction + intrinsic motivation?''')

=== Need satisfaction and frustration ===
Within BPNT, psychological needs can either be satisfied or frustrated depending on the extent to which a person's environment supports or obstructs those needs. 

Need satisfaction occurs when our environments allow for experiences where the psychological need can be fulfilled. It is considered psychologically nourishing and supports motivation, psychological growth, effective functioning, and wellbeing (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013) ('''studies for this, i.e. impacts of need satisfaction''')

In contrast, need frustration occurs when a psychological need is actively obstructed or undermined (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013). ('''more empirical evidence, impacts of need frustration''')

Importantly, need frustration is not simply the absence of need satisfaction. A person may experience low need satisfaction because they have fewer opportunities to fulfill a need, whereas need frustration involves an environment that actively thwarts or undermines a need. 

===Relatedness===
Relatedness refers to the need to feel connected to others, including both the need to care for others and to feel cared for, valued, and significant to others (Van den Broeck et al., 2016). 

('''More info?''')

==== Relatedness satisfaction and frustration ====
Relatedness satisfaction involves experiencing genuine connection and closeness to others, and a sense of belonging, whereas relatedness frustration involves experiences of rejection, exclusion, disconnection, or loneliness (Chen et al., 2015). 

('''More info/end of section?''')

{{RoundBoxTop|theme=3}}
[[File:Case Icon.png|left|20px|]] A few weeks later, Harry and Caitlin are invited to a neighbourhood barbecue. 

Harry spends the afternoon talking with several neighbours and is included in plans for another get-together the following weekend. He leaves feeling welcomed and like he is beginning to belong in the community. However, later that week he notices that several neighbours have organised another gathering without inviting him. 

During the barbecue, Caitlin enjoys chatting with people. When one neighbour later invites her over for coffee, she politely declines and does not suggest another time. Although no one has rejected or excluded her. 

Harry’s experience at the barbecue illustrates relatedness satisfaction because he feels welcomed, included, and valued by others, giving him a sense of connection and belonging. When he is later deliberately left out of plans, this may represent relatedness frustration, because the opportunity for connection is undermined through exclusion.

Caitlin’s experience is different. By repeatedly declining invitations and keeping some distance, she may have fewer opportunities to experience meaningful connection, resulting in relatively low relatedness satisfaction. However, because others are still inviting and including her, her need for relatedness is not necessarily being actively thwarted.{{RoundBoxBottom}}

==Attachment theory and styles==
[[wikipedia:Attachment_theory|Attachment theory]] ''('''Issues with wikipage, still include?''')'' was first developed by John Bowlby to explain the anxiety and distress infants experience when separated from their caregivers ('''source'''). Bowlby observed that infants use attachment behaviours, such as crying, clinging, following, to prevent separation or re-establish proximity to their caregivers (Bowlby, 1958). ''He proposed that these behaviours form part of an attachment behavioural system (ABS), an innate psychobiological mechanism that motivates infants to seek and maintain closeness to an attachment figure, reasoning the system is evolutionary based as infants that stayed close to caregivers would be more likely to survive to reproductive age (Bowlby, 1982). '''sentence too long'''''

Although Bowlby considered the ABS to be universal, he recognised that infants could differ in how attachment was experienced and expressed. He theorised that early experiences with caregivers contribute to internal working models, mental representations of expectations of whether attachment figures are available and responsive, and whether the self is worthy of care and support. These expectations are thought to guide an infants response to situations that activate their ABS, including whether the infant seeks support, intensifies attachment behaviours, or minimises them (Bretherton &amp; Munholland, 2008; Collins &amp; Allard, 2004; Sherman et al., 2015). 

[[wikipedia:Mary_Ainsworth|Mary Ainsworth]] extended Bowlby's work by examining how individual differences in attachment were expressed in infant's behaviour through the [[wikipedia:Strange_situation|Strange Situation procedure]]. The procedure involved observing infants during brief separations and reunions with a caregiver, focusing primarily on exploration, separation and reunion responses, and reactions to a stranger (Ainsworth et al., 1978). Through this, Ainsworth identified three infant attachment patterns, Secure, Anxious-ambivalent/, and Anxious-avoidant—with disorganised-disoriented attachment later identified by Main and Solomon (1986) to describe infant behaviours that did not fit comfortably within Ainsworth’s original classifications (See Table 1.)

Table 1.

''Infant Attachment Patterns, Associated Caregiving Experiences, and Attachment Strategies''
{| class=&quot;wikitable&quot;
|+
!Infant attachment style
!Typical attachment response
!Associated caregiving experiences
!Internal working model
|-
|Secure attachment
|Uses caregiver as a secure base, exploring environment independently while seeking proximity and comfort when distressed. 
|Associated with caregiving that is generally sensitive, responsive, and consistent. 
|Expects caregiver will be available and responsive when support is required. Attachment needs can therefore expressed distress without intensifying or suppressing attachment behaviour.
|-
|Anxious-ambivalent attachment
|Remains highly attentive to  caregiver availability while exploring. May become easily distressed by separation and seeks frequent proximity, attention, or reassurance, while sometimes difficult to soothe. 
|Associated with caregiving that may be inconsistent or unpredictable.
|


Expects caregiver to be inconsistent, causing infant to become attentive to caregiver’s availability and intensify attachment signals in an attempt to obtain a response. 
|-
|Anxious-avoidant attachment
|May appear unusually independent and spend more time focused on objects, activities, or exploration than on caregiver. Less likely to openly seek comfort or reassurance from the caregiver. 
|Associated with caregiving that may be relatively unresponsive, rejecting, or uncomfortable with expressions of distress. 
|Expects attempts to obtain comfort or support as unlikely to be met with a responsive reaction. Causes infant to minimise or suppress attachment signals.
|-
|Disorganised-disoriented attachment
|Displays contradictory, confused, or disoriented attachment behaviour and may alternate between proximity-seeking and avoidance without a consistent strategy.
|Associated with caregiving that is frightening, frightened, highly disrupted, or unpredictable.Has been found at higher rates in some contexts involving significant adversity. 
|Difficult to explain through one coherent internal working model as infant does not appear to have a consistent strategy for obtaining comfort.

One proposed explanation is that  caregiver may simultaneously represent a source of safety and a source of fear or uncertainty, creating conflict between approaching the caregiver for protection and moving away from them.
|}
''Note''. Caregiving experiences are associated with, rather than solely determining, infant attachment patterns. Adapted from (Ainsworth et al., 1978), Benoit (2004), Main and Solomon (1986), Sherman et al. (2015), Granqvist et al. (2017), Vaughn and Waters (1990), and Zeanah et al. (1997).

{{RoundBoxTop|theme=2}}
;Knowledge check [[File:Quiz.png|left|20px|]]
&lt;quiz display=simple&gt;
{How do internal working models help explain differences between infant attachment patterns?
|type=&quot;()&quot;}
- They determine how strongly an infant is biologically attached to their caregiver.
|| Internal working models do not determine whether an infant '''has''' an attachment to their caregiver. Instead, they shape expectations about whether caregivers will be available and responsive, which can influence how the infant seeks comfort and responds when the attachment system is activated.
+ They shape expectations about whether caregivers will be available and responsive when support is needed.
|| Yes. Internal working models develop through attachment experiences and shape expectations about whether attachment figures will be available and responsive.
- They determine how much distress every infant experiences during separation.
|| Internal working models can influence how infants respond when distressed, but they do not simply determine how much separation distress an infant experiences.
&lt;/quiz&gt;

{{RoundBoxBottom}}

===Adult attachment theory===
Attachment theory was later extended beyond infancy to explain how attachment may continue into adulthood. Hazan and Shaver (1987) were among the first to construct a self-report measure of adult attachment patterns, though this was in the context of romantic relationships. Their measure was based on the idea that individual differences in the ways adults engage in romantic relationships echo Ainsworth's classifications.

Bartholomew (1990), and Bartholomew and Horowitz (1991) later created a four-factor moled of adult attachment, proposing that attachment in adulthood could be understood through two underlying dimensions:
* Model of self: Reflects a person's sense of self-worth and whether they feel worthy of love and support. (Bartholomew, 1990)
* Model of others: Reflects whether a person expects others to be available, trustworthy, and supportive (Bartholomew, 1990)
Combining positive and negative models of the self and others produced four adult attachment styles, Secure, Anxious-preoccupied, Dismissive-avoidant, Fearful-avoidant (Alareqe et al., 2021). 

==== Attachment anxiety and avoidance ====
Although Bartholomew's model describes four attachment styles, contemporary adult attachment research often assess attachment along the continuous dimensions of attachment anxiety and attachment avoidance
* Attachment anxiety: the degree to which individuals worry about being underappreciated or abandoned by their romantic partners   (Simpson &amp; Steven Rholes, 2017).
* Attachment avoidance: the degree to which individuals are comfortable with closeness and emotional intimacy in relationships (Simpson &amp; Steven Rholes, 2017).[[File:Four Adult Attachment Styles Based on Models of Self and Others and Attachment Anxiety and Avoidance.svg|thumb|465x465px|'''''Figure 2'''.'' Diagram of Bartholomew’s four adult attachment styles based on models of self and others, and their correspondence with attachment anxiety and attachment avoidance.                                                                                      ''Note''. Adapted from Alareqe et al. (2021), Bartholomew (1990), Bartholomew and Horowitz (1991), and Morse et al. (2012).]]
Using factor and hierarchical cluster analyses, Brennan et al. (1998) identified attachment anxiety and avoidance as two underlying dimensions of adult attachment and demonstrated that different combination of these dimensions broadly correspond to Bartholomew and Horowitz's four attachment styles (see Figure 2.).

Because contemporary research commonly measures attachment along the continuous dimensions of attachment anxiety and avoidance, this chapter draws on evidence from both dimensional and categorical approaches when examining attachment and relatedness. Where studies report findings for attachment anxiety and avoidance, these findings are interpreted in relation to the attachment styles they are most consistent with based on their established dimensional profiles. However, these interpretations should be used cautiously, as dimensional findings do not directly demonstrate effects for categorical attachment styles.

{{RoundBoxTop|theme=3}}
[[File:Case Icon.png|left|20px|]] continue case study{{RoundBoxBottom}}

{{RoundBoxTop|theme=2}}
;Knowledge check [[File:Quiz.png|left|20px|]]
&lt;quiz display=simple&gt;
{Adult attachment is completely determined by experiences in infancy.
|type=&quot;()&quot;}
+ TRUE.
|| Not quite. Early attachment experiences may contribute to the development of internal working models, but attachment is not considered permanently fixed and may change across later experiences and relationships.
- FALSE.
|| Correct. Early attachment experiences may influence internal working models and later attachment patterns, but adult attachment is not completely determined by infancy and may change across time and experience.
&lt;/quiz&gt;

{{RoundBoxBottom}}

==Attachment styles and the need for relatedness==

* Self-determination theory proposes that relatedness is a universal psychological need, suggesting that all individuals have a need to feel connected, valued, and that they belong.
* However, attachment styles may influence how this need is experienced, expressed, pursued, or satisfied.
* An important focus of this section will therefore be whether attachment styles actually influence the strength of the need for relatedness itself, or whether they primarily affect the way individuals respond to and regulate that need.
* The section will also consider whether differences in attachment style are associated with relatedness need satisfaction or frustration, rather than simply differences in how much relatedness people need.
* Finally, the chapter will examine whether the relationship may work in both directions, with repeated experiences of relatedness satisfaction or frustration potentially contributing to changes in attachment over time.

{{RoundBoxTop|theme=4}}
Information to be added for book chapter: Research evidence examining attachment anxiety/avoidance, relatedness motivation, basic psychological need satisfaction/frustration, and possible reciprocal effects between attachment and relatedness.
{{RoundBoxBottom}}

==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
* [[wikipedia:Attachment_in_adults|Attachment in adults]] (Wikipedia)
* [[wikipedia:Self-determination_theory|Self-determination theory]] (Wikipedia)

==References==
{{Hanging indent|1=

Ainsworth, M. D. S., Blehar, M. C., Waters, E., &amp; Wall, S. (1978). ''Patterns of attachment: A psychological study of the strange situation''. Lawrence Erlbaum. 

Bartholomew, K. (1990). Avoidance of Intimacy: An Attachment Perspective. ''Journal of Social and Personal Relationships'', 7(2), 147–178. https://doi.org/10.1177/0265407590072001 

Bartholomew, K., &amp; Horowitz, L. (1991). Attachment Styles Among Young Adults: A Test of a Four-Category Model. ''Journal of Personality and Social Psychology'', 61, 226–244. https://doi.org/10.1037/0022-3514.61.2.226 

Benoit, D. (2004). Infant-parent attachment: Definition, types, antecedents, measurement and outcome. ''Paediatrics &amp; Child Health'', 9(8), 541–545. https://doi.org/10.1093/pch/9.8.541 

Bowlby, J. (1958). The nature of the child's tie to his mother. ''Int J Psychoanal'', 39(5), 350–373. 

Bowlby, J. (1982). Attachment and loss: Retrospect and prospect. American ''Journal of Orthopsychiatry'', 52(4), 664–678. https://doi.org/10.1111/j.1939-0025.1982.tb01456.x 

Bretherton, I., &amp; Munholland, K. A. (2008). Internal working models in attachment relationships: Elaborating a central construct in attachment theory. In ''Handbook of attachment: Theory, research, and clinical applications'', 2nd ed. (pp. 102–127). The Guilford Press. 

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. ''Motivation and Emotion'', 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1 

Collins, N. L., &amp; Allard, L. M. (2003). Cognitive Representations of Attachment: The Content and Function of Working Models. In Garth J. O. Fletcher &amp; M. S. Clark (Eds.), ''Blackwell Handbook of Social Psychology: Interpersonal Processes'' (pp. 60–85). Blackwell Publishing. https://doi.org/https://doi.org/10.1002/9780470998557.ch3 

Deci, E. L., &amp; Ryan, R. M. (2000). The &quot;What&quot; and &quot;Why&quot; of Goal Pursuits: Human Needs and the Self-Determination of Behavior. ''Psychological Inquiry'', 11(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 

Duschinsky, R. (2018). Disorganization, fear and attachment: working towards clarification. ''Infant Ment Health J'', 39(1), 17–29. https://doi.org/10.1002/imhj.21689 

Granqvist, P., Sroufe, L. A., Dozier, M., Hesse, E., Steele, M., van Ijzendoorn, M., Solomon, J., Schuengel, C., Fearon, P., Bakermans-Kranenburg, M., Steele, H., Cassidy, J., Carlson, E., Madigan, S., Jacobvitz, D., Foster, S., Behrens, K., Rifkin-Graboi, A., Gribneau, N.,…Duschinsky, R. (2017). Disorganized attachment in infancy: a review of the phenomenon and its implications for clinicians and policy-makers. ''Attachment &amp; Human Development'', 19(6), 534–558. https://doi.org/10.1080/14616734.2017.1354040 

Hazan, C., &amp; Shaver, P. (1987). Romantic love conceptualized as an attachment process. ''J Pers Soc Psychol'', 52(3), 511–524. https://doi.org/10.1037//0022-351

Main, M., &amp; Solomon, J. (1986). Discovery of An Insecure Disorganized Disoriented Attachment Pattern. In T. B. Brazelton &amp; M. W. Yogman (Eds.), ''Affective development in infancy'' (pp. 95–124). Ablex Publishing. 

Perasso, G. (2023). Strange Situation Procedure (SSP). In T. K. Shackelford (Ed.), ''Encyclopedia of Sexual Psychology and Behavior''. Springer, Cham. https://doi.org/https://doi.org/10.1007/978-3-031-08956-5_128-1 

Ryan, R. M., &amp; Deci, E. L. (2002). Overview of self-determination theory: An organismic-dialectical perspective. In ''Handbook of self-determination research''. (pp. 3–33). University of Rochester Press. 

Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology'', 61, 101860. https://doi.org/https://doi.org/10.1016/j.cedpsych.2020.101860 

Sherman, L. J., Rice, K., &amp; Cassidy, J. (2015). Infant capacities related to building internal working models of attachment figures: A theoretical and empirical review. ''Developmental Review'', 37, 109–141. https://doi.org/https://doi.org/10.1016/j.dr.2015.06.001 

Sroufe, L. A. (1988). The role of infant-caregiver attachment in development. In ''Clinical implications of attachment''. (pp. 18–38). Lawrence Erlbaum Associates, Inc. 

Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A Review of Self-Determination Theory’s Basic Psychological Needs at Work. ''Journal of Management'', 42(5), 1195-1229. https://doi.org/10.1177/0149206316632058 

Vansteenkiste, M., &amp; Ryan, R. (2013). On Psychological Growth and Vulnerability: Basic Psychological Need Satisfaction and Need Frustration as a Unifying Principle. ''Journal of Psychotherapy Integration'', 23, 263–280. https://doi.org/10.1037/a0032359 

Vaughn, B. E., &amp; Waters, E. (1990). Attachment Behavior at Home and in the Laboratory: Q-Sort Observations and Strange Situation Classifications of One-Year-Olds. ''Child Development'', 61(6), 1965–1973. https://doi.org/10.2307/1130850 

Zeanah, C. H., Berlin, L. J., &amp; Boris, N. W. (2011). Practitioner review: clinical applications of attachment theory and research for infants and young children. ''J Child Psychol Psychiatry'', 52(8), 819–833. https://doi.org/10.1111/j.1469-7610.2011.02399.x 

Zeanah, C. H., Boris, N. W., &amp; Larrieu, J. A. (1997). Infant Development and Developmental Risk: A Review of the Past 10 Years. ''Journal of the American Academy of Child &amp; Adolescent Psychiatry'', 36(2), 165–178. https://doi.org/https://doi.org/10.1097/00004583-199702000-00007 

}}

==External links==
* [https://www.attachmentproject.com/attachment-theory/john-bowlby/ Bowlby and attachment theory: insights and legacy] (attachmentproject.com)
* [https://www.simplypsychology.org/self-determination-theory.html Self-determination theory of motivation] (simplypsychology.org)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Relationships/Attachment]]
[[Category:Motivation and emotion/Book/Needs/Psychological/Relatedness]]</text>
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      <text bytes="26372" sha1="syauuyke1wmxijatr340mx0cbv77t29" xml:space="preserve">{{title|Attachment styles and relatedness motivation:&lt;br&gt;How do attachment styles shape the need for relatedness?}}
__TOC__
==Overview==
{{RoundBoxTop|theme=3}}

[[File:People and stands at the Museum Reserve, Orientation Week MS-5342 012 002.jpg|thumb|'''Figure 1'''. People and stands at the Museum Reserve, Orientation Week]]


Harry and Caitlin have both recently moved to a new neighbourhood and are adjusting to their new community. 

Harry makes an effort to meet people by attending local social events. He enjoys feeling included, but when plans are made without him or a message goes unanswered, he wonders whether people actually like him. After spending time with his new neighbours, he replays conversations and worries about whether he said or did something wrong.

Caitlin also enjoys meeting her neighbours and likes being included in group activities. She chats easily with people at events but often turns down invitations to spend more time together. When conversations turn more personal or neighbours begin trying to get to know her better, she changes the subject, leaves early, and may decide to avoid the next event. Although she enjoys being part of the neighbourhood, she finds keeping some distance more comfortable. 

Harry and Caitlin both appear to value connection and belonging, yet their need for relatedness seems to be experienced and expressed in very different ways
{{RoundBoxBottom}}
Relatedness, the need to feel connected, cared for, and significant to others (Van den Broeck et al., 2016), is considered a basic psychological need within [[wikipedia:Self-determination_theory|self-determination theory]]. Satisfaction of relatedness is associated with positive psychological functioning, whereas frustration of relatedness is associated poorer psychological functioning (Chen et al., 2015) '''(more detail?)''', highlighting the importance of understanding the factors that support or interfere with relatedness satisfaction.  However, despite relatedness being proposed as a universal psychological need, individuals differ in how they seek connection and experience relatedness satisfaction. 

One factor that may explain these differences is attachment style. Attachment theory proposes that experiences with attachment figures during infancy contribute to expectations about the availability and responsiveness of others, which influences how attachment-related needs are regulated and expressed. In adulthood, secure, anxious-preoccupied, dismissive-avoidant, and fearful-avoidant attachment styles are associated with different patterns of seeking and responding to connection and support. 

'''(link to chapter aims)'''

This chapter investigates whether adult attachment styles shape how relatedness is experienced, expressed, pursued, and satisfied or influence the need for relatedness itself. Additionally, it considers whether experiences of relatedness satisfaction or frustration may contribute to changes in attachment style over time.
{{RoundBoxTop|theme=1}}
;Focus questions [[File:Crystal Clear app ktip.svg|left|20px|]]
* How do different attachment styles influence the way the need for relatedness is experienced and expressed?
* How might experiences of relatedness satisfaction or frustration shape attachment over time?

{{RoundBoxBottom}}

==Self-determination theory and relatedness==
[[wikipedia:Self-determination_theory|Self-determination theory]] (SDT) is an approach to human motivation that seeks to explain the conditions that support or undermine motivation and psychological wellbeing.

A central proposition of SDT is the that individuals have inherent tendencies towards psychological growth, mastery, and connection with others (Ryan &amp; Deci, 2002). 

Within SDT [[wikipedia:Self-determination_theory#:~:text=Summary%20of%20the%20SDT%20mini%2Dtheories|six mini-theories]] address different aspects of motivation and psychological functioning. Of particular relevance to this chapter is the Basic Psychological Needs Theory (BPNT), which proposes that individuals must satisfy three [[wikipedia:Self-determination_theory#:~:text=%5B18%5D-,Basic%20psychological%20needs,-edit|basic psychological needs]], autonomy, competence, and relatedness, for healthy psychological growth and wellbeing ('''Source'''). Satisfaction of these needs is not only important for, psychological growth, effective functioning, and wellbeing, but has been linked to more intrinsic forms of motivation (Deci &amp; Ryan, 2000; Ryan &amp; Deci, 2020) ('''additional source for need satisfaction + intrinsic motivation?''')

=== Need satisfaction and frustration ===
Within BPNT, psychological needs can either be satisfied or frustrated depending on the extent to which a person's environment supports or obstructs those needs. 

Need satisfaction occurs when our environments allow for experiences where the psychological need can be fulfilled. It is considered psychologically nourishing and supports motivation, psychological growth, effective functioning, and wellbeing (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013) ('''studies for this, i.e. impacts of need satisfaction''')

In contrast, need frustration occurs when a psychological need is actively obstructed or undermined (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013). ('''more empirical evidence, impacts of need frustration''')

Importantly, need frustration is not simply the absence of need satisfaction. A person may experience low need satisfaction because they have fewer opportunities to fulfill a need, whereas need frustration involves an environment that actively thwarts or undermines a need. 

===Relatedness===
Relatedness refers to the need to feel connected to others, including both the need to care for others and to feel cared for, valued, and significant to others (Van den Broeck et al., 2016). 

('''More info?''')

==== Relatedness satisfaction and frustration ====
Relatedness satisfaction involves experiencing genuine connection and closeness to others, and a sense of belonging, whereas relatedness frustration involves experiences of rejection, exclusion, disconnection, or loneliness (Chen et al., 2015). 

('''More info/end of section?''')

{{RoundBoxTop|theme=3}}
[[File:Case Icon.png|left|20px|]] A few weeks later, Harry and Caitlin are invited to a neighbourhood barbecue. 

Harry spends the afternoon talking with several neighbours and is included in plans for another get-together the following weekend. He leaves feeling welcomed and like he is beginning to belong in the community. However, later that week he notices that several neighbours have organised another gathering without inviting him. 

During the barbecue, Caitlin enjoys chatting with people. When one neighbour later invites her over for coffee, she politely declines and does not suggest another time. Although no one has rejected or excluded her. 

Harry’s experience at the barbecue illustrates relatedness satisfaction because he feels welcomed, included, and valued by others, giving him a sense of connection and belonging. When he is later deliberately left out of plans, this may represent relatedness frustration, because the opportunity for connection is undermined through exclusion.

Caitlin’s experience is different. By repeatedly declining invitations and keeping some distance, she may have fewer opportunities to experience meaningful connection, resulting in relatively low relatedness satisfaction. However, because others are still inviting and including her, her need for relatedness is not necessarily being actively thwarted.{{RoundBoxBottom}}

==Attachment theory and styles==
[[wikipedia:Attachment_theory|Attachment theory]] ''('''Issues with wikipage, still include?''')'' was first developed by John Bowlby to explain the anxiety and distress infants experience when separated from their caregivers ('''source'''). Bowlby observed that infants use attachment behaviours, such as crying, clinging, following, to prevent separation or re-establish proximity to their caregivers (Bowlby, 1958). ''He proposed that these behaviours form part of an attachment behavioural system (ABS), an innate psychobiological mechanism that motivates infants to seek and maintain closeness to an attachment figure, reasoning the system is evolutionary based as infants that stayed close to caregivers would be more likely to survive to reproductive age (Bowlby, 1982). '''sentence too long'''''

Although Bowlby considered the ABS to be universal, he recognised that infants could differ in how attachment was experienced and expressed. He theorised that early experiences with caregivers contribute to internal working models, mental representations of expectations of whether attachment figures are available and responsive, and whether the self is worthy of care and support. These expectations are thought to guide an infants response to situations that activate their ABS, including whether the infant seeks support, intensifies attachment behaviours, or minimises them (Bretherton &amp; Munholland, 2008; Collins &amp; Allard, 2004; Sherman et al., 2015). 

[[wikipedia:Mary_Ainsworth|Mary Ainsworth]] extended Bowlby's work by examining how individual differences in attachment were expressed in infant's behaviour through the [[wikipedia:Strange_situation|Strange Situation procedure]]. The procedure involved observing infants during brief separations and reunions with a caregiver, focusing primarily on exploration, separation and reunion responses, and reactions to a stranger (Ainsworth et al., 1978). Through this, Ainsworth identified three infant attachment patterns, Secure, Anxious-ambivalent/, and Anxious-avoidant—with disorganised-disoriented attachment later identified by Main and Solomon (1986) to describe infant behaviours that did not fit comfortably within Ainsworth’s original classifications (See Table 1.)

Table 1.

''Infant Attachment Patterns, Associated Caregiving Experiences, and Attachment Strategies''
{| class=&quot;wikitable&quot;
|+
!Infant attachment style
!Typical attachment response
!Associated caregiving experiences
!Internal working model
|-
|Secure attachment
|Uses caregiver as a secure base, exploring environment independently while seeking proximity and comfort when distressed. 
|Associated with caregiving that is generally sensitive, responsive, and consistent. 
|Expects caregiver will be available and responsive when support is required. Attachment needs can therefore expressed distress without intensifying or suppressing attachment behaviour.
|-
|Anxious-ambivalent attachment
|Remains highly attentive to  caregiver availability while exploring. May become easily distressed by separation and seeks frequent proximity, attention, or reassurance, while sometimes difficult to soothe. 
|Associated with caregiving that may be inconsistent or unpredictable.
|


Expects caregiver to be inconsistent, causing infant to become attentive to caregiver’s availability and intensify attachment signals in an attempt to obtain a response. 
|-
|Anxious-avoidant attachment
|May appear unusually independent and spend more time focused on objects, activities, or exploration than on caregiver. Less likely to openly seek comfort or reassurance from the caregiver. 
|Associated with caregiving that may be relatively unresponsive, rejecting, or uncomfortable with expressions of distress. 
|Expects attempts to obtain comfort or support as unlikely to be met with a responsive reaction. Causes infant to minimise or suppress attachment signals.
|-
|Disorganised-disoriented attachment
|Displays contradictory, confused, or disoriented attachment behaviour and may alternate between proximity-seeking and avoidance without a consistent strategy.
|Associated with caregiving that is frightening, frightened, highly disrupted, or unpredictable.Has been found at higher rates in some contexts involving significant adversity. 
|Difficult to explain through one coherent internal working model as infant does not appear to have a consistent strategy for obtaining comfort.

One proposed explanation is that  caregiver may simultaneously represent a source of safety and a source of fear or uncertainty, creating conflict between approaching the caregiver for protection and moving away from them.
|}
''Note''. Caregiving experiences are associated with, rather than solely determining, infant attachment patterns. Adapted from (Ainsworth et al., 1978), Benoit (2004), Main and Solomon (1986), Sherman et al. (2015), Granqvist et al. (2017), Vaughn and Waters (1990), and Zeanah et al. (1997).

{{RoundBoxTop|theme=2}}
;Knowledge check [[File:Quiz.png|left|20px|]]
&lt;quiz display=simple&gt;
{How do internal working models help explain differences between infant attachment patterns?
|type=&quot;()&quot;}
- They determine how strongly an infant is biologically attached to their caregiver.
|| Internal working models do not determine whether an infant '''has''' an attachment to their caregiver. Instead, they shape expectations about whether caregivers will be available and responsive, which can influence how the infant seeks comfort and responds when the attachment system is activated.
+ They shape expectations about whether caregivers will be available and responsive when support is needed.
|| Yes. Internal working models develop through attachment experiences and shape expectations about whether attachment figures will be available and responsive.
- They determine how much distress every infant experiences during separation.
|| Internal working models can influence how infants respond when distressed, but they do not simply determine how much separation distress an infant experiences.
&lt;/quiz&gt;

{{RoundBoxBottom}}

===Adult attachment theory===
Attachment theory was later extended beyond infancy to explain how attachment may continue into adulthood. Hazan and Shaver (1987) were among the first to construct a self-report measure of adult attachment patterns, though this was in the context of romantic relationships. Their measure was based on the idea that individual differences in the ways adults engage in romantic relationships echo Ainsworth's classifications.

Bartholomew (1990), and Bartholomew and Horowitz (1991) later created a four-factor moled of adult attachment, proposing that attachment in adulthood could be understood through two underlying dimensions:
* Model of self: Reflects a person's sense of self-worth and whether they feel worthy of love and support. (Bartholomew, 1990)
* Model of others: Reflects whether a person expects others to be available, trustworthy, and supportive (Bartholomew, 1990)
Combining positive and negative models of the self and others produced four adult attachment styles, Secure, Anxious-preoccupied, Dismissive-avoidant, Fearful-avoidant (Alareqe et al., 2021). 

==== Attachment anxiety and avoidance ====
Although Bartholomew's model describes four attachment styles, contemporary adult attachment research often assess attachment along the continuous dimensions of attachment anxiety and attachment avoidance
* Attachment anxiety: the degree to which individuals worry about being underappreciated or abandoned by their romantic partners   (Simpson &amp; Steven Rholes, 2017).
* Attachment avoidance: the degree to which individuals are comfortable with closeness and emotional intimacy in relationships (Simpson &amp; Steven Rholes, 2017).[[File:Four Adult Attachment Styles Based on Models of Self and Others and Attachment Anxiety and Avoidance.svg|thumb|465x465px|'''''Figure 2'''.'' Diagram of Bartholomew’s four adult attachment styles based on models of self and others, and their correspondence with attachment anxiety and attachment avoidance.                                                                                      ''Note''. Adapted from Alareqe et al. (2021), Bartholomew (1990), Bartholomew and Horowitz (1991), Kang et al. (2015), and Morse et al. (2012).]]
Using factor and hierarchical cluster analyses, Brennan et al. (1998) identified attachment anxiety and avoidance as two underlying dimensions of adult attachment and demonstrated that different combination of these dimensions broadly correspond to Bartholomew and Horowitz's four attachment styles (see Figure 2.).

Because contemporary research commonly measures attachment along the continuous dimensions of attachment anxiety and avoidance, this chapter draws on evidence from both dimensional and categorical approaches when examining attachment and relatedness. Where studies report findings for attachment anxiety and avoidance, these findings are interpreted in relation to the attachment styles they are most consistent with based on their established dimensional profiles. However, these interpretations should be used cautiously, as dimensional findings do not directly demonstrate effects for categorical attachment styles.

{{RoundBoxTop|theme=3}}
[[File:Case Icon.png|left|20px|]] continue case study{{RoundBoxBottom}}

{{RoundBoxTop|theme=2}}
;Knowledge check [[File:Quiz.png|left|20px|]]
&lt;quiz display=simple&gt;
{Adult attachment is completely determined by experiences in infancy.
|type=&quot;()&quot;}
+ TRUE.
|| Not quite. Early attachment experiences may contribute to the development of internal working models, but attachment is not considered permanently fixed and may change across later experiences and relationships.
- FALSE.
|| Correct. Early attachment experiences may influence internal working models and later attachment patterns, but adult attachment is not completely determined by infancy and may change across time and experience.
&lt;/quiz&gt;

{{RoundBoxBottom}}

==Attachment styles and the need for relatedness==

* Self-determination theory proposes that relatedness is a universal psychological need, suggesting that all individuals have a need to feel connected, valued, and that they belong.
* However, attachment styles may influence how this need is experienced, expressed, pursued, or satisfied.
* An important focus of this section will therefore be whether attachment styles actually influence the strength of the need for relatedness itself, or whether they primarily affect the way individuals respond to and regulate that need.
* The section will also consider whether differences in attachment style are associated with relatedness need satisfaction or frustration, rather than simply differences in how much relatedness people need.
* Finally, the chapter will examine whether the relationship may work in both directions, with repeated experiences of relatedness satisfaction or frustration potentially contributing to changes in attachment over time.

{{RoundBoxTop|theme=4}}
Information to be added for book chapter: Research evidence examining attachment anxiety/avoidance, relatedness motivation, basic psychological need satisfaction/frustration, and possible reciprocal effects between attachment and relatedness.
{{RoundBoxBottom}}

==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
* [[wikipedia:Attachment_in_adults|Attachment in adults]] (Wikipedia)
* [[wikipedia:Self-determination_theory|Self-determination theory]] (Wikipedia)
* [[Motivation and emotion/Book/2016/Attachment type and emotion|Attachment type and emotion]] (Wikiversity)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Wikiversity)

==References==
{{Hanging indent|1=

Ainsworth, M. D. S., Blehar, M. C., Waters, E., &amp; Wall, S. (1978). ''Patterns of attachment: A psychological study of the strange situation''. Lawrence Erlbaum. 

Bartholomew, K. (1990). Avoidance of Intimacy: An Attachment Perspective. ''Journal of Social and Personal Relationships'', 7(2), 147–178. https://doi.org/10.1177/0265407590072001 

Bartholomew, K., &amp; Horowitz, L. (1991). Attachment Styles Among Young Adults: A Test of a Four-Category Model. ''Journal of Personality and Social Psychology'', 61, 226–244. https://doi.org/10.1037/0022-3514.61.2.226 

Benoit, D. (2004). Infant-parent attachment: Definition, types, antecedents, measurement and outcome. ''Paediatrics &amp; Child Health'', 9(8), 541–545. https://doi.org/10.1093/pch/9.8.541 

Bowlby, J. (1958). The nature of the child's tie to his mother. ''Int J Psychoanal'', 39(5), 350–373. 

Bowlby, J. (1982). Attachment and loss: Retrospect and prospect. American ''Journal of Orthopsychiatry'', 52(4), 664–678. https://doi.org/10.1111/j.1939-0025.1982.tb01456.x 

Bretherton, I., &amp; Munholland, K. A. (2008). Internal working models in attachment relationships: Elaborating a central construct in attachment theory. In ''Handbook of attachment: Theory, research, and clinical applications'', 2nd ed. (pp. 102–127). The Guilford Press. 

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. ''Motivation and Emotion'', 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1 

Collins, N. L., &amp; Allard, L. M. (2003). Cognitive Representations of Attachment: The Content and Function of Working Models. In Garth J. O. Fletcher &amp; M. S. Clark (Eds.), ''Blackwell Handbook of Social Psychology: Interpersonal Processes'' (pp. 60–85). Blackwell Publishing. https://doi.org/https://doi.org/10.1002/9780470998557.ch3 

Deci, E. L., &amp; Ryan, R. M. (2000). The &quot;What&quot; and &quot;Why&quot; of Goal Pursuits: Human Needs and the Self-Determination of Behavior. ''Psychological Inquiry'', 11(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 

Duschinsky, R. (2018). Disorganization, fear and attachment: working towards clarification. ''Infant Ment Health J'', 39(1), 17–29. https://doi.org/10.1002/imhj.21689 

Granqvist, P., Sroufe, L. A., Dozier, M., Hesse, E., Steele, M., van Ijzendoorn, M., Solomon, J., Schuengel, C., Fearon, P., Bakermans-Kranenburg, M., Steele, H., Cassidy, J., Carlson, E., Madigan, S., Jacobvitz, D., Foster, S., Behrens, K., Rifkin-Graboi, A., Gribneau, N.,…Duschinsky, R. (2017). Disorganized attachment in infancy: a review of the phenomenon and its implications for clinicians and policy-makers. ''Attachment &amp; Human Development'', 19(6), 534–558. https://doi.org/10.1080/14616734.2017.1354040 

Hazan, C., &amp; Shaver, P. (1987). Romantic love conceptualized as an attachment process. ''J Pers Soc Psychol'', 52(3), 511–524. https://doi.org/10.1037//0022-351

Main, M., &amp; Solomon, J. (1986). Discovery of An Insecure Disorganized Disoriented Attachment Pattern. In T. B. Brazelton &amp; M. W. Yogman (Eds.), ''Affective development in infancy'' (pp. 95–124). Ablex Publishing. 

Perasso, G. (2023). Strange Situation Procedure (SSP). In T. K. Shackelford (Ed.), ''Encyclopedia of Sexual Psychology and Behavior''. Springer, Cham. https://doi.org/https://doi.org/10.1007/978-3-031-08956-5_128-1 

Ryan, R. M., &amp; Deci, E. L. (2002). Overview of self-determination theory: An organismic-dialectical perspective. In ''Handbook of self-determination research''. (pp. 3–33). University of Rochester Press. 

Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology'', 61, 101860. https://doi.org/https://doi.org/10.1016/j.cedpsych.2020.101860 

Sherman, L. J., Rice, K., &amp; Cassidy, J. (2015). Infant capacities related to building internal working models of attachment figures: A theoretical and empirical review. ''Developmental Review'', 37, 109–141. https://doi.org/https://doi.org/10.1016/j.dr.2015.06.001 

Sroufe, L. A. (1988). The role of infant-caregiver attachment in development. In ''Clinical implications of attachment''. (pp. 18–38). Lawrence Erlbaum Associates, Inc. 

Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A Review of Self-Determination Theory’s Basic Psychological Needs at Work. ''Journal of Management'', 42(5), 1195-1229. https://doi.org/10.1177/0149206316632058 

Vansteenkiste, M., &amp; Ryan, R. (2013). On Psychological Growth and Vulnerability: Basic Psychological Need Satisfaction and Need Frustration as a Unifying Principle. ''Journal of Psychotherapy Integration'', 23, 263–280. https://doi.org/10.1037/a0032359 

Vaughn, B. E., &amp; Waters, E. (1990). Attachment Behavior at Home and in the Laboratory: Q-Sort Observations and Strange Situation Classifications of One-Year-Olds. ''Child Development'', 61(6), 1965–1973. https://doi.org/10.2307/1130850 

Zeanah, C. H., Berlin, L. J., &amp; Boris, N. W. (2011). Practitioner review: clinical applications of attachment theory and research for infants and young children. ''J Child Psychol Psychiatry'', 52(8), 819–833. https://doi.org/10.1111/j.1469-7610.2011.02399.x 

Zeanah, C. H., Boris, N. W., &amp; Larrieu, J. A. (1997). Infant Development and Developmental Risk: A Review of the Past 10 Years. ''Journal of the American Academy of Child &amp; Adolescent Psychiatry'', 36(2), 165–178. https://doi.org/https://doi.org/10.1097/00004583-199702000-00007 

}}

==External links==
* [https://www.attachmentproject.com/attachment-theory/john-bowlby/ Bowlby and attachment theory: insights and legacy] (attachmentproject.com)
* [https://www.simplypsychology.org/self-determination-theory.html Self-determination theory of motivation] (simplypsychology.org)
* [https://selfdeterminationtheory.org/theory/ Theory] (selfdeterminationtheory.org)
* [https://youtu.be/GHHCy1IHTUc Maunder and Hunter: intro to adult attachment] (YouTube.com)

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      <text bytes="26433" sha1="1jpurriirhwmq9873krzan8th3x3fxo" xml:space="preserve">{{title|Attachment styles and relatedness motivation:&lt;br&gt;How do attachment styles shape the need for relatedness?}}
__TOC__
==Overview==
{{RoundBoxTop|theme=3}}

[[File:People and stands at the Museum Reserve, Orientation Week MS-5342 012 002.jpg|thumb|'''Figure 1'''. People and stands at the Museum Reserve, Orientation Week]]


Harry and Caitlin have both recently moved to a new neighbourhood and are adjusting to their new community. 

Harry makes an effort to meet people by attending local social events. He enjoys feeling included, but when plans are made without him or a message goes unanswered, he wonders whether people actually like him. After spending time with his new neighbours, he replays conversations and worries about whether he said or did something wrong.

Caitlin also enjoys meeting her neighbours and likes being included in group activities. She chats easily with people at events but often turns down invitations to spend more time together. When conversations turn more personal or neighbours begin trying to get to know her better, she changes the subject, leaves early, and may decide to avoid the next event. Although she enjoys being part of the neighbourhood, she finds keeping some distance more comfortable. 

Harry and Caitlin both appear to value connection and belonging, yet their need for relatedness seems to be experienced and expressed in very different ways
{{RoundBoxBottom}}
Relatedness, the need to feel connected, cared for, and significant to others (Van den Broeck et al., 2016), is considered a basic psychological need within [[wikipedia:Self-determination_theory|self-determination theory]]. Satisfaction of relatedness is associated with positive psychological functioning, whereas frustration of relatedness is associated poorer psychological functioning (Chen et al., 2015) '''(more detail?)''', highlighting the importance of understanding the factors that support or interfere with relatedness satisfaction.  However, despite relatedness being proposed as a universal psychological need, individuals differ in how they seek connection and experience relatedness satisfaction. 

One factor that may explain these differences is attachment style. Attachment theory proposes that experiences with attachment figures during infancy contribute to expectations about the availability and responsiveness of others, which influences how attachment-related needs are regulated and expressed. In adulthood, secure, anxious-preoccupied, dismissive-avoidant, and fearful-avoidant attachment styles are associated with different patterns of seeking and responding to connection and support. 

This chapter investigates whether adult attachment styles shape how relatedness is experienced, expressed, pursued, and satisfied or influence the need for relatedness itself. Additionally, it considers whether experiences of relatedness satisfaction or frustration may contribute to changes in attachment style over time.
{{Robelbox|theme=1|title=Focus questions|iconwidth=48px|icon=Crystal Clear app ktip.svg}}
* How do different attachment styles influence the way the need for relatedness is experienced and expressed?
* How might experiences of relatedness satisfaction or frustration shape attachment over time?
{{Robelbox-close}}

==Self-determination theory and relatedness==
[[wikipedia:Self-determination_theory|Self-determination theory]] (SDT) is an approach to human motivation that seeks to explain the conditions that support or undermine motivation and psychological wellbeing.

A central proposition of SDT is the that individuals have inherent tendencies towards psychological growth, mastery, and connection with others (Ryan &amp; Deci, 2002). 

Within SDT [[wikipedia:Self-determination_theory#:~:text=Summary%20of%20the%20SDT%20mini%2Dtheories|six mini-theories]] address different aspects of motivation and psychological functioning. Of particular relevance to this chapter is the Basic Psychological Needs Theory (BPNT), which proposes that individuals must satisfy three [[wikipedia:Self-determination_theory#:~:text=%5B18%5D-,Basic%20psychological%20needs,-edit|basic psychological needs]], autonomy, competence, and relatedness, for healthy psychological growth and wellbeing ('''Source'''). Satisfaction of these needs is not only important for, psychological growth, effective functioning, and wellbeing, but has been linked to more intrinsic forms of motivation (Deci &amp; Ryan, 2000; Ryan &amp; Deci, 2020) ('''additional source for need satisfaction + intrinsic motivation?''')

=== Need satisfaction and frustration ===
Within BPNT, psychological needs can either be satisfied or frustrated depending on the extent to which a person's environment supports or obstructs those needs. 

Need satisfaction occurs when our environments allow for experiences where the psychological need can be fulfilled. It is considered psychologically nourishing and supports motivation, psychological growth, effective functioning, and wellbeing (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013) ('''studies for this, i.e. impacts of need satisfaction''')

In contrast, need frustration occurs when a psychological need is actively obstructed or undermined (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013). ('''more empirical evidence, impacts of need frustration''')

Importantly, need frustration is not simply the absence of need satisfaction. A person may experience low need satisfaction because they have fewer opportunities to fulfill a need, whereas need frustration involves an environment that actively thwarts or undermines a need. 

===Relatedness===
Relatedness refers to the need to feel connected to others, including both the need to care for others and to feel cared for, valued, and significant to others (Van den Broeck et al., 2016). 

('''More info?''')

==== Relatedness satisfaction and frustration ====
Relatedness satisfaction involves experiencing genuine connection and closeness to others, and a sense of belonging, whereas relatedness frustration involves experiences of rejection, exclusion, disconnection, or loneliness (Chen et al., 2015). 

('''More info/end of section?''')

{{RoundBoxTop|theme=3}}
[[File:Case Icon.png|left|20px|]] A few weeks later, Harry and Caitlin are invited to a neighbourhood barbecue. 

Harry spends the afternoon talking with several neighbours and is included in plans for another get-together the following weekend. He leaves feeling welcomed and like he is beginning to belong in the community. However, later that week he notices that several neighbours have organised another gathering without inviting him. 

During the barbecue, Caitlin enjoys chatting with people. When one neighbour later invites her over for coffee, she politely declines and does not suggest another time. Although no one has rejected or excluded her. 

Harry’s experience at the barbecue illustrates relatedness satisfaction because he feels welcomed, included, and valued by others, giving him a sense of connection and belonging. When he is later deliberately left out of plans, this may represent relatedness frustration, because the opportunity for connection is undermined through exclusion.

Caitlin’s experience is different. By repeatedly declining invitations and keeping some distance, she may have fewer opportunities to experience meaningful connection, resulting in relatively low relatedness satisfaction. However, because others are still inviting and including her, her need for relatedness is not necessarily being actively thwarted.{{RoundBoxBottom}}

==Attachment theory and styles==
[[wikipedia:Attachment_theory|Attachment theory]] ''('''Issues with wikipage, still include?''')'' was first developed by John Bowlby to explain the anxiety and distress infants experience when separated from their caregivers ('''source'''). Bowlby observed that infants use attachment behaviours, such as crying, clinging, following, to prevent separation or re-establish proximity to their caregivers (Bowlby, 1958). ''He proposed that these behaviours form part of an attachment behavioural system (ABS), an innate psychobiological mechanism that motivates infants to seek and maintain closeness to an attachment figure, reasoning the system is evolutionary based as infants that stayed close to caregivers would be more likely to survive to reproductive age (Bowlby, 1982). '''sentence too long'''''

Although Bowlby considered the ABS to be universal, he recognised that infants could differ in how attachment was experienced and expressed. He theorised that early experiences with caregivers contribute to internal working models, mental representations of expectations of whether attachment figures are available and responsive, and whether the self is worthy of care and support. These expectations are thought to guide an infants response to situations that activate their ABS, including whether the infant seeks support, intensifies attachment behaviours, or minimises them (Bretherton &amp; Munholland, 2008; Collins &amp; Allard, 2004; Sherman et al., 2015). 

[[wikipedia:Mary_Ainsworth|Mary Ainsworth]] extended Bowlby's work by examining how individual differences in attachment were expressed in infant's behaviour through the [[wikipedia:Strange_situation|Strange Situation procedure]]. The procedure involved observing infants during brief separations and reunions with a caregiver, focusing primarily on exploration, separation and reunion responses, and reactions to a stranger (Ainsworth et al., 1978). Through this, Ainsworth identified three infant attachment patterns, Secure, Anxious-ambivalent/, and Anxious-avoidant—with disorganised-disoriented attachment later identified by Main and Solomon (1986) to describe infant behaviours that did not fit comfortably within Ainsworth’s original classifications (See Table 1.)

Table 1.

''Infant Attachment Patterns, Associated Caregiving Experiences, and Attachment Strategies''
{| class=&quot;wikitable&quot;
|+
!Infant attachment style
!Typical attachment response
!Associated caregiving experiences
!Internal working model
|-
|Secure attachment
|Uses caregiver as a secure base, exploring environment independently while seeking proximity and comfort when distressed. 
|Associated with caregiving that is generally sensitive, responsive, and consistent. 
|Expects caregiver will be available and responsive when support is required. Attachment needs can therefore expressed distress without intensifying or suppressing attachment behaviour.
|-
|Anxious-ambivalent attachment
|Remains highly attentive to  caregiver availability while exploring. May become easily distressed by separation and seeks frequent proximity, attention, or reassurance, while sometimes difficult to soothe. 
|Associated with caregiving that may be inconsistent or unpredictable.
|


Expects caregiver to be inconsistent, causing infant to become attentive to caregiver’s availability and intensify attachment signals in an attempt to obtain a response. 
|-
|Anxious-avoidant attachment
|May appear unusually independent and spend more time focused on objects, activities, or exploration than on caregiver. Less likely to openly seek comfort or reassurance from the caregiver. 
|Associated with caregiving that may be relatively unresponsive, rejecting, or uncomfortable with expressions of distress. 
|Expects attempts to obtain comfort or support as unlikely to be met with a responsive reaction. Causes infant to minimise or suppress attachment signals.
|-
|Disorganised-disoriented attachment
|Displays contradictory, confused, or disoriented attachment behaviour and may alternate between proximity-seeking and avoidance without a consistent strategy.
|Associated with caregiving that is frightening, frightened, highly disrupted, or unpredictable.Has been found at higher rates in some contexts involving significant adversity. 
|Difficult to explain through one coherent internal working model as infant does not appear to have a consistent strategy for obtaining comfort.

One proposed explanation is that  caregiver may simultaneously represent a source of safety and a source of fear or uncertainty, creating conflict between approaching the caregiver for protection and moving away from them.
|}
''Note''. Caregiving experiences are associated with, rather than solely determining, infant attachment patterns. Adapted from (Ainsworth et al., 1978), Benoit (2004), Main and Solomon (1986), Sherman et al. (2015), Granqvist et al. (2017), Vaughn and Waters (1990), and Zeanah et al. (1997).
{{RoundBoxTop|theme=2}}
{{Robelbox|theme=2|title=Knowledge Check!|iconwidth=48px|icon=Quiz.png}}
&lt;quiz display=simple&gt;
{How do internal working models help explain differences between infant attachment patterns?
|type=&quot;()&quot;}
- They determine how strongly an infant is biologically attached to their caregiver.
|| Internal working models do not determine whether an infant '''has''' an attachment to their caregiver. Instead, they shape expectations about whether caregivers will be available and responsive, which can influence how the infant seeks comfort and responds when the attachment system is activated.
+ They shape expectations about whether caregivers will be available and responsive when support is needed.
|| Yes. Internal working models develop through attachment experiences and shape expectations about whether attachment figures will be available and responsive.
- They determine how much distress every infant experiences during separation.
|| Internal working models can influence how infants respond when distressed, but they do not simply determine how much separation distress an infant experiences.
&lt;/quiz&gt;
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===Adult attachment theory===
Attachment theory was later extended beyond infancy to explain how attachment may continue into adulthood. Hazan and Shaver (1987) were among the first to construct a self-report measure of adult attachment patterns, though this was in the context of romantic relationships. Their measure was based on the idea that individual differences in the ways adults engage in romantic relationships echo Ainsworth's classifications.

Bartholomew (1990), and Bartholomew and Horowitz (1991) later created a four-factor moled of adult attachment, proposing that attachment in adulthood could be understood through two underlying dimensions:
* Model of self: Reflects a person's sense of self-worth and whether they feel worthy of love and support. (Bartholomew, 1990)
* Model of others: Reflects whether a person expects others to be available, trustworthy, and supportive (Bartholomew, 1990)
Combining positive and negative models of the self and others produced four adult attachment styles, Secure, Anxious-preoccupied, Dismissive-avoidant, Fearful-avoidant (Alareqe et al., 2021). 

==== Attachment anxiety and avoidance ====
Although Bartholomew's model describes four attachment styles, contemporary adult attachment research often assess attachment along the continuous dimensions of attachment anxiety and attachment avoidance
* Attachment anxiety: the degree to which individuals worry about being underappreciated or abandoned by their romantic partners   (Simpson &amp; Steven Rholes, 2017).
* Attachment avoidance: the degree to which individuals are comfortable with closeness and emotional intimacy in relationships (Simpson &amp; Steven Rholes, 2017).[[File:Four Adult Attachment Styles Based on Models of Self and Others and Attachment Anxiety and Avoidance.svg|thumb|465x465px|'''''Figure 2'''.'' Diagram of Bartholomew’s four adult attachment styles based on models of self and others, and their correspondence with attachment anxiety and attachment avoidance.                                                                                      ''Note''. Adapted from Alareqe et al. (2021), Bartholomew (1990), Bartholomew and Horowitz (1991), Kang et al. (2015), and Morse et al. (2012).]]
Using factor and hierarchical cluster analyses, Brennan et al. (1998) identified attachment anxiety and avoidance as two underlying dimensions of adult attachment and demonstrated that different combination of these dimensions broadly correspond to Bartholomew and Horowitz's four attachment styles (see Figure 2.).

Because contemporary research commonly measures attachment along the continuous dimensions of attachment anxiety and avoidance, this chapter draws on evidence from both dimensional and categorical approaches when examining attachment and relatedness. Where studies report findings for attachment anxiety and avoidance, these findings are interpreted in relation to the attachment styles they are most consistent with based on their established dimensional profiles. However, these interpretations should be used cautiously, as dimensional findings do not directly demonstrate effects for categorical attachment styles.

{{RoundBoxTop|theme=3}}
[[File:Case Icon.png|left|20px|]] continue case study
{{RoundBoxBottom}}

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{{Robelbox|theme=2|title=Knowledge Check!|iconwidth=48px|icon=Quiz.png}}
&lt;quiz display=simple&gt;
{Adult attachment is completely determined by experiences in infancy.
|type=&quot;()&quot;}
+ TRUE.
|| Not quite. Early attachment experiences may contribute to the development of internal working models, but attachment is not considered permanently fixed and may change across later experiences and relationships.
- FALSE.
|| Correct. Early attachment experiences may influence internal working models and later attachment patterns, but adult attachment is not completely determined by infancy and may change across time and experience.
&lt;/quiz&gt;
{{Robelbox-close}}
{{RoundBoxBottom}}

==Attachment styles and the need for relatedness==

* Self-determination theory proposes that relatedness is a universal psychological need, suggesting that all individuals have a need to feel connected, valued, and that they belong.
* However, attachment styles may influence how this need is experienced, expressed, pursued, or satisfied.
* An important focus of this section will therefore be whether attachment styles actually influence the strength of the need for relatedness itself, or whether they primarily affect the way individuals respond to and regulate that need.
* The section will also consider whether differences in attachment style are associated with relatedness need satisfaction or frustration, rather than simply differences in how much relatedness people need.
* Finally, the chapter will examine whether the relationship may work in both directions, with repeated experiences of relatedness satisfaction or frustration potentially contributing to changes in attachment over time.

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Information to be added for book chapter: Research evidence examining attachment anxiety/avoidance, relatedness motivation, basic psychological need satisfaction/frustration, and possible reciprocal effects between attachment and relatedness.
{{RoundBoxBottom}}

==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
* [[wikipedia:Attachment_in_adults|Attachment in adults]] (Wikipedia)
* [[wikipedia:Self-determination_theory|Self-determination theory]] (Wikipedia)
* [[Motivation and emotion/Book/2016/Attachment type and emotion|Attachment type and emotion]] (Wikiversity)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Wikiversity)

==References==
{{Hanging indent|1=

Ainsworth, M. D. S., Blehar, M. C., Waters, E., &amp; Wall, S. (1978). ''Patterns of attachment: A psychological study of the strange situation''. Lawrence Erlbaum. 

Bartholomew, K. (1990). Avoidance of Intimacy: An Attachment Perspective. ''Journal of Social and Personal Relationships'', 7(2), 147–178. https://doi.org/10.1177/0265407590072001 

Bartholomew, K., &amp; Horowitz, L. (1991). Attachment Styles Among Young Adults: A Test of a Four-Category Model. ''Journal of Personality and Social Psychology'', 61, 226–244. https://doi.org/10.1037/0022-3514.61.2.226 

Benoit, D. (2004). Infant-parent attachment: Definition, types, antecedents, measurement and outcome. ''Paediatrics &amp; Child Health'', 9(8), 541–545. https://doi.org/10.1093/pch/9.8.541 

Bowlby, J. (1958). The nature of the child's tie to his mother. ''Int J Psychoanal'', 39(5), 350–373. 

Bowlby, J. (1982). Attachment and loss: Retrospect and prospect. American ''Journal of Orthopsychiatry'', 52(4), 664–678. https://doi.org/10.1111/j.1939-0025.1982.tb01456.x 

Bretherton, I., &amp; Munholland, K. A. (2008). Internal working models in attachment relationships: Elaborating a central construct in attachment theory. In ''Handbook of attachment: Theory, research, and clinical applications'', 2nd ed. (pp. 102–127). The Guilford Press. 

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. ''Motivation and Emotion'', 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1 

Collins, N. L., &amp; Allard, L. M. (2003). Cognitive Representations of Attachment: The Content and Function of Working Models. In Garth J. O. Fletcher &amp; M. S. Clark (Eds.), ''Blackwell Handbook of Social Psychology: Interpersonal Processes'' (pp. 60–85). Blackwell Publishing. https://doi.org/https://doi.org/10.1002/9780470998557.ch3 

Deci, E. L., &amp; Ryan, R. M. (2000). The &quot;What&quot; and &quot;Why&quot; of Goal Pursuits: Human Needs and the Self-Determination of Behavior. ''Psychological Inquiry'', 11(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 

Duschinsky, R. (2018). Disorganization, fear and attachment: working towards clarification. ''Infant Ment Health J'', 39(1), 17–29. https://doi.org/10.1002/imhj.21689 

Granqvist, P., Sroufe, L. A., Dozier, M., Hesse, E., Steele, M., van Ijzendoorn, M., Solomon, J., Schuengel, C., Fearon, P., Bakermans-Kranenburg, M., Steele, H., Cassidy, J., Carlson, E., Madigan, S., Jacobvitz, D., Foster, S., Behrens, K., Rifkin-Graboi, A., Gribneau, N.,…Duschinsky, R. (2017). Disorganized attachment in infancy: a review of the phenomenon and its implications for clinicians and policy-makers. ''Attachment &amp; Human Development'', 19(6), 534–558. https://doi.org/10.1080/14616734.2017.1354040 

Hazan, C., &amp; Shaver, P. (1987). Romantic love conceptualized as an attachment process. ''J Pers Soc Psychol'', 52(3), 511–524. https://doi.org/10.1037//0022-351

Main, M., &amp; Solomon, J. (1986). Discovery of An Insecure Disorganized Disoriented Attachment Pattern. In T. B. Brazelton &amp; M. W. Yogman (Eds.), ''Affective development in infancy'' (pp. 95–124). Ablex Publishing. 

Perasso, G. (2023). Strange Situation Procedure (SSP). In T. K. Shackelford (Ed.), ''Encyclopedia of Sexual Psychology and Behavior''. Springer, Cham. https://doi.org/https://doi.org/10.1007/978-3-031-08956-5_128-1 

Ryan, R. M., &amp; Deci, E. L. (2002). Overview of self-determination theory: An organismic-dialectical perspective. In ''Handbook of self-determination research''. (pp. 3–33). University of Rochester Press. 

Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology'', 61, 101860. https://doi.org/https://doi.org/10.1016/j.cedpsych.2020.101860 

Sherman, L. J., Rice, K., &amp; Cassidy, J. (2015). Infant capacities related to building internal working models of attachment figures: A theoretical and empirical review. ''Developmental Review'', 37, 109–141. https://doi.org/https://doi.org/10.1016/j.dr.2015.06.001 

Sroufe, L. A. (1988). The role of infant-caregiver attachment in development. In ''Clinical implications of attachment''. (pp. 18–38). Lawrence Erlbaum Associates, Inc. 

Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A Review of Self-Determination Theory’s Basic Psychological Needs at Work. ''Journal of Management'', 42(5), 1195-1229. https://doi.org/10.1177/0149206316632058 

Vansteenkiste, M., &amp; Ryan, R. (2013). On Psychological Growth and Vulnerability: Basic Psychological Need Satisfaction and Need Frustration as a Unifying Principle. ''Journal of Psychotherapy Integration'', 23, 263–280. https://doi.org/10.1037/a0032359 

Vaughn, B. E., &amp; Waters, E. (1990). Attachment Behavior at Home and in the Laboratory: Q-Sort Observations and Strange Situation Classifications of One-Year-Olds. ''Child Development'', 61(6), 1965–1973. https://doi.org/10.2307/1130850 

Zeanah, C. H., Berlin, L. J., &amp; Boris, N. W. (2011). Practitioner review: clinical applications of attachment theory and research for infants and young children. ''J Child Psychol Psychiatry'', 52(8), 819–833. https://doi.org/10.1111/j.1469-7610.2011.02399.x 

Zeanah, C. H., Boris, N. W., &amp; Larrieu, J. A. (1997). Infant Development and Developmental Risk: A Review of the Past 10 Years. ''Journal of the American Academy of Child &amp; Adolescent Psychiatry'', 36(2), 165–178. https://doi.org/https://doi.org/10.1097/00004583-199702000-00007 

}}

==External links==
* [https://www.attachmentproject.com/attachment-theory/john-bowlby/ Bowlby and attachment theory: insights and legacy] (attachmentproject.com)
* [https://www.simplypsychology.org/self-determination-theory.html Self-determination theory of motivation] (simplypsychology.org)
* [https://selfdeterminationtheory.org/theory/ Theory] (selfdeterminationtheory.org)
* [https://youtu.be/GHHCy1IHTUc Maunder and Hunter: intro to adult attachment] (YouTube.com)

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__TOC__
==Overview==
{{RoundBoxTop|theme=3}}

[[File:People and stands at the Museum Reserve, Orientation Week MS-5342 012 002.jpg|thumb|'''Figure 1'''. People and stands at the Museum Reserve, Orientation Week]]


Harry and Caitlin have both recently moved to a new neighbourhood and are adjusting to their new community. 

Harry makes an effort to meet people by attending local social events. He enjoys feeling included, but when plans are made without him or a message goes unanswered, he wonders whether people actually like him. After spending time with his new neighbours, he replays conversations and worries about whether he said or did something wrong.

Caitlin also enjoys meeting her neighbours and likes being included in group activities. She chats easily with people at events but often turns down invitations to spend more time together. When conversations turn more personal or neighbours begin trying to get to know her better, she changes the subject, leaves early, and may decide to avoid the next event. Although she enjoys being part of the neighbourhood, she finds keeping some distance more comfortable. 

Harry and Caitlin both appear to value connection and belonging, yet their need for relatedness seems to be experienced and expressed in very different ways
{{RoundBoxBottom}}
Relatedness, the need to feel connected, cared for, and significant to others (Van den Broeck et al., 2016), is considered a basic psychological need within [[wikipedia:Self-determination_theory|self-determination theory]]. Satisfaction of relatedness is associated with positive psychological functioning, whereas frustration of relatedness is associated poorer psychological functioning (Chen et al., 2015) '''(more detail?)''', highlighting the importance of understanding the factors that support or interfere with relatedness satisfaction.  However, despite relatedness being proposed as a universal psychological need, individuals differ in how they seek connection and experience relatedness satisfaction. 

One factor that may explain these differences is attachment style. Attachment theory proposes that experiences with attachment figures during infancy contribute to expectations about the availability and responsiveness of others, which influences how attachment-related needs are regulated and expressed. In adulthood, secure, anxious-preoccupied, dismissive-avoidant, and fearful-avoidant attachment styles are associated with different patterns of seeking and responding to connection and support. 

This chapter investigates whether adult attachment styles shape how relatedness is experienced, expressed, pursued, and satisfied or influence the need for relatedness itself. Additionally, it considers whether experiences of relatedness satisfaction or frustration may contribute to changes in attachment style over time.
{{Robelbox|theme=1|title=Focus questions|iconwidth=48px|icon=Crystal Clear app ktip.svg}}
* How do different attachment styles influence the way the need for relatedness is experienced and expressed?
* How might experiences of relatedness satisfaction or frustration shape attachment over time?
{{Robelbox-close}}

==Self-Determination theory and relatedness==
[[wikipedia:Self-determination_theory|Self-determination theory]] (SDT) is an approach to human motivation that seeks to explain the conditions that support or undermine motivation and psychological wellbeing.

A central proposition of SDT is the that individuals have inherent tendencies towards psychological growth, mastery, and connection with others (Ryan &amp; Deci, 2002). 

Within SDT [[wikipedia:Self-determination_theory#:~:text=Summary%20of%20the%20SDT%20mini%2Dtheories|six mini-theories]] address different aspects of motivation and psychological functioning. Of particular relevance to this chapter is the Basic Psychological Needs Theory (BPNT), which proposes that individuals must satisfy three [[wikipedia:Self-determination_theory#:~:text=%5B18%5D-,Basic%20psychological%20needs,-edit|basic psychological needs]], autonomy, competence, and relatedness, for healthy psychological growth and wellbeing ('''Source'''). Satisfaction of these needs is not only important for, psychological growth, effective functioning, and wellbeing, but has been linked to more intrinsic forms of motivation (Deci &amp; Ryan, 2000; Ryan &amp; Deci, 2020) ('''additional source for need satisfaction + intrinsic motivation?''')

=== Need satisfaction and frustration ===
Within BPNT, psychological needs can either be satisfied or frustrated depending on the extent to which a person's environment supports or obstructs those needs. 

Need satisfaction occurs when our environments allow for experiences where the psychological need can be fulfilled. It is considered psychologically nourishing and supports motivation, psychological growth, effective functioning, and wellbeing (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013) ('''studies for this, i.e. impacts of need satisfaction''')

In contrast, need frustration occurs when a psychological need is actively obstructed or undermined (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013). ('''more empirical evidence, impacts of need frustration''')

Importantly, need frustration is not simply the absence of need satisfaction. A person may experience low need satisfaction because they have fewer opportunities to fulfill a need, whereas need frustration involves an environment that actively thwarts or undermines a need. 

===Relatedness===
Relatedness refers to the need to feel connected to others, including both the need to care for others and to feel cared for, valued, and significant to others (Van den Broeck et al., 2016). 

('''More info?''')

==== Relatedness satisfaction and frustration ====
Relatedness satisfaction involves experiencing genuine connection and closeness to others, and a sense of belonging, whereas relatedness frustration involves experiences of rejection, exclusion, disconnection, or loneliness (Chen et al., 2015). 

('''More info/end of section?''')

{{RoundBoxTop|theme=3}}
[[File:Case Icon.png|left|20px|]] A few weeks later, Harry and Caitlin are invited to a neighbourhood barbecue. 

Harry spends the afternoon talking with several neighbours and is included in plans for another get-together the following weekend. He leaves feeling welcomed and like he is beginning to belong in the community. However, later that week he notices that several neighbours have organised another gathering without inviting him. 

During the barbecue, Caitlin enjoys chatting with people. When one neighbour later invites her over for coffee, she politely declines and does not suggest another time. Although no one has rejected or excluded her. 

Harry’s experience at the barbecue illustrates relatedness satisfaction because he feels welcomed, included, and valued by others, giving him a sense of connection and belonging. When he is later deliberately left out of plans, this may represent relatedness frustration, because the opportunity for connection is undermined through exclusion.

Caitlin’s experience is different. By repeatedly declining invitations and keeping some distance, she may have fewer opportunities to experience meaningful connection, resulting in relatively low relatedness satisfaction. However, because others are still inviting and including her, her need for relatedness is not necessarily being actively thwarted.{{RoundBoxBottom}}

==Attachment theory and styles==
[[wikipedia:Attachment_theory|Attachment theory]] ''('''Issues with wikipage, still include?''')'' was first developed by John Bowlby to explain the anxiety and distress infants experience when separated from their caregivers ('''source'''). Bowlby observed that infants use attachment behaviours, such as crying, clinging, following, to prevent separation or re-establish proximity to their caregivers (Bowlby, 1958). ''He proposed that these behaviours form part of an attachment behavioural system (ABS), an innate psychobiological mechanism that motivates infants to seek and maintain closeness to an attachment figure, reasoning the system is evolutionary based as infants that stayed close to caregivers would be more likely to survive to reproductive age (Bowlby, 1982). '''sentence too long'''''

Although Bowlby considered the ABS to be universal, he recognised that infants could differ in how attachment was experienced and expressed. He theorised that early experiences with caregivers contribute to internal working models, mental representations of expectations of whether attachment figures are available and responsive, and whether the self is worthy of care and support. These expectations are thought to guide an infants response to situations that activate their ABS, including whether the infant seeks support, intensifies attachment behaviours, or minimises them (Bretherton &amp; Munholland, 2008; Collins &amp; Allard, 2004; Sherman et al., 2015). 

[[wikipedia:Mary_Ainsworth|Mary Ainsworth]] extended Bowlby's work by examining how individual differences in attachment were expressed in infant's behaviour through the [[wikipedia:Strange_situation|Strange Situation procedure]]. The procedure involved observing infants during brief separations and reunions with a caregiver, focusing primarily on exploration, separation and reunion responses, and reactions to a stranger (Ainsworth et al., 1978). Through this, Ainsworth identified three infant attachment patterns, Secure, Anxious-ambivalent/, and Anxious-avoidant—with disorganised-disoriented attachment later identified by Main and Solomon (1986) to describe infant behaviours that did not fit comfortably within Ainsworth’s original classifications (See Table 1.)

Table 1.

''Infant Attachment Patterns, Associated Caregiving Experiences, and Attachment Strategies''
{| class=&quot;wikitable&quot;
|+
!Infant attachment style
!Typical attachment response
!Associated caregiving experiences
!Internal working model
|-
|Secure attachment
|Uses caregiver as a secure base, exploring environment independently while seeking proximity and comfort when distressed. 
|Associated with caregiving that is generally sensitive, responsive, and consistent. 
|Expects caregiver will be available and responsive when support is required. Attachment needs can therefore expressed distress without intensifying or suppressing attachment behaviour.
|-
|Anxious-ambivalent attachment
|Remains highly attentive to  caregiver availability while exploring. May become easily distressed by separation and seeks frequent proximity, attention, or reassurance, while sometimes difficult to soothe. 
|Associated with caregiving that may be inconsistent or unpredictable.
|


Expects caregiver to be inconsistent, causing infant to become attentive to caregiver’s availability and intensify attachment signals in an attempt to obtain a response. 
|-
|Anxious-avoidant attachment
|May appear unusually independent and spend more time focused on objects, activities, or exploration than on caregiver. Less likely to openly seek comfort or reassurance from the caregiver. 
|Associated with caregiving that may be relatively unresponsive, rejecting, or uncomfortable with expressions of distress. 
|Expects attempts to obtain comfort or support as unlikely to be met with a responsive reaction. Causes infant to minimise or suppress attachment signals.
|-
|Disorganised-disoriented attachment
|Displays contradictory, confused, or disoriented attachment behaviour and may alternate between proximity-seeking and avoidance without a consistent strategy.
|Associated with caregiving that is frightening, frightened, highly disrupted, or unpredictable.Has been found at higher rates in some contexts involving significant adversity. 
|Difficult to explain through one coherent internal working model as infant does not appear to have a consistent strategy for obtaining comfort.

One proposed explanation is that  caregiver may simultaneously represent a source of safety and a source of fear or uncertainty, creating conflict between approaching the caregiver for protection and moving away from them.
|}
''Note''. Caregiving experiences are associated with, rather than solely determining, infant attachment patterns. Adapted from (Ainsworth et al., 1978), Benoit (2004), Main and Solomon (1986), Sherman et al. (2015), Granqvist et al. (2017), Vaughn and Waters (1990), and Zeanah et al. (1997).
{{RoundBoxTop|theme=2}}
{{Robelbox|theme=2|title=Knowledge Check!|iconwidth=48px|icon=Quiz.png}}
&lt;quiz display=simple&gt;
{How do internal working models help explain differences between infant attachment patterns?
|type=&quot;()&quot;}
- They determine how strongly an infant is biologically attached to their caregiver.
|| Internal working models do not determine whether an infant '''has''' an attachment to their caregiver. Instead, they shape expectations about whether caregivers will be available and responsive, which can influence how the infant seeks comfort and responds when the attachment system is activated.
+ They shape expectations about whether caregivers will be available and responsive when support is needed.
|| Yes. Internal working models develop through attachment experiences and shape expectations about whether attachment figures will be available and responsive.
- They determine how much distress every infant experiences during separation.
|| Internal working models can influence how infants respond when distressed, but they do not simply determine how much separation distress an infant experiences.
&lt;/quiz&gt;
{{Robelbox-close}}
{{RoundBoxBottom}}

===Adult attachment theory===
Attachment theory was later extended beyond infancy to explain how attachment may continue into adulthood. Hazan and Shaver (1987) were among the first to construct a self-report measure of adult attachment patterns, though this was in the context of romantic relationships. Their measure was based on the idea that individual differences in the ways adults engage in romantic relationships echo Ainsworth's classifications.

Bartholomew (1990), and Bartholomew and Horowitz (1991) later created a four-factor moled of adult attachment, proposing that attachment in adulthood could be understood through two underlying dimensions:
* Model of self: Reflects a person's sense of self-worth and whether they feel worthy of love and support. (Bartholomew, 1990)
* Model of others: Reflects whether a person expects others to be available, trustworthy, and supportive (Bartholomew, 1990)
Combining positive and negative models of the self and others produced four adult attachment styles, Secure, Anxious-preoccupied, Dismissive-avoidant, Fearful-avoidant (Alareqe et al., 2021). 

==== Attachment anxiety and avoidance ====
Although Bartholomew's model describes four attachment styles, contemporary adult attachment research often assess attachment along the continuous dimensions of attachment anxiety and attachment avoidance
* Attachment anxiety: the degree to which individuals worry about being underappreciated or abandoned by their romantic partners   (Simpson &amp; Steven Rholes, 2017).
* Attachment avoidance: the degree to which individuals are comfortable with closeness and emotional intimacy in relationships (Simpson &amp; Steven Rholes, 2017).[[File:Four Adult Attachment Styles Based on Models of Self and Others and Attachment Anxiety and Avoidance.svg|thumb|465x465px|'''''Figure 2'''.'' Diagram of Bartholomew’s four adult attachment styles based on models of self and others, and their correspondence with attachment anxiety and attachment avoidance.                                                                                      ''Note''. Adapted from Alareqe et al. (2021), Bartholomew (1990), Bartholomew and Horowitz (1991), Kang et al. (2015), and Morse et al. (2012).]]
Using factor and hierarchical cluster analyses, Brennan et al. (1998) identified attachment anxiety and avoidance as two underlying dimensions of adult attachment and demonstrated that different combination of these dimensions broadly correspond to Bartholomew and Horowitz's four attachment styles (see Figure 2.).

Because contemporary research commonly measures attachment along the continuous dimensions of attachment anxiety and avoidance, this chapter draws on evidence from both dimensional and categorical approaches when examining attachment and relatedness. Where studies report findings for attachment anxiety and avoidance, these findings are interpreted in relation to the attachment styles they are most consistent with based on their established dimensional profiles. However, these interpretations should be used cautiously, as dimensional findings do not directly demonstrate effects for categorical attachment styles.

{{RoundBoxTop|theme=3}}
[[File:Case Icon.png|left|20px|]] continue case study
{{RoundBoxBottom}}

{{RoundBoxTop|theme=2}}
{{Robelbox|theme=2|title=Knowledge Check!|iconwidth=48px|icon=Quiz.png}}
&lt;quiz display=simple&gt;
{Adult attachment is completely determined by experiences in infancy.
|type=&quot;()&quot;}
+ TRUE.
|| Not quite. Early attachment experiences may contribute to the development of internal working models, but attachment is not considered permanently fixed and may change across later experiences and relationships.
- FALSE.
|| Correct. Early attachment experiences may influence internal working models and later attachment patterns, but adult attachment is not completely determined by infancy and may change across time and experience.
&lt;/quiz&gt;
{{Robelbox-close}}
{{RoundBoxBottom}}

==Attachment styles and the need for relatedness==

* Self-determination theory proposes that relatedness is a universal psychological need, suggesting that all individuals have a need to feel connected, valued, and that they belong.
* However, attachment styles may influence how this need is experienced, expressed, pursued, or satisfied.
* An important focus of this section will therefore be whether attachment styles actually influence the strength of the need for relatedness itself, or whether they primarily affect the way individuals respond to and regulate that need.
* The section will also consider whether differences in attachment style are associated with relatedness need satisfaction or frustration, rather than simply differences in how much relatedness people need.
* Finally, the chapter will examine whether the relationship may work in both directions, with repeated experiences of relatedness satisfaction or frustration potentially contributing to changes in attachment over time.

{{RoundBoxTop|theme=4}}
Information to be added for book chapter: Research evidence examining attachment anxiety/avoidance, relatedness motivation, basic psychological need satisfaction/frustration, and possible reciprocal effects between attachment and relatedness.
{{RoundBoxBottom}}

==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
* [[wikipedia:Attachment_in_adults|Attachment in adults]] (Wikipedia)
* [[wikipedia:Self-determination_theory|Self-determination theory]] (Wikipedia)
* [[Motivation and emotion/Book/2016/Attachment type and emotion|Attachment type and emotion]] (Wikiversity)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Wikiversity)

==References==
{{Hanging indent|1=

Ainsworth, M. D. S., Blehar, M. C., Waters, E., &amp; Wall, S. (1978). ''Patterns of attachment: A psychological study of the strange situation''. Lawrence Erlbaum. 

Bartholomew, K. (1990). Avoidance of Intimacy: An Attachment Perspective. ''Journal of Social and Personal Relationships'', 7(2), 147–178. https://doi.org/10.1177/0265407590072001 

Bartholomew, K., &amp; Horowitz, L. (1991). Attachment Styles Among Young Adults: A Test of a Four-Category Model. ''Journal of Personality and Social Psychology'', 61, 226–244. https://doi.org/10.1037/0022-3514.61.2.226 

Benoit, D. (2004). Infant-parent attachment: Definition, types, antecedents, measurement and outcome. ''Paediatrics &amp; Child Health'', 9(8), 541–545. https://doi.org/10.1093/pch/9.8.541 

Bowlby, J. (1958). The nature of the child's tie to his mother. ''Int J Psychoanal'', 39(5), 350–373. 

Bowlby, J. (1982). Attachment and loss: Retrospect and prospect. American ''Journal of Orthopsychiatry'', 52(4), 664–678. https://doi.org/10.1111/j.1939-0025.1982.tb01456.x 

Bretherton, I., &amp; Munholland, K. A. (2008). Internal working models in attachment relationships: Elaborating a central construct in attachment theory. In ''Handbook of attachment: Theory, research, and clinical applications'', 2nd ed. (pp. 102–127). The Guilford Press. 

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. ''Motivation and Emotion'', 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1 

Collins, N. L., &amp; Allard, L. M. (2003). Cognitive Representations of Attachment: The Content and Function of Working Models. In Garth J. O. Fletcher &amp; M. S. Clark (Eds.), ''Blackwell Handbook of Social Psychology: Interpersonal Processes'' (pp. 60–85). Blackwell Publishing. https://doi.org/https://doi.org/10.1002/9780470998557.ch3 

Deci, E. L., &amp; Ryan, R. M. (2000). The &quot;What&quot; and &quot;Why&quot; of Goal Pursuits: Human Needs and the Self-Determination of Behavior. ''Psychological Inquiry'', 11(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 

Duschinsky, R. (2018). Disorganization, fear and attachment: working towards clarification. ''Infant Ment Health J'', 39(1), 17–29. https://doi.org/10.1002/imhj.21689 

Granqvist, P., Sroufe, L. A., Dozier, M., Hesse, E., Steele, M., van Ijzendoorn, M., Solomon, J., Schuengel, C., Fearon, P., Bakermans-Kranenburg, M., Steele, H., Cassidy, J., Carlson, E., Madigan, S., Jacobvitz, D., Foster, S., Behrens, K., Rifkin-Graboi, A., Gribneau, N.,…Duschinsky, R. (2017). Disorganized attachment in infancy: a review of the phenomenon and its implications for clinicians and policy-makers. ''Attachment &amp; Human Development'', 19(6), 534–558. https://doi.org/10.1080/14616734.2017.1354040 

Hazan, C., &amp; Shaver, P. (1987). Romantic love conceptualized as an attachment process. ''J Pers Soc Psychol'', 52(3), 511–524. https://doi.org/10.1037//0022-351

Main, M., &amp; Solomon, J. (1986). Discovery of An Insecure Disorganized Disoriented Attachment Pattern. In T. B. Brazelton &amp; M. W. Yogman (Eds.), ''Affective development in infancy'' (pp. 95–124). Ablex Publishing. 

Perasso, G. (2023). Strange Situation Procedure (SSP). In T. K. Shackelford (Ed.), ''Encyclopedia of Sexual Psychology and Behavior''. Springer, Cham. https://doi.org/https://doi.org/10.1007/978-3-031-08956-5_128-1 

Ryan, R. M., &amp; Deci, E. L. (2002). Overview of self-determination theory: An organismic-dialectical perspective. In ''Handbook of self-determination research''. (pp. 3–33). University of Rochester Press. 

Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology'', 61, 101860. https://doi.org/https://doi.org/10.1016/j.cedpsych.2020.101860 

Sherman, L. J., Rice, K., &amp; Cassidy, J. (2015). Infant capacities related to building internal working models of attachment figures: A theoretical and empirical review. ''Developmental Review'', 37, 109–141. https://doi.org/https://doi.org/10.1016/j.dr.2015.06.001 

Sroufe, L. A. (1988). The role of infant-caregiver attachment in development. In ''Clinical implications of attachment''. (pp. 18–38). Lawrence Erlbaum Associates, Inc. 

Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A Review of Self-Determination Theory’s Basic Psychological Needs at Work. ''Journal of Management'', 42(5), 1195-1229. https://doi.org/10.1177/0149206316632058 

Vansteenkiste, M., &amp; Ryan, R. (2013). On Psychological Growth and Vulnerability: Basic Psychological Need Satisfaction and Need Frustration as a Unifying Principle. ''Journal of Psychotherapy Integration'', 23, 263–280. https://doi.org/10.1037/a0032359 

Vaughn, B. E., &amp; Waters, E. (1990). Attachment Behavior at Home and in the Laboratory: Q-Sort Observations and Strange Situation Classifications of One-Year-Olds. ''Child Development'', 61(6), 1965–1973. https://doi.org/10.2307/1130850 

Zeanah, C. H., Berlin, L. J., &amp; Boris, N. W. (2011). Practitioner review: clinical applications of attachment theory and research for infants and young children. ''J Child Psychol Psychiatry'', 52(8), 819–833. https://doi.org/10.1111/j.1469-7610.2011.02399.x 

Zeanah, C. H., Boris, N. W., &amp; Larrieu, J. A. (1997). Infant Development and Developmental Risk: A Review of the Past 10 Years. ''Journal of the American Academy of Child &amp; Adolescent Psychiatry'', 36(2), 165–178. https://doi.org/https://doi.org/10.1097/00004583-199702000-00007 

}}

==External links==
* [https://www.attachmentproject.com/attachment-theory/john-bowlby/ Bowlby and attachment theory: insights and legacy] (attachmentproject.com)
* [https://www.simplypsychology.org/self-determination-theory.html Self-determination theory of motivation] (simplypsychology.org)
* [https://selfdeterminationtheory.org/theory/ Theory] (selfdeterminationtheory.org)
* [https://youtu.be/GHHCy1IHTUc Maunder and Hunter: intro to adult attachment] (YouTube.com)

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__TOC__
==Overview==
{{RoundBoxTop|theme=3}}

[[File:People and stands at the Museum Reserve, Orientation Week MS-5342 012 002.jpg|thumb|'''Figure 1'''. People and stands at the Museum Reserve, Orientation Week]]


Harry and Caitlin have both recently moved to a new neighbourhood and are adjusting to their new community. 

Harry makes an effort to meet people by attending local social events. He enjoys feeling included, but when plans are made without him or a message goes unanswered, he wonders whether people actually like him. After spending time with his new neighbours, he replays conversations and worries about whether he said or did something wrong.

Caitlin also enjoys meeting her neighbours and likes being included in group activities. She chats easily with people at events but often turns down invitations to spend more time together. When conversations turn more personal or neighbours begin trying to get to know her better, she changes the subject, leaves early, and may decide to avoid the next event. Although she enjoys being part of the neighbourhood, she finds keeping some distance more comfortable. 

Harry and Caitlin both appear to value connection and belonging, yet their need for relatedness seems to be experienced and expressed in very different ways
{{RoundBoxBottom}}
Relatedness, the need to feel connected, cared for, and significant to others (Van den Broeck et al., 2016), is considered a basic psychological need within [[wikipedia:Self-determination_theory|self-determination theory]]. Satisfaction of relatedness is associated with positive psychological functioning, whereas frustration of relatedness is associated poorer psychological functioning (Chen et al., 2015) '''(more detail?)''', highlighting the importance of understanding the factors that support or interfere with relatedness satisfaction.  However, despite relatedness being proposed as a universal psychological need, individuals differ in how they seek connection and experience relatedness satisfaction. 

One factor that may explain these differences is attachment style. Attachment theory proposes that experiences with attachment figures during infancy contribute to expectations about the availability and responsiveness of others, which influences how attachment-related needs are regulated and expressed. In adulthood, secure, anxious-preoccupied, dismissive-avoidant, and fearful-avoidant attachment styles are associated with different patterns of seeking and responding to connection and support. 

This chapter investigates whether adult attachment styles shape how relatedness is experienced, expressed, pursued, and satisfied or influence the need for relatedness itself. Additionally, it considers whether experiences of relatedness satisfaction or frustration may contribute to changes in attachment style over time.
{{Robelbox|theme=1|title=Focus questions|iconwidth=48px|icon=Crystal Clear app ktip.svg}}
* How do different attachment styles influence the way the need for relatedness is experienced and expressed?
* How might experiences of relatedness satisfaction or frustration shape attachment over time?
{{Robelbox-close}}

==Self-Determination theory and relatedness==
[[wikipedia:Self-determination_theory|Self-determination theory]] (SDT) is an approach to human motivation that seeks to explain the conditions that support or undermine motivation and psychological wellbeing.

A central proposition of SDT is the that individuals have inherent tendencies towards psychological growth, mastery, and connection with others (Ryan &amp; Deci, 2002). 

Within SDT [[wikipedia:Self-determination_theory#:~:text=Summary%20of%20the%20SDT%20mini%2Dtheories|six mini-theories]] address different aspects of motivation and psychological functioning. Of particular relevance to this chapter is the Basic Psychological Needs Theory (BPNT), which proposes that individuals must satisfy three [[wikipedia:Self-determination_theory#:~:text=%5B18%5D-,Basic%20psychological%20needs,-edit|basic psychological needs]], autonomy, competence, and relatedness, for healthy psychological growth and wellbeing ('''Source'''). Satisfaction of these needs is not only important for, psychological growth, effective functioning, and wellbeing, but has been linked to more intrinsic forms of motivation (Deci &amp; Ryan, 2000; Ryan &amp; Deci, 2020) ('''additional source for need satisfaction + intrinsic motivation?''')

=== Need satisfaction and frustration ===
Within BPNT, psychological needs can either be satisfied or frustrated depending on the extent to which a person's environment supports or obstructs those needs. 

Need satisfaction occurs when our environments allow for experiences where the psychological need can be fulfilled. It is considered psychologically nourishing and supports motivation, psychological growth, effective functioning, and wellbeing (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013) ('''studies for this, i.e. impacts of need satisfaction''')

In contrast, need frustration occurs when a psychological need is actively obstructed or undermined (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013). ('''more empirical evidence, impacts of need frustration''')

Importantly, need frustration is not simply the absence of need satisfaction. A person may experience low need satisfaction because they have fewer opportunities to fulfill a need, whereas need frustration involves an environment that actively thwarts or undermines a need. 

===Relatedness===
Relatedness refers to the need to feel connected to others, including both the need to care for others and to feel cared for, valued, and significant to others (Van den Broeck et al., 2016). 

('''More info?''')

==== Relatedness satisfaction and frustration ====
Relatedness satisfaction involves experiencing genuine connection and closeness to others, and a sense of belonging, whereas relatedness frustration involves experiences of rejection, exclusion, disconnection, or loneliness (Chen et al., 2015). 

('''More info/end of section?''')

{{RoundBoxTop|theme=3}}
[[File:Case Icon.png|left|20px|]] A few weeks later, Harry and Caitlin are invited to a neighbourhood barbecue. 

Harry spends the afternoon talking with several neighbours and is included in plans for another get-together the following weekend. He leaves feeling welcomed and like he is beginning to belong in the community. However, later that week he notices that several neighbours have organised another gathering without inviting him. 

During the barbecue, Caitlin enjoys chatting with people. When one neighbour later invites her over for coffee, she politely declines and does not suggest another time. Although no one has rejected or excluded her. 

Harry’s experience at the barbecue illustrates relatedness satisfaction because he feels welcomed, included, and valued by others, giving him a sense of connection and belonging. When he is later deliberately left out of plans, this may represent relatedness frustration, because the opportunity for connection is undermined through exclusion.

Caitlin’s experience is different. By repeatedly declining invitations and keeping some distance, she may have fewer opportunities to experience meaningful connection, resulting in relatively low relatedness satisfaction. However, because others are still inviting and including her, her need for relatedness is not necessarily being actively thwarted.{{RoundBoxBottom}}

==Attachment theory and styles==
[[wikipedia:Attachment_theory|Attachment theory]] ''('''Issues with wikipage, still include?''')'' was first developed by John Bowlby to explain the anxiety and distress infants experience when separated from their caregivers ('''source'''). Bowlby observed that infants use attachment behaviours, such as crying, clinging, following, to prevent separation or re-establish proximity to their caregivers (Bowlby, 1958). ''He proposed that these behaviours form part of an attachment behavioural system (ABS), an innate psychobiological mechanism that motivates infants to seek and maintain closeness to an attachment figure, reasoning the system is evolutionary based as infants that stayed close to caregivers would be more likely to survive to reproductive age (Bowlby, 1982). '''sentence too long'''''

Although Bowlby considered the ABS to be universal, he recognised that infants could differ in how attachment was experienced and expressed. He theorised that early experiences with caregivers contribute to internal working models, mental representations of expectations of whether attachment figures are available and responsive, and whether the self is worthy of care and support. These expectations are thought to guide an infants response to situations that activate their ABS, including whether the infant seeks support, intensifies attachment behaviours, or minimises them (Bretherton &amp; Munholland, 2008; Collins &amp; Allard, 2004; Sherman et al., 2015). 

[[wikipedia:Mary_Ainsworth|Mary Ainsworth]] extended Bowlby's work by examining how individual differences in attachment were expressed in infant's behaviour through the [[wikipedia:Strange_situation|Strange Situation procedure]]. The procedure involved observing infants during brief separations and reunions with a caregiver, focusing primarily on exploration, separation and reunion responses, and reactions to a stranger (Ainsworth et al., 1978). Through this, Ainsworth identified three infant attachment patterns, Secure, Anxious-ambivalent/, and Anxious-avoidant—with disorganised-disoriented attachment later identified by Main and Solomon (1986) to describe infant behaviours that did not fit comfortably within Ainsworth’s original classifications (See Table 1.)

'''Table 1'''.

''Infant Attachment Patterns, Associated Caregiving Experiences, and Attachment Strategies''
{| class=&quot;wikitable&quot;
|+
!Infant attachment style
!Typical attachment response
!Associated caregiving experiences
!Internal working model
|-
|Secure attachment
|Uses caregiver as a secure base, exploring environment independently while seeking proximity and comfort when distressed. 
|Associated with caregiving that is generally sensitive, responsive, and consistent. 
|Expects caregiver will be available and responsive when support is required. Attachment needs can therefore expressed distress without intensifying or suppressing attachment behaviour.
|-
|Anxious-ambivalent attachment
|Remains highly attentive to  caregiver availability while exploring. May become easily distressed by separation and seeks frequent proximity, attention, or reassurance, while sometimes difficult to soothe. 
|Associated with caregiving that may be inconsistent or unpredictable.
|


Expects caregiver to be inconsistent, causing infant to become attentive to caregiver’s availability and intensify attachment signals in an attempt to obtain a response. 
|-
|Anxious-avoidant attachment
|May appear unusually independent and spend more time focused on objects, activities, or exploration than on caregiver. Less likely to openly seek comfort or reassurance from the caregiver. 
|Associated with caregiving that may be relatively unresponsive, rejecting, or uncomfortable with expressions of distress. 
|Expects attempts to obtain comfort or support as unlikely to be met with a responsive reaction. Causes infant to minimise or suppress attachment signals.
|-
|Disorganised-disoriented attachment
|Displays contradictory, confused, or disoriented attachment behaviour and may alternate between proximity-seeking and avoidance without a consistent strategy.
|Associated with caregiving that is frightening, frightened, highly disrupted, or unpredictable.Has been found at higher rates in some contexts involving significant adversity. 
|Difficult to explain through one coherent internal working model as infant does not appear to have a consistent strategy for obtaining comfort.

One proposed explanation is that  caregiver may simultaneously represent a source of safety and a source of fear or uncertainty, creating conflict between approaching the caregiver for protection and moving away from them.
|}
''Note''. Caregiving experiences are associated with, rather than solely determining, infant attachment patterns. Adapted from (Ainsworth et al., 1978), Benoit (2004), Main and Solomon (1986), Sherman et al. (2015), Granqvist et al. (2017), Vaughn and Waters (1990), and Zeanah et al. (1997).
{{RoundBoxTop|theme=2}}
{{Robelbox|theme=2|title=Knowledge Check!|iconwidth=48px|icon=Quiz.png}}
&lt;quiz display=simple&gt;
{How do internal working models help explain differences between infant attachment patterns?
|type=&quot;()&quot;}
- They determine how strongly an infant is biologically attached to their caregiver.
|| Internal working models do not determine whether an infant '''has''' an attachment to their caregiver. Instead, they shape expectations about whether caregivers will be available and responsive, which can influence how the infant seeks comfort and responds when the attachment system is activated.
+ They shape expectations about whether caregivers will be available and responsive when support is needed.
|| Yes. Internal working models develop through attachment experiences and shape expectations about whether attachment figures will be available and responsive.
- They determine how much distress every infant experiences during separation.
|| Internal working models can influence how infants respond when distressed, but they do not simply determine how much separation distress an infant experiences.
&lt;/quiz&gt;
{{Robelbox-close}}
{{RoundBoxBottom}}

===Adult attachment theory===
Attachment theory was later extended beyond infancy to explain how attachment may continue into adulthood. Hazan and Shaver (1987) were among the first to construct a self-report measure of adult attachment patterns, though this was in the context of romantic relationships. Their measure was based on the idea that individual differences in the ways adults engage in romantic relationships echo Ainsworth's classifications.

Bartholomew (1990), and Bartholomew and Horowitz (1991) later created a four-factor moled of adult attachment, proposing that attachment in adulthood could be understood through two underlying dimensions:
* Model of self: Reflects a person's sense of self-worth and whether they feel worthy of love and support. (Bartholomew, 1990)
* Model of others: Reflects whether a person expects others to be available, trustworthy, and supportive (Bartholomew, 1990)
Combining positive and negative models of the self and others produced four adult attachment styles, Secure, Anxious-preoccupied, Dismissive-avoidant, Fearful-avoidant (Alareqe et al., 2021). 

==== Attachment anxiety and avoidance ====
Although Bartholomew's model describes four attachment styles, contemporary adult attachment research often assess attachment along the continuous dimensions of attachment anxiety and attachment avoidance
* Attachment anxiety: the degree to which individuals worry about being underappreciated or abandoned by their romantic partners   (Simpson &amp; Steven Rholes, 2017).
* Attachment avoidance: the degree to which individuals are comfortable with closeness and emotional intimacy in relationships (Simpson &amp; Steven Rholes, 2017).[[File:Four Adult Attachment Styles Based on Models of Self and Others and Attachment Anxiety and Avoidance.svg|thumb|465x465px|'''Figure 2'''. Diagram of Bartholomew’s four adult attachment styles based on models of self and others, and their correspondence with attachment anxiety and attachment avoidance.                                                                                      ''Note''. Adapted from Alareqe et al. (2021), Bartholomew (1990), Bartholomew and Horowitz (1991), Kang et al. (2015), and Morse et al. (2012).]]
Using factor and hierarchical cluster analyses, Brennan et al. (1998) identified attachment anxiety and avoidance as two underlying dimensions of adult attachment and demonstrated that different combination of these dimensions broadly correspond to Bartholomew and Horowitz's four attachment styles (see Figure 2).

Because contemporary research commonly measures attachment along the continuous dimensions of attachment anxiety and avoidance, this chapter draws on evidence from both dimensional and categorical approaches when examining attachment and relatedness. Where studies report findings for attachment anxiety and avoidance, these findings are interpreted in relation to the attachment styles they are most consistent with based on their established dimensional profiles. However, these interpretations should be used cautiously, as dimensional findings do not directly demonstrate effects for categorical attachment styles.

{{RoundBoxTop|theme=3}}
[[File:Case Icon.png|left|20px|]] continue case study
{{RoundBoxBottom}}

{{RoundBoxTop|theme=2}}
{{Robelbox|theme=2|title=Knowledge Check!|iconwidth=48px|icon=Quiz.png}}
&lt;quiz display=simple&gt;
{Adult attachment is completely determined by experiences in infancy.
|type=&quot;()&quot;}
+ TRUE.
|| Not quite. Early attachment experiences may contribute to the development of internal working models, but attachment is not considered permanently fixed and may change across later experiences and relationships.
- FALSE.
|| Correct. Early attachment experiences may influence internal working models and later attachment patterns, but adult attachment is not completely determined by infancy and may change across time and experience.
&lt;/quiz&gt;
{{Robelbox-close}}
{{RoundBoxBottom}}

==Attachment styles and the need for relatedness==

* Self-determination theory proposes that relatedness is a universal psychological need, suggesting that all individuals have a need to feel connected, valued, and that they belong.
* However, attachment styles may influence how this need is experienced, expressed, pursued, or satisfied.
* An important focus of this section will therefore be whether attachment styles actually influence the strength of the need for relatedness itself, or whether they primarily affect the way individuals respond to and regulate that need.
* The section will also consider whether differences in attachment style are associated with relatedness need satisfaction or frustration, rather than simply differences in how much relatedness people need.
* Finally, the chapter will examine whether the relationship may work in both directions, with repeated experiences of relatedness satisfaction or frustration potentially contributing to changes in attachment over time.

{{RoundBoxTop|theme=4}}
Information to be added for book chapter: Research evidence examining attachment anxiety/avoidance, relatedness motivation, basic psychological need satisfaction/frustration, and possible reciprocal effects between attachment and relatedness.
{{RoundBoxBottom}}

==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
* [[wikipedia:Attachment_in_adults|Attachment in adults]] (Wikipedia)
* [[wikipedia:Self-determination_theory|Self-determination theory]] (Wikipedia)
* [[Motivation and emotion/Book/2016/Attachment type and emotion|Attachment type and emotion]] (Wikiversity)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Wikiversity)

==References==
{{Hanging indent|1=

Ainsworth, M. D. S., Blehar, M. C., Waters, E., &amp; Wall, S. (1978). ''Patterns of attachment: A psychological study of the strange situation''. Lawrence Erlbaum. 

Bartholomew, K. (1990). Avoidance of Intimacy: An Attachment Perspective. ''Journal of Social and Personal Relationships'', 7(2), 147–178. https://doi.org/10.1177/0265407590072001 

Bartholomew, K., &amp; Horowitz, L. (1991). Attachment Styles Among Young Adults: A Test of a Four-Category Model. ''Journal of Personality and Social Psychology'', 61, 226–244. https://doi.org/10.1037/0022-3514.61.2.226 

Benoit, D. (2004). Infant-parent attachment: Definition, types, antecedents, measurement and outcome. ''Paediatrics &amp; Child Health'', 9(8), 541–545. https://doi.org/10.1093/pch/9.8.541 

Bowlby, J. (1958). The nature of the child's tie to his mother. ''Int J Psychoanal'', 39(5), 350–373. 

Bowlby, J. (1982). Attachment and loss: Retrospect and prospect. American ''Journal of Orthopsychiatry'', 52(4), 664–678. https://doi.org/10.1111/j.1939-0025.1982.tb01456.x 

Bretherton, I., &amp; Munholland, K. A. (2008). Internal working models in attachment relationships: Elaborating a central construct in attachment theory. In ''Handbook of attachment: Theory, research, and clinical applications'', 2nd ed. (pp. 102–127). The Guilford Press. 

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. ''Motivation and Emotion'', 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1 

Collins, N. L., &amp; Allard, L. M. (2003). Cognitive Representations of Attachment: The Content and Function of Working Models. In Garth J. O. Fletcher &amp; M. S. Clark (Eds.), ''Blackwell Handbook of Social Psychology: Interpersonal Processes'' (pp. 60–85). Blackwell Publishing. https://doi.org/https://doi.org/10.1002/9780470998557.ch3 

Deci, E. L., &amp; Ryan, R. M. (2000). The &quot;What&quot; and &quot;Why&quot; of Goal Pursuits: Human Needs and the Self-Determination of Behavior. ''Psychological Inquiry'', 11(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 

Duschinsky, R. (2018). Disorganization, fear and attachment: working towards clarification. ''Infant Ment Health J'', 39(1), 17–29. https://doi.org/10.1002/imhj.21689 

Granqvist, P., Sroufe, L. A., Dozier, M., Hesse, E., Steele, M., van Ijzendoorn, M., Solomon, J., Schuengel, C., Fearon, P., Bakermans-Kranenburg, M., Steele, H., Cassidy, J., Carlson, E., Madigan, S., Jacobvitz, D., Foster, S., Behrens, K., Rifkin-Graboi, A., Gribneau, N.,…Duschinsky, R. (2017). Disorganized attachment in infancy: a review of the phenomenon and its implications for clinicians and policy-makers. ''Attachment &amp; Human Development'', 19(6), 534–558. https://doi.org/10.1080/14616734.2017.1354040 

Hazan, C., &amp; Shaver, P. (1987). Romantic love conceptualized as an attachment process. ''J Pers Soc Psychol'', 52(3), 511–524. https://doi.org/10.1037//0022-351

Main, M., &amp; Solomon, J. (1986). Discovery of An Insecure Disorganized Disoriented Attachment Pattern. In T. B. Brazelton &amp; M. W. Yogman (Eds.), ''Affective development in infancy'' (pp. 95–124). Ablex Publishing. 

Perasso, G. (2023). Strange Situation Procedure (SSP). In T. K. Shackelford (Ed.), ''Encyclopedia of Sexual Psychology and Behavior''. Springer, Cham. https://doi.org/https://doi.org/10.1007/978-3-031-08956-5_128-1 

Ryan, R. M., &amp; Deci, E. L. (2002). Overview of self-determination theory: An organismic-dialectical perspective. In ''Handbook of self-determination research''. (pp. 3–33). University of Rochester Press. 

Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology'', 61, 101860. https://doi.org/https://doi.org/10.1016/j.cedpsych.2020.101860 

Sherman, L. J., Rice, K., &amp; Cassidy, J. (2015). Infant capacities related to building internal working models of attachment figures: A theoretical and empirical review. ''Developmental Review'', 37, 109–141. https://doi.org/https://doi.org/10.1016/j.dr.2015.06.001 

Sroufe, L. A. (1988). The role of infant-caregiver attachment in development. In ''Clinical implications of attachment''. (pp. 18–38). Lawrence Erlbaum Associates, Inc. 

Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A Review of Self-Determination Theory’s Basic Psychological Needs at Work. ''Journal of Management'', 42(5), 1195-1229. https://doi.org/10.1177/0149206316632058 

Vansteenkiste, M., &amp; Ryan, R. (2013). On Psychological Growth and Vulnerability: Basic Psychological Need Satisfaction and Need Frustration as a Unifying Principle. ''Journal of Psychotherapy Integration'', 23, 263–280. https://doi.org/10.1037/a0032359 

Vaughn, B. E., &amp; Waters, E. (1990). Attachment Behavior at Home and in the Laboratory: Q-Sort Observations and Strange Situation Classifications of One-Year-Olds. ''Child Development'', 61(6), 1965–1973. https://doi.org/10.2307/1130850 

Zeanah, C. H., Berlin, L. J., &amp; Boris, N. W. (2011). Practitioner review: clinical applications of attachment theory and research for infants and young children. ''J Child Psychol Psychiatry'', 52(8), 819–833. https://doi.org/10.1111/j.1469-7610.2011.02399.x 

Zeanah, C. H., Boris, N. W., &amp; Larrieu, J. A. (1997). Infant Development and Developmental Risk: A Review of the Past 10 Years. ''Journal of the American Academy of Child &amp; Adolescent Psychiatry'', 36(2), 165–178. https://doi.org/https://doi.org/10.1097/00004583-199702000-00007 

}}

==External links==
* [https://www.attachmentproject.com/attachment-theory/john-bowlby/ Bowlby and attachment theory: insights and legacy] (attachmentproject.com)
* [https://www.simplypsychology.org/self-determination-theory.html Self-determination theory of motivation] (simplypsychology.org)
* [https://selfdeterminationtheory.org/theory/ Theory] (selfdeterminationtheory.org)
* [https://youtu.be/GHHCy1IHTUc Maunder and Hunter: intro to adult attachment] (YouTube.com)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Relationships/Attachment]]
[[Category:Motivation and emotion/Book/Needs/Psychological/Relatedness]]</text>
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      <text bytes="26336" sha1="j78wcxpotc2do560qb3d5i3muh9ak1m" xml:space="preserve">{{title|Attachment styles and relatedness motivation:&lt;br&gt;How do attachment styles shape the need for relatedness?}}
__TOC__
==Overview==
{{RoundBoxTop|theme=3}}

[[File:People and stands at the Museum Reserve, Orientation Week MS-5342 012 002.jpg|thumb|'''Figure 1'''. People and stands at the Museum Reserve, Orientation Week]]


Harry and Caitlin have both recently moved to a new neighbourhood and are adjusting to their new community. 

Harry makes an effort to meet people by attending local social events. He enjoys feeling included, but when plans are made without him or a message goes unanswered, he wonders whether people actually like him. After spending time with his new neighbours, he replays conversations and worries about whether he said or did something wrong.

Caitlin also enjoys meeting her neighbours and likes being included in group activities. She chats easily with people at events but often turns down invitations to spend more time together. When conversations turn more personal or neighbours begin trying to get to know her better, she changes the subject, leaves early, and may decide to avoid the next event. Although she enjoys being part of the neighbourhood, she finds keeping some distance more comfortable. 

Harry and Caitlin both appear to value connection and belonging, yet their need for relatedness seems to be experienced and expressed in very different ways
{{RoundBoxBottom}}
Relatedness, the need to feel connected, cared for, and significant to others (Van den Broeck et al., 2016), is considered a basic psychological need within [[wikipedia:Self-determination_theory|self-determination theory]]. Satisfaction of relatedness is associated with positive psychological functioning, whereas frustration of relatedness is associated poorer psychological functioning (Chen et al., 2015) '''(more detail?)''', highlighting the importance of understanding the factors that support or interfere with relatedness satisfaction.  However, despite relatedness being proposed as a universal psychological need, individuals differ in how they seek connection and experience relatedness satisfaction. 

One factor that may explain these differences is attachment style. Attachment theory proposes that experiences with attachment figures during infancy contribute to expectations about the availability and responsiveness of others, which influences how attachment-related needs are regulated and expressed. In adulthood, secure, anxious-preoccupied, dismissive-avoidant, and fearful-avoidant attachment styles are associated with different patterns of seeking and responding to connection and support. 

This chapter investigates whether adult attachment styles shape how relatedness is experienced, expressed, pursued, and satisfied or influence the need for relatedness itself. Additionally, it considers whether experiences of relatedness satisfaction or frustration may contribute to changes in attachment style over time.
{{Robelbox|theme=1|title=Focus questions|iconwidth=48px|icon=Crystal Clear app ktip.svg}}
* How do different attachment styles influence the way the need for relatedness is experienced and expressed?
* How might experiences of relatedness satisfaction or frustration shape attachment over time?
{{Robelbox-close}}

==Self-Determination theory and relatedness==
[[wikipedia:Self-determination_theory|Self-determination theory]] (SDT) is an approach to human motivation that seeks to explain the conditions that support or undermine motivation and psychological wellbeing.

A central proposition of SDT is the that individuals have inherent tendencies towards psychological growth, mastery, and connection with others (Ryan &amp; Deci, 2002). 

Within SDT [[wikipedia:Self-determination_theory#:~:text=Summary%20of%20the%20SDT%20mini%2Dtheories|six mini-theories]] address different aspects of motivation and psychological functioning. Of particular relevance to this chapter is the Basic Psychological Needs Theory (BPNT), which proposes that individuals must satisfy three [[wikipedia:Self-determination_theory#:~:text=%5B18%5D-,Basic%20psychological%20needs,-edit|basic psychological needs]], autonomy, competence, and relatedness, for healthy psychological growth and wellbeing (Deci &amp; Ryan, 2000). Satisfaction of these needs is not only important for, psychological growth, effective functioning, and wellbeing, but has been linked to more intrinsic forms of motivation (Deci &amp; Ryan, 2000; Ryan &amp; Deci, 2020) ('''additional source for need satisfaction + intrinsic motivation?''')

=== Need satisfaction and frustration ===
Within BPNT, psychological needs can either be satisfied or frustrated depending on the extent to which a person's environment supports or obstructs those needs. 

Need satisfaction occurs when our environments allow for experiences where the psychological need can be fulfilled. It is considered psychologically nourishing and supports motivation, psychological growth, effective functioning, and wellbeing (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013). In contrast, need frustration occurs when a psychological need is actively obstructed or undermined (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013).

Importantly, need frustration is not simply the absence of need satisfaction. A person may experience low need satisfaction because they have fewer opportunities to fulfill a need, whereas need frustration involves an environment that actively thwarts or undermines a need. 

===Relatedness===
Relatedness refers to the need to feel connected to others, including both the need to care for others and to feel cared for, valued, and significant to others (Van den Broeck et al., 2016). 

('''More info?''')

==== Relatedness satisfaction and frustration ====
Relatedness satisfaction involves experiencing genuine connection and closeness to others, and a sense of belonging, whereas relatedness frustration involves experiences of rejection, exclusion, disconnection, or loneliness (Chen et al., 2015). 

('''More info/end of section?''')

{{RoundBoxTop|theme=3}}
[[File:Case Icon.png|left|20px|]] A few weeks later, Harry and Caitlin are invited to a neighbourhood barbecue. 

Harry spends the afternoon talking with several neighbours and is included in plans for another get-together the following weekend. He leaves feeling welcomed and like he is beginning to belong in the community. However, later that week he notices that several neighbours have organised another gathering without inviting him. 

During the barbecue, Caitlin enjoys chatting with people. When one neighbour later invites her over for coffee, she politely declines and does not suggest another time. Although no one has rejected or excluded her. 

Harry’s experience at the barbecue illustrates relatedness satisfaction because he feels welcomed, included, and valued by others, giving him a sense of connection and belonging. When he is later deliberately left out of plans, this may represent relatedness frustration, because the opportunity for connection is undermined through exclusion.

Caitlin’s experience is different. By repeatedly declining invitations and keeping some distance, she may have fewer opportunities to experience meaningful connection, resulting in relatively low relatedness satisfaction. However, because others are still inviting and including her, her need for relatedness is not necessarily being actively thwarted.{{RoundBoxBottom}}

==Attachment theory and styles==
[[wikipedia:Attachment_theory|Attachment theory]] ''('''Issues with wikipage, still include?''')'' was first developed by John Bowlby to explain the anxiety and distress infants experience when separated from their caregivers ('''source'''). Bowlby observed that infants use attachment behaviours, such as crying, clinging, following, to prevent separation or re-establish proximity to their caregivers (Bowlby, 1958). ''He proposed that these behaviours form part of an attachment behavioural system (ABS), an innate psychobiological mechanism that motivates infants to seek and maintain closeness to an attachment figure, reasoning the system is evolutionary based as infants that stayed close to caregivers would be more likely to survive to reproductive age (Bowlby, 1982). '''sentence too long'''''

Although Bowlby considered the ABS to be universal, he recognised that infants could differ in how attachment was experienced and expressed. He theorised that early experiences with caregivers contribute to internal working models, mental representations of expectations of whether attachment figures are available and responsive, and whether the self is worthy of care and support. These expectations are thought to guide an infants response to situations that activate their ABS, including whether the infant seeks support, intensifies attachment behaviours, or minimises them (Bretherton &amp; Munholland, 2008; Collins &amp; Allard, 2004; Sherman et al., 2015). 

[[wikipedia:Mary_Ainsworth|Mary Ainsworth]] extended Bowlby's work by examining how individual differences in attachment were expressed in infant's behaviour through the [[wikipedia:Strange_situation|Strange Situation procedure]]. The procedure involved observing infants during brief separations and reunions with a caregiver, focusing primarily on exploration, separation and reunion responses, and reactions to a stranger (Ainsworth et al., 1978). Through this, Ainsworth identified three infant attachment patterns, Secure, Anxious-ambivalent/, and Anxious-avoidant—with disorganised-disoriented attachment later identified by Main and Solomon (1986) to describe infant behaviours that did not fit comfortably within Ainsworth’s original classifications (See Table 1.)

'''Table 1'''.

''Infant Attachment Patterns, Associated Caregiving Experiences, and Attachment Strategies''
{| class=&quot;wikitable&quot;
|+
!Infant attachment style
!Typical attachment response
!Associated caregiving experiences
!Internal working model
|-
|Secure attachment
|Uses caregiver as a secure base, exploring environment independently while seeking proximity and comfort when distressed. 
|Associated with caregiving that is generally sensitive, responsive, and consistent. 
|Expects caregiver will be available and responsive when support is required. Attachment needs can therefore expressed distress without intensifying or suppressing attachment behaviour.
|-
|Anxious-ambivalent attachment
|Remains highly attentive to  caregiver availability while exploring. May become easily distressed by separation and seeks frequent proximity, attention, or reassurance, while sometimes difficult to soothe. 
|Associated with caregiving that may be inconsistent or unpredictable.
|


Expects caregiver to be inconsistent, causing infant to become attentive to caregiver’s availability and intensify attachment signals in an attempt to obtain a response. 
|-
|Anxious-avoidant attachment
|May appear unusually independent and spend more time focused on objects, activities, or exploration than on caregiver. Less likely to openly seek comfort or reassurance from the caregiver. 
|Associated with caregiving that may be relatively unresponsive, rejecting, or uncomfortable with expressions of distress. 
|Expects attempts to obtain comfort or support as unlikely to be met with a responsive reaction. Causes infant to minimise or suppress attachment signals.
|-
|Disorganised-disoriented attachment
|Displays contradictory, confused, or disoriented attachment behaviour and may alternate between proximity-seeking and avoidance without a consistent strategy.
|Associated with caregiving that is frightening, frightened, highly disrupted, or unpredictable.Has been found at higher rates in some contexts involving significant adversity. 
|Difficult to explain through one coherent internal working model as infant does not appear to have a consistent strategy for obtaining comfort.

One proposed explanation is that  caregiver may simultaneously represent a source of safety and a source of fear or uncertainty, creating conflict between approaching the caregiver for protection and moving away from them.
|}
&lt;nowiki&gt;''Note''&lt;/nowiki&gt;. Caregiving experiences are associated with, rather than solely determining, infant attachment patterns. Adapted from (Ainsworth et al., 1978), Benoit (2004), Main and Solomon (1986), Sherman et al. (2015), Granqvist et al. (2017), Vaughn and Waters (1990), and Zeanah et al. (1997).

{{RoundBoxTop|theme=2}}
{{Robelbox|theme=2|title=Knowledge Check!|iconwidth=48px|icon=Quiz.png}}
&lt;quiz display=simple&gt;
{How do internal working models help explain differences between infant attachment patterns?
|type=&quot;()&quot;}
- They determine how strongly an infant is biologically attached to their caregiver.
|| Internal working models do not determine whether an infant '''has''' an attachment to their caregiver. Instead, they shape expectations about whether caregivers will be available and responsive, which can influence how the infant seeks comfort and responds when the attachment system is activated.
+ They shape expectations about whether caregivers will be available and responsive when support is needed.
|| Yes. Internal working models develop through attachment experiences and shape expectations about whether attachment figures will be available and responsive.
- They determine how much distress every infant experiences during separation.
|| Internal working models can influence how infants respond when distressed, but they do not simply determine how much separation distress an infant experiences.
&lt;/quiz&gt;
{{Robelbox-close}}
{{RoundBoxBottom}}

===Adult attachment theory===
Attachment theory was later extended beyond infancy to explain how attachment may continue into adulthood. Hazan and Shaver (1987) were among the first to construct a self-report measure of adult attachment patterns, though this was in the context of romantic relationships. Their measure was based on the idea that individual differences in the ways adults engage in romantic relationships echo Ainsworth's classifications.

Bartholomew (1990), and Bartholomew and Horowitz (1991) later created a four-factor moled of adult attachment, proposing that attachment in adulthood could be understood through two underlying dimensions:
* Model of self: Reflects a person's sense of self-worth and whether they feel worthy of love and support. (Bartholomew, 1990)
* Model of others: Reflects whether a person expects others to be available, trustworthy, and supportive (Bartholomew, 1990)
Combining positive and negative models of the self and others produced four adult attachment styles, Secure, Anxious-preoccupied, Dismissive-avoidant, Fearful-avoidant (Alareqe et al., 2021). 

==== Attachment anxiety and avoidance ====
Although Bartholomew's model describes four attachment styles, contemporary adult attachment research often assess attachment along the continuous dimensions of attachment anxiety and attachment avoidance
* Attachment anxiety: the degree to which individuals worry about being underappreciated or abandoned by their romantic partners   (Simpson &amp; Steven Rholes, 2017).
* Attachment avoidance: the degree to which individuals are comfortable with closeness and emotional intimacy in relationships (Simpson &amp; Steven Rholes, 2017).[[File:Four Adult Attachment Styles Based on Models of Self and Others and Attachment Anxiety and Avoidance.svg|thumb|465x465px|'''Figure 2'''. Diagram of Bartholomew’s four adult attachment styles based on models of self and others, and their correspondence with attachment anxiety and attachment avoidance.                                                                                      ''Note''. Adapted from Alareqe et al. (2021), Bartholomew (1990), Bartholomew and Horowitz (1991), Kang et al. (2015), and Morse et al. (2012).]]
Using factor and hierarchical cluster analyses, Brennan et al. (1998) identified attachment anxiety and avoidance as two underlying dimensions of adult attachment and demonstrated that different combination of these dimensions broadly correspond to Bartholomew and Horowitz's four attachment styles (see Figure 2).

Because contemporary research commonly measures attachment along the continuous dimensions of attachment anxiety and avoidance, this chapter draws on evidence from both dimensional and categorical approaches when examining attachment and relatedness. Where studies report findings for attachment anxiety and avoidance, these findings are interpreted in relation to the attachment styles they are most consistent with based on their established dimensional profiles. However, these interpretations should be used cautiously, as dimensional findings do not directly demonstrate effects for categorical attachment styles.

{{RoundBoxTop|theme=3}}
[[File:Case Icon.png|left|20px|]] continue case study
{{RoundBoxBottom}}

{{RoundBoxTop|theme=2}}
{{Robelbox|theme=2|title=Knowledge Check!|iconwidth=48px|icon=Quiz.png}}
&lt;quiz display=simple&gt;
{Adult attachment is completely determined by experiences in infancy.
|type=&quot;()&quot;}
+ TRUE.
|| Not quite. Early attachment experiences may contribute to the development of internal working models, but attachment is not considered permanently fixed and may change across later experiences and relationships.
- FALSE.
|| Correct. Early attachment experiences may influence internal working models and later attachment patterns, but adult attachment is not completely determined by infancy and may change across time and experience.
&lt;/quiz&gt;
{{Robelbox-close}}
{{RoundBoxBottom}}

==Attachment styles and the need for relatedness==

* Self-determination theory proposes that relatedness is a universal psychological need, suggesting that all individuals have a need to feel connected, valued, and that they belong.
* However, attachment styles may influence how this need is experienced, expressed, pursued, or satisfied.
* An important focus of this section will therefore be whether attachment styles actually influence the strength of the need for relatedness itself, or whether they primarily affect the way individuals respond to and regulate that need.
* The section will also consider whether differences in attachment style are associated with relatedness need satisfaction or frustration, rather than simply differences in how much relatedness people need.
* Finally, the chapter will examine whether the relationship may work in both directions, with repeated experiences of relatedness satisfaction or frustration potentially contributing to changes in attachment over time.

{{RoundBoxTop|theme=4}}
Information to be added for book chapter: Research evidence examining attachment anxiety/avoidance, relatedness motivation, basic psychological need satisfaction/frustration, and possible reciprocal effects between attachment and relatedness.
{{RoundBoxBottom}}

==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
* [[wikipedia:Attachment_in_adults|Attachment in adults]] (Wikipedia)
* [[wikipedia:Self-determination_theory|Self-determination theory]] (Wikipedia)
* [[Motivation and emotion/Book/2016/Attachment type and emotion|Attachment type and emotion]] (Wikiversity)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Wikiversity)

==References==
{{Hanging indent|1=

Ainsworth, M. D. S., Blehar, M. C., Waters, E., &amp; Wall, S. (1978). ''Patterns of attachment: A psychological study of the strange situation''. Lawrence Erlbaum. 

Bartholomew, K. (1990). Avoidance of Intimacy: An Attachment Perspective. ''Journal of Social and Personal Relationships'', 7(2), 147–178. https://doi.org/10.1177/0265407590072001 

Bartholomew, K., &amp; Horowitz, L. (1991). Attachment Styles Among Young Adults: A Test of a Four-Category Model. ''Journal of Personality and Social Psychology'', 61, 226–244. https://doi.org/10.1037/0022-3514.61.2.226 

Benoit, D. (2004). Infant-parent attachment: Definition, types, antecedents, measurement and outcome. ''Paediatrics &amp; Child Health'', 9(8), 541–545. https://doi.org/10.1093/pch/9.8.541 

Bowlby, J. (1958). The nature of the child's tie to his mother. ''Int J Psychoanal'', 39(5), 350–373. 

Bowlby, J. (1982). Attachment and loss: Retrospect and prospect. American ''Journal of Orthopsychiatry'', 52(4), 664–678. https://doi.org/10.1111/j.1939-0025.1982.tb01456.x 

Bretherton, I., &amp; Munholland, K. A. (2008). Internal working models in attachment relationships: Elaborating a central construct in attachment theory. In ''Handbook of attachment: Theory, research, and clinical applications'', 2nd ed. (pp. 102–127). The Guilford Press. 

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. ''Motivation and Emotion'', 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1 

Collins, N. L., &amp; Allard, L. M. (2003). Cognitive Representations of Attachment: The Content and Function of Working Models. In Garth J. O. Fletcher &amp; M. S. Clark (Eds.), ''Blackwell Handbook of Social Psychology: Interpersonal Processes'' (pp. 60–85). Blackwell Publishing. https://doi.org/https://doi.org/10.1002/9780470998557.ch3 

Deci, E. L., &amp; Ryan, R. M. (2000). The &quot;What&quot; and &quot;Why&quot; of Goal Pursuits: Human Needs and the Self-Determination of Behavior. ''Psychological Inquiry'', 11(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 

Duschinsky, R. (2018). Disorganization, fear and attachment: working towards clarification. ''Infant Ment Health J'', 39(1), 17–29. https://doi.org/10.1002/imhj.21689 

Granqvist, P., Sroufe, L. A., Dozier, M., Hesse, E., Steele, M., van Ijzendoorn, M., Solomon, J., Schuengel, C., Fearon, P., Bakermans-Kranenburg, M., Steele, H., Cassidy, J., Carlson, E., Madigan, S., Jacobvitz, D., Foster, S., Behrens, K., Rifkin-Graboi, A., Gribneau, N.,…Duschinsky, R. (2017). Disorganized attachment in infancy: a review of the phenomenon and its implications for clinicians and policy-makers. ''Attachment &amp; Human Development'', 19(6), 534–558. https://doi.org/10.1080/14616734.2017.1354040 

Hazan, C., &amp; Shaver, P. (1987). Romantic love conceptualized as an attachment process. ''J Pers Soc Psychol'', 52(3), 511–524. https://doi.org/10.1037//0022-351

Main, M., &amp; Solomon, J. (1986). Discovery of An Insecure Disorganized Disoriented Attachment Pattern. In T. B. Brazelton &amp; M. W. Yogman (Eds.), ''Affective development in infancy'' (pp. 95–124). Ablex Publishing. 

Perasso, G. (2023). Strange Situation Procedure (SSP). In T. K. Shackelford (Ed.), ''Encyclopedia of Sexual Psychology and Behavior''. Springer, Cham. https://doi.org/https://doi.org/10.1007/978-3-031-08956-5_128-1 

Ryan, R. M., &amp; Deci, E. L. (2002). Overview of self-determination theory: An organismic-dialectical perspective. In ''Handbook of self-determination research''. (pp. 3–33). University of Rochester Press. 

Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology'', 61, 101860. https://doi.org/https://doi.org/10.1016/j.cedpsych.2020.101860 

Sherman, L. J., Rice, K., &amp; Cassidy, J. (2015). Infant capacities related to building internal working models of attachment figures: A theoretical and empirical review. ''Developmental Review'', 37, 109–141. https://doi.org/https://doi.org/10.1016/j.dr.2015.06.001 

Sroufe, L. A. (1988). The role of infant-caregiver attachment in development. In ''Clinical implications of attachment''. (pp. 18–38). Lawrence Erlbaum Associates, Inc. 

Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A Review of Self-Determination Theory’s Basic Psychological Needs at Work. ''Journal of Management'', 42(5), 1195-1229. https://doi.org/10.1177/0149206316632058 

Vansteenkiste, M., &amp; Ryan, R. (2013). On Psychological Growth and Vulnerability: Basic Psychological Need Satisfaction and Need Frustration as a Unifying Principle. ''Journal of Psychotherapy Integration'', 23, 263–280. https://doi.org/10.1037/a0032359 

Vaughn, B. E., &amp; Waters, E. (1990). Attachment Behavior at Home and in the Laboratory: Q-Sort Observations and Strange Situation Classifications of One-Year-Olds. ''Child Development'', 61(6), 1965–1973. https://doi.org/10.2307/1130850 

Zeanah, C. H., Berlin, L. J., &amp; Boris, N. W. (2011). Practitioner review: clinical applications of attachment theory and research for infants and young children. ''J Child Psychol Psychiatry'', 52(8), 819–833. https://doi.org/10.1111/j.1469-7610.2011.02399.x 

Zeanah, C. H., Boris, N. W., &amp; Larrieu, J. A. (1997). Infant Development and Developmental Risk: A Review of the Past 10 Years. ''Journal of the American Academy of Child &amp; Adolescent Psychiatry'', 36(2), 165–178. https://doi.org/https://doi.org/10.1097/00004583-199702000-00007 

}}

==External links==
* [https://www.attachmentproject.com/attachment-theory/john-bowlby/ Bowlby and attachment theory: insights and legacy] (attachmentproject.com)
* [https://www.simplypsychology.org/self-determination-theory.html Self-determination theory of motivation] (simplypsychology.org)
* [https://selfdeterminationtheory.org/theory/ Theory] (selfdeterminationtheory.org)
* [https://youtu.be/GHHCy1IHTUc Maunder and Hunter: intro to adult attachment] (YouTube.com)

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__TOC__
==Overview==
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[[File:People and stands at the Museum Reserve, Orientation Week MS-5342 012 002.jpg|thumb|'''Figure 1'''. People and stands at the Museum Reserve, Orientation Week]]


Harry and Caitlin have both recently moved to a new neighbourhood and are adjusting to their new community. 

Harry makes an effort to meet people by attending local social events. He enjoys feeling included, but when plans are made without him or a message goes unanswered, he wonders whether people actually like him. After spending time with his new neighbours, he replays conversations and worries about whether he said or did something wrong.

Caitlin also enjoys meeting her neighbours and likes being included in group activities. She chats easily with people at events but often turns down invitations to spend more time together. When conversations turn more personal or neighbours begin trying to get to know her better, she changes the subject, leaves early, and may decide to avoid the next event. Although she enjoys being part of the neighbourhood, she finds keeping some distance more comfortable. 

Harry and Caitlin both appear to value connection and belonging, yet their need for relatedness seems to be experienced and expressed in very different ways
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Relatedness, the need to feel connected, cared for, and significant to others (Van den Broeck et al., 2016), is considered a basic psychological need within [[wikipedia:Self-determination_theory|self-determination theory]]. Satisfaction of relatedness is associated with positive psychological functioning, whereas frustration of relatedness is associated poorer psychological functioning (Chen et al., 2015) '''(more detail?)''', highlighting the importance of understanding the factors that support or interfere with relatedness satisfaction.  However, despite relatedness being proposed as a universal psychological need, individuals differ in how they seek connection and experience relatedness satisfaction. 

One factor that may explain these differences is attachment style. Attachment theory proposes that experiences with attachment figures during infancy contribute to expectations about the availability and responsiveness of others, which influences how attachment-related needs are regulated and expressed. In adulthood, secure, anxious-preoccupied, dismissive-avoidant, and fearful-avoidant attachment styles are associated with different patterns of seeking and responding to connection and support. 

This chapter investigates whether adult attachment styles shape how relatedness is experienced, expressed, pursued, and satisfied or influence the need for relatedness itself. Additionally, it considers whether experiences of relatedness satisfaction or frustration may contribute to changes in attachment style over time.
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* How do different attachment styles influence the way the need for relatedness is experienced and expressed?
* How might experiences of relatedness satisfaction or frustration shape attachment over time?
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==Self-Determination theory and relatedness==
[[wikipedia:Self-determination_theory|Self-determination theory]] (SDT) is an approach to human motivation that seeks to explain the conditions that support or undermine motivation and psychological wellbeing.

A central proposition of SDT is the that individuals have inherent tendencies towards psychological growth, mastery, and connection with others (Ryan &amp; Deci, 2002). 

Within SDT [[wikipedia:Self-determination_theory#:~:text=Summary%20of%20the%20SDT%20mini%2Dtheories|six mini-theories]] address different aspects of motivation and psychological functioning. Of particular relevance to this chapter is the Basic Psychological Needs Theory (BPNT), which proposes that individuals must satisfy three [[wikipedia:Self-determination_theory#:~:text=%5B18%5D-,Basic%20psychological%20needs,-edit|basic psychological needs]], autonomy, competence, and relatedness, for healthy psychological growth and wellbeing (Deci &amp; Ryan, 2000). Satisfaction of these needs is not only important for, psychological growth, effective functioning, and wellbeing, but has been linked to more intrinsic forms of motivation (Deci &amp; Ryan, 2000; Ryan &amp; Deci, 2020).

=== Need satisfaction and frustration ===
Within BPNT, psychological needs can either be satisfied or frustrated depending on the extent to which a person's environment supports or obstructs those needs. 

Need satisfaction occurs when our environments allow for experiences where the psychological need can be fulfilled. It is considered psychologically nourishing and supports motivation, psychological growth, effective functioning, and wellbeing (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013). In contrast, need frustration occurs when a psychological need is actively obstructed or undermined (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013).

Importantly, need frustration is not simply the absence of need satisfaction. A person may experience low need satisfaction because they have fewer opportunities to fulfill a need, whereas need frustration involves an environment that actively thwarts or undermines a need. 

===Relatedness===
Relatedness refers to the  need to feel connected to others, including both the need to care for others and to feel cared for, valued, and significant to others (Van den Broeck et al., 2016). 

Support for relatedness as a universal need has been found across different cultural groups. For example, Chen et al. (2015), found that satisfaction of relatedness, autonomy, and competence was positively associated with wellbeing across samples from Belgium, China, Peru, and the United States. This suggests that the importance of relatedness is not limited to a particular cultural context, although the ways in which connection is expressed or pursued may vary. 

Relatedness satisfaction involves experiencing genuine connection and closeness to others, and a sense of belonging, whereas relatedness frustration involves experiences of rejection, exclusion, disconnection, or loneliness (Chen et al., 2015). 

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[[File:Case Icon.png|left|20px|]] A few weeks later, Harry and Caitlin are invited to a neighbourhood barbecue. 

Harry spends the afternoon talking with several neighbours and is included in plans for another get-together the following weekend. He leaves feeling welcomed and like he is beginning to belong in the community. However, later that week he notices that several neighbours have organised another gathering without inviting him. 

During the barbecue, Caitlin enjoys chatting with people. When one neighbour later invites her over for coffee, she politely declines and does not suggest another time. Although no one has rejected or excluded her. 

Harry’s experience at the barbecue illustrates relatedness satisfaction because he feels welcomed, included, and valued by others, giving him a sense of connection and belonging. When he is later deliberately left out of plans, this may represent relatedness frustration, because the opportunity for connection is undermined through exclusion.

Caitlin’s experience is different. By repeatedly declining invitations and keeping some distance, she may have fewer opportunities to experience meaningful connection, resulting in relatively low relatedness satisfaction. However, because others are still inviting and including her, her need for relatedness is not necessarily being actively thwarted.{{RoundBoxBottom}}

==Attachment theory and styles==
[[wikipedia:Attachment_theory|Attachment theory]] was first developed by John Bowlby to explain the anxiety and distress infants experience when separated from their caregivers. Bowlby observed that infants use attachment behaviours, such as crying, clinging, following, to prevent separation or re-establish proximity to their caregivers (Bowlby, 1958). He proposed that these behaviours form part of an attachment behavioural system (ABS), an innate psychobiological mechanism that motivates infants to seek and maintain closeness to an attachment figure. Bowlby (1982) argued that this system has an evolutionary function, as infants who remained close to caregivers would have been more likely to survive to reproductive age.

Although Bowlby considered the ABS to be universal, he recognised that infants could differ in how attachment was experienced and expressed. He theorised that early experiences with caregivers contribute to internal working models, mental representations of expectations of whether attachment figures are available and responsive, and whether the self is worthy of care and support. These expectations are thought to guide an infants response to situations that activate their ABS, including whether the infant seeks support, intensifies attachment behaviours, or minimises them (Bretherton &amp; Munholland, 2008; Collins &amp; Allard, 2004; Sherman et al., 2015). 

[[wikipedia:Mary_Ainsworth|Mary Ainsworth]] extended Bowlby's work by examining how individual differences in attachment were expressed in infant's behaviour through the [[wikipedia:Strange_situation|Strange Situation procedure]]. The procedure involved observing infants during brief separations and reunions with a caregiver, focusing primarily on exploration, separation and reunion responses, and reactions to a stranger (Ainsworth et al., 1978). Through this, Ainsworth identified three infant attachment patterns, Secure, Anxious-ambivalent/, and Anxious-avoidant—with disorganised-disoriented attachment later identified by Main and Solomon (1986) to describe infant behaviours that did not fit comfortably within Ainsworth’s original classifications (See Table 1.)

'''Table 1'''.

''Infant Attachment Patterns, Associated Caregiving Experiences, and Attachment Strategies''
{| class=&quot;wikitable&quot;
|+
!Infant attachment style
!Typical attachment response
!Associated caregiving experiences
!Internal working model
|-
|Secure attachment
|Uses caregiver as a secure base, exploring environment independently while seeking proximity and comfort when distressed. 
|Associated with caregiving that is generally sensitive, responsive, and consistent. 
|Expects caregiver will be available and responsive when support is required. Attachment needs can therefore expressed distress without intensifying or suppressing attachment behaviour.
|-
|Anxious-ambivalent attachment
|Remains highly attentive to  caregiver availability while exploring. May become easily distressed by separation and seeks frequent proximity, attention, or reassurance, while sometimes difficult to soothe. 
|Associated with caregiving that may be inconsistent or unpredictable.
|

Expects caregiver to be inconsistent, causing infant to become attentive to caregiver’s availability and intensify attachment signals in an attempt to obtain a response (hyperactivating strategy). 
|-
|Anxious-avoidant attachment
|May appear unusually independent and spend more time focused on objects, activities, or exploration than on caregiver. Less likely to openly seek comfort or reassurance from the caregiver. 
|Associated with caregiving that may be relatively unresponsive, rejecting, or uncomfortable with expressions of distress. 
|Expects attempts to obtain comfort or support as unlikely to be met with a responsive reaction. Causes infant to minimise or suppress attachment signals (deactivating stratergy).
|-
|Disorganised-disoriented attachment
|Displays contradictory, confused, or disoriented attachment behaviour and may alternate between proximity-seeking and avoidance without a consistent strategy.
|Associated with caregiving that is frightening, frightened, highly disrupted, or unpredictable.Has been found at higher rates in some contexts involving significant adversity. 
|Difficult to explain through one coherent internal working model as infant does not appear to have a consistent strategy for obtaining comfort.

One proposed explanation is that  caregiver may simultaneously represent a source of safety and a source of fear or uncertainty, creating conflict between approaching the caregiver for protection and moving away from them.
|}
''Note''. Caregiving experiences are associated with, rather than solely determining, infant attachment patterns. Adapted from (Ainsworth et al., 1978), Benoit (2004), Main and Solomon (1986), Sherman et al. (2015), Granqvist et al. (2017), Vaughn and Waters (1990), and Zeanah et al. (1997).

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&lt;quiz display=simple&gt;
{How do internal working models help explain differences between infant attachment patterns?
|type=&quot;()&quot;}
- They determine how strongly an infant is biologically attached to their caregiver.
|| Internal working models do not determine whether an infant '''has''' an attachment to their caregiver. Instead, they shape expectations about whether caregivers will be available and responsive, which can influence how the infant seeks comfort and responds when the attachment system is activated.
+ They shape expectations about whether caregivers will be available and responsive when support is needed.
|| Yes. Internal working models develop through attachment experiences and shape expectations about whether attachment figures will be available and responsive.
- They determine how much distress every infant experiences during separation.
|| Internal working models can influence how infants respond when distressed, but they do not simply determine how much separation distress an infant experiences.
&lt;/quiz&gt;
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===Adult attachment theory===
Attachment theory was later extended beyond infancy to explain how attachment may continue into adulthood. Hazan and Shaver (1987) were among the first to construct a self-report measure of adult attachment patterns, though this was in the context of romantic relationships. Their measure was based on the idea that individual differences in the ways adults engage in romantic relationships echo Ainsworth's classifications.

Bartholomew (1990), and Bartholomew and Horowitz (1991) later created a four-factor moled of adult attachment, proposing that attachment in adulthood could be understood through two underlying dimensions:
* Model of self: Reflects a person's sense of self-worth and whether they feel worthy of love and support. (Bartholomew, 1990)
* Model of others: Reflects whether a person expects others to be available, trustworthy, and supportive (Bartholomew, 1990)
Combining positive and negative models of the self and others produced four adult attachment styles, Secure, Anxious-preoccupied, Dismissive-avoidant, Fearful-avoidant (Alareqe et al., 2021). 

==== Attachment anxiety and avoidance ====
Although Bartholomew's model describes four attachment styles, contemporary adult attachment research often assess attachment along the continuous dimensions of attachment anxiety and attachment avoidance
* Attachment anxiety: the degree to which individuals worry about being underappreciated or abandoned by their romantic partners   (Simpson &amp; Steven Rholes, 2017).
* Attachment avoidance: the degree to which individuals are comfortable with closeness and emotional intimacy in relationships (Simpson &amp; Steven Rholes, 2017).[[File:Four Adult Attachment Styles Based on Models of Self and Others and Attachment Anxiety and Avoidance.svg|thumb|465x465px|'''Figure 2'''. Diagram of Bartholomew’s four adult attachment styles based on models of self and others, and their correspondence with attachment anxiety and attachment avoidance.                                                                                      ''Note''. Adapted from Alareqe et al. (2021), Bartholomew (1990), Bartholomew and Horowitz (1991), Kang et al. (2015), and Morse et al. (2012).]]
Using factor and hierarchical cluster analyses, Brennan et al. (1998) identified attachment anxiety and avoidance as two underlying dimensions of adult attachment and demonstrated that different combination of these dimensions broadly correspond to Bartholomew and Horowitz's four attachment styles (see Figure 2).

Because contemporary research commonly measures attachment along the continuous dimensions of attachment anxiety and avoidance, this chapter draws on evidence from both dimensional and categorical approaches when examining attachment and relatedness. Where studies report findings for attachment anxiety and avoidance, these findings are interpreted in relation to the attachment styles they are most consistent with based on their established dimensional profiles. However, these interpretations should be used cautiously, as dimensional findings do not directly demonstrate effects for categorical attachment styles.

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[[File:Case Icon.png|left|20px|]] continue case study
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{Adult attachment is completely determined by experiences in infancy.
|type=&quot;()&quot;}
+ TRUE.
|| Not quite. Early attachment experiences may contribute to the development of internal working models, but attachment is not considered permanently fixed and may change across later experiences and relationships.
- FALSE.
|| Correct. Early attachment experiences may influence internal working models and later attachment patterns, but adult attachment is not completely determined by infancy and may change across time and experience.
&lt;/quiz&gt;
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== Attachment styles and the need for relatedness ==
Self-determination theory proposes that relatedness is a universal psychological need, suggesting that individuals require experiences of connection, belonging, and significance to others. However, attachment theory indicates that people differ considerably in how they approach closeness, interpret the availability of others, and respond when connection is uncertain or threatened. This raises an important question: do attachment styles influence the strength of the need for relatedness itself, or do they primarily influence how that need is experienced, expressed, pursued, and satisfied?

At first glance, behavioural differences between attachment styles could be interpreted as differences in relatedness need strength. For example, anxious-preoccupied attachment is characterised by strong proximity-seeking and concern about acceptance, which could suggest a greater need for relatedness, while dismissive-avoidant attachment is associated with greater interpersonal distance and self-reliance, which could appear to indicate a weaker need. However, differences in the outward pursuit of connection do not necessarily demonstrate differences in the underlying psychological need. They may instead reflect different strategies for regulating a need that remains important across attachment orientations.

=== '''Does attachment style influence the strength of the relatedness need?''' ===
Research examining the need to belong provides mixed evidence regarding whether attachment styles differ in the strength of their motivation for connection. Although the need to belong is not identical to SDT's relatedness construct, it provides useful converging evidence as both concern the psychological importance of social connection and acceptance.

Lavigne et al. (2011) distinguished between two orientations towards belonging, a growth orientation, in which social connection is pursued as a source of development and positive experience, and a deficit-reduction orientation, in which connection is pursued to compensate for feelings of social deficiency or insecurity. In their third study, secure attachment positively predicted a growth orientation, whereas preoccupied attachment positively predicted a deficit-reduction orientation and a stronger self-reported need to belong. Dismissing-avoidant attachment, in contrast, negatively predicted both deficit-reduction orientation and reported need to belong. These findings could be interpreted as evidence that preoccupied individuals possess a stronger need for connection while dismissing individuals possess a weaker one.

However, this interpretation requires caution. Lavigne et al. (2011) relied on self-report measures in a predominantly university sample and used a correlational design, meaning the findings cannot establish whether attachment causes differences in relatedness motivation. More importantly, self-reported strength of belonging may itself be influenced by attachment regulation. Individuals with a dismissive-avoidant attachment style may consciously minimise the importance of connection as part of a deactivating strategy, whereas preoccupied individuals may be particularly aware of and focused on unmet connection needs. Consequently, differences in reported need may reflect differences in awareness, expression, or regulation rather than actual differences in whether the underlying need exists.

This interpretation is supported by Leary et al. (2013), who found that need to belong was distinguishable from attachment insecurity rather than simply representing another measure of insecure attachment. Their findings challenge the assumption that high attachment anxiety can be equated with a stronger relatedness need, or that high avoidance necessarily indicates a weaker one. Instead, attachment insecurity and the strength of belonging motivation appear to represent related but distinct constructs.

Experimental evidence concerning dismissive and avoidant attachment further challenges the idea that these individuals have little need for connection Carvallo and Gabriel (2006) specifically examined individuals with dismissing-avoidant attachment, who commonly report comfort without close interpersonal involvement. Despite this apparent self-sufficiency, highly dismissing participants showed increased positive affect and state self-esteem after receiving social. If dismissing individuals genuinely possessed little need for connection, social acceptance would be expected to have relatively little psychological value. Instead, their positive response suggests that the need for connection may remain psychologically significant even when it is consciously downplayed or behaviourally avoided.

MacDonald and Borsook (2010)provide converging experimental evidence. In a brief social-interaction study, participants high and low in attachment avoidance interacted with either a highly positive or mildly negative confederate. Both groups reported greater feelings of connection following the positive interaction, and the effect was actually stronger among participants higher in avoidance. Although the study involved a small sample and measured immediate feelings of connection rather than SDT relatedness satisfaction, the findings provide further evidence that avoidant individuals remain responsive to positive social experiences.

Taken together, these studies suggest that attachment style may have a stronger influence on the '''orientation and expression of relatedness motivation''' than on the existence of the need itself. Preoccupied attachment may heighten conscious concern with acceptance and belonging, whereas dismissive attachment may involve downplaying or suppressing the importance of connection. However, evidence that avoidant individuals continue to respond positively to acceptance and connection is difficult to reconcile with the claim that they simply possess a weaker underlying need for relatedness.

=== '''Attachment and relatedness satisfaction''' ===
A separate question is whether attachment influences how successfully the need for relatedness is satisfied. Here, the evidence is somewhat stronger.

Lin (2016) directly examined attachment in relation to SDT relatedness satisfaction through Facebook use. Secure and anxious attachment were associated with pathways in which greater Facebook use was linked with higher relatedness satisfaction. In contrast, avoidant attachment was not associated with using Facebook in the same way to obtain relatedness satisfaction. These findings suggest that attachment may influence '''how individuals attempt to satisfy relatedness'''. Anxiously attached individuals appeared more likely to use social interaction as a means of pursuing connection, whereas avoidantly attached individuals did not appear to use this particular social context in the same way. Importantly, Lin's findings do not show that individuals with anxious-avoidant attachment style possess less need for relatedness. Facebook represents only one possible route through which connection can be pursued, and the cross-sectional design cannot establish whether attachment caused differences in Facebook behaviour or relatedness satisfaction. The results are therefore better interpreted as evidence that attachment may influence the '''strategies through which relatedness is pursued and obtained''', rather than whether the need exists.

Wei et al. (2005) provides broader evidence linking attachment insecurity with psychological need satisfaction. They found that higher attachment anxiety and avoidance were both associated with lower overall satisfaction of autonomy, competence, and relatedness, with the two attachment dimensions together explaining a substantial proportion of variance in basic psychological need satisfaction. Need satisfaction also mediated associations between attachment insecurity and psychological distress. However, the three psychological needs were combined, meaning it is not possible to determine whether relatedness specifically accounted for these effects. In addition, because the study was cross-sectional, the mediation model should not be interpreted as demonstrating that attachment insecurity causes low need satisfaction, which then causes distress.

More recent evidence improves on this limitation by considering relatedness separately. Chen et al. (2026) found that both attachment anxiety and attachment avoidance were negatively associated specifically with relatedness satisfaction among Chinese university students. '''Importantly, attachment anxiety showed its strongest negative associations with competence and autonomy satisfaction, whereas attachment avoidance was most strongly associated with lower relatedness satisfaction.''' 

This finding is difficult to explain through a simple ‘anxious individuals need more, avoidant individuals need less’ account. Instead, it suggests that different attachment styles may interfere with successful relatedness satisfaction. Chen et al. (2026) proposed that anxiously attached individuals may struggle to satisfy relatedness despite actively seeking closeness and reassurance, because heightened concern about rejection and uncertainty about others’ availability can make reassurance difficult to maintain. In contrast, avoidantly attached individuals may restrict opportunities for relatedness satisfaction by maintaining emotional distance, prioritising self-reliance, and being less willing to seek support or engage with opportunities for closeness. In both cases, the underlying need for relatedness may remain present, while the strategies used to regulate that need reduce the likelihood that it will be consistently satisfied

=== '''Attachment and relatedness frustration''' ===
Attachment may also influence how individuals respond when relatedness is threatened or frustrated. DeWall et al. (2012) examined neural responses during simulated social exclusion and found contrasting patterns for attachment anxiety and avoidance. Higher attachment anxiety was associated with greater activation in neural regions implicated in rejection-related distress, whereas higher avoidance was associated with reduced activation in these regions.

These findings are consistent with the hyperactivating and deactivating strategies described in attachment theory. Attachment anxiety appears to involve heightened sensitivity to signs of exclusion or rejection, whereas avoidance may involve dampening or suppressing responses to relatedness threat ('''source'''). However, reduced reactivity among avoidant participants should not be interpreted as evidence that rejection is psychologically irrelevant or that the need for relatedness is absent. When considered alongside Carvallo and Gabriel (2006) and MacDonald and Borsook (2010), a different interpretation becomes more plausible, avoidant individuals may suppress or deactivate responses to threatened connection while still benefiting psychologically when connection and acceptance are available.

This distinction is important because relatedness frustration concerns the '''active thwarting''' of connection, whereas attachment style concerns the strategies used to respond to that threat. Attachment anxiety may therefore amplify the experience and expression of relatedness frustration, while attachment avoidance may reduce its overt expression. Neither pattern necessarily demonstrates a fundamental difference in whether relatedness is needed.

=== '''Can relatedness experiences shape attachment over time?''' ===
The relationship between attachment and relatedness may also operate in the opposite direction. Much of the research discussed above implicitly assumes that attachment style influences later experiences of connection. However, attachment is not completely fixed, and repeated experiences of psychological need satisfaction may also contribute to greater attachment security.

La Guardia et al. (2000) examined variations in attachment security across different relationships and found that people did not necessarily display the same level of security with every relational partner. Greater fulfilment of autonomy, competence, and relatedness within a particular relationship was associated with greater attachment security and more positive models of self and others within that relationship. These findings challenge a strictly one-directional model in which early attachment determines later interpersonal functioning.

At the same time, La Guardia et al. (2000) did not demonstrate that relatedness satisfaction alone caused increases in attachment security. The effects remained when relatedness was removed from the overall need-satisfaction measure, indicating that autonomy and competence also contributed to attachment security. The study therefore supports a broader '''reciprocal model''' in which attachment may shape how individuals seek and experience connection, while need-supportive experiences may in turn reinforce more secure expectations about the self and others.

==Conclusion==
* The Conclusion is arguably the most important section
* Draft clear take-home message(s), even at the topic development stage
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
* [[wikipedia:Attachment_in_adults|Attachment in adults]] (Wikipedia)
* [[wikipedia:Self-determination_theory|Self-determination theory]] (Wikipedia)
* [[Motivation and emotion/Book/2016/Attachment type and emotion|Attachment type and emotion]] (Wikiversity)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Wikiversity)

==References==
{{Hanging indent|1=

Ainsworth, M. D. S., Blehar, M. C., Waters, E., &amp; Wall, S. (1978). ''Patterns of attachment: A psychological study of the strange situation''. Lawrence Erlbaum. 

Bartholomew, K. (1990). Avoidance of Intimacy: An Attachment Perspective. ''Journal of Social and Personal Relationships'', 7(2), 147–178. https://doi.org/10.1177/0265407590072001 

Bartholomew, K., &amp; Horowitz, L. (1991). Attachment Styles Among Young Adults: A Test of a Four-Category Model. ''Journal of Personality and Social Psychology'', 61, 226–244. https://doi.org/10.1037/0022-3514.61.2.226 

Benoit, D. (2004). Infant-parent attachment: Definition, types, antecedents, measurement and outcome. ''Paediatrics &amp; Child Health'', 9(8), 541–545. https://doi.org/10.1093/pch/9.8.541 

Bowlby, J. (1958). The nature of the child's tie to his mother. ''Int J Psychoanal'', 39(5), 350–373. 

Bowlby, J. (1982). Attachment and loss: Retrospect and prospect. American ''Journal of Orthopsychiatry'', 52(4), 664–678. https://doi.org/10.1111/j.1939-0025.1982.tb01456.x 

Bretherton, I., &amp; Munholland, K. A. (2008). Internal working models in attachment relationships: Elaborating a central construct in attachment theory. In ''Handbook of attachment: Theory, research, and clinical applications'', 2nd ed. (pp. 102–127). The Guilford Press. 

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. ''Motivation and Emotion'', 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1 

Collins, N. L., &amp; Allard, L. M. (2003). Cognitive Representations of Attachment: The Content and Function of Working Models. In Garth J. O. Fletcher &amp; M. S. Clark (Eds.), ''Blackwell Handbook of Social Psychology: Interpersonal Processes'' (pp. 60–85). Blackwell Publishing. https://doi.org/https://doi.org/10.1002/9780470998557.ch3 

Deci, E. L., &amp; Ryan, R. M. (2000). The &quot;What&quot; and &quot;Why&quot; of Goal Pursuits: Human Needs and the Self-Determination of Behavior. ''Psychological Inquiry'', 11(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 

Duschinsky, R. (2018). Disorganization, fear and attachment: working towards clarification. ''Infant Ment Health J'', 39(1), 17–29. https://doi.org/10.1002/imhj.21689 

Granqvist, P., Sroufe, L. A., Dozier, M., Hesse, E., Steele, M., van Ijzendoorn, M., Solomon, J., Schuengel, C., Fearon, P., Bakermans-Kranenburg, M., Steele, H., Cassidy, J., Carlson, E., Madigan, S., Jacobvitz, D., Foster, S., Behrens, K., Rifkin-Graboi, A., Gribneau, N.,…Duschinsky, R. (2017). Disorganized attachment in infancy: a review of the phenomenon and its implications for clinicians and policy-makers. ''Attachment &amp; Human Development'', 19(6), 534–558. https://doi.org/10.1080/14616734.2017.1354040 

Hazan, C., &amp; Shaver, P. (1987). Romantic love conceptualized as an attachment process. ''J Pers Soc Psychol'', 52(3), 511–524. https://doi.org/10.1037//0022-351

Main, M., &amp; Solomon, J. (1986). Discovery of An Insecure Disorganized Disoriented Attachment Pattern. In T. B. Brazelton &amp; M. W. Yogman (Eds.), ''Affective development in infancy'' (pp. 95–124). Ablex Publishing. 

Perasso, G. (2023). Strange Situation Procedure (SSP). In T. K. Shackelford (Ed.), ''Encyclopedia of Sexual Psychology and Behavior''. Springer, Cham. https://doi.org/https://doi.org/10.1007/978-3-031-08956-5_128-1 

Ryan, R. M., &amp; Deci, E. L. (2002). Overview of self-determination theory: An organismic-dialectical perspective. In ''Handbook of self-determination research''. (pp. 3–33). University of Rochester Press. 

Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology'', 61, 101860. https://doi.org/https://doi.org/10.1016/j.cedpsych.2020.101860 

Sherman, L. J., Rice, K., &amp; Cassidy, J. (2015). Infant capacities related to building internal working models of attachment figures: A theoretical and empirical review. ''Developmental Review'', 37, 109–141. https://doi.org/https://doi.org/10.1016/j.dr.2015.06.001 

Sroufe, L. A. (1988). The role of infant-caregiver attachment in development. In ''Clinical implications of attachment''. (pp. 18–38). Lawrence Erlbaum Associates, Inc. 

Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A Review of Self-Determination Theory’s Basic Psychological Needs at Work. ''Journal of Management'', 42(5), 1195-1229. https://doi.org/10.1177/0149206316632058 

Vansteenkiste, M., &amp; Ryan, R. (2013). On Psychological Growth and Vulnerability: Basic Psychological Need Satisfaction and Need Frustration as a Unifying Principle. ''Journal of Psychotherapy Integration'', 23, 263–280. https://doi.org/10.1037/a0032359 

Vaughn, B. E., &amp; Waters, E. (1990). Attachment Behavior at Home and in the Laboratory: Q-Sort Observations and Strange Situation Classifications of One-Year-Olds. ''Child Development'', 61(6), 1965–1973. https://doi.org/10.2307/1130850 

Zeanah, C. H., Berlin, L. J., &amp; Boris, N. W. (2011). Practitioner review: clinical applications of attachment theory and research for infants and young children. ''J Child Psychol Psychiatry'', 52(8), 819–833. https://doi.org/10.1111/j.1469-7610.2011.02399.x 

Zeanah, C. H., Boris, N. W., &amp; Larrieu, J. A. (1997). Infant Development and Developmental Risk: A Review of the Past 10 Years. ''Journal of the American Academy of Child &amp; Adolescent Psychiatry'', 36(2), 165–178. https://doi.org/https://doi.org/10.1097/00004583-199702000-00007 

}}

==External links==
* [https://www.attachmentproject.com/attachment-theory/john-bowlby/ Bowlby and attachment theory: insights and legacy] (attachmentproject.com)
* [https://www.simplypsychology.org/self-determination-theory.html Self-determination theory of motivation] (simplypsychology.org)
* [https://selfdeterminationtheory.org/theory/ Theory] (selfdeterminationtheory.org)
* [https://youtu.be/GHHCy1IHTUc Maunder and Hunter: intro to adult attachment] (YouTube.com)

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      <text bytes="40445" sha1="d5sci6uzo0gqeb90s9qw2py04iyt0ns" xml:space="preserve">{{title|Attachment styles and relatedness motivation:&lt;br&gt;How do attachment styles shape the need for relatedness?}}
__TOC__
==Overview==
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[[File:People and stands at the Museum Reserve, Orientation Week MS-5342 012 002.jpg|thumb|'''Figure 1'''. People and stands at the Museum Reserve, Orientation Week]]


Harry and Caitlin have both recently moved to a new neighbourhood and are adjusting to their new community. 

Harry makes an effort to meet people by attending local social events. He enjoys feeling included, but when plans are made without him or a message goes unanswered, he wonders whether people actually like him. After spending time with his new neighbours, he replays conversations and worries about whether he said or did something wrong.

Caitlin also enjoys meeting her neighbours and likes being included in group activities. She chats easily with people at events but often turns down invitations to spend more time together. When conversations turn more personal or neighbours begin trying to get to know her better, she changes the subject, leaves early, and may decide to avoid the next event. Although she enjoys being part of the neighbourhood, she finds keeping some distance more comfortable. 

Harry and Caitlin both appear to value connection and belonging, yet their need for relatedness seems to be experienced and expressed in very different ways
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Relatedness, the need to feel connected, cared for, and significant to others (Van den Broeck et al., 2016), is considered a basic psychological need within [[wikipedia:Self-determination_theory|self-determination theory]]. Satisfaction of relatedness is associated with positive psychological functioning, whereas frustration of relatedness is associated poorer psychological functioning (Chen et al., 2015) '''(more detail?)''', highlighting the importance of understanding the factors that support or interfere with relatedness satisfaction.  However, despite relatedness being proposed as a universal psychological need, individuals differ in how they seek connection and experience relatedness satisfaction. 

One factor that may explain these differences is attachment style. Attachment theory proposes that experiences with attachment figures during infancy contribute to expectations about the availability and responsiveness of others, which influences how attachment-related needs are regulated and expressed. In adulthood, secure, anxious-preoccupied, dismissive-avoidant, and fearful-avoidant attachment styles are associated with different patterns of seeking and responding to connection and support. 

This chapter investigates whether adult attachment styles shape how relatedness is experienced, expressed, pursued, and satisfied or influence the need for relatedness itself. Additionally, it considers whether experiences of relatedness satisfaction or frustration may contribute to changes in attachment style over time.
{{Robelbox|theme=1|title=Focus questions|iconwidth=48px|icon=Crystal Clear app ktip.svg}}
* How do different attachment styles influence the way the need for relatedness is experienced and expressed?
* How might experiences of relatedness satisfaction or frustration shape attachment over time?
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==Self-Determination theory and relatedness==
[[wikipedia:Self-determination_theory|Self-determination theory]] (SDT) is an approach to human motivation that seeks to explain the conditions that support or undermine motivation and psychological wellbeing.

A central proposition of SDT is the that individuals have inherent tendencies towards psychological growth, mastery, and connection with others (Ryan &amp; Deci, 2002). 

Within SDT [[wikipedia:Self-determination_theory#:~:text=Summary%20of%20the%20SDT%20mini%2Dtheories|six mini-theories]] address different aspects of motivation and psychological functioning. Of particular relevance to this chapter is the Basic Psychological Needs Theory (BPNT), which proposes that individuals must satisfy three [[wikipedia:Self-determination_theory#:~:text=%5B18%5D-,Basic%20psychological%20needs,-edit|basic psychological needs]], autonomy, competence, and relatedness, for healthy psychological growth and wellbeing (Deci &amp; Ryan, 2000). Satisfaction of these needs is not only important for, psychological growth, effective functioning, and wellbeing, but has been linked to more intrinsic forms of motivation (Deci &amp; Ryan, 2000; Ryan &amp; Deci, 2020).

=== Need satisfaction and frustration ===
Within BPNT, psychological needs can either be satisfied or frustrated depending on the extent to which a person's environment supports or obstructs those needs. 

Need satisfaction occurs when our environments allow for experiences where the psychological need can be fulfilled. It is considered psychologically nourishing and supports motivation, psychological growth, effective functioning, and wellbeing (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013). In contrast, need frustration occurs when a psychological need is actively obstructed or undermined (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013).

Importantly, need frustration is not simply the absence of need satisfaction. A person may experience low need satisfaction because they have fewer opportunities to fulfill a need, whereas need frustration involves an environment that actively thwarts or undermines a need. 

===Relatedness===
Relatedness refers to the  need to feel connected to others, including both the need to care for others and to feel cared for, valued, and significant to others (Van den Broeck et al., 2016). 

Support for relatedness as a universal need has been found across different cultural groups. For example, Chen et al. (2015), found that satisfaction of relatedness, autonomy, and competence was positively associated with wellbeing across samples from Belgium, China, Peru, and the United States. This suggests that the importance of relatedness is not limited to a particular cultural context, although the ways in which connection is expressed or pursued may vary. 

Relatedness satisfaction involves experiencing genuine connection and closeness to others, and a sense of belonging, whereas relatedness frustration involves experiences of rejection, exclusion, disconnection, or loneliness (Chen et al., 2015). 

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[[File:Case Icon.png|left|20px|]] A few weeks later, Harry and Caitlin are invited to a neighbourhood barbecue. 

Harry spends the afternoon talking with several neighbours and is included in plans for another get-together the following weekend. He leaves feeling welcomed and like he is beginning to belong in the community. However, later that week he notices that several neighbours have organised another gathering without inviting him. 

During the barbecue, Caitlin enjoys chatting with people. When one neighbour later invites her over for coffee, she politely declines and does not suggest another time. Although no one has rejected or excluded her. 

Harry’s experience at the barbecue illustrates relatedness satisfaction because he feels welcomed, included, and valued by others, giving him a sense of connection and belonging. When he is later deliberately left out of plans, this may represent relatedness frustration, because the opportunity for connection is undermined through exclusion.

Caitlin’s experience is different. By repeatedly declining invitations and keeping some distance, she may have fewer opportunities to experience meaningful connection, resulting in relatively low relatedness satisfaction. However, because others are still inviting and including her, her need for relatedness is not necessarily being actively thwarted.{{RoundBoxBottom}}

==Attachment theory and styles==
[[wikipedia:Attachment_theory|Attachment theory]] was first developed by John Bowlby to explain the anxiety and distress infants experience when separated from their caregivers. Bowlby observed that infants use attachment behaviours, such as crying, clinging, following, to prevent separation or re-establish proximity to their caregivers (Bowlby, 1958). He proposed that these behaviours form part of an attachment behavioural system (ABS), an innate psychobiological mechanism that motivates infants to seek and maintain closeness to an attachment figure. Bowlby (1982) argued that this system has an evolutionary function, as infants who remained close to caregivers would have been more likely to survive to reproductive age.

Although Bowlby considered the ABS to be universal, he recognised that infants could differ in how attachment was experienced and expressed. He theorised that early experiences with caregivers contribute to internal working models, mental representations of expectations of whether attachment figures are available and responsive, and whether the self is worthy of care and support. These expectations are thought to guide an infants response to situations that activate their ABS, including whether the infant seeks support, intensifies attachment behaviours, or minimises them (Bretherton &amp; Munholland, 2008; Collins &amp; Allard, 2004; Sherman et al., 2015). 

[[wikipedia:Mary_Ainsworth|Mary Ainsworth]] extended Bowlby's work by examining how individual differences in attachment were expressed in infant's behaviour through the [[wikipedia:Strange_situation|Strange Situation procedure]]. The procedure involved observing infants during brief separations and reunions with a caregiver, focusing primarily on exploration, separation and reunion responses, and reactions to a stranger (Ainsworth et al., 1978). Through this, Ainsworth identified three infant attachment patterns, Secure, Anxious-ambivalent/, and Anxious-avoidant—with disorganised-disoriented attachment later identified by Main and Solomon (1986) to describe infant behaviours that did not fit comfortably within Ainsworth’s original classifications (See Table 1.)

'''Table 1'''.

''Infant Attachment Patterns, Associated Caregiving Experiences, and Attachment Strategies''
{| class=&quot;wikitable&quot;
|+
!Infant attachment style
!Typical attachment response
!Associated caregiving experiences
!Internal working model
|-
|Secure attachment
|Uses caregiver as a secure base, exploring environment independently while seeking proximity and comfort when distressed. 
|Associated with caregiving that is generally sensitive, responsive, and consistent. 
|Expects caregiver will be available and responsive when support is required. Attachment needs can therefore expressed distress without intensifying or suppressing attachment behaviour.
|-
|Anxious-ambivalent attachment
|Remains highly attentive to  caregiver availability while exploring. May become easily distressed by separation and seeks frequent proximity, attention, or reassurance, while sometimes difficult to soothe. 
|Associated with caregiving that may be inconsistent or unpredictable.
|

Expects caregiver to be inconsistent, causing infant to become attentive to caregiver’s availability and intensify attachment signals in an attempt to obtain a response (hyperactivating strategy). 
|-
|Anxious-avoidant attachment
|May appear unusually independent and spend more time focused on objects, activities, or exploration than on caregiver. Less likely to openly seek comfort or reassurance from the caregiver. 
|Associated with caregiving that may be relatively unresponsive, rejecting, or uncomfortable with expressions of distress. 
|Expects attempts to obtain comfort or support as unlikely to be met with a responsive reaction. Causes infant to minimise or suppress attachment signals (deactivating stratergy).
|-
|Disorganised-disoriented attachment
|Displays contradictory, confused, or disoriented attachment behaviour and may alternate between proximity-seeking and avoidance without a consistent strategy.
|Associated with caregiving that is frightening, frightened, highly disrupted, or unpredictable.Has been found at higher rates in some contexts involving significant adversity. 
|Difficult to explain through one coherent internal working model as infant does not appear to have a consistent strategy for obtaining comfort.

One proposed explanation is that  caregiver may simultaneously represent a source of safety and a source of fear or uncertainty, creating conflict between approaching the caregiver for protection and moving away from them.
|}
''Note''. Caregiving experiences are associated with, rather than solely determining, infant attachment patterns. Adapted from (Ainsworth et al., 1978), Benoit (2004), Main and Solomon (1986), Sherman et al. (2015), Granqvist et al. (2017), Vaughn and Waters (1990), and Zeanah et al. (1997).

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{{Robelbox|theme=2|title=Knowledge Check!|iconwidth=48px|icon=Quiz.png}}
&lt;quiz display=simple&gt;
{How do internal working models help explain differences between infant attachment patterns?
|type=&quot;()&quot;}
- They determine how strongly an infant is biologically attached to their caregiver.
|| Internal working models do not determine whether an infant '''has''' an attachment to their caregiver. Instead, they shape expectations about whether caregivers will be available and responsive, which can influence how the infant seeks comfort and responds when the attachment system is activated.
+ They shape expectations about whether caregivers will be available and responsive when support is needed.
|| Yes. Internal working models develop through attachment experiences and shape expectations about whether attachment figures will be available and responsive.
- They determine how much distress every infant experiences during separation.
|| Internal working models can influence how infants respond when distressed, but they do not simply determine how much separation distress an infant experiences.
&lt;/quiz&gt;
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===Adult attachment theory===
Attachment theory was later extended beyond infancy to explain how attachment may continue into adulthood. Hazan and Shaver (1987) were among the first to construct a self-report measure of adult attachment patterns, though this was in the context of romantic relationships. Their measure was based on the idea that individual differences in the ways adults engage in romantic relationships echo Ainsworth's classifications.

Bartholomew (1990), and Bartholomew and Horowitz (1991) later created a four-factor moled of adult attachment, proposing that attachment in adulthood could be understood through two underlying dimensions:
* Model of self: Reflects a person's sense of self-worth and whether they feel worthy of love and support. (Bartholomew, 1990)
* Model of others: Reflects whether a person expects others to be available, trustworthy, and supportive (Bartholomew, 1990)
Combining positive and negative models of the self and others produced four adult attachment styles, Secure, Anxious-preoccupied, Dismissive-avoidant, Fearful-avoidant (Alareqe et al., 2021). 

==== Attachment anxiety and avoidance ====
Although Bartholomew's model describes four attachment styles, contemporary adult attachment research often assess attachment along the continuous dimensions of attachment anxiety and attachment avoidance
* Attachment anxiety: the degree to which individuals worry about being underappreciated or abandoned by their romantic partners   (Simpson &amp; Steven Rholes, 2017).
* Attachment avoidance: the degree to which individuals are comfortable with closeness and emotional intimacy in relationships (Simpson &amp; Steven Rholes, 2017).[[File:Four Adult Attachment Styles Based on Models of Self and Others and Attachment Anxiety and Avoidance.svg|thumb|465x465px|'''Figure 2'''. Diagram of Bartholomew’s four adult attachment styles based on models of self and others, and their correspondence with attachment anxiety and attachment avoidance.                                                                                      ''Note''. Adapted from Alareqe et al. (2021), Bartholomew (1990), Bartholomew and Horowitz (1991), Kang et al. (2015), and Morse et al. (2012).]]
Using factor and hierarchical cluster analyses, Brennan et al. (1998) identified attachment anxiety and avoidance as two underlying dimensions of adult attachment and demonstrated that different combination of these dimensions broadly correspond to Bartholomew and Horowitz's four attachment styles (see Figure 2).

Because contemporary research commonly measures attachment along the continuous dimensions of attachment anxiety and avoidance, this chapter draws on evidence from both dimensional and categorical approaches when examining attachment and relatedness. Where studies report findings for attachment anxiety and avoidance, these findings are interpreted in relation to the attachment styles they are most consistent with based on their established dimensional profiles. However, these interpretations should be used cautiously, as dimensional findings do not directly demonstrate effects for categorical attachment styles.

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[[File:Case Icon.png|left|20px|]] continue case study
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&lt;quiz display=simple&gt;
{Adult attachment is completely determined by experiences in infancy.
|type=&quot;()&quot;}
+ TRUE.
|| Not quite. Early attachment experiences may contribute to the development of internal working models, but attachment is not considered permanently fixed and may change across later experiences and relationships.
- FALSE.
|| Correct. Early attachment experiences may influence internal working models and later attachment patterns, but adult attachment is not completely determined by infancy and may change across time and experience.
&lt;/quiz&gt;
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== Attachment styles and the need for relatedness ==
Self-determination theory proposes that relatedness is a universal psychological need, suggesting that individuals require experiences of connection, belonging, and significance to others. However, attachment theory indicates that people differ considerably in how they approach closeness, interpret the availability of others, and respond when connection is uncertain or threatened. This raises an important question: do attachment styles influence the strength of the need for relatedness itself, or do they primarily influence how that need is experienced, expressed, pursued, and satisfied?

At first glance, behavioural differences between attachment styles could be interpreted as differences in relatedness need strength. For example, anxious-preoccupied attachment is characterised by strong proximity-seeking and concern about acceptance, which could suggest a greater need for relatedness, while dismissive-avoidant attachment is associated with greater interpersonal distance and self-reliance, which could appear to indicate a weaker need. However, differences in the outward pursuit of connection do not necessarily demonstrate differences in the underlying psychological need. They may instead reflect different strategies for regulating a need that remains important across attachment orientations.

=== '''Does attachment style influence the strength of the relatedness need?''' ===
Research examining the need to belong provides mixed evidence regarding whether attachment styles differ in the strength of their motivation for connection. Although the need to belong is not identical to SDT's relatedness construct, it provides useful converging evidence as both concern the psychological importance of social connection and acceptance.

Lavigne et al. (2011) distinguished between two orientations towards belonging, a growth orientation, in which social connection is pursued as a source of development and positive experience, and a deficit-reduction orientation, in which connection is pursued to compensate for feelings of social deficiency or insecurity. In their third study, secure attachment positively predicted a growth orientation, whereas preoccupied attachment positively predicted a deficit-reduction orientation and a stronger self-reported need to belong. Dismissing-avoidant attachment, in contrast, negatively predicted both deficit-reduction orientation and reported need to belong. These findings could be interpreted as evidence that preoccupied individuals possess a stronger need for connection while dismissing individuals possess a weaker one.

However, this interpretation requires caution. Lavigne et al. (2011) relied on self-report measures in a predominantly university sample and used a correlational design, meaning the findings cannot establish whether attachment causes differences in relatedness motivation. More importantly, self-reported strength of belonging may itself be influenced by attachment regulation. Individuals with a dismissive-avoidant attachment style may consciously minimise the importance of connection as part of a deactivating strategy, whereas preoccupied individuals may be particularly aware of and focused on unmet connection needs. Consequently, differences in reported need may reflect differences in awareness, expression, or regulation rather than actual differences in whether the underlying need exists.

This interpretation is supported by Leary et al. (2013), who found that need to belong was distinguishable from attachment insecurity rather than simply representing another measure of insecure attachment. Their findings challenge the assumption that high attachment anxiety can be equated with a stronger relatedness need, or that high avoidance necessarily indicates a weaker one. Instead, attachment insecurity and the strength of belonging motivation appear to represent related but distinct constructs.

Experimental evidence concerning dismissive and avoidant attachment further challenges the idea that these individuals have little need for connection Carvallo and Gabriel (2006) specifically examined individuals with dismissing-avoidant attachment, who commonly report comfort without close interpersonal involvement. Despite this apparent self-sufficiency, highly dismissing participants showed increased positive affect and state self-esteem after receiving social. If dismissing individuals genuinely possessed little need for connection, social acceptance would be expected to have relatively little psychological value. Instead, their positive response suggests that the need for connection may remain psychologically significant even when it is consciously downplayed or behaviourally avoided.

MacDonald and Borsook (2010)provide converging experimental evidence. In a brief social-interaction study, participants high and low in attachment avoidance interacted with either a highly positive or mildly negative confederate. Both groups reported greater feelings of connection following the positive interaction, and the effect was actually stronger among participants higher in avoidance. Although the study involved a small sample and measured immediate feelings of connection rather than SDT relatedness satisfaction, the findings provide further evidence that avoidant individuals remain responsive to positive social experiences.

Taken together, these studies suggest that attachment style may have a stronger influence on the experience and expression of relatedness motivation than on the existence of the need itself. Preoccupied attachment may heighten conscious concern with acceptance and belonging, whereas dismissive attachment may involve downplaying or suppressing the importance of connection. However, evidence that avoidant individuals continue to respond positively to acceptance and connection is difficult to reconcile with the claim that they simply possess a weaker underlying need for relatedness.

=== '''Attachment and relatedness satisfaction''' ===
A separate question is whether attachment influences how successfully the need for relatedness is satisfied. Here, the evidence is somewhat stronger.

Lin (2016) directly examined attachment in relation to SDT relatedness satisfaction through Facebook use. Secure and anxious attachment were associated with pathways in which greater Facebook use was linked with higher relatedness satisfaction. In contrast, avoidant attachment was not associated with using Facebook in the same way to obtain relatedness satisfaction. These findings suggest that attachment may influence how individuals attempt to satisfy relatedness. Anxiously attached individuals appeared more likely to use social interaction as a means of pursuing connection, whereas avoidantly attached individuals did not appear to use this particular social context in the same way. Importantly, Lin's findings do not show that individuals with anxious-avoidant attachment style possess less need for relatedness. Facebook represents only one possible route through which connection can be pursued, and the cross-sectional design cannot establish whether attachment caused differences in Facebook behaviour or relatedness satisfaction. The results are therefore better interpreted as evidence that attachment may influence the strategies through which relatedness is pursued and obtained, rather than whether the need exists.

Wei et al. (2005) provides broader evidence linking attachment insecurity with psychological need satisfaction. They found that higher attachment anxiety and avoidance were both associated with lower overall satisfaction of autonomy, competence, and relatedness, with the two attachment dimensions together explaining a substantial proportion of variance in basic psychological need satisfaction. Need satisfaction also mediated associations between attachment insecurity and psychological distress. However, the three psychological needs were combined, meaning it is not possible to determine whether relatedness specifically accounted for these effects. In addition, because the study was cross-sectional, the mediation model should not be interpreted as demonstrating that attachment insecurity causes low need satisfaction, which then causes distress.

More recent evidence improves on this limitation by considering relatedness separately. Chen et al. (2026) found that both attachment anxiety and attachment avoidance were negatively associated specifically with relatedness satisfaction among Chinese university students. Importantly, attachment anxiety showed its strongest negative associations with competence and autonomy satisfaction, whereas attachment avoidance was most strongly associated with lower relatedness satisfaction. 

This finding is difficult to explain through a simple ‘anxious individuals need more, avoidant individuals need less’ account. Instead, it suggests that different attachment styles may interfere with successful relatedness satisfaction. Chen et al. (2026) proposed that anxiously attached individuals may struggle to satisfy relatedness despite actively seeking closeness and reassurance, because heightened concern about rejection and uncertainty about others’ availability can make reassurance difficult to maintain. In contrast, avoidantly attached individuals may restrict opportunities for relatedness satisfaction by maintaining emotional distance, prioritising self-reliance, and being less willing to seek support or engage with opportunities for closeness. In both cases, the underlying need for relatedness may remain present, while the strategies used to regulate that need reduce the likelihood that it will be consistently satisfied

Secure and fearful-avoidant attachment provide further insight into how attachment may shape relatedness. Lavigne et al. (2011) found that secure attachment positively predicted a growth-oriented approach to belonging, while Lin (2016) linked secure attachment with greater relatedness satisfaction and wellbeing. This suggests that secure attachment may support a more adaptive experience of relatedness, as individuals are generally more comfortable seeking and accepting connection and are more likely to expect others to be available and responsive

While research specifically examining fearful-avoidant attachment and relatedness is limited, its combination of high attachment anxiety and avoidance provides some indication of how relatedness may be experienced. As established previously, individuals with fearful-avoidant attachment may desire connection while simultaneously expecting rejection or feeling uncomfortable with closeness. Consistent with this, Lavigne et al. (2011) found that fearful attachment was marginally negatively associated with a growth orientation towards belonging, suggesting that connection may be approached less as a secure source of growth. However, because relatively few studies have examined fearful-avoidant attachment specifically in relation to SDT relatedness, conclusions should remain cautious. Evidence from dimensional research nevertheless suggests that the combined influence of anxiety and avoidance may make relatedness particularly difficult to pursue and satisfy consistently.

=== '''Attachment and relatedness frustration''' ===
Attachment may also influence how individuals respond when relatedness is threatened or frustrated. DeWall et al. (2012) examined neural responses during simulated social exclusion and found contrasting patterns for attachment anxiety and avoidance. Higher attachment anxiety was associated with greater activation in neural regions implicated in rejection-related distress, whereas higher avoidance was associated with reduced activation in these regions.

These findings are consistent with the hyperactivating and deactivating strategies described in attachment theory. Attachment anxiety appears to involve heightened sensitivity to signs of exclusion or rejection, whereas avoidance may involve dampening or suppressing responses to relatedness threat ('''source'''). However, reduced reactivity among avoidant participants should not be interpreted as evidence that rejection is psychologically irrelevant or that the need for relatedness is absent. When considered alongside Carvallo and Gabriel (2006) and MacDonald and Borsook (2010), a different interpretation becomes more plausible, avoidant individuals may suppress or deactivate responses to threatened connection while still benefiting psychologically when connection and acceptance are available.

This distinction is important because relatedness frustration concerns the '''active thwarting''' of connection, whereas attachment style concerns the strategies used to respond to that threat. Attachment anxiety may therefore amplify the experience and expression of relatedness frustration, while attachment avoidance may reduce its overt expression. Neither pattern necessarily demonstrates a fundamental difference in whether relatedness is needed.

=== '''Can relatedness experiences shape attachment over time?''' ===
The relationship between attachment and relatedness may also operate in the opposite direction. Much of the research discussed above implicitly assumes that attachment style influences later experiences of connection. However, attachment is not completely fixed, and repeated experiences of psychological need satisfaction may also contribute to greater attachment security.

La Guardia et al. (2000) examined variations in attachment security across different relationships and found that people did not necessarily display the same level of security with every relational partner. Greater fulfilment of autonomy, competence, and relatedness within a particular relationship was associated with greater attachment security and more positive models of self and others within that relationship. These findings challenge a strictly one-directional model in which early attachment determines later interpersonal functioning.

At the same time, La Guardia et al. (2000) did not demonstrate that relatedness satisfaction alone caused increases in attachment security. The effects remained when relatedness was removed from the overall need-satisfaction measure, indicating that autonomy and competence also contributed to attachment security. The study therefore supports a broader '''reciprocal model''' in which attachment may shape how individuals seek and experience connection, while need-supportive experiences may in turn reinforce more secure expectations about the self and others.

==Conclusion==
Different attachment styles appear to shape how the need for relatedness is experienced, expressed, and satisfied rather than whether the need exists. Secure attachment is generally associated with comfort in connection, while anxious-preoccupied attachment involves heightened concern about acceptance and stronger reassurance-seeking. Dismissive-avoidant attachment involves greater distance and deactivation, whereas fearful-avoidant attachment combines a desire for closeness with fear of rejection. 

Relatedness experiences may also shape attachment over time. Repeated experiences of acceptance, support, and connection may strengthen attachment security, while rejection or exclusion may reinforce insecure expectations. In real-world settings, this means that outward behaviour should not be taken as a direct indicator of how much connection a person needs.
{{tip|Attachment style appears to shape how the need for relatedness is experienced and experienced, rather than whether the need exists. Additionally, experiences of acceptance, support, rejection, or exclusion may contribute to changes in attachment over time.
}}

==See also==
* [[wikipedia:Attachment_in_adults|Attachment in adults]] (Wikipedia)
* [[wikipedia:Self-determination_theory|Self-determination theory]] (Wikipedia)
* [[Motivation and emotion/Book/2016/Attachment type and emotion|Attachment type and emotion]] (Wikiversity)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Wikiversity)

==References==
{{Hanging indent|1=

Ainsworth, M. D. S., Blehar, M. C., Waters, E., &amp; Wall, S. (1978). ''Patterns of attachment: A psychological study of the strange situation''. Lawrence Erlbaum. 

Bartholomew, K. (1990). Avoidance of Intimacy: An Attachment Perspective. ''Journal of Social and Personal Relationships'', 7(2), 147–178. https://doi.org/10.1177/0265407590072001 

Bartholomew, K., &amp; Horowitz, L. (1991). Attachment Styles Among Young Adults: A Test of a Four-Category Model. ''Journal of Personality and Social Psychology'', 61, 226–244. https://doi.org/10.1037/0022-3514.61.2.226 

Benoit, D. (2004). Infant-parent attachment: Definition, types, antecedents, measurement and outcome. ''Paediatrics &amp; Child Health'', 9(8), 541–545. https://doi.org/10.1093/pch/9.8.541 

Bowlby, J. (1958). The nature of the child's tie to his mother. ''Int J Psychoanal'', 39(5), 350–373. 

Bowlby, J. (1982). Attachment and loss: Retrospect and prospect. American ''Journal of Orthopsychiatry'', 52(4), 664–678. https://doi.org/10.1111/j.1939-0025.1982.tb01456.x 

Bretherton, I., &amp; Munholland, K. A. (2008). Internal working models in attachment relationships: Elaborating a central construct in attachment theory. In ''Handbook of attachment: Theory, research, and clinical applications'', 2nd ed. (pp. 102–127). The Guilford Press. 

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. ''Motivation and Emotion'', 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1 

Collins, N. L., &amp; Allard, L. M. (2003). Cognitive Representations of Attachment: The Content and Function of Working Models. In Garth J. O. Fletcher &amp; M. S. Clark (Eds.), ''Blackwell Handbook of Social Psychology: Interpersonal Processes'' (pp. 60–85). Blackwell Publishing. https://doi.org/https://doi.org/10.1002/9780470998557.ch3 

Deci, E. L., &amp; Ryan, R. M. (2000). The &quot;What&quot; and &quot;Why&quot; of Goal Pursuits: Human Needs and the Self-Determination of Behavior. ''Psychological Inquiry'', 11(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01 

Duschinsky, R. (2018). Disorganization, fear and attachment: working towards clarification. ''Infant Ment Health J'', 39(1), 17–29. https://doi.org/10.1002/imhj.21689 

Granqvist, P., Sroufe, L. A., Dozier, M., Hesse, E., Steele, M., van Ijzendoorn, M., Solomon, J., Schuengel, C., Fearon, P., Bakermans-Kranenburg, M., Steele, H., Cassidy, J., Carlson, E., Madigan, S., Jacobvitz, D., Foster, S., Behrens, K., Rifkin-Graboi, A., Gribneau, N.,…Duschinsky, R. (2017). Disorganized attachment in infancy: a review of the phenomenon and its implications for clinicians and policy-makers. ''Attachment &amp; Human Development'', 19(6), 534–558. https://doi.org/10.1080/14616734.2017.1354040 

Hazan, C., &amp; Shaver, P. (1987). Romantic love conceptualized as an attachment process. ''J Pers Soc Psychol'', 52(3), 511–524. https://doi.org/10.1037//0022-351

Main, M., &amp; Solomon, J. (1986). Discovery of An Insecure Disorganized Disoriented Attachment Pattern. In T. B. Brazelton &amp; M. W. Yogman (Eds.), ''Affective development in infancy'' (pp. 95–124). Ablex Publishing. 

Perasso, G. (2023). Strange Situation Procedure (SSP). In T. K. Shackelford (Ed.), ''Encyclopedia of Sexual Psychology and Behavior''. Springer, Cham. https://doi.org/https://doi.org/10.1007/978-3-031-08956-5_128-1 

Ryan, R. M., &amp; Deci, E. L. (2002). Overview of self-determination theory: An organismic-dialectical perspective. In ''Handbook of self-determination research''. (pp. 3–33). University of Rochester Press. 

Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology'', 61, 101860. https://doi.org/https://doi.org/10.1016/j.cedpsych.2020.101860 

Sherman, L. J., Rice, K., &amp; Cassidy, J. (2015). Infant capacities related to building internal working models of attachment figures: A theoretical and empirical review. ''Developmental Review'', 37, 109–141. https://doi.org/https://doi.org/10.1016/j.dr.2015.06.001 

Sroufe, L. A. (1988). The role of infant-caregiver attachment in development. In ''Clinical implications of attachment''. (pp. 18–38). Lawrence Erlbaum Associates, Inc. 

Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A Review of Self-Determination Theory’s Basic Psychological Needs at Work. ''Journal of Management'', 42(5), 1195-1229. https://doi.org/10.1177/0149206316632058 

Vansteenkiste, M., &amp; Ryan, R. (2013). On Psychological Growth and Vulnerability: Basic Psychological Need Satisfaction and Need Frustration as a Unifying Principle. ''Journal of Psychotherapy Integration'', 23, 263–280. https://doi.org/10.1037/a0032359 

Vaughn, B. E., &amp; Waters, E. (1990). Attachment Behavior at Home and in the Laboratory: Q-Sort Observations and Strange Situation Classifications of One-Year-Olds. ''Child Development'', 61(6), 1965–1973. https://doi.org/10.2307/1130850 

Zeanah, C. H., Berlin, L. J., &amp; Boris, N. W. (2011). Practitioner review: clinical applications of attachment theory and research for infants and young children. ''J Child Psychol Psychiatry'', 52(8), 819–833. https://doi.org/10.1111/j.1469-7610.2011.02399.x 

Zeanah, C. H., Boris, N. W., &amp; Larrieu, J. A. (1997). Infant Development and Developmental Risk: A Review of the Past 10 Years. ''Journal of the American Academy of Child &amp; Adolescent Psychiatry'', 36(2), 165–178. https://doi.org/https://doi.org/10.1097/00004583-199702000-00007 

}}

==External links==
* [https://www.attachmentproject.com/attachment-theory/john-bowlby/ Bowlby and attachment theory: insights and legacy] (attachmentproject.com)
* [https://www.simplypsychology.org/self-determination-theory.html Self-determination theory of motivation] (simplypsychology.org)
* [https://selfdeterminationtheory.org/theory/ Theory] (selfdeterminationtheory.org)
* [https://youtu.be/GHHCy1IHTUc Maunder and Hunter: intro to adult attachment] (YouTube.com)

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[[Category:Motivation and emotion/Book/Needs/Psychological/Relatedness]]</text>
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      <text bytes="43654" sha1="pmx4rwvz6a48o3ovn0ejjpga1z6mjy7" xml:space="preserve">{{title|Attachment styles and relatedness motivation:&lt;br&gt;How do attachment styles shape the need for relatedness?}}
__TOC__
==Overview==
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[[File:People and stands at the Museum Reserve, Orientation Week MS-5342 012 002.jpg|thumb|'''Figure 1'''. People and stands at the Museum Reserve, Orientation Week]]


Harry and Caitlin have both recently moved to a new neighbourhood and are adjusting to their new community. 

Harry makes an effort to meet people by attending local social events. He enjoys feeling included, but when plans are made without him or a message goes unanswered, he wonders whether people actually like him. After spending time with his new neighbours, he replays conversations and worries about whether he said or did something wrong.

Caitlin also enjoys meeting her neighbours and likes being included in group activities. She chats easily with people at events but often turns down invitations to spend more time together. When conversations turn more personal or neighbours begin trying to get to know her better, she changes the subject, leaves early, and may decide to avoid the next event. Although she enjoys being part of the neighbourhood, she finds keeping some distance more comfortable. 

Harry and Caitlin both appear to value connection and belonging, yet their need for relatedness seems to be experienced and expressed in very different ways
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Relatedness, the need to feel connected, cared for, and significant to others (Van den Broeck et al., 2016), is considered a basic psychological need within [[wikipedia:Self-determination_theory|self-determination theory]]. Satisfaction of relatedness is associated with positive psychological functioning, whereas frustration of relatedness is associated poorer psychological functioning (Chen et al., 2015) '''(more detail?)''', highlighting the importance of understanding the factors that support or interfere with relatedness satisfaction.  However, despite relatedness being proposed as a universal psychological need, individuals differ in how they seek connection and experience relatedness satisfaction. 

One factor that may explain these differences is attachment style. Attachment theory proposes that experiences with attachment figures during infancy contribute to expectations about the availability and responsiveness of others, which influences how attachment-related needs are regulated and expressed. In adulthood, secure, anxious-preoccupied, dismissive-avoidant, and fearful-avoidant attachment styles are associated with different patterns of seeking and responding to connection and support. 

This chapter investigates whether adult attachment styles shape how relatedness is experienced, expressed, pursued, and satisfied, or influences the need for relatedness itself. Additionally, it considers whether experiences of relatedness satisfaction or frustration may contribute to changes in attachment style over time.
{{Robelbox|theme=1|title=Focus questions|iconwidth=48px|icon=Crystal Clear app ktip.svg}}
* How do different attachment styles influence the way the need for relatedness is experienced and expressed?
* How might experiences of relatedness satisfaction or frustration shape attachment over time?
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==Self-Determination theory and relatedness==
[[wikipedia:Self-determination_theory|Self-determination theory]] (SDT) is an approach to human motivation that seeks to explain the conditions that support or undermine motivation and psychological wellbeing.

A central proposition of SDT is the that individuals have inherent tendencies towards psychological growth, mastery, and connection with others (Ryan &amp; Deci, 2002). 

Within SDT [[wikipedia:Self-determination_theory#:~:text=Summary%20of%20the%20SDT%20mini%2Dtheories|six mini-theories]] address different aspects of motivation and psychological functioning. Of particular relevance to this chapter is the Basic Psychological Needs Theory (BPNT), which proposes that individuals must satisfy three [[wikipedia:Self-determination_theory#:~:text=%5B18%5D-,Basic%20psychological%20needs,-edit|basic psychological needs]], autonomy, competence, and relatedness, for healthy psychological growth and wellbeing (Deci &amp; Ryan, 2000). Satisfaction of these needs is not only important for, psychological growth, effective functioning, and wellbeing, but has been linked to more intrinsic forms of motivation (Deci &amp; Ryan, 2000; Ryan &amp; Deci, 2020).

=== Need satisfaction and frustration ===
Within BPNT, psychological needs can either be satisfied or frustrated depending on the extent to which a person's environment supports or obstructs those needs. 

Need satisfaction occurs when the environment allow for experiences where the psychological need can be fulfilled. It is considered psychologically nourishing and supports motivation, psychological growth, effective functioning, and wellbeing (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013). In contrast, need frustration occurs when a psychological need is actively obstructed or undermined (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013).

Importantly, need frustration is not simply the absence of need satisfaction. A person may experience low need satisfaction because they have fewer opportunities to fulfill a need, whereas need frustration involves an environment that actively thwarts or undermines a need. 

===Relatedness===
Relatedness refers to the  need to feel connected to others, including both the need to care for others and to feel cared for, valued, and significant to others (Van den Broeck et al., 2016). 

Support for relatedness as a universal need has been found across different cultural groups. For example, Chen et al., (2015), found that satisfaction of relatedness, autonomy, and competence was positively associated with wellbeing across samples from Belgium, China, Peru, and the United States. This suggests that the importance of relatedness is not limited to a particular cultural context, although the ways in which connection is expressed or pursued may vary. 

Relatedness satisfaction involves experiencing genuine connection and closeness to others, and a sense of belonging, whereas relatedness frustration involves experiences of rejection, exclusion, disconnection, or loneliness (Chen et al., 2015). 

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[[File:Case Icon.png|left|20px|]] A few weeks later, Harry and Caitlin are invited to a neighbourhood barbecue. 

Harry spends the afternoon talking with several neighbours and is included in plans for another get-together the following weekend. He leaves feeling welcomed and like he is beginning to belong in the community. However, later that week he notices that several neighbours have organised another gathering without inviting him. 

During the barbecue, Caitlin enjoys chatting with people. When one neighbour later invites her over for coffee, she politely declines and does not suggest another time. Although no one has rejected or excluded her. 

Harry’s experience at the barbecue illustrates relatedness satisfaction because he feels welcomed, included, and valued by others, giving him a sense of connection and belonging. When he is later deliberately left out of plans, this may represent relatedness frustration, because the opportunity for connection is undermined through exclusion.

Caitlin’s experience is different. By repeatedly declining invitations and keeping some distance, she may have fewer opportunities to experience meaningful connection, resulting in relatively low relatedness satisfaction. However, because others are still inviting and including her, her need for relatedness is not necessarily being actively thwarted.{{RoundBoxBottom}}

==Attachment theory and styles==
[[wikipedia:Attachment_theory|Attachment theory]] was first developed by John Bowlby to explain the anxiety and distress infants experience when separated from their caregivers. Bowlby observed that infants use attachment behaviours, such as crying, clinging, following, to prevent separation or re-establish proximity to their caregivers (Bowlby, 1958). He proposed that these behaviours form part of an attachment behavioural system (ABS), an innate psychobiological mechanism that motivates infants to seek and maintain closeness to an attachment figure. Bowlby (1982) argued that this system has an evolutionary function, as infants who remained close to caregivers would have been more likely to survive to reproductive age.

Although Bowlby considered the ABS to be universal, he recognised that infants could differ in how attachment was experienced and expressed. He theorised that early experiences with caregivers contribute to internal working models, mental representations of expectations of whether attachment figures are available and responsive, and whether the self is worthy of care and support. These expectations are thought to guide an infant's response to situations that activate their ABS, including whether the infant seeks support, intensifies attachment behaviours, or minimises them (Bretherton &amp; Munholland, 2008; Collins &amp; Allard, 2004; Sherman et al., 2015). 

[[wikipedia:Mary_Ainsworth|Mary Ainsworth]] extended Bowlby's work by examining how individual differences in attachment were expressed in infant's behaviour through the [[wikipedia:Strange_situation|Strange Situation procedure]]. The procedure involved observing infants during brief separations and reunions with a caregiver, focusing primarily on exploration, separation and reunion responses, and reactions to a stranger (Ainsworth et al., 1978). Through this, Ainsworth identified three infant attachment patterns, Secure, Anxious-ambivalent/, and Anxious-avoidant—with disorganised-disoriented attachment later identified by Main and Solomon (1986) to describe infant behaviours that did not fit comfortably within Ainsworth’s original classifications (See Table 1.)

'''Table 1'''.

''Infant Attachment Patterns, Associated Caregiving Experiences, and Attachment Strategies''
{| class=&quot;wikitable&quot;
|+
!Infant attachment style
!Typical attachment response
!Associated caregiving experiences
!Internal working model
|-
|Secure attachment
|Uses caregiver as a secure base, exploring environment independently while seeking proximity and comfort when distressed. 
|Associated with caregiving that is generally sensitive, responsive, and consistent. 
|Expects caregiver will be available and responsive when support is required. Attachment needs can therefore expressed distress without intensifying or suppressing attachment behaviour.
|-
|Anxious-ambivalent attachment
|Remains highly attentive to  caregiver availability while exploring. May become easily distressed by separation and seeks frequent proximity, attention, or reassurance, while sometimes difficult to soothe. 
|Associated with caregiving that may be inconsistent or unpredictable.
|

Expects caregiver to be inconsistent, causing infant to become attentive to caregiver’s availability and intensify attachment signals in an attempt to obtain a response (hyperactivating strategy). 
|-
|Anxious-avoidant attachment
|May appear unusually independent and spend more time focused on objects, activities, or exploration than on caregiver. Less likely to openly seek comfort or reassurance from the caregiver. 
|Associated with caregiving that may be relatively unresponsive, rejecting, or uncomfortable with expressions of distress. 
|Expects attempts to obtain comfort or support as unlikely to be met with a responsive reaction. Causes infant to minimise or suppress attachment signals (deactivating stratergy).
|-
|Disorganised-disoriented attachment
|Displays contradictory, confused, or disoriented attachment behaviour and may alternate between proximity-seeking and avoidance without a consistent strategy.
|Associated with caregiving that is frightening, frightened, highly disrupted, or unpredictable.Has been found at higher rates in some contexts involving significant adversity. 
|Difficult to explain through one coherent internal working model as infant does not appear to have a consistent strategy for obtaining comfort.

One proposed explanation is that  caregiver may simultaneously represent a source of safety and a source of fear or uncertainty, creating conflict between approaching the caregiver for protection and moving away from them.
|}
''Note''. Caregiving experiences are associated with, rather than solely determining, infant attachment patterns. Adapted from (Ainsworth et al., 1978), Benoit (2004), Main and Solomon (1986), Sherman et al. (2015), Granqvist et al. (2017), Vaughn and Waters (1990), and Zeanah et al. (1997).

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{{Robelbox|theme=2|title=Knowledge Check!|iconwidth=48px|icon=Quiz.png}}
&lt;quiz display=simple&gt;
{How do internal working models help explain differences between infant attachment patterns?
|type=&quot;()&quot;}
- They determine how strongly an infant is biologically attached to their caregiver.
|| Internal working models do not determine whether an infant '''has''' an attachment to their caregiver. Instead, they shape expectations about whether caregivers will be available and responsive, which can influence how the infant seeks comfort and responds when the attachment system is activated.
+ They shape expectations about whether caregivers will be available and responsive when support is needed.
|| Yes. Internal working models develop through attachment experiences and shape expectations about whether attachment figures will be available and responsive.
- They determine how much distress every infant experiences during separation.
|| Internal working models can influence how infants respond when distressed, but they do not simply determine how much separation distress an infant experiences.
&lt;/quiz&gt;
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===Adult attachment theory===
Attachment theory was later extended beyond infancy to explain how attachment may continue into adulthood. Hazan and Shaver (1987) were among the first to construct a self-report measure of adult attachment patterns, though this was in the context of romantic relationships. Their measure was based on the idea that individual differences in the ways adults engage in romantic relationships echo Ainsworth's classifications.

Bartholomew (1990), and Bartholomew and Horowitz (1991) later created a four-factor moled of adult attachment, proposing that attachment in adulthood could be understood through two underlying dimensions:
* Model of self: Reflects a person's sense of self-worth and whether they feel worthy of love and support. (Bartholomew, 1990)
* Model of others: Reflects whether a person expects others to be available, trustworthy, and supportive (Bartholomew, 1990)
Combining positive and negative models of the self and others produced four adult attachment styles, Secure, Anxious-preoccupied, Dismissive-avoidant, Fearful-avoidant (Alareqe et al., 2021). 

==== Attachment anxiety and avoidance ====
Although Bartholomew's model describes four attachment styles, contemporary adult attachment research often assess attachment along the continuous dimensions of attachment anxiety and attachment avoidance
* Attachment anxiety: the degree to which individuals worry about being underappreciated or abandoned by their romantic partners   (Simpson &amp; Steven Rholes, 2017).
* Attachment avoidance: the degree to which individuals are comfortable with closeness and emotional intimacy in relationships (Simpson &amp; Steven Rholes, 2017).[[File:Four Adult Attachment Styles Based on Models of Self and Others and Attachment Anxiety and Avoidance.svg|thumb|465x465px|'''Figure 2'''. Diagram of Bartholomew’s four adult attachment styles based on models of self and others, and their correspondence with attachment anxiety and attachment avoidance.                                                                                      ''Note''. Adapted from Alareqe et al. (2021), Bartholomew (1990), Bartholomew and Horowitz (1991), Kang et al. (2015), and Morse et al. (2012).]]
Using factor and hierarchical cluster analyses, Brennan et al. (1998) identified attachment anxiety and avoidance as two underlying dimensions of adult attachment and demonstrated that different combinations of these dimensions broadly correspond to Bartholomew and Horowitz's four attachment styles (see Figure 2).

Because contemporary research commonly measures attachment along the continuous dimensions of attachment anxiety and avoidance, this chapter draws on evidence from both dimensional and categorical approaches when examining attachment and relatedness. Where studies report findings for attachment anxiety and avoidance, these findings are interpreted in relation to the attachment styles they are most consistent with based on their established dimensional profiles. However, these interpretations should be used cautiously, as dimensional findings do not directly demonstrate effects for categorical attachment styles.

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{Adult attachment is completely determined by experiences in infancy.
|type=&quot;()&quot;}
+ TRUE.
|| Not quite. Early attachment experiences may contribute to the development of internal working models, but attachment is not considered permanently fixed and may change across later experiences and relationships.
- FALSE.
|| Correct. Early attachment experiences may influence internal working models and later attachment patterns, but adult attachment is not completely determined by infancy and may change across time and experience.
&lt;/quiz&gt;
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== Attachment styles and the need for relatedness ==
Self-determination theory proposes that relatedness is a universal psychological need, suggesting that individuals require experiences of connection, belonging, and significance to others. However, attachment theory indicates that people differ considerably in how they approach closeness, interpret the availability of others, and respond when connection is uncertain or threatened. This raises an important question: do attachment styles influence the strength of the need for relatedness itself, or do they primarily influence how that need is experienced, expressed, pursued, and satisfied?

At first glance, behavioural differences between attachment styles could be interpreted as differences in relatedness strength. For example, anxious-preoccupied attachment is characterised by strong proximity-seeking and concern about acceptance, which could suggest a greater need for relatedness, while dismissive-avoidant attachment is associated with greater interpersonal distance and self-reliance, which could appear to indicate a weaker need. However, differences in the outward pursuit of connection do not necessarily demonstrate differences in the underlying psychological need. They may instead reflect different strategies for regulating a need that remains important across attachment orientations.

=== '''Does attachment style influence the strength of the relatedness need?''' ===
Research examining the need to belong provides mixed evidence regarding whether attachment styles differ in the strength of their motivation for connection. Although the need to belong is not identical to SDT's relatedness construct, it provides useful converging evidence as both concern the psychological importance of social connection and acceptance.

Lavigne et al. (2011) distinguished between two orientations towards belonging, a growth orientation, in which social connection is pursued as a source of development and positive experience, and a deficit-reduction orientation, in which connection is pursued to compensate for feelings of social deficiency or insecurity. In their third study, secure attachment positively predicted a growth orientation, whereas preoccupied attachment positively predicted a deficit-reduction orientation and a stronger self-reported need to belong. Dismissing-avoidant attachment, in contrast, negatively predicted both deficit-reduction orientation and reported need to belong. These findings could be interpreted as evidence that preoccupied individuals possess a stronger need for connection while dismissive-avoidant individuals possess a weaker one.

However, this interpretation requires caution. Lavigne et al. (2011) relied on self-report measures in a predominantly university sample and used a correlational design, meaning the findings cannot establish whether attachment causes differences in relatedness motivation. More importantly, self-reported strength of belonging may itself be influenced by attachment regulation. Individuals with a dismissive-avoidant attachment style may consciously minimise the importance of connection as part of a deactivating strategy, whereas preoccupied individuals may be particularly aware of and focused on unmet connection needs. Consequently, differences in reported need may reflect differences in awareness, expression, or regulation rather than actual differences in whether the underlying need exists.

This interpretation is supported by Leary et al. (2013), who found that need to belong was distinguishable from attachment insecurity rather than simply representing another measure of insecure attachment. Their findings challenge the assumption that high attachment anxiety can be equated with a stronger relatedness need, or that high avoidance necessarily indicates a weaker one. Instead, attachment insecurity and the strength of belonging motivation appear to represent related but distinct constructs.

Experimental evidence concerning dismissive and avoidant attachment further challenges the idea that these individuals have little need for connection Carvallo and Gabriel (2006) specifically examined individuals with dismissing-avoidant attachment, who commonly report comfort without close interpersonal involvement. Despite this apparent self-sufficiency, highly dismissing participants showed increased positive affect and state self-esteem after receiving social. If dismissing individuals genuinely possessed little need for connection, social acceptance would be expected to have relatively little psychological value. Instead, their positive response suggests that the need for connection may remain psychologically significant even when it is consciously downplayed or behaviourally avoided.

MacDonald and Borsook (2010) provide converging experimental evidence. In a brief social-interaction study, participants high and low in attachment avoidance interacted with either a highly positive or mildly negative confederate. Both groups reported greater feelings of connection following the positive interaction, and the effect was actually stronger among participants higher in avoidance. Although the study involved a small sample and measured immediate feelings of connection rather than SDT relatedness satisfaction, the findings provide further evidence that avoidant individuals remain responsive to positive social experiences.

Taken together, these studies suggest that attachment style may have a stronger influence on the experience and expression of relatedness motivation than on the existence of the need itself. Preoccupied attachment may heighten conscious concern with acceptance and belonging, whereas dismissive attachment may involve downplaying or suppressing the importance of connection. However, evidence that avoidant individuals continue to respond positively to acceptance and connection is difficult to reconcile with the claim that they simply possess a weaker underlying need for relatedness.

=== '''Attachment and relatedness satisfaction''' ===
A separate question is whether attachment influences how successfully the need for relatedness is satisfied. Here, the evidence is somewhat stronger.

Lin (2016) directly examined attachment in relation to SDT relatedness satisfaction through Facebook use. Secure and anxious attachment were associated with pathways in which greater Facebook use was linked with higher relatedness satisfaction. In contrast, avoidant attachment was not associated with using Facebook in the same way to obtain relatedness satisfaction. These findings suggest that attachment may influence how individuals attempt to satisfy relatedness. Anxiously attached individuals appeared more likely to use social interaction as a means of pursuing connection, whereas avoidantly attached individuals did not appear to use this particular social context in the same way. Importantly, Lin's findings do not show that individuals with anxious-avoidant attachment style possess less need for relatedness. Facebook represents only one possible route through which connection can be pursued, and the cross-sectional design cannot establish whether attachment caused differences in Facebook behaviour or relatedness satisfaction. The results are therefore better interpreted as evidence that attachment may influence the strategies through which relatedness is pursued and obtained, rather than whether the need exists.

Wei et al. (2005) provides broader evidence linking attachment insecurity with psychological need satisfaction. They found that higher attachment anxiety and avoidance were both associated with lower overall satisfaction of autonomy, competence, and relatedness, with the two attachment dimensions together explaining a substantial proportion of variance in basic psychological need satisfaction. Need satisfaction also mediated associations between attachment insecurity and psychological distress. However, the three psychological needs were combined, meaning it is not possible to determine whether relatedness specifically accounted for these effects. In addition, because the study was cross-sectional, the mediation model should not be interpreted as demonstrating that attachment insecurity causes low need satisfaction, which then causes distress.

More recent evidence improves on this limitation by considering relatedness separately. Chen et al. (2026) found that both attachment anxiety and attachment avoidance were negatively associated specifically with relatedness satisfaction among Chinese university students. Importantly, attachment anxiety showed its strongest negative associations with competence and autonomy satisfaction, whereas attachment avoidance was most strongly associated with lower relatedness satisfaction. 

This finding is difficult to explain through a simple ‘anxious individuals need more, avoidant individuals need less’ account. Instead, it suggests that different attachment styles may interfere with successful relatedness satisfaction. Chen et al. (2026) proposed that anxiously attached individuals may struggle to satisfy relatedness despite actively seeking closeness and reassurance, because heightened concern about rejection and uncertainty about others’ availability can make reassurance difficult to maintain. In contrast, avoidantly attached individuals may restrict opportunities for relatedness satisfaction by maintaining emotional distance, prioritising self-reliance, and being less willing to seek support or engage with opportunities for closeness. In both cases, the underlying need for relatedness may remain present, while the strategies used to regulate that need reduce the likelihood that it will be consistently satisfied

Secure and fearful-avoidant attachment provide further insight into how attachment may shape relatedness. Lavigne et al. (2011) found that secure attachment positively predicted a growth-oriented approach to belonging, while Lin (2016) linked secure attachment with greater relatedness satisfaction and wellbeing. This suggests that secure attachment may support a more adaptive experience of relatedness, as individuals are generally more comfortable seeking and accepting connection and are more likely to expect others to be available and responsive

While research specifically examining fearful-avoidant attachment and relatedness is limited, its combination of high attachment anxiety and avoidance provides some indication of how relatedness may be experienced. As established previously, individuals with fearful-avoidant attachment may desire connection while simultaneously expecting rejection or feeling uncomfortable with closeness. Consistent with this, Lavigne et al. (2011) found that fearful attachment was marginally negatively associated with a growth orientation towards belonging, suggesting that connection may be approached less as a secure source of growth. However, because relatively few studies have examined fearful-avoidant attachment specifically in relation to SDT relatedness, conclusions should remain cautious. Evidence from dimensional research nevertheless suggests that the combined influence of anxiety and avoidance may make relatedness particularly difficult to pursue and satisfy consistently.

=== '''Attachment and relatedness frustration''' ===
Attachment may also influence how individuals respond when relatedness is threatened or frustrated. DeWall et al. (2012) examined neural responses during simulated social exclusion and found contrasting patterns for attachment anxiety and avoidance. Higher attachment anxiety was associated with greater activation in neural regions implicated in rejection-related distress, whereas higher avoidance was associated with reduced activation in these regions.

These findings are consistent with the hyperactivating and deactivating strategies described in attachment theory. Attachment anxiety appears to involve heightened sensitivity to signs of exclusion or rejection, whereas avoidance may involve dampening or suppressing responses to relatedness threat ('''source'''). However, reduced reactivity among avoidant participants should not be interpreted as evidence that rejection is psychologically irrelevant or that the need for relatedness is absent. When considered alongside Carvallo and Gabriel (2006) and MacDonald and Borsook (2010), a different interpretation becomes more plausible, avoidant individuals may suppress or deactivate responses to threatened connection while still benefiting psychologically when connection and acceptance are available.

This distinction is important because relatedness frustration concerns the active thwarting of connection, whereas attachment style concerns the strategies used to respond to that threat. Attachment anxiety may therefore amplify the experience and expression of relatedness frustration, while attachment avoidance may reduce its overt expression. Neither pattern necessarily demonstrates a fundamental difference in whether relatedness is needed.

=== '''Can relatedness experiences shape attachment over time?''' ===
The relationship between attachment and relatedness may also operate in the opposite direction. Much of the research discussed above implicitly assumes that attachment style influences later experiences of connection. However, attachment is not completely fixed, and repeated experiences of psychological need satisfaction may also contribute to greater attachment security.

La Guardia et al. (2000) examined variations in attachment security across different relationships and found that people did not necessarily display the same level of security with every relational partner. Greater fulfilment of autonomy, competence, and relatedness within a particular relationship was associated with greater attachment security and more positive models of self and others within that relationship. These findings challenge a strictly one-directional model in which early attachment determines later interpersonal functioning.

At the same time, La Guardia et al. (2000) did not demonstrate that relatedness satisfaction alone caused increases in attachment security. The effects remained when relatedness was removed from the overall need-satisfaction measure, indicating that autonomy and competence also contributed to attachment security. The study therefore supports a broader '''reciprocal model''' in which attachment may shape how individuals seek and experience connection, while need-supportive experiences may in turn reinforce more secure expectations about the self and others.

==Conclusion==
Different attachment styles appear to shape how the need for relatedness is experienced, expressed, and satisfied rather than whether the need exists. Secure attachment is generally associated with comfort in connection, while anxious-preoccupied attachment involves heightened concern about acceptance and stronger reassurance-seeking. Dismissive-avoidant attachment involves greater distance and deactivation, whereas fearful-avoidant attachment combines a desire for closeness with fear of rejection. 

Relatedness experiences may also shape attachment over time. Repeated experiences of acceptance, support, and connection may strengthen attachment security, while rejection or exclusion may reinforce insecure expectations. In real-world settings, this means that outward behaviour should not be taken as a direct indicator of how much connection a person needs. 

{{tip|Attachment style appears to shape how the need for relatedness is experienced and experienced, rather than whether the need exists. Additionally, experiences of acceptance, support, rejection, or exclusion may contribute to changes in attachment over time.
}}

==See also==
* [[wikipedia:Attachment_in_adults|Attachment in adults]] (Wikipedia)
* [[wikipedia:Self-determination_theory|Self-determination theory]] (Wikipedia)
* [[Motivation and emotion/Book/2016/Attachment type and emotion|Attachment type and emotion]] (Wikiversity)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Wikiversity)

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{{Hanging indent|1=

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}}

==External links==
* [https://www.attachmentproject.com/attachment-theory/john-bowlby/ Bowlby and attachment theory: insights and legacy] (attachmentproject.com)
* [https://www.simplypsychology.org/self-determination-theory.html Self-determination theory of motivation] (simplypsychology.org)
* [https://selfdeterminationtheory.org/theory/ Theory] (selfdeterminationtheory.org)
* [https://youtu.be/GHHCy1IHTUc Maunder and Hunter: intro to adult attachment] (YouTube.com)

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[[Category:Motivation and emotion/Book/Needs/Psychological/Relatedness]]</text>
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__TOC__
==Overview==
{{RoundBoxTop|theme=3}}

[[File:People and stands at the Museum Reserve, Orientation Week MS-5342 012 002.jpg|thumb|'''Figure 1'''. People and stands at the Museum Reserve, Orientation Week]]


Harry and Caitlin have both recently moved to a new neighbourhood and are adjusting to their new community. 

Harry makes an effort to meet people by attending local social events. He enjoys feeling included, but when plans are made without him or a message goes unanswered, he wonders whether people actually like him. After spending time with his new neighbours, he replays conversations and worries about whether he said or did something wrong.

Caitlin also enjoys meeting her neighbours and likes being included in group activities. She chats easily with people at events but often turns down invitations to spend more time together. When conversations turn more personal or neighbours begin trying to get to know her better, she changes the subject, leaves early, and may decide to avoid the next event. Although she enjoys being part of the neighbourhood, she finds keeping some distance more comfortable. 

Harry and Caitlin both appear to value connection and belonging, yet their need for relatedness seems to be experienced and expressed in very different ways
{{RoundBoxBottom}}
Relatedness, the need to feel connected, cared for, and significant to others (Van den Broeck et al., 2016), is considered a basic psychological need within [[wikipedia:Self-determination_theory|self-determination theory]]. Satisfaction of relatedness is associated with positive psychological functioning, whereas frustration of relatedness is associated poorer psychological functioning (Chen et al., 2015) '''(more detail?)''', highlighting the importance of understanding the factors that support or interfere with relatedness satisfaction.  However, despite relatedness being proposed as a universal psychological need, individuals differ in how they seek connection and experience relatedness satisfaction. 

One factor that may explain these differences is attachment style. Attachment theory proposes that experiences with attachment figures during infancy contribute to expectations about the availability and responsiveness of others, which influences how attachment-related needs are regulated and expressed. In adulthood, secure, anxious-preoccupied, dismissive-avoidant, and fearful-avoidant attachment styles are associated with different patterns of seeking and responding to connection and support. 

This chapter investigates whether adult attachment styles shape how relatedness is experienced, expressed, pursued, and satisfied, or influences the need for relatedness itself. Additionally, it considers whether experiences of relatedness satisfaction or frustration may contribute to changes in attachment style over time.
{{Robelbox|theme=1|title=Focus questions|iconwidth=48px|icon=Crystal Clear app ktip.svg}}
* How do different attachment styles influence the way the need for relatedness is experienced and expressed?
* How might experiences of relatedness satisfaction or frustration shape attachment over time?
{{Robelbox-close}}

==Self-Determination theory and relatedness==
[[wikipedia:Self-determination_theory|Self-determination theory]] (SDT) is an approach to human motivation that seeks to explain the conditions that support or undermine motivation and psychological wellbeing.

A central proposition of SDT is the that individuals have inherent tendencies towards psychological growth, mastery, and connection with others (Ryan &amp; Deci, 2002). 

Within SDT [[wikipedia:Self-determination_theory#:~:text=Summary%20of%20the%20SDT%20mini%2Dtheories|six mini-theories]] address different aspects of motivation and psychological functioning. Of particular relevance to this chapter is the Basic Psychological Needs Theory (BPNT), which proposes that individuals must satisfy three [[wikipedia:Self-determination_theory#:~:text=%5B18%5D-,Basic%20psychological%20needs,-edit|basic psychological needs]], autonomy, competence, and relatedness, for healthy psychological growth and wellbeing (Deci &amp; Ryan, 2000). Satisfaction of these needs is not only important for, psychological growth, effective functioning, and wellbeing, but has been linked to more intrinsic forms of motivation (Deci &amp; Ryan, 2000; Ryan &amp; Deci, 2020).

=== Need satisfaction and frustration ===
Within BPNT, psychological needs can either be satisfied or frustrated depending on the extent to which a person's environment supports or obstructs those needs. 

Need satisfaction occurs when the environment allow for experiences where the psychological need can be fulfilled. It is considered psychologically nourishing and supports motivation, psychological growth, effective functioning, and wellbeing (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013). In contrast, need frustration occurs when a psychological need is actively obstructed or undermined (Chen et al., 2015; Vansteenkiste &amp; Ryan, 2013).

Importantly, need frustration is not simply the absence of need satisfaction. A person may experience low need satisfaction because they have fewer opportunities to fulfill a need, whereas need frustration involves an environment that actively thwarts or undermines a need. 

===Relatedness===
Relatedness refers to the  need to feel connected to others, including both the need to care for others and to feel cared for, valued, and significant to others (Van den Broeck et al., 2016). 

Support for relatedness as a universal need has been found across different cultural groups. For example, Chen et al., (2015), found that satisfaction of relatedness, autonomy, and competence was positively associated with wellbeing across samples from Belgium, China, Peru, and the United States. This suggests that the importance of relatedness is not limited to a particular cultural context, although the ways in which connection is expressed or pursued may vary. 

Relatedness satisfaction involves experiencing genuine connection and closeness to others, and a sense of belonging, whereas relatedness frustration involves experiences of rejection, exclusion, disconnection, or loneliness (Chen et al., 2015). 

{{RoundBoxTop|theme=3}}
[[File:Case Icon.png|left|20px|]] A few weeks later, Harry and Caitlin are invited to a neighbourhood barbecue. 

Harry spends the afternoon talking with several neighbours and is included in plans for another get-together the following weekend. He leaves feeling welcomed and like he is beginning to belong in the community. However, later that week he notices that several neighbours have organised another gathering without inviting him. 

During the barbecue, Caitlin enjoys chatting with people. When one neighbour later invites her over for coffee, she politely declines and does not suggest another time. Although no one has rejected or excluded her. 

Harry’s experience at the barbecue illustrates relatedness satisfaction because he feels welcomed, included, and valued by others, giving him a sense of connection and belonging. When he is later deliberately left out of plans, this may represent relatedness frustration, because the opportunity for connection is undermined through exclusion.

Caitlin’s experience is different. By repeatedly declining invitations and keeping some distance, she may have fewer opportunities to experience meaningful connection, resulting in relatively low relatedness satisfaction. However, because others are still inviting and including her, her need for relatedness is not necessarily being actively thwarted.{{RoundBoxBottom}}

==Attachment theory and styles==
[[wikipedia:Attachment_theory|Attachment theory]] was first developed by John Bowlby to explain the anxiety and distress infants experience when separated from their caregivers. Bowlby observed that infants use attachment behaviours, such as crying, clinging, following, to prevent separation or re-establish proximity to their caregivers (Bowlby, 1958). He proposed that these behaviours form part of an attachment behavioural system (ABS), an innate psychobiological mechanism that motivates infants to seek and maintain closeness to an attachment figure. Bowlby (1982) argued that this system has an evolutionary function, as infants who remained close to caregivers would have been more likely to survive to reproductive age.

Although Bowlby considered the ABS to be universal, he recognised that infants could differ in how attachment was experienced and expressed. He theorised that early experiences with caregivers contribute to internal working models, mental representations of expectations of whether attachment figures are available and responsive, and whether the self is worthy of care and support. These expectations are thought to guide an infant's response to situations that activate their ABS, including whether the infant seeks support, intensifies attachment behaviours, or minimises them (Bretherton &amp; Munholland, 2008; Collins &amp; Allard, 2004; Sherman et al., 2015). 

[[wikipedia:Mary_Ainsworth|Mary Ainsworth]] extended Bowlby's work by examining how individual differences in attachment were expressed in infant's behaviour through the [[wikipedia:Strange_situation|Strange Situation procedure]]. The procedure involved observing infants during brief separations and reunions with a caregiver, focusing primarily on exploration, separation and reunion responses, and reactions to a stranger (Ainsworth et al., 1978). Through this, Ainsworth identified three infant attachment patterns, Secure, Anxious-ambivalent/, and Anxious-avoidant—with disorganised-disoriented attachment later identified by Main and Solomon (1986) to describe infant behaviours that did not fit comfortably within Ainsworth’s original classifications (See Table 1.)

'''Table 1'''.

''Infant Attachment Patterns, Associated Caregiving Experiences, and Attachment Strategies''
{| class=&quot;wikitable&quot;
|+
!Infant attachment style
!Typical attachment response
!Associated caregiving experiences
!Internal working model
|-
|Secure attachment
|Uses caregiver as a secure base, exploring environment independently while seeking proximity and comfort when distressed. 
|Associated with caregiving that is generally sensitive, responsive, and consistent. 
|Expects caregiver will be available and responsive when support is required. Attachment needs can therefore expressed distress without intensifying or suppressing attachment behaviour.
|-
|Anxious-ambivalent attachment
|Remains highly attentive to  caregiver availability while exploring. May become easily distressed by separation and seeks frequent proximity, attention, or reassurance, while sometimes difficult to soothe. 
|Associated with caregiving that may be inconsistent or unpredictable.
|

Expects caregiver to be inconsistent, causing infant to become attentive to caregiver’s availability and intensify attachment signals in an attempt to obtain a response (hyperactivating strategy). 
|-
|Anxious-avoidant attachment
|May appear unusually independent and spend more time focused on objects, activities, or exploration than on caregiver. Less likely to openly seek comfort or reassurance from the caregiver. 
|Associated with caregiving that may be relatively unresponsive, rejecting, or uncomfortable with expressions of distress. 
|Expects attempts to obtain comfort or support as unlikely to be met with a responsive reaction. Causes infant to minimise or suppress attachment signals (deactivating stratergy).
|-
|Disorganised-disoriented attachment
|Displays contradictory, confused, or disoriented attachment behaviour and may alternate between proximity-seeking and avoidance without a consistent strategy.
|Associated with caregiving that is frightening, frightened, highly disrupted, or unpredictable.Has been found at higher rates in some contexts involving significant adversity. 
|Difficult to explain through one coherent internal working model as infant does not appear to have a consistent strategy for obtaining comfort.

One proposed explanation is that  caregiver may simultaneously represent a source of safety and a source of fear or uncertainty, creating conflict between approaching the caregiver for protection and moving away from them.
|}
''Note''. Caregiving experiences are associated with, rather than solely determining, infant attachment patterns. Adapted from (Ainsworth et al., 1978), Benoit (2004), Main and Solomon (1986), Sherman et al. (2015), Granqvist et al. (2017), Vaughn and Waters (1990), and Zeanah et al. (1997).

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{How do internal working models help explain differences between infant attachment patterns?
|type=&quot;()&quot;}
- They determine how strongly an infant is biologically attached to their caregiver.
|| Internal working models do not determine whether an infant '''has''' an attachment to their caregiver. Instead, they shape expectations about whether caregivers will be available and responsive, which can influence how the infant seeks comfort and responds when the attachment system is activated.
+ They shape expectations about whether caregivers will be available and responsive when support is needed.
|| Yes. Internal working models develop through attachment experiences and shape expectations about whether attachment figures will be available and responsive.
- They determine how much distress every infant experiences during separation.
|| Internal working models can influence how infants respond when distressed, but they do not simply determine how much separation distress an infant experiences.
&lt;/quiz&gt;
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===Adult attachment theory===
Attachment theory was later extended beyond infancy to explain how attachment may continue into adulthood. Hazan and Shaver (1987) were among the first to construct a self-report measure of adult attachment patterns, though this was in the context of romantic relationships. Their measure was based on the idea that individual differences in the ways adults engage in romantic relationships echo Ainsworth's classifications.

Bartholomew (1990), and Bartholomew and Horowitz (1991) later created a four-factor moled of adult attachment, proposing that attachment in adulthood could be understood through two underlying dimensions:
* Model of self: Reflects a person's sense of self-worth and whether they feel worthy of love and support. (Bartholomew, 1990)
* Model of others: Reflects whether a person expects others to be available, trustworthy, and supportive (Bartholomew, 1990)
Combining positive and negative models of the self and others produced four adult attachment styles, Secure, Anxious-preoccupied, Dismissive-avoidant, Fearful-avoidant (Alareqe et al., 2021). 

==== Attachment anxiety and avoidance ====
Although Bartholomew's model describes four attachment styles, contemporary adult attachment research often assess attachment along the continuous dimensions of attachment anxiety and attachment avoidance
* Attachment anxiety: the degree to which individuals worry about being underappreciated or abandoned by their romantic partners   (Simpson &amp; Steven Rholes, 2017).
* Attachment avoidance: the degree to which individuals are comfortable with closeness and emotional intimacy in relationships (Simpson &amp; Steven Rholes, 2017).[[File:Four Adult Attachment Styles Based on Models of Self and Others and Attachment Anxiety and Avoidance.svg|thumb|465x465px|'''Figure 2'''. Diagram of Bartholomew’s four adult attachment styles based on models of self and others, and their correspondence with attachment anxiety and attachment avoidance.                                                                                      ''Note''. Adapted from Alareqe et al. (2021), Bartholomew (1990), Bartholomew and Horowitz (1991), Kang et al. (2015), and Morse et al. (2012).]]
Using factor and hierarchical cluster analyses, Brennan et al. (1998) identified attachment anxiety and avoidance as two underlying dimensions of adult attachment and demonstrated that different combinations of these dimensions broadly correspond to Bartholomew and Horowitz's four attachment styles (see Figure 2).

Because contemporary research commonly measures attachment along the continuous dimensions of attachment anxiety and avoidance, this chapter draws on evidence from both dimensional and categorical approaches when examining attachment and relatedness. Where studies report findings for attachment anxiety and avoidance, these findings are interpreted in relation to the attachment styles they are most consistent with based on their established dimensional profiles. However, these interpretations should be used cautiously, as dimensional findings do not directly demonstrate effects for categorical attachment styles.

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{Adult attachment is completely determined by experiences in infancy.
|type=&quot;()&quot;}
+ TRUE.
|| Not quite. Early attachment experiences may contribute to the development of internal working models, but attachment is not considered permanently fixed and may change across later experiences and relationships.
- FALSE.
|| Correct. Early attachment experiences may influence internal working models and later attachment patterns, but adult attachment is not completely determined by infancy and may change across time and experience.
&lt;/quiz&gt;
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== Attachment styles and the need for relatedness ==
SDT proposes relatedness as a universal psychological need, yet attachment theory indicates that people differ in how they approach closeness, interpret other's availability, and respond when connection is uncertain. This raises an important question: do attachment styles influence the strength of the need for relatedness itself, or do they primarily influence how that need is experienced, expressed, pursued, and satisfied?

=== '''Does attachment style influence the strength of the relatedness need?''' ===
Research on the need to belong provides mixed evidence regarding whether attachment styles differ in the strength of their motivation for connection. Although belonging is not identical to SDT relatedness, it offers useful converging evidence as both concern the psychological importance of social connection and acceptance.

Lavigne et al. (2011) distinguished between two orientations towards belonging, a growth orientation, in which social connection is pursued as a source of development and positive experience, and a deficit-reduction orientation, in which connection is pursued to compensate for feelings of social deficiency or insecurity. They found secure attachment positively predicted a growth orientation, whereas preoccupied attachment positively predicted a deficit-reduction orientation and a stronger self-reported need to belong. Dismissing-avoidant attachment, in contrast, negatively predicted both deficit-reduction orientation and reported need to belong. These findings could be interpreted as evidence that preoccupied individuals possess a stronger need for connection while dismissive-avoidant individuals possess a weaker one.

However, this interpretation requires caution. Lavigne et al. (2011) relied on self-report measures in a predominantly university sample and used a correlational design, meaning the findings cannot establish whether attachment causes differences in relatedness motivation. More importantly, self-reported strength of belonging may itself be influenced by attachment regulation. Individuals with a dismissive-avoidant attachment style may consciously minimise the importance of connection as part of a deactivating strategy, whereas preoccupied individuals may be particularly aware of and focused on unmet connection needs. Consequently, differences in reported need may reflect differences in awareness, expression, or regulation rather than actual differences in whether the underlying need exists.

This interpretation is supported by Leary et al. (2013), who found that need to belong was distinguishable from attachment insecurity rather than simply representing another measure of insecure attachment. Their findings challenge the assumption that high attachment anxiety can be equated with a stronger relatedness need, or that high avoidance necessarily indicates a weaker one. Instead, attachment insecurity and the strength of belonging motivation appear to represent related but distinct constructs.

Experimental evidence concerning dismissive and avoidant attachment further challenges the idea that these individuals have little need for connection Carvallo and Gabriel (2006) specifically examined individuals with dismissing-avoidant attachment, who commonly report comfort without close interpersonal involvement. Despite this apparent self-sufficiency, highly dismissing participants showed increased positive affect and state self-esteem after receiving social. If dismissing individuals genuinely possessed little need for connection, social acceptance would be expected to have relatively little psychological value. Instead, their positive response suggests that the need for connection may remain psychologically significant even when it is consciously downplayed or behaviourally avoided.

MacDonald and Borsook (2010) provide converging experimental evidence. In a brief social-interaction study, participants high and low in attachment avoidance interacted with either a highly positive or mildly negative confederate. Both groups reported greater feelings of connection following the positive interaction, and the effect was actually stronger among participants higher in avoidance. Although the study involved a small sample and measured immediate feelings of connection rather than SDT relatedness satisfaction, the findings provide further evidence that avoidant individuals remain responsive to positive social experiences.

Taken together, these studies suggest that attachment style may have a stronger influence on the experience and expression of relatedness motivation than on the existence of the need itself. Preoccupied attachment may heighten conscious concern with acceptance and belonging, whereas dismissive attachment may involve downplaying or suppressing the importance of connection. However, evidence that avoidant individuals continue to respond positively to acceptance and connection is difficult to reconcile with the claim that they simply possess a weaker underlying need for relatedness.

=== '''Attachment and relatedness satisfaction''' ===
A separate question is whether attachment influences how successfully the need for relatedness is satisfied. Here, the evidence is somewhat stronger.

Lin (2016) directly examined attachment in relation to SDT relatedness satisfaction through Facebook use. Secure and anxious attachment were associated with pathways in which greater Facebook use was linked with higher relatedness satisfaction. In contrast, avoidant attachment was not associated with using Facebook in the same way to obtain relatedness satisfaction. These findings suggest that attachment may influence how individuals attempt to satisfy relatedness. Anxiously attached individuals appeared more likely to use social interaction as a means of pursuing connection, whereas avoidantly attached individuals did not appear to use this particular social context in the same way. Importantly, Lin's findings do not show that individuals with anxious-avoidant attachment style possess less need for relatedness. Facebook represents only one possible route through which connection can be pursued, and the cross-sectional design cannot establish whether attachment caused differences in Facebook behaviour or relatedness satisfaction. The results are therefore better interpreted as evidence that attachment may influence the strategies through which relatedness is pursued and obtained, rather than whether the need exists.

Wei et al. (2005) provides broader evidence linking attachment insecurity with psychological need satisfaction. They found that higher attachment anxiety and avoidance were both associated with lower overall satisfaction of autonomy, competence, and relatedness, with the two attachment dimensions together explaining a substantial proportion of variance in basic psychological need satisfaction. Need satisfaction also mediated associations between attachment insecurity and psychological distress. However, the three psychological needs were combined, meaning it is not possible to determine whether relatedness specifically accounted for these effects. In addition, because the study was cross-sectional, the mediation model should not be interpreted as demonstrating that attachment insecurity causes low need satisfaction, which then causes distress.

More recent evidence improves on this limitation by considering relatedness separately. Chen et al. (2026) found that both attachment anxiety and attachment avoidance were negatively associated specifically with relatedness satisfaction among Chinese university students. Importantly, attachment anxiety showed its strongest negative associations with competence and autonomy satisfaction, whereas attachment avoidance was most strongly associated with lower relatedness satisfaction. 

This finding is difficult to explain through a simple ‘anxious individuals need more, avoidant individuals need less’ account. Instead, it suggests that different attachment styles may interfere with successful relatedness satisfaction. Chen et al. (2026) proposed that anxiously attached individuals may struggle to satisfy relatedness despite actively seeking closeness and reassurance, because heightened concern about rejection and uncertainty about others’ availability can make reassurance difficult to maintain. In contrast, avoidantly attached individuals may restrict opportunities for relatedness satisfaction by maintaining emotional distance, prioritising self-reliance, and being less willing to seek support or engage with opportunities for closeness. In both cases, the underlying need for relatedness may remain present, while the strategies used to regulate that need reduce the likelihood that it will be consistently satisfied

Secure and fearful-avoidant attachment provide further insight into how attachment may shape relatedness. Lavigne et al. (2011) found that secure attachment positively predicted a growth-oriented approach to belonging, while Lin (2016) linked secure attachment with greater relatedness satisfaction and wellbeing. This suggests that secure attachment may support a more adaptive experience of relatedness, as individuals are generally more comfortable seeking and accepting connection and are more likely to expect others to be available and responsive

While research specifically examining fearful-avoidant attachment and relatedness is limited, its combination of high attachment anxiety and avoidance provides some indication of how relatedness may be experienced. As established previously, individuals with fearful-avoidant attachment may desire connection while simultaneously expecting rejection or feeling uncomfortable with closeness. Consistent with this, Lavigne et al. (2011) found that fearful attachment was marginally negatively associated with a growth orientation towards belonging, suggesting that connection may be approached less as a secure source of growth. However, because relatively few studies have examined fearful-avoidant attachment specifically in relation to SDT relatedness, conclusions should remain cautious. Evidence from dimensional research nevertheless suggests that the combined influence of anxiety and avoidance may make relatedness particularly difficult to pursue and satisfy consistently.

=== '''Attachment and relatedness frustration''' ===
Attachment may also influence how individuals respond when relatedness is threatened or frustrated. DeWall et al. (2012) examined neural responses during simulated social exclusion and found contrasting patterns for attachment anxiety and avoidance. Higher attachment anxiety was associated with greater activation in neural regions implicated in rejection-related distress, whereas higher avoidance was associated with reduced activation in these regions.

These findings are consistent with the hyperactivating and deactivating strategies described in attachment theory. Attachment anxiety appears to involve heightened sensitivity to signs of exclusion or rejection, whereas avoidance may involve dampening or suppressing responses to relatedness threat ('''source'''). However, reduced reactivity among avoidant participants should not be interpreted as evidence that rejection is psychologically irrelevant or that the need for relatedness is absent. When considered alongside Carvallo and Gabriel (2006) and MacDonald and Borsook (2010), a different interpretation becomes more plausible, avoidant individuals may suppress or deactivate responses to threatened connection while still benefiting psychologically when connection and acceptance are available.

This distinction is important because relatedness frustration concerns the active thwarting of connection, whereas attachment style concerns the strategies used to respond to that threat. Attachment anxiety may therefore amplify the experience and expression of relatedness frustration, while attachment avoidance may reduce its overt expression. Neither pattern necessarily demonstrates a fundamental difference in whether relatedness is needed.

=== '''Can relatedness experiences shape attachment over time?''' ===
The relationship between attachment and relatedness may also operate in the opposite direction. Much of the research discussed above implicitly assumes that attachment style influences later experiences of connection. However, attachment is not completely fixed, and repeated experiences of psychological need satisfaction may also contribute to greater attachment security.

La Guardia et al. (2000) examined variations in attachment security across different relationships and found that people did not necessarily display the same level of security with every relational partner. Greater fulfilment of autonomy, competence, and relatedness within a particular relationship was associated with greater attachment security and more positive models of self and others within that relationship. These findings challenge a strictly one-directional model in which early attachment determines later interpersonal functioning.

At the same time, La Guardia et al. (2000) did not demonstrate that relatedness satisfaction alone caused increases in attachment security. The effects remained when relatedness was removed from the overall need-satisfaction measure, indicating that autonomy and competence also contributed to attachment security. The study therefore supports a broader '''reciprocal model''' in which attachment may shape how individuals seek and experience connection, while need-supportive experiences may in turn reinforce more secure expectations about the self and others.

==Conclusion==
Different attachment styles appear to shape how the need for relatedness is experienced, expressed, and satisfied rather than whether the need exists. Secure attachment is generally associated with comfort in connection, while anxious-preoccupied attachment involves heightened concern about acceptance and stronger reassurance-seeking. Dismissive-avoidant attachment involves greater distance and deactivation, whereas fearful-avoidant attachment combines a desire for closeness with fear of rejection. 

Relatedness experiences may also shape attachment over time. Repeated experiences of acceptance, support, and connection may strengthen attachment security, while rejection or exclusion may reinforce insecure expectations. In real-world settings, this means that outward behaviour should not be taken as a direct indicator of how much connection a person needs. 

{{tip|Attachment style appears to shape how the need for relatedness is experienced and experienced, rather than whether the need exists. Additionally, experiences of acceptance, support, rejection, or exclusion may contribute to changes in attachment over time.
}}

==See also==
* [[wikipedia:Attachment_in_adults|Attachment in adults]] (Wikipedia)
* [[wikipedia:Self-determination_theory|Self-determination theory]] (Wikipedia)
* [[Motivation and emotion/Book/2016/Attachment type and emotion|Attachment type and emotion]] (Wikiversity)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Wikiversity)

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{{Hanging indent|1=

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}}

==External links==
* [https://www.attachmentproject.com/attachment-theory/john-bowlby/ Bowlby and attachment theory: insights and legacy] (attachmentproject.com)
* [https://www.simplypsychology.org/self-determination-theory.html Self-determination theory of motivation] (simplypsychology.org)
* [https://selfdeterminationtheory.org/theory/ Theory] (selfdeterminationtheory.org)
* [https://youtu.be/GHHCy1IHTUc Maunder and Hunter: intro to adult attachment] (YouTube.com)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Relationships/Attachment]]
[[Category:Motivation and emotion/Book/Needs/Psychological/Relatedness]]</text>
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      <text bytes="1153" sha1="8hwb8so9rxc5uhhglsm38gf2n6v66d3" xml:space="preserve">== About me ==
Hi! My name is Salma and I am in my third year of [https://www.canberra.edu.au/course/780AA/4/2023 Bachelor of Science in Psychology]. 
[[File:Gingerbread, raspberry + dark chocolate.jpg|thumb|225x225px|Gingerbread cookie cake with raspberry buttercream and dark chocolate ganache I made.]]

=== Interests ===
My personal interests are: 

* Crocheting and Sewing
* Playing netball
* Baking
* Scrolling Pinterest ([https://pin.it/2HiPJfd8s find my account here])

== Book chapter topic ==
The book chapter I'm working on is [[Motivation and emotion/Book/2026/Attachment styles and relatedness motivation|Attachment styles and relatedness motivation]]

== Social contributions ==

# [[Talk:Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Made a comment sharing relevant sources and tips.]]
# [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/457888?entry_id=813984 Made a suggestion on potential changes to overview]
# [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FAdaptive_versus_maladaptive_self-reflection&amp;diff=2831012&amp;oldid=2828912 Fixed a typo]</text>
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      <format>text/x-wiki</format>
      <text bytes="3101" sha1="fhn5uieia4dl82l16crontm578myynh" xml:space="preserve">== About me ==
Hi! My name is Salma and I'm a third year Bachelor of Science in Psychology student at the [[University of Canberra|University of Canberra (UC)]], breadth majoring in Forensic and Legal Psychology.  

Alongside my studies, I have gained experience in a range of support roles, including disability support and youth mental health. I currently work as a Youth Peer Support Coach where I support young people through recovery-oriented, person-centred practice. These experiences have strengthened my interest in mental health, recovery, advocacy and the importance of creating supportive environments where people feel heard and empowered. You can find my LinkedIn [https://www.linkedin.com/in/salma-adam-a0b186326/ here].  

Through my academic studies and professional experience, I have developed a particular interest in clinical and forensic psychology. My long-term aspiration is to become a registered psychologist, with the goal of pursuing further postgraduate study and developing expertise in both clinical and forensic practice.  
[[File:Gingerbread, raspberry + dark chocolate.jpg|thumb|225x225px|Gingerbread cookie cake with raspberry buttercream and dark chocolate ganache I made.]]

=== Interests ===
Outside of my studies, I enjoy a range of hobbies, including: 

* Crocheting and sewing
* Playing netball
* Baking, particularly cakes and other desserts
* Finding creative inspiration on Pinterest ([https://pin.it/2HiPJfd8s find my account here])
* Spending time with my goddaughters
* Reading, specifically romantasy. My favourite books are the [https://rickriordan.com/series/percy-jackson-and-the-olympians/ Percy Jackson] and all associated series  
* Travelling, recently visited London and Japan
* Drawing and painting

== Book chapter topic ==
The book chapter I'm working on is [[Motivation and emotion/Book/2026/Attachment styles and relatedness motivation|Attachment styles and relatedness motivation]]

== Social contributions ==

# [[Talk:Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Made a comment sharing relevant sources and tips.]]
# [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/457888?entry_id=813984 Made a suggestion on potential changes to overview]
# [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FAdaptive_versus_maladaptive_self-reflection&amp;diff=2831012&amp;oldid=2828912 Fixed a typo]
# [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/465111?entry_id=824403 Commented potential changes to environmental and social factors section.] 
# [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/464954 Asked for clarification on using Wikiversity citations alongside APA 7 referencing]
# [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/465940 Started a feedback thread for students with extensions to share ideas and support each other]
# [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/465940?entry_id=825841 Gave feedback on improving chapter focus and alignment with the central topic question]</text>
      <sha1>fhn5uieia4dl82l16crontm578myynh</sha1>
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      <id>2841340</id>
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      <timestamp>2026-10-18T18:46:14Z</timestamp>
      <contributor>
        <username>HawaSA</username>
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      <text bytes="3358" sha1="2w8efzw6tcw786l0fo08y8l249n3wqi" xml:space="preserve">== About me ==
Hi! My name is Salma and I'm a third year Bachelor of Science in Psychology student at the [[University of Canberra|University of Canberra (UC)]], breadth majoring in Forensic and Legal Psychology.  

Alongside my studies, I have gained experience in a range of support roles, including disability support and youth mental health. I currently work as a Youth Peer Support Coach where I support young people through recovery-oriented, person-centred practice. These experiences have strengthened my interest in mental health, recovery, advocacy and the importance of creating supportive environments where people feel heard and empowered. You can find my LinkedIn [https://www.linkedin.com/in/salma-adam-a0b186326/ here].  

Through my academic studies and professional experience, I have developed a particular interest in clinical and forensic psychology. My long-term aspiration is to become a registered psychologist, with the goal of pursuing further postgraduate study and developing expertise in both clinical and forensic practice.  
[[File:Gingerbread, raspberry + dark chocolate.jpg|thumb|225x225px|Gingerbread cookie cake with raspberry buttercream and dark chocolate ganache I made.]]

=== Interests ===
Outside of my studies, I enjoy a range of hobbies, including: 

* Crocheting and sewing
* Playing netball
* Baking, particularly cakes and other desserts
* Finding creative inspiration on Pinterest ([https://pin.it/2HiPJfd8s find my account here])
* Spending time with my goddaughters
* Reading, specifically romantasy. My favourite books are the [https://rickriordan.com/series/percy-jackson-and-the-olympians/ Percy Jackson] and all associated series  
* Travelling, recently visited London and Japan
* Drawing and painting

== Book chapter topic ==
The book chapter I'm working on is [[Motivation and emotion/Book/2026/Attachment styles and relatedness motivation|Attachment styles and relatedness motivation]]

== Social contributions ==

# [[Talk:Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Made a comment sharing relevant sources and tips.]]
# [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/457888?entry_id=813984 Made a suggestion on potential changes to overview]
# [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FAdaptive_versus_maladaptive_self-reflection&amp;diff=2831012&amp;oldid=2828912 Fixed a typo]
# [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/465111?entry_id=824403 Commented potential changes to environmental and social factors section.] 
# [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/464954 Asked for clarification on using Wikiversity citations alongside APA 7 referencing]
# [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/465940 Started a feedback thread for students with extensions to share ideas and support each other]
# [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/465940?entry_id=825841 Gave feedback on improving chapter focus and alignment with the central topic question]
# [[:File:Four Adult Attachment Styles Based on Models of Self and Others and Attachment Anxiety and Avoidance.svg|Created and uploaded a diagram illustrating the four adult attachment styles and their correspondence with attachment anxiety and avoidance]]</text>
      <sha1>2w8efzw6tcw786l0fo08y8l249n3wqi</sha1>
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  <page>
    <title>Motivation and emotion/Book/2026/Expectancy-value theory of educational motivation</title>
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        <id>3105303</id>
      </contributor>
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      <text bytes="35916" sha1="f2bi25zpcdm7mnucjimjczfp89l6489" xml:space="preserve">{{title|Expectancy-value theory of educational motivation:&lt;br&gt;What is expectancy-value theory and how can it be applied to understand and enhance educational motivation?}}
__TOC__
==Overview ==
{| style=&quot;width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;&quot;
|-
! style=&quot;background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;&quot; | Imagine this scenario
|-
| style=&quot;border-radius:0 0 12px 12px; padding:8px; border:0;&quot; |
&lt;div style=&quot;background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;&quot;&gt;
[[File:Motivation Laptop.svg|150px|alt=A student reflecting on their motivation to learn]]
&lt;br&gt;
&lt;span style=&quot;line-height:1.2; display:block; margin-top:2px;&quot;&gt;
'''Figure 1'''. A student reflecting on their motivation to learn.
&lt;/span&gt;
&lt;/div&gt;
You're sitting at your desk, working through a short maths quiz before dinner. The first question looks familiar, yet you pause, unsure whether you can solve it. You read it again, feeling a small wave of hesitation and mild frustration as you try to work out where to begin, see Figure 1.
After a moment, you recall solving a similar problem last week, and your teacher mentioned you were on the right track. This memory gives you a small boost of confidence, enough to try the first step. As you work through the question, you start thinking about why you’re even doing this quiz. You remind yourself that completing these tasks helps you prepare for the upcoming test and supports your longer‑term academic goals.
This shift in mindset increases your confidence and clarifies the importance of the task. The quiz feels more manageable, and you start working through the first question. With this renewed sense of direction, you continue working through the quiz.

This scenario demonstrates how expectancy and task value shape a learner’s motivation during routine academic activities. Expectancy-value theory provides a clear framework for understanding how changes in confidence and task value affect a learner’s motivation. This theory proposes that motivation increases when learners feel capable of succeeding and when they view a task as important, useful, or aligned with their goals.
|}

The scenario above shows how small shifts in confidence and perceived value can make everyday learning tasks feel either overwhelming or manageable. Many students experience fluctuating motivation during routine academic tasks, which can make learning feel overwhelming or discouraging. Expectancy-value theory helps explain this pattern by showing how confidence (expectancy beliefs) and perceived importance or usefulness (task values) shape a learner’s motivation. This theory provides a [[wikipedia:Social_cognition|social-cognitive]] explanation of why students choose to engage in learning activities and offers evidence-based strategies to strengthen both expectancy beliefs and task values. The following sections outline these core components and show how to apply them in educational settings to support more adaptive learning behaviours.

{| style=&quot;width:100%; background:#CBF2D3; color:black; border-radius:12px; border:0;&quot;
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! style=&quot;background:#96E25B; color:black; border-radius:12px 12px 0 0; border:0;&quot; | Focus questions
|-
| style=&quot;border-radius:0 0 12px 12px; padding:10px; border:0;&quot; |
* What is expectancy-value theory?
* How do social‑cognitive models explain educational motivation?
* How do expectancy beliefs influence educational motivation?
* How do task values influence educational motivation?
* How can expectancy-value theory be used to enhance motivation in educational settings?
|}

== What is expectancy-value theory? ==

[[File:Situated Expectancy-Value Theory SEVT Diagram.png|thumb|right|450px|'''Figure 2.''' Conceptual diagram illustrating expectancy‑value theory (EVT). Diagram created by author.]]
Expectancy-value theory comes from research on student motivation, especially the work of Eccles and Wigfield (2000, 2002,). The theory says that students are motivated by two main things: how confident they feel about doing a task and how much they value the task, which is seen in a conceptual flow chart in Figure 2. Expectancy is about whether a student believes they can succeed and while task value describes how important, useful, or enjoyable the task feels. Together these ideas shape how students approach schoolwork, how much effort they put in, and how long they keep trying. An example of this would be a student is more likely to study for a maths test if they feel capable and believe the test will help them reach future goals (Eccles &amp; Wigfield, 2002).

The theory includes several components that help explain why student respond differently to the same task. Expectancy refer’s to beliefs about success, while task value includes four parts: intrinsic value, utility value, attainment value, and cost, (Eccles &amp; Wigfield, 2002). Intrinsic value is the level of enjoyment a student gets from the task, utility value is about how well the task aligns with future goals, attainment value is the about how important doing well in the task is to the student. Cost refer’s to the downsides of doing the task, such as the amount of effort, time or stress required for the task. Theses components influence how worthwhile a task feels and how much time and energy students are willing to invest. Table 1 summarises these components with definitions and examples.

Although expectancy-value theory is widely used, researchers have pointed out some limitations. Pintrach (2003) argues that the theory focuses too much on logical decision-making and does not fully consider emotional or social influences. Flake et al. (2015) also note that theory does not clearly explain how expectancies and values develop or why they differ between students. These critiques have led to updates of the theory which includes adding the “S” (situated) to EVT, which evolved EVT into situated expectancy-value theory (SEVT). This contempory work emphaises how motivation changes across different contexts and learning environments (Eccles &amp; Wigfield, 2020). This new theory reflects a meaningful extension of EVT, highlighting how context actively shapes motivation.

==How do social-cognitive models explain educational motivation?==

Social-cognitive models explain educational motivation by emphasising the beliefs students hold about their abilities and the value they assign to learning tasks. Bandura’s self-efficacy theory proposes that learners’ confidence in their capability to succeed strongly influences the choices they make, the effort they invest, and their persistence when facing challenges (Bandura, 1997). Building on this work, Pajares (1996) demonstrates that self-efficacy beliefs are powerful predictors of academic performance because they shape how students interpret difficulty and regulate their learning. Pajares and Schunk (2009) further explain that self-efficacy develops through experiences such as mastery, feedback, and social comparison, which means classroom environments play a central role in shaping motivation. Social-cognitive models also highlight the importance of students’ beliefs about the value of academic tasks, with Eccles and Wigfield (2002) noting that motivation increases when learners view an activity as important, enjoyable, or useful for future goals. Together, these perspectives show that educational motivation is influenced by how students think about themselves and how they evaluate the learning activities they encounter. This perspective sets up a clear link to expectancy-value theory, which similarly emphasises how motivation is shaped by both personal beliefs and environmental influences.

Self-efficacy theory and expectancy-value theory share an important similarity: both recognise that motivation is shaped not only by internal beliefs but also by the environment in which learning occurs. Self-efficacy develops through experiences such as mastery, feedback, and social comparison, which means classroom conditions and teacher support directly influence how confident students feel (Pajares &amp; Schunk, 2009). EVT makes a similar point through the development of situated expectancy-value theory (SEVT), which emphasises that expectancies and task values shift depending on the learning context. In both models, motivation is not fixed within the individual but is shaped by the interaction between personal beliefs and environmental factors. This overlap reflects the broader nature-versus-nurture debate, showing that educational motivation emerges from both internal psychological processes (nature) and external influences such as teaching practices, feedback, and classroom climate (nurture).

== How do expectancy beliefs influence educational motivation? ==
Expectancy beliefs refer to students’ judgements about how capable they are of completing a task successfully. Eccles and Wigfield (2002) explain that these beliefs come from students' past achievements, their self-concept, and how difficult they think the task will be. When students believe they can succeed, they are more willing to start a task, put effort in and keep going when challenges arise or the task becomes more difficult. This makes expectancy beliefs a key part of understanding why some students engage strongly with schoolwork while others hold back.

Bandura (1997), Pajares (1996), and Pajares and Schunk (2009) are key social-cognitive researchers who show how strongly expectancy beliefs influence students’ effort, persistence, and academic performance. Bandura’s work demonstrates that when students feel capable, they try harder and keep going when the task becomes difficult. Pajares (1996) adds that these beliefs shape how students interpret challenges and manage their learning. Pajares and Schunk (2009) explain that expectancy beliefs grow through experiences like mastery, feedback, and seeing others succeed. This suggests that classroom environments and teacher support play an important role in building students’ confidence. Together, these researchers show that expectancy beliefs are central to understanding why students engage differently with schoolwork.

Expectancy beliefs help explain educational motivation because students who believe they can succeed are more likely to engage with learning tasks, keep trying when things get difficult and choose activities that support their academic progress (Eccles &amp; Wigfield, 2002; Bandura, 1997). These beliefs shape how students understand classroom demands and influence how much effort they are willing to put in (Pajares, 1996). This is why students with similar abilities can show very different levels of motivation: it is not only their actual skill that matters, but what they believe they can achieve (Eccles &amp; Wigfield, 2002). Expectancy beliefs act as a motivational filter that guide how students approach schoolwork.

Although expectancy beliefs are strong predictors of motivation, researchers point out several limitations. Critics argue that these models focus too heavily on cognitive judgements and overlook the emotional and contextual factors that influence how students engage. Pajares (1996) and Bandura (1997) show that confidence alone cannot fully explain motivation, especially when anxiety, stress, or negative classroom climates reduce students’ willingness to participate. A student may believe they are capable but still disengage if the environment feels overwhelming or unsupportive. These critiques highlight why newer approaches, such as situated expectancy-value theory (SEVT), emphasise how motivation shifts across different learning contexts.

== How do task values influence educational motivation? ==
Task value describes how important, enjoyable, or useful students perceive a learning activity to be. Eccles and Wigfield (2000, 2002) explain that these evaluations play a major role in shaping motivation because they influence how worthwhile students believe a task is. When students see value in what they are learning, they are more likely to participate and invest effort.

Eccles and Wigfield (2000, 2002) emphasise that task values are central to expectancy-value theory because they explain most of the variation in why students choose certain learning activities. Intrinsic value, utility value, attainment value, and cost together account for the majority of the model, showing that motivation is shaped not just by whether students think they can succeed, but by how worthwhile they believe the task is. These values influence decisions such as which subjects’ students pursue, how much effort they invest, and whether they persist when work becomes challenging. By highlighting the importance of enjoyment, usefulness, personal significance, and perceived cost, task values help explain why students engage differently even when their abilities are similar.

Research supports the importance of task values by showing that students are more motivated when they find learning activities enjoyable or personally meaningful (Eccles &amp; Wigfield, 2000). Utility value also plays a major role, with studies demonstrating that students invest more effort when they believe the task will help them achieve future goals (Harackiewicz &amp; Hulleman 2009). These findings reinforce the central claim of expectancy-value theory: students engage more deeply with task they see as worthwhile, either because they enjoy the activity, believe it will help them in the future, or view it as personally important.

More recent work highlights the importance of cost, showing that high perceived effort, stress and anxiety, or time demands can reduce motivation even when other values are string (Flake et al., 2015). Cost captures the negative side of engaging in a task, and research demonstrates that these perceptions can undermine students’ willingness to participate even when they find the activity enjoyable or useful. This helps explain why motivation can drop in situations where the workload feels overwhelming or emotionally demanding.

Task values help explain educational motivation because students are more likely to engage with learning activities, they see as enjoyable, important, or useful. When students believe a task is worthwhile, they are more willing to invest effort and persist through challenges. This perspective shows how socio-cognitive models account for differences in motivation by focusing on how students evaluate the worth of academic tasks.

Intrinsic subjective task value refers to the enjoyment or interest students expect from a learning activity. In SEVT, this is understood as situated intrinsic value, meaning that enjoyment is shaped by the learner’s immediate context rather that being a stable personal trait. Eccles and Wigfield (2020) argue that these contextual influences are central to how task values form and change. This is why the “S” was added to EVT: to emphasise that value is always shaped by the learner’s developmental, cultural, and situational context.

Task value research has been critiqued for focusing mainly on cognitive evaluations and overlooking how emotions, social pressures, and classroom climate shape students’ perceptions of value. Researchers also note that the different types of value can blur together in real learning situations, making them difficult to distinguish clearly (Eccles, 2005; Flake et al., 2015). These critiques highlight the need for approaches that consider how students’ experiences and environments influenct the value they assign to learning tasks.

{| class=&quot;wikitable&quot; style=&quot;margin: auto;&quot;
|-
! style=&quot;background:#B3BBE4;{{Text color default}};&quot; | Component 
! style=&quot;background:#B3BBE4;{{Text color default}};&quot; | Definition 
! style=&quot;background:#B3BBE4;{{Text color default}};&quot; | Example in education
|-
| style=&quot;background:#CEEEF4;{{Text color default}};&quot; | '''Expectancy''' 
| style=&quot;background:#CEEEF4;{{Text color default}};&quot; | Belief about ability to succeed 
| style=&quot;background:#CEEEF4;{{Text color default}};&quot; | &quot;I can pass this exam if I study.&quot;
|-
| style=&quot;background:#CEEEF4;;{{Text color default}};&quot; | '''Intrinsic value''' 
| style=&quot;background:#CEEEF4;{{Text color default}};&quot; | Enjoyment or interest in the task 
| style=&quot;background:#CEEEF4;{{Text color default}};&quot; | &quot;I enjoy learning psychology.&quot;
|-
| style=&quot;background:#CEEEF4;{{Text color default}};&quot; | '''Utility value''' 
| style=&quot;background:#CEEEF4;{{Text color default}};&quot; | Usefulness for future goals 
| style=&quot;background:#CEEEF4;{{Text color default}};&quot; | &quot;This unit is required for my degree.&quot;
|-
| style=&quot;background:#CEEEF4;{{Text color default}};&quot; | '''Attainment value''' 
| style=&quot;background:#CEEEF4;{{Text color default}};&quot; | Importance to identity 
| style=&quot;background:#CEEEF4;{{Text color default}};&quot; | &quot;Being good at maths matters to me.&quot;
|-
| style=&quot;background:#CEEEF4;{{Text color default}};&quot; | '''Cost''' 
| style=&quot;background:#CEEEF4;{{Text color default}};&quot; | Negative aspects of engagement 
| style=&quot;background:#CEEEF4;{{Text color default}};&quot; | &quot;This assignment is stressful and time-consuming.&quot;
|}

'''Table 1.''' Key components of expectancy-value theory and their relevance to educational motivation.

{| style=&quot;width:100%; background:#FFE1F4; color:black; border-radius:12px; border:0; padding:2px;&quot;
|-
! style=&quot;background:#F9C3E5; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;&quot; | Imagine this scenario
|-
| style=&quot;border-radius:0 0 12px 12px; padding:8px; border:0;&quot; |
&lt;div style=&quot;background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;&quot;&gt;

[[File:Science Lab at Pace Brantley Preparatory School.jpg|Science_Lab_at_Pace_Brantley_Preparatory_School|150px|alt= Science student's engaging in a group activity]]
&lt;br&gt;
&lt;span style=&quot;line-height:1.2; display:block; margin-top:2px;&quot;&gt;
'''Figure 3.'''. Science student's engaging in a group activity.
&lt;/span&gt;
&lt;/div&gt;
You are sitting in a crowded classroom during a weekly science workshop. The activity involves a group problem-solving task that requires quick thinking and collaboration. As the task begins, you notice that the instructions feel unclear, and your group members start discussing ideas rapidly. You hesitate, unsure whether your contribution will be helpful. This uncertainty lowers your confidence, even though you usually feel capable when working on similar material in quieter settings. The noise in the room makes it difficult to concentrate, and you begin to question whether the task is worth the effort at this moment. You remind yourself that the activity is part of your assessment, but the immediate pressure and social dynamics make the task feel less manageable.

This situation contrasts with the scenario at the beginning of this book chapter, where motivation was shaped by stable beliefs about ability and long-term goals. In the current example, motivation shifts in response to the environment, social interactions, and moment-to-moment changes in confidence. Situated expectancy-value theory explains these fluctuations by emphasising that expectancies and values are influenced by context and can vary across settings and activities (Eccles &amp; Wigfield, 2020). Figure 3 illustrates how these situational influences interact with expectancy and task value, showing that motivation is shaped not only by learners’ beliefs but also by the conditions in which learning occurs. The learner’s confidence decreases because the classroom environment feels overwhelming, and the value of the task changes because the immediate demands differ from previous experiences. 
|}

This scenario illustrates how expectancy and value can fluctuate in response to environmental and social cues, which reflects the situational perspective introduced in contemporary extensions of expectancy-value theory. Unlike the earlier example in the first scenario where motivation was guided by stable beliefs and long-term goals, this scenario shows how context can rapidly alter confidence and perceived task value. Situated expectancy-value theory highlights that motivation is shaped not only by what learners believe and value but also by the conditions under which learning takes place (Eccles &amp; Wigfield, 2020).

{| style=&quot;width:100%; background:#DBEAFA; color:black; border-radius:12px; border:0; padding:2px;&quot;
|-
! style=&quot;background:#B2E4FF; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;&quot; | What's happening in this space?
|-
| style=&quot;border-radius:0 0 12px 12px; padding:8px; border:0;&quot; |
'''The move towards situated expectancy-value theory'''&lt;br&gt;

Early EVT (Eccles et al., 1983) focused on stable beliefs about competence and task value. Later refinements clarified how social influences (teachers, parents, and peers) shape these beliefs. SEVT (2020) reframes motivation as dynamic and situated, showing that expectancies and values shift in response to classroom context, feedback, identity, and social interactions.&lt;br&gt;

''' The MUSIC model of motivation '''&lt;br&gt;
&lt;div style=&quot;background-color:#F6F4E7;{{Text color default}}; padding:8px; width:150px; float:right; text-align:center;&quot;&gt;
[[File:TED stage logo from Flickr (cropped).jpg|150px|alt=TED talk icon|link=https://www.youtube.com/watch?v=De5U-GE4YkE]]
&lt;br&gt;
&lt;span style=&quot;line-height:1.2; display:block; margin-top:2px;&quot;&gt;
'''''Figure 4'''. Expectancy-Value Theory, Motivating Others (Ep. 3), Brett D. Jones''
&lt;/span&gt;
&lt;/div&gt;
A recent extension of situated expectancy-value theory is the MUSIC Model of Motivation developed by Brett D. Jones. This model helps explain how motivation shifts across different learning environments, which is the key difference between EVT and SEVT. The first scenario in this chapter reflects traditional EVT, where motivation is guided by stable beliefs about ability and long-term goals (Eccles &amp; Wigfield, 2002). The second scenario reflects SEVT, where confidence and task value change in response to immediate environmental demands (Eccles &amp; Wigfield, 2020). The MUSIC model builds on this situational perspective by identifying five classroom features that shape students’ moment-to-moment motivation: empowerment, usefulness, success, interest, and caring. Empowerment helps students feel more in control of their learning, which can strengthen both expectancy beliefs and task value. Usefulness reflects how relevant a task feels to students’ goals and future needs, consistent with utility value (Eccles &amp; Wigfield, 2002). Success relates to students’ confidence in their ability to achieve desired outcomes. Interest captures the enjoyment and engagement students experience during learning, which aligns with intrinsic value (Eccles &amp; Wigfield, 2002). Caring reflects the supportive relationships in the classroom, which SEVT identifies as a key influence on how expectancies and values shift across contexts. Jones explains in his Motivating Others talk (Episode 3) that these elements help teachers design learning experiences that support students’ confidence and perceived value in different situations, which can be seen in Figure 4. The MUSIC model therefore extends EVT by showing how educators can intentionally shape classroom conditions to strengthen motivation in real time, a claim supported by intervention research demonstrating that increasing perceived usefulness enhances performance and retention (Canning et al., 2018).
|}

== How can expectancy-value theory be used to enhance motivation in educational settings? ==

Expectancy-value theory can be applied in several practical ways to strengthen students’ motivation in educational settings. By targeting expectancy beliefs, task values and perceived cost, educators can shape how students think about their abilityies, the importance of learning activities, and the effort required to complete them. The following sections outline key strategies grounded in EVT and explain how each can support more consistent and sustained engagement.

===Strngthening expectancy beliefs===

Strengthening expectany beliefs is one way Evt can be used to enhance motivation in educational settings. Students are more willing to engage when they believe they can succees,  and teachers can support this by providing support and guidance with how to approach tasks, breaking the work into manageable steps and providing clear feedback, in doing so will help build confidence strengthening their expectancy beliefs and enhancing motivation. Demonstrating effective strategies, such as thinking aloud while problem solving or showing how to organise information, helps students to see what successful performance looks like. Research shows that confidence develops through repeated experiences of mastery and supportive information, which increases students’ willingness to attempt challenging tasks (Bandura, 1997; Pajares &amp; Schunk, 2009). By helping students build a realistic sense of competence, educators create conditions where expectancy beliefs contribute to stronger and more sustained motivation.

===Enhancing task value===

Enhancing task values is another way EVT can be applied to strengthen motivation in educational settings. Students are more likely to engage when they see learning activities as relevant, useful, or personally meaningful, therefore teachers can support this by explaining how tasks connect to future goals or real-world situations. Highlighting the purpose behind an activity helps students understand why it matters, while providing eaxamples of how skills are used outside the classroom can increase perceived usefulness. Research shows that when students recognise the value of what they are learning, they invest more effort and show greater persistence (Eccled &amp; Wigfield, 2002; Harackiewicz &amp; Hulleman, 2009). By making the significance of academic tasks clear, educators can help students develop stronger and more eduring task values.

===Reducing perceived cost===

Reducing perceived cost is another way EVT can be applied to strengthen motivation in educational settings. Students are less willing to engage when tasks feel overwhelming, stressful, or too time-consuming, and research shows that these experiences can lower motivation (Flake et al., 2015). Teachers can support students by creating classroom environments that minimise these pressure through manageable workloads, breaking tasks into smaller steps, and offering opportunities for autonomy. Supportive classroom climates also help reduce stress and anxiety, making students more comfortable asking questions and attempting challenging work. Lowering perceived cost has been shown to increase engagement even when students already hold high intrinsic, utitility, or attainment value for a task (Flake et al., 2015), meaning that reducing stress and workload pressure can still make a meaningful difference for learners who otherwise see the activity as valuable.

===Harackiewicz &amp; Hulleman's (2009), utility-value intervention===

A practical example of EVT in educational settings is the utility-value intervention, where students complete a short writing task that asks them to explain how a learning activity connects to their personal goals or future plans. This process helps students recognise the usefuleness of what they are learning, which increases task value and encourages greater engagement. Howerver, the writing component can be difficult for students with lower literacy skills, which limits the effectiveness of the intervention for those who may benefit from it the most. Half redundant in terms that it boosts motivation in those who may not particularly need it and reduce confidence in those that do. Despite this limitation, the approach has been shown to improve motivation and academic performance, particularly for students with lower initial expectancy beliefs (Harackiewicz &amp; Hulleman, 2009).

===Critique for applying EVT in educational settings===

Increasing task values or expectancy beliefs may have a limited impact when students face broader structural barriers such as poor teaching quality, limited resources, or high levels of stress and anxiety. These conditions can restrict students’ opportunities to engage, even when they recognise the value of a task or believe they can succeed. EVT-based strategies also rely on ongoing support, and without consistent reinforcement they can be difficult to maintain over time (Eccles &amp; Wigfield, 2002).

== Knowledge checkpoint ==
{| style=&quot;width:50%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;&quot;
|-
! style=&quot;background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;&quot; | &lt;big&gt;Quiz&lt;/big&gt;
|-
| style=&quot;border-radius:0 0 12px 12px; padding:2px; border:0;&quot; |

&lt;div style=&quot;margin-top:-15px;&quot;&gt;
&lt;quiz display=simple&gt;
{Which component of expectancy-value theory refers to a student's belief about their ability to succeed?
|type=&quot;()&quot;}
+ Expectancy
- Intrinsic value
- Utility value
- Cost

{Which value component of EVT reflects how enjoyable or interesting a task is?
|type=&quot;()&quot;}
- Attainment value
+ Intrinsic value
- Utility value
- Cost

{What was added to the updated theory SEVT that was not a component of traditional EVT?
|type=&quot;()&quot;}
- Stable, long-term beliefs about ability
- The inclusion of cost value
+ The idea that motivation is shaped by situational and contextual factors
- The addition of attainment value
}
&lt;/quiz&gt;
&lt;/div&gt;

|}

==Conclusion==

Expectancy-value theory offers a clear and practical framework for understanding why students engage with learning tasks and how their motivation can be strengthened in educational settings. Expectancy beliefs shape students’ confidence in their ability to succeed, influencing effort, persistence, and engagement. Task values determine how important, interesting or useful a learning activity feels, guiding students’ willingness to invest time and energy. Together, these components show motivation increases when students believe they can succeed and when they view tasks as meaningful relevant or aligned with their personal goals.
Applying EVT in classrooms involves strengthening expectancy beliefs through supportive feedback and structured guidance, enhancing task calues by emphasising relevance and usefulness, and reducing perceived cost by minimising stress, workload pressure, and emotional barriers. These strategies help create learning environments where students are more willing to participate, persist, and engage with academic tasks. Overall, EVT provides educators with a practical, evidence-based approach for improving student motivations in everyday classroom contexts.

{| style=&quot;width:100%; background:#FEFB9F; color:black; border-radius:12px; border:0;&quot;
|-
! style=&quot;background:#FFD208; color:black; border-radius:12px 12px 0 0; border:0;&quot; | Take-home messages
|-
| style=&quot;border-radius:0 0 12px 12px; padding:10px; border:0;&quot; |
* Students engage more when they feel capable and see value in the task.
* Clear feedback, manageable steps, and modelling strategies help build expectancy beliefs.
* Connecting tasks to real-world relevance strengthens task value.
*Reducing stress, workload pressure, and anxiety lowers perceived cost, supporting engagement.
*Motivation is context-sensitive, meaning classroom climate and task design matter.
|}

== See also ==

*[[Achievement motivation]] (Book chapter 2011)

*[[wikipedia:Educational_psychology|Educational psychology]] (Wikipedia)

*[[wikipedia:Expectancy-value_theory|Expectancy-value theory]] (Wikipedia)

*[[wikipedia:Motivation|Motivation]] (Wikipedia)

== External links ==

*[https://study.com/academy/lesson/video/the-expectancy-value-theory-of-motivation.html Expactancy-value theory video] (Study.com)

*[https://www.simplypsychology.org/differences-between-extrinsic-and-intrinsic-motivation.html Extrinsic vs. Intrinsic Motivation: What’s the Difference?] (Verywell Mind article)

*[https://education.okstate.edu/site-files/documents/motivation-classrooms/motivation-minute-expectancy-value-theory.pdf Motivation minute: Expectancy-value theory] (Oklahoma State University, professional teaching resource)

*[https://www.youtube.com/watch?v=De5U-GE4YkE Expectancy-Value Theory - Motivating Others Ep. 3] (Ted talk by Brett D. Jones, PhD, Professor at Virginia Tech)

==References insert italics where neccessary==

{{Hanging indent|1=

Bandura, A. (1997). Self-efficacy: The exercise of control. W. H. Freeman.

Canning, E. A., Harackiewicz, J. M., Priniski, S. J., Hecht, C. A., Tibbetts, Y., &amp; Hyde, J. S. (2018). Improving performance and retention in introductory biology with a utility-value intervention. Journal of Educational Psychology, 110(6), 834–849. https://doi.org/10.1037/edu0000244

Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot &amp; C. S. Dweck (Eds.), Handbook of competence and motivation (pp. 105–121). Guilford Press.

Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., &amp; Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), Achievement and achievement motives (pp. 75–146). W. H. Freeman.

Eccles, J. S., &amp; Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual Review of Psychology, 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153

Eccles, J. S., &amp; Wigfield, A. (2020). From expectancy–value theory to situated expectancy–value theory: A developmental, social cognitive, and sociocultural perspective on motivation. Contemporary Educational Psychology, 61, Article 101859. https://doi.org/10.1016/j.cedpsych.2020.101859

EricEdwardWilson714. (2021, July 21). Science lab at Pace Brantley Preparatory School [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Science_Lab_at_Pace_Brantley_Preparatory_School.jpg

Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., &amp; Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. Contemporary Educational Psychology, 41, 232–244. https://doi.org/10.1016/j.cedpsych.2015.03.002

Harackiewicz, J. M., &amp; Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. Annual Review of Psychology, 69, 409–435. https://doi.org/10.1146/annurev-psych-122216-011725

Hulleman, C. S., &amp; Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. Science, 326(5958), 1410–1412. https://doi.org/10.1126/science.1177067

Lazowski, R. A., &amp; Hulleman, C. S. (2016). Motivation Interventions in Education: A Meta-Analytic Review. Review of Educational Research, 86(2), 602–640. https://doi.org/10.3102/0034654315617832

Pajares, F. (1996). Self-efficacy beliefs in academic settings. Review of Educational Research, 66(4), 543–578. https://doi.org/10.3102/00346543066004543

Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation in Learning and Teaching Contexts. Journal of Educational Psychology, 95(4), 667–686. https://doi.org/10.1037/0022-0663.95.4.667

S00246164. (2025). Motivation Laptop.svg [SVG image]. Wikiversity. https://en.wikiversity.org/wiki/File:Motivation_Laptop.svg 

Schunk, D. H., &amp; Pajares, F. (2009). Self-efficacy theory. In K. R. Wentzel &amp; A. Wigfield (Eds.), Handbook of motivation at school (pp. 35–53). Routledge.

Wigfield, A., &amp; Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. Developmental Review, 30, 1–35. https://doi.org/10.1016/j.dr.2009.12.001 

Wigfield, A., &amp; Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81. https://doi.org/10.1006/ceps.1999.1015

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      <text bytes="16857" sha1="tdfw7zslboq4hftla83ratj0y1v88sl" xml:space="preserve">{{title|Emotional effects of incarceration on Indigenous Australians:&lt;br&gt;What are the emotional effects of incarceration on Indigenous Australians? }}
__TOC__

==Overview==
{{RoundBoxTop|theme=12}}
[[File:Kakadu (AU), Kakadu National Park, Anbangbang Rock Shelter -- 2019 -- 4106.jpg|thumb|250px|'''Figure 1'''. Emotional wellbeing for Indigenous Australians is viewed as health, connected with the land, culture, and community.]]

; Case study
In January of 2021, an unnamed incarcerated Aboriginal woman on remand at the [[w:Alexander Maconochie Centre|Alexander Maconochie Centre in the ACT]] was allegedly strip searched by four guards in riot gear, within view of male detainees (Larkin, 2021). The woman is a victim of a previous sexual assault.

This case, amongst others, has caused concern among health care professionals who work with Aboriginal women detainees (Larkin, 2021). For many First Nations communities, the showing of a woman's sensitive body parts is considered sacred to women's business (Thompson &amp; Archibald-Binge, 2020). This lore and culture has been practised for thousands of years. The separation of men's and women's business, and strict traditions and customs is central to many [[w:Australian Aboriginal culture|Aboriginal cultures]]. The conduct and nature of these traditions recognises and respects particular roles, ceremony and lore sacred to men and women (Sydney Nature Team, 2025). The customs and practices within men's and women's business are strict and if the rules are broken, harsh punishment is to follow. 

&quot;If women's business is conducted in front of males, cultural shame is likely to be the result. This is extremely distressing and would stay with the woman for a long time,&quot; (Thompson &amp; Archibald-Binge, 2020).

This local case, alongside many others, acknowledges how the absence of cultural safety within institutional practice can undermine Indigenous wellbeing. This chapter explores the social and emotional wellbeing model and the emotional effects of incarceration on Indigenous Australians. 

{{RoundBoxBottom}}

* Introduction to the problem: Indigenous Australians are incarcerated at a disproportionately high rate, accounting for 37% of all persons in custody as of March 2025 (ABS, 2025).
* &quot;Research shows that imprisonment has negative impacts on the physical and mental health of incarcerated individuals, and these impacts persist after release.&quot; - (Impacts of Imprisonment | Bugmy Bar Book, 2023) {{ic|Include page numbers for quotes (APA style)}}
* Incarceration significantly implicates{{huh}} the cultural and relational connections to land and kin which are directly correlational with wellbeing for many Indigenous Australians. 
* Introduction to the model/theory: Social and Emotional Wellbeing (SEWB) model was developed to support and strengthen Indigenous mental health --&gt; The SEWB model is a holistic, multi-dimensional concept of wellbeing which takes into account the impacts of the history of colonisation (Dudgeon, 2026).
* How incarceration negatively impacts Indigenous emotional wellbeing --&gt; which also affects mental health. 
* The SEWB model recognises that connection to land, sea, culture, and spirituality contribute to wellbeing.
* Incarceration affects SEWB domains --&gt; physical separation from family members, restricted cultural practice, removal from country. 
* Why does this matter? ...Access to culturally safe, responsive, and person-centred services is essential to improving the emotional wellbeing of Indigenous Australians in custody (Department of the Prime Minister and Cabinet, 2017). --&gt; Essential that psychological science be informed by Indigenous understandings of wellbeing.

{{RoundBoxTop|theme=11}}
'''Focus questions'''

* What is the relationship between incarceration and the emotional wellbeing of Indigenous Australians?
* What broader factors are affected by high rates of offending and imprisonment among First Nations people?
* What is the Social and Emotional Wellbeing (SEWB) model? 
* How does incarceration affect the domains of social and emotional wellbeing?
* What does the Social and Emotional Wellbeing model contribute that westernised frameworks don't?
{{RoundBoxBottom}}

==Incarceration and emotional wellbeing==
'''Focus question:''' ''What is the relationship between incarceration and the emotional wellbeing of Indigenous Australians?''
==What contributes to high offending rates and imprisonment among First Nations people?==
'''Focus question:''' ''What broader factors are affected by high rates of offending and imprisonment among First Nations people?''
===Modifiable factors===
====Education====
====Employment====
====Housing====
====Removal from family====
====Living in a single-parent family====
====Experience of physical harm====
====Physical and mental health====
====Financial stress====
====Alcohol and drug use====
====Adverse childhood experiences====

==Social and Emotional Wellbeing==
'''Focus question:''' ''What is the Social and Emotional Wellbeing (SEWB) model?'' 
Social and Emotional Wellbeing (SEWB) is a stepped care model which is dedicated to focalising Aboriginal and Torres Strait Islander social and emotional wellbeing and mental health. The term social and emotional wellbeing (SEWB) is used by many Aboriginal and Torres Strait Islander people to describe the social, emotional, spiritual, and cultural wellbeing of a person (Gee et al., 2014). 
According to Gee et al., (2014), SEWB is the preferred term used to describe an individual's wellbeing as it corresponds with a holistic view of health, compared to using terms such as mental health and mental illness as it is perceived as medical terms that focalise on problems, and do not properly describe all the factors that make up and influence wellbeing.  

The SEWB framework has nine principles that define the concept of SEWB:
# Aboriginal and Torres Strait Islander health is viewed in a holistic context that encompasses mental, physical, cultural, and spiritual health. Land is central to wellbeing. The disruption of these interrelations will result in Aboriginal and Torres Strait Islander ill health (Dudgeon et al., 2014, p. xxiv). 
# Self-determination is central to the provision of Aboriginal and Torres Strait Islander health services (Dudgeon et al., 2014, p. xxiv).
# Culturally valid understandings must inform the provision of services and must guide assessment, care, and management of Aboriginal and Torres Strait Islander peoples health problems generally, and mental health problems in particular (Dudgeon et al., 2014, p. xxiv). 
# Trauma and loss which has been present since European invasion are a direct outcome of the disruption to cultural wellbeing. Trauma and loss of this magnitude continue to have intergenerational effects. This concept must be recognised (Dudgeon et al., 2014, p. xxiv). 
# The human rights of Aboriginal and Torres Strait Islander peoples must be recognised and respected. Human rights relevant to mental illness must be specifically addressed (Dudgeon et al., 2014, p. xxiv). 
# Racism, stigma, environmental adversity and social disadvantage constitute ongoing stressors and have negative impacts on Aboriginal and Torres Strait Islander people's mental health and wellbeing (Dudgeon et al., 2014, p. xxiv). 
# Recognition of the centrality of Aboriginal and Torres Strait Islander family and kinship must be recognised as well as the broader concepts of family and the bonds of reciprocal affection, responsibility and sharing (Dudgeon et al., 2014, p. xxiv). 
# Aboriginal or Torres Strait Islander culture or groups are not singular, but rather hundreds of groupings, languages, kinships, tribes, and ways of living and being. Aboriginal or Torres Strait Islander peoples may currently live in urban, rural, or remote settings, in urbanised, traditional, or other lifestyles and frequently move between these ways of living (Dudgeon et al., 2014, p. xxiv).
# Aboriginal and Torres Strait Islander peoples have great strengths, creativity, and endurance and a deep understanding of the relationships between human beings and their environment (Dudgeon et al., 2014, p. xxiv).

[[File:Determinants of social and emotional wellbeing.png|thumb|300px|'''Figure 1'''. Determinants of social and emotional wellbeing. Adapted from [Dudgeon &amp; Walker, 2015].]]

Figure 1, displays that the SEWB of individuals, families and communities are shaped by connections to body, mind and emotions, family and kinship, community, culture, land, and spirituality. ‘Connection’ refers to the diverse ways in which people experience and express these various domains of SEWB throughout the course of their lives. The nature of these connections are affected by the differentiation of needs across the lifespan (childhood, youth, adulthood, and old age) (Gee et al., 2014, p. 57). The disruption of these connections can result in higher likeliness of experiencing poorer SEWB (Gee at l., 2014, p. 58). 

==How incarceration affects SEWB domains==
'''Focus question:''' ''How does incarceration affect the domains of social and emotional wellbeing?''
* colonial impact (colonisation) --&gt; cultural, economic, and social bases of Indigenous lives and health has been significantly impacted by colonialism (&quot;through disease, massacre, dispossession of lands, relocation, forced labor, removal of children, and enforced cultural assimilation.&quot;)(Battams et al., 2021)

==Connection to community==
* Separation
* Limited/restrictive nature of visitation

==Connection to country==
* Removal from country
* Inability to participate or attend (in/to) cultural practices (ceremonies, obligations etc).
* Reference to opening case study, not only is incarceration and the criminal justice system preventing cultural agency for Indigenous Australians, but it is complicit in the cultural discrimination of Aboriginal lore and culture (Larkin, 2021). This point is quite direct; further elaborate.
* Identity within country and within the land.

==Emotional and mental wellbeing==
* Direct implications on wellbeing due to incarceration.

===Emotional resilience, and protective factors===
'''Focus Question:''' ''What factors improve/support emotional resilience during and after incarceration?''
===Why the Social and Emotional Wellbeing model?===
'''Focus Question:''' ''What does the Social and Emotional Wellbeing model contribute that Westernised frameworks don't?''
* Western definitions of mental health do not align with Aboriginal perspectives of health and wellbeing which endorse a more holistic approach to their conceptualisation (Harrison, 2021).

==Figures==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]]

* For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure; this can be the figure in the scenario
* For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples
* Images must be embedded from [[commons:|Wikimedia Commons]] which hosts free-to-use media such as photos, diagrams, graphs, video, and audio
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text)
* Cite each figure at least once in the main text (e.g., see Figure 2)

==Learning features==
;Quizzes
* One or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=simple&gt;
{The purpose of quizzes is to provide an interactive learning feature:
|type=&quot;()&quot;}
+ True
- False

{Long and complex quiz questions are recommended:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

==Future directions/recommendations==
Note: this section could be added to discuss future directions, and ways to improve the emotional wellbeing of Indigenous Australians in custody.

==Conclusion==
* Arguably the most important section
* Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking
* For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
List [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity)
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)
* [[w:Self determination theory|Self determination theory]] (Wikipedia)
* [[Motivation and emotion/Assessment/Topic/Checklist|Topic development - Checklist]] (Wikiversity)
* [https://en.wikipedia.org/wiki/Indigenous_Australians_and_crime Indigenous incarceration]
* [https://en.wikipedia.org/wiki/Closing_the_Gap Closing the gap]

==References==
{{Hanging indent|1=

Australian Bureau of Statistics. (2025). ''Corrective services, Australia, March quarter 2025''. https://www.abs.gov.au/statistics/people/crime-and-justice/corrective-services-australia/latest-release

Australian Institute of Health and Welfare. (2025). ''Social and emotional wellbeing''. https://www.aihw.gov.au/reports/indigenous-mental-health-suicide-prevention/social-emotional-wellbeing

Battams, S., Delany-Crowe, T., Fisher, M., Wright, L., Krieg, A., McDermott, D., &amp; Baum, F. (2021). Applying crime prevention and health promotion frameworks to the problem of high incarceration rates for Aboriginal and Torres Strait Islander populations: Lessons from a case study from Victoria. ''International Indigenous Policy Journal'', ''12''(2), 1–29. https://doi.org/10.18584/iipj.2021.12.2.10208

Department of the Prime Minister and Cabinet. (2017, April 4). ''National strategic framework for Aboriginal and Torres Strait Islander peoples' mental health and social and emotional wellbeing 2017–2023''. Australian Indigenous HealthInfoNet. https://healthinfonet.ecu.edu.au/key-resources/policies-and-strategies/33834/

Dudgeon, P. (2026, May 26). ''Pat Dudgeon AM FAPS on developing the social and emotional wellbeing model to support Indigenous communities''. Australian Psychological Society. https://psychology.org.au/insights/pat-dudgeon-am-sewb-model

Dudgeon, P., &amp; Walker, R. (2015). Decolonising Australian psychology: Discourses, strategies, and practice. ''Journal of Social and Political Psychology'', ''3''(1). https://doi.org/10.5964/jspp.v3i1.4857

}}

==External links==
* [https://www.aihw.gov.au/reports/indigenous-australians/closing-the-gap-targets-key-findings-implications/contents/criminal-justice Closing the Gap targets: Key findings – Criminal justice] (Australian Institute of Health and Welfare)
* [https://www.myiacfp.org/the-relationship-between-justice-system-involvement-and-the-social-and-emotional-wellbeing-sewb-of-aboriginal-and-torres-strait-islander-youth/ The relationship between justice system involvement and the social and emotional wellbeing (SEWB) of Aboriginal and Torres Strait Islander youth] (IACFP)
* [https://bugmybarbook.org.au/chapters/imprisonment/ Imprisonment] (Bugmy Bar Book)
* [https://theconversation.com/excessive-strip-searching-shines-light-on-discrimination-of-aboriginal-women-in-the-criminal-justice-system-163969 Excessive strip searching shines light on discrimination of Aboriginal women in the criminal justice system] (The Conversation)
* [https://www.smh.com.au/national/nsw/aboriginal-girl-fights-to-exclude-men-from-seeing-strip-search-footage-20200310-p548pu.html Aboriginal girl fights to exclude men from seeing strip search footage] (Sydney Morning Herald)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
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__TOC__

==Overview==
{{RoundBoxTop|theme=12}}
[[File:Kakadu (AU), Kakadu National Park, Anbangbang Rock Shelter -- 2019 -- 4106.jpg|thumb|250px|'''Figure 1'''. Emotional wellbeing for Indigenous Australians is viewed as health, connected with the land, culture, and community.]]

; Case study
In January of 2021, an unnamed incarcerated Aboriginal woman on remand at the [[w:Alexander Maconochie Centre|Alexander Maconochie Centre in the ACT]] was allegedly strip searched by four guards in riot gear, within view of male detainees (Larkin, 2021). The woman is a victim of a previous sexual assault.

This case, amongst others, has caused concern among health care professionals who work with Aboriginal women detainees (Larkin, 2021). For many First Nations communities, the showing of a woman's sensitive body parts is considered sacred to women's business (Thompson &amp; Archibald-Binge, 2020). This lore and culture has been practised for thousands of years. The separation of men's and women's business, and strict traditions and customs is central to many [[w:Australian Aboriginal culture|Aboriginal cultures]]. The conduct and nature of these traditions recognises and respects particular roles, ceremony and lore sacred to men and women (Sydney Nature Team, 2025). The customs and practices within men's and women's business are strict and if the rules are broken, harsh punishment is to follow. 

&quot;If women's business is conducted in front of males, cultural shame is likely to be the result. This is extremely distressing and would stay with the woman for a long time,&quot; (Thompson &amp; Archibald-Binge, 2020).

This local case, alongside many others, acknowledges how the absence of cultural safety within institutional practice can undermine Indigenous wellbeing. This chapter explores the social and emotional wellbeing model and the emotional effects of incarceration on Indigenous Australians. 

{{RoundBoxBottom}}

* Introduction to the problem: Indigenous Australians are incarcerated at a disproportionately high rate, accounting for 37% of all persons in custody as of March 2025 (ABS, 2025).
* &quot;Research shows that imprisonment has negative impacts on the physical and mental health of incarcerated individuals, and these impacts persist after release.&quot; - (Impacts of Imprisonment | Bugmy Bar Book, 2023) {{ic|Include page numbers for quotes (APA style)}}
* Incarceration significantly implicates{{huh}} the cultural and relational connections to land and kin which are directly correlational with wellbeing for many Indigenous Australians. 
* Introduction to the model/theory: Social and Emotional Wellbeing (SEWB) model was developed to support and strengthen Indigenous mental health --&gt; The SEWB model is a holistic, multi-dimensional concept of wellbeing which takes into account the impacts of the history of colonisation (Dudgeon, 2026).
* How incarceration negatively impacts Indigenous emotional wellbeing --&gt; which also affects mental health. 
* The SEWB model recognises that connection to land, sea, culture, and spirituality contribute to wellbeing.
* Incarceration affects SEWB domains --&gt; physical separation from family members, restricted cultural practice, removal from country. 
* Why does this matter? ...Access to culturally safe, responsive, and person-centred services is essential to improving the emotional wellbeing of Indigenous Australians in custody (Department of the Prime Minister and Cabinet, 2017). --&gt; Essential that psychological science be informed by Indigenous understandings of wellbeing.

{{RoundBoxTop|theme=11}}
'''Focus questions'''

* What is the relationship between incarceration and the emotional wellbeing of Indigenous Australians?
* What broader factors are affected by high rates of offending and imprisonment among First Nations people?
* What is the Social and Emotional Wellbeing (SEWB) model? 
* How does incarceration affect the domains of social and emotional wellbeing?
* What does the Social and Emotional Wellbeing model contribute that westernised frameworks don't?
{{RoundBoxBottom}}

==Incarceration and emotional wellbeing==
'''Focus question:''' ''What is the relationship between incarceration and the emotional wellbeing of Indigenous Australians?''
==What contributes to high offending rates and imprisonment among First Nations people?==
'''Focus question:''' ''What broader factors are affected by high rates of offending and imprisonment among First Nations people?''
===Modifiable factors===
====Education====
====Employment====
====Housing====
====Removal from family====
====Living in a single-parent family====
====Experience of physical harm====
====Physical and mental health====
====Financial stress====
====Alcohol and drug use====
====Adverse childhood experiences====

==Social and Emotional Wellbeing==
'''Focus question:''' ''What is the Social and Emotional Wellbeing (SEWB) model?'' 
Social and Emotional Wellbeing (SEWB) is a stepped care model which is dedicated to focalising Aboriginal and Torres Strait Islander social and emotional wellbeing and mental health. The term social and emotional wellbeing (SEWB) is used by many Aboriginal and Torres Strait Islander people to describe the social, emotional, spiritual, and cultural wellbeing of a person (Gee et al., 2014). 
According to Gee et al., (2014), SEWB is the preferred term used to describe an individual's wellbeing as it corresponds with a holistic view of health, compared to using terms such as mental health and mental illness as it is perceived as medical terms that focalise on problems, and do not properly describe all the factors that make up and influence wellbeing.  

The SEWB framework has nine principles that define the concept of SEWB:
# Aboriginal and Torres Strait Islander health is viewed in a holistic context that encompasses mental, physical, cultural, and spiritual health. Land is central to wellbeing. The disruption of these interrelations will result in Aboriginal and Torres Strait Islander ill health (Dudgeon et al., 2014, p. xxiv). 
# Self-determination is central to the provision of Aboriginal and Torres Strait Islander health services (Dudgeon et al., 2014, p. xxiv).
# Culturally valid understandings must inform the provision of services and must guide assessment, care, and management of Aboriginal and Torres Strait Islander peoples health problems generally, and mental health problems in particular (Dudgeon et al., 2014, p. xxiv). 
# Trauma and loss which has been present since European invasion are a direct outcome of the disruption to cultural wellbeing. Trauma and loss of this magnitude continue to have intergenerational effects. This concept must be recognised (Dudgeon et al., 2014, p. xxiv). 
# The human rights of Aboriginal and Torres Strait Islander peoples must be recognised and respected. Human rights relevant to mental illness must be specifically addressed (Dudgeon et al., 2014, p. xxiv). 
# Racism, stigma, environmental adversity and social disadvantage constitute ongoing stressors and have negative impacts on Aboriginal and Torres Strait Islander people's mental health and wellbeing (Dudgeon et al., 2014, p. xxiv). 
# Recognition of the centrality of Aboriginal and Torres Strait Islander family and kinship must be recognised as well as the broader concepts of family and the bonds of reciprocal affection, responsibility and sharing (Dudgeon et al., 2014, p. xxiv). 
# Aboriginal or Torres Strait Islander culture or groups are not singular, but rather hundreds of groupings, languages, kinships, tribes, and ways of living and being. Aboriginal or Torres Strait Islander peoples may currently live in urban, rural, or remote settings, in urbanised, traditional, or other lifestyles and frequently move between these ways of living (Dudgeon et al., 2014, p. xxiv).
# Aboriginal and Torres Strait Islander peoples have great strengths, creativity, and endurance and a deep understanding of the relationships between human beings and their environment (Dudgeon et al., 2014, p. xxiv).

[[File:Determinants of social and emotional wellbeing.png|thumb|300px|'''Figure 1'''. Determinants of social and emotional wellbeing. Adapted from [Dudgeon &amp; Walker, 2015].]]

Figure 1, displays that the SEWB of individuals, families and communities are shaped by connections to body, mind and emotions, family and kinship, community, culture, land, and spirituality. ‘Connection’ refers to the diverse ways in which people experience and express these various domains of SEWB throughout the course of their lives. The nature of these connections are affected by the differentiation of needs across the lifespan (childhood, youth, adulthood, and old age) (Gee et al., 2014, p. 57). The disruption of these connections can result in higher likeliness of experiencing poorer SEWB (Gee at l., 2014, p. 58). 

==How incarceration affects SEWB domains==
'''Focus question:''' ''How does incarceration affect the domains of social and emotional wellbeing?''
* colonial impact (colonisation) --&gt; cultural, economic, and social bases of Indigenous lives and health has been significantly impacted by colonialism (&quot;through disease, massacre, dispossession of lands, relocation, forced labor, removal of children, and enforced cultural assimilation.&quot;)(Battams et al., 2021)

==Connection to community==
* Separation
* Limited/restrictive nature of visitation

==Connection to country==
* Removal from country
* Inability to participate or attend (in/to) cultural practices (ceremonies, obligations etc).
* Reference to opening case study, not only is incarceration and the criminal justice system preventing cultural agency for Indigenous Australians, but it is complicit in the cultural discrimination of Aboriginal lore and culture (Larkin, 2021). This point is quite direct; further elaborate.
* Identity within country and within the land.

==Emotional and mental wellbeing==
* Direct implications on wellbeing due to incarceration.

===Emotional resilience, and protective factors===
'''Focus Question:''' ''What factors improve/support emotional resilience during and after incarceration?''
===Why the Social and Emotional Wellbeing model?===
'''Focus Question:''' ''What does the Social and Emotional Wellbeing model contribute that Westernised frameworks don't?''
* Western definitions of mental health do not align with Aboriginal perspectives of health and wellbeing which endorse a more holistic approach to their conceptualisation (Harrison, 2021).

==Figures==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]]

* For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure; this can be the figure in the scenario
* For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples
* Images must be embedded from [[commons:|Wikimedia Commons]] which hosts free-to-use media such as photos, diagrams, graphs, video, and audio
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text)
* Cite each figure at least once in the main text (e.g., see Figure 2)

==Learning features==
;Quizzes
* One or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=simple&gt;
{The purpose of quizzes is to provide an interactive learning feature:
|type=&quot;()&quot;}
+ True
- False

{Long and complex quiz questions are recommended:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

==Future directions/recommendations==
Note: this section could be added to discuss future directions, and ways to improve the emotional wellbeing of Indigenous Australians in custody.

==Conclusion==
* Arguably the most important section
* Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking
* For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
* [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity)
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)
* [[w:Self determination theory|Self determination theory]] (Wikipedia)
* [[Motivation and emotion/Assessment/Topic/Checklist|Topic development - Checklist]] (Wikiversity)
* [https://en.wikipedia.org/wiki/Indigenous_Australians_and_crime Indigenous incarceration]
* [https://en.wikipedia.org/wiki/Closing_the_Gap Closing the gap]

==References==
{{Hanging indent|1=

Australian Bureau of Statistics. (2025). ''Corrective services, Australia, March quarter 2025''. https://www.abs.gov.au/statistics/people/crime-and-justice/corrective-services-australia/latest-release

Australian Institute of Health and Welfare. (2025). ''Social and emotional wellbeing''. https://www.aihw.gov.au/reports/indigenous-mental-health-suicide-prevention/social-emotional-wellbeing

Battams, S., Delany-Crowe, T., Fisher, M., Wright, L., Krieg, A., McDermott, D., &amp; Baum, F. (2021). Applying crime prevention and health promotion frameworks to the problem of high incarceration rates for Aboriginal and Torres Strait Islander populations: Lessons from a case study from Victoria. ''International Indigenous Policy Journal'', ''12''(2), 1–29. https://doi.org/10.18584/iipj.2021.12.2.10208

Department of the Prime Minister and Cabinet. (2017, April 4). ''National strategic framework for Aboriginal and Torres Strait Islander peoples' mental health and social and emotional wellbeing 2017–2023''. Australian Indigenous HealthInfoNet. https://healthinfonet.ecu.edu.au/key-resources/policies-and-strategies/33834/

Dudgeon, P. (2026, May 26). ''Pat Dudgeon AM FAPS on developing the social and emotional wellbeing model to support Indigenous communities''. Australian Psychological Society. https://psychology.org.au/insights/pat-dudgeon-am-sewb-model

Dudgeon, P., &amp; Walker, R. (2015). Decolonising Australian psychology: Discourses, strategies, and practice. ''Journal of Social and Political Psychology'', ''3''(1). https://doi.org/10.5964/jspp.v3i1.4857

}}

==External links==
* [https://www.aihw.gov.au/reports/indigenous-australians/closing-the-gap-targets-key-findings-implications/contents/criminal-justice Closing the Gap targets: Key findings – Criminal justice] (Australian Institute of Health and Welfare)
* [https://www.myiacfp.org/the-relationship-between-justice-system-involvement-and-the-social-and-emotional-wellbeing-sewb-of-aboriginal-and-torres-strait-islander-youth/ The relationship between justice system involvement and the social and emotional wellbeing (SEWB) of Aboriginal and Torres Strait Islander youth] (IACFP)
* [https://bugmybarbook.org.au/chapters/imprisonment/ Imprisonment] (Bugmy Bar Book)
* [https://theconversation.com/excessive-strip-searching-shines-light-on-discrimination-of-aboriginal-women-in-the-criminal-justice-system-163969 Excessive strip searching shines light on discrimination of Aboriginal women in the criminal justice system] (The Conversation)
* [https://www.smh.com.au/national/nsw/aboriginal-girl-fights-to-exclude-men-from-seeing-strip-search-footage-20200310-p548pu.html Aboriginal girl fights to exclude men from seeing strip search footage] (Sydney Morning Herald)

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__TOC__

==Overview==
{{RoundBoxTop|theme=12}}
[[File:Kakadu (AU), Kakadu National Park, Anbangbang Rock Shelter -- 2019 -- 4106.jpg|thumb|250px|'''Figure 1'''. Emotional wellbeing for Indigenous Australians is viewed as health, connected with the land, culture, and community.]]

; Case study
In January of 2021, an unnamed incarcerated Aboriginal woman on remand at the [[w:Alexander Maconochie Centre|Alexander Maconochie Centre in the ACT]] was allegedly strip searched by four guards in riot gear, within view of male detainees (Larkin, 2021). The woman is a victim of a previous sexual assault.

This case, amongst others, has caused concern among health care professionals who work with Aboriginal women detainees (Larkin, 2021). For many First Nations communities, the showing of a woman's sensitive body parts is considered sacred to women's business (Thompson &amp; Archibald-Binge, 2020). This lore and culture has been practised for thousands of years. The separation of men's and women's business, and strict traditions and customs is central to many [[w:Australian Aboriginal culture|Aboriginal cultures]]. The conduct and nature of these traditions recognises and respects particular roles, ceremony and lore sacred to men and women (Sydney Nature Team, 2025). The customs and practices within men's and women's business are strict and if the rules are broken, harsh punishment is to follow. 

&quot;If women's business is conducted in front of males, cultural shame is likely to be the result. This is extremely distressing and would stay with the woman for a long time,&quot; (Thompson &amp; Archibald-Binge, 2020).

This local case, alongside many others, acknowledges how the absence of cultural safety within institutional practice can undermine Indigenous wellbeing. This chapter explores the social and emotional wellbeing model and the emotional effects of incarceration on Indigenous Australians. 

{{RoundBoxBottom}}

* Introduction to the problem: Indigenous Australians are incarcerated at a disproportionately high rate, accounting for 37% of all persons in custody as of March 2025 (ABS, 2025).
* &quot;Research shows that imprisonment has negative impacts on the physical and mental health of incarcerated individuals, and these impacts persist after release.&quot; - (Impacts of Imprisonment | Bugmy Bar Book, 2023) {{ic|Include page numbers for quotes (APA style)}}
* Incarceration significantly implicates{{huh}} the cultural and relational connections to land and kin which are directly correlational with wellbeing for many Indigenous Australians. 
* Introduction to the model/theory: Social and Emotional Wellbeing (SEWB) model was developed to support and strengthen Indigenous mental health --&gt; The SEWB model is a holistic, multi-dimensional concept of wellbeing which takes into account the impacts of the history of colonisation (Dudgeon, 2026).
* How incarceration negatively impacts Indigenous emotional wellbeing --&gt; which also affects mental health. 
* The SEWB model recognises that connection to land, sea, culture, and spirituality contribute to wellbeing.
* Incarceration affects SEWB domains --&gt; physical separation from family members, restricted cultural practice, removal from country. 
* Why does this matter? ...Access to culturally safe, responsive, and person-centred services is essential to improving the emotional wellbeing of Indigenous Australians in custody (Department of the Prime Minister and Cabinet, 2017). --&gt; Essential that psychological science be informed by Indigenous understandings of wellbeing.

{{RoundBoxTop|theme=11}}
'''Focus questions'''

* What is the relationship between incarceration and the emotional wellbeing of Indigenous Australians?
* What broader factors are affected by high rates of offending and imprisonment among First Nations people?
* What is the Social and Emotional Wellbeing (SEWB) model? 
* How does incarceration affect the domains of social and emotional wellbeing?
* What does the Social and Emotional Wellbeing model contribute that westernised frameworks don't?
{{RoundBoxBottom}}

==Incarceration and emotional wellbeing==
'''Focus question:''' ''What is the relationship between incarceration and the emotional wellbeing of Indigenous Australians?''

The relationship between incarceration and the emotional wellbeing of Indigenous Australians is bidirectional. Targeted discrimination and intergenerational trauma have undermined the health and wellbeing of Australia’s Aboriginal and Torres Strait Islander population, which directly leads to significantly poorer health status, social impoverishment and inequity resulting in the over-representation of Aboriginal people in Australian prisons” (Kendall et al., 2020). The relationship between poor mental health and contact with the criminal justice system is well established, and systemic issues in the criminal justice system can intensify mental health problems (Harrison et al., 2024). In 2021, the census-based estimated resident population of Aboriginal and Torres Strait Islander peoples was 3.8% of the total Australian population (ABS). In the June quarter of 2026, there were 18,396 Aboriginal and Torres Strait Islander prisoners, which accounts for 37% of the custodial population in Australia (Australian Bureau of Statistics [ABS], 2026). 

People in prison are disproportionately affected by poorer physical, mental, and social outcomes, with greater healthcare needs than the broader Australian population. They have higher rates of mental health conditions, chronic conditions, communicable disease, acquired brain injury, tobacco smoking, high-risk alcohol consumption, recent illicit drug use, and recent injecting drug use than the general population (AIHW 2026). As described by Haney (2003), the implication of incarceration on the individual often causes long-term consequences due to experiencing pain, deprivation, and extremely atypical patterns and norms of living and interacting with others, which is dysfunctional in periods post-incarceration. He argues that individuals are forced to quickly adapt to the institutional routine, where they are deprived of privacy and liberty, subjected to a diminished, stigmatised status, and live in sparse material conditions which overall are stressful and unpleasant for the individual. 

===Mental disorder and incarceration===
The relationship between poor mental health and engagement with the justice system is well established (Harrison et al., 2024). The prevalence of mental disorder among the general prison population is much higher than in the community, but there are complex links between incarceration, social adversity and poor mental health for Indigenous people (Shepherd et al., 2016). Indigenous Australians are incarcerated at a disproportionately high rate compared to non-indigenous Australians (ABS, 2026). In Hefferen et al.,’s (2012) study estimating the prevalence of mental disorder in a representative sample of Aboriginal and Torres Strait Islander people in Queensland prisons, the 12 month prevalence of mental disorder was 73% among men and 86% among women. Anxiety, depression, and psychosis, are particularly high in women (Heffernan et al., 2012). Research shows that individuals who experience several forms of disadvantage such as racism and gender discrimination, are more likely to experience poor health (Bastos et al., 2018).

==What contributes to high offending rates and imprisonment among First Nations people?==
'''Focus question:''' ''What broader factors are affected by high rates of offending and imprisonment among First Nations people?''
===Modifiable factors===
====Education====
====Employment====
====Housing====
====Removal from family====
====Living in a single-parent family====
====Experience of physical harm====
====Physical and mental health====
====Financial stress====
====Alcohol and drug use====
====Adverse childhood experiences====

==Social and Emotional Wellbeing==
'''Focus question:''' ''What is the Social and Emotional Wellbeing (SEWB) model?'' 
Social and Emotional Wellbeing (SEWB) is a stepped care model which is dedicated to focalising Aboriginal and Torres Strait Islander social and emotional wellbeing and mental health. The term social and emotional wellbeing (SEWB) is used by many Aboriginal and Torres Strait Islander people to describe the social, emotional, spiritual, and cultural wellbeing of a person (Gee et al., 2014). 
According to Gee et al., (2014), SEWB is the preferred term used to describe an individual's wellbeing as it corresponds with a holistic view of health, compared to using terms such as mental health and mental illness as it is perceived as medical terms that focalise on problems, and do not properly describe all the factors that make up and influence wellbeing.  

The SEWB framework has nine principles that define the concept of SEWB:
# Aboriginal and Torres Strait Islander health is viewed in a holistic context that encompasses mental, physical, cultural, and spiritual health. Land is central to wellbeing. The disruption of these interrelations will result in Aboriginal and Torres Strait Islander ill health (Dudgeon et al., 2014, p. xxiv). 
# Self-determination is central to the provision of Aboriginal and Torres Strait Islander health services (Dudgeon et al., 2014, p. xxiv).
# Culturally valid understandings must inform the provision of services and must guide assessment, care, and management of Aboriginal and Torres Strait Islander peoples health problems generally, and mental health problems in particular (Dudgeon et al., 2014, p. xxiv). 
# Trauma and loss which has been present since European invasion are a direct outcome of the disruption to cultural wellbeing. Trauma and loss of this magnitude continue to have intergenerational effects. This concept must be recognised (Dudgeon et al., 2014, p. xxiv). 
# The human rights of Aboriginal and Torres Strait Islander peoples must be recognised and respected. Human rights relevant to mental illness must be specifically addressed (Dudgeon et al., 2014, p. xxiv). 
# Racism, stigma, environmental adversity and social disadvantage constitute ongoing stressors and have negative impacts on Aboriginal and Torres Strait Islander people's mental health and wellbeing (Dudgeon et al., 2014, p. xxiv). 
# Recognition of the centrality of Aboriginal and Torres Strait Islander family and kinship must be recognised as well as the broader concepts of family and the bonds of reciprocal affection, responsibility and sharing (Dudgeon et al., 2014, p. xxiv). 
# Aboriginal or Torres Strait Islander culture or groups are not singular, but rather hundreds of groupings, languages, kinships, tribes, and ways of living and being. Aboriginal or Torres Strait Islander peoples may currently live in urban, rural, or remote settings, in urbanised, traditional, or other lifestyles and frequently move between these ways of living (Dudgeon et al., 2014, p. xxiv).
# Aboriginal and Torres Strait Islander peoples have great strengths, creativity, and endurance and a deep understanding of the relationships between human beings and their environment (Dudgeon et al., 2014, p. xxiv).

[[File:Determinants of social and emotional wellbeing.png|thumb|300px|'''Figure 1'''. Determinants of social and emotional wellbeing. Adapted from [Dudgeon &amp; Walker, 2015].]]

Figure 1, displays that the SEWB of individuals, families and communities are shaped by connections to body, mind and emotions, family and kinship, community, culture, land, and spirituality. ‘Connection’ refers to the diverse ways in which people experience and express these various domains of SEWB throughout the course of their lives. The nature of these connections are affected by the differentiation of needs across the lifespan (childhood, youth, adulthood, and old age) (Gee et al., 2014, p. 57). The disruption of these connections can result in higher likeliness of experiencing poorer SEWB (Gee at l., 2014, p. 58). 

==How incarceration affects SEWB domains==
'''Focus question:''' ''How does incarceration affect the domains of social and emotional wellbeing?''
* colonial impact (colonisation) --&gt; cultural, economic, and social bases of Indigenous lives and health has been significantly impacted by colonialism (&quot;through disease, massacre, dispossession of lands, relocation, forced labor, removal of children, and enforced cultural assimilation.&quot;)(Battams et al., 2021)

==Connection to community==
* Separation
* Limited/restrictive nature of visitation

==Connection to country==
* Removal from country
* Inability to participate or attend (in/to) cultural practices (ceremonies, obligations etc).
* Reference to opening case study, not only is incarceration and the criminal justice system preventing cultural agency for Indigenous Australians, but it is complicit in the cultural discrimination of Aboriginal lore and culture (Larkin, 2021). This point is quite direct; further elaborate.
* Identity within country and within the land.

==Emotional and mental wellbeing==
* Direct implications on wellbeing due to incarceration.

===Emotional resilience, and protective factors===
'''Focus Question:''' ''What factors improve/support emotional resilience during and after incarceration?''
===Why the Social and Emotional Wellbeing model?===
'''Focus Question:''' ''What does the Social and Emotional Wellbeing model contribute that Westernised frameworks don't?''
* Western definitions of mental health do not align with Aboriginal perspectives of health and wellbeing which endorse a more holistic approach to their conceptualisation (Harrison, 2021).

==Figures==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]]

* For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure; this can be the figure in the scenario
* For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples
* Images must be embedded from [[commons:|Wikimedia Commons]] which hosts free-to-use media such as photos, diagrams, graphs, video, and audio
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text)
* Cite each figure at least once in the main text (e.g., see Figure 2)

==Learning features==
;Quizzes
* One or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=simple&gt;
{The purpose of quizzes is to provide an interactive learning feature:
|type=&quot;()&quot;}
+ True
- False

{Long and complex quiz questions are recommended:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

==Future directions/recommendations==
Note: this section could be added to discuss future directions, and ways to improve the emotional wellbeing of Indigenous Australians in custody.

==Conclusion==
* Arguably the most important section
* Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking
* For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
* [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity)
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)
* [[w:Self determination theory|Self determination theory]] (Wikipedia)
* [[Motivation and emotion/Assessment/Topic/Checklist|Topic development - Checklist]] (Wikiversity)
* [https://en.wikipedia.org/wiki/Indigenous_Australians_and_crime Indigenous incarceration]
* [https://en.wikipedia.org/wiki/Closing_the_Gap Closing the gap]

==References==
{{Hanging indent|1=

Australian Bureau of Statistics. (2025). ''Corrective services, Australia, March quarter 2025''. https://www.abs.gov.au/statistics/people/crime-and-justice/corrective-services-australia/latest-release

Australian Institute of Health and Welfare. (2025). ''Social and emotional wellbeing''. https://www.aihw.gov.au/reports/indigenous-mental-health-suicide-prevention/social-emotional-wellbeing

Battams, S., Delany-Crowe, T., Fisher, M., Wright, L., Krieg, A., McDermott, D., &amp; Baum, F. (2021). Applying crime prevention and health promotion frameworks to the problem of high incarceration rates for Aboriginal and Torres Strait Islander populations: Lessons from a case study from Victoria. ''International Indigenous Policy Journal'', ''12''(2), 1–29. https://doi.org/10.18584/iipj.2021.12.2.10208

Department of the Prime Minister and Cabinet. (2017, April 4). ''National strategic framework for Aboriginal and Torres Strait Islander peoples' mental health and social and emotional wellbeing 2017–2023''. Australian Indigenous HealthInfoNet. https://healthinfonet.ecu.edu.au/key-resources/policies-and-strategies/33834/

Dudgeon, P. (2026, May 26). ''Pat Dudgeon AM FAPS on developing the social and emotional wellbeing model to support Indigenous communities''. Australian Psychological Society. https://psychology.org.au/insights/pat-dudgeon-am-sewb-model

Dudgeon, P., &amp; Walker, R. (2015). Decolonising Australian psychology: Discourses, strategies, and practice. ''Journal of Social and Political Psychology'', ''3''(1). https://doi.org/10.5964/jspp.v3i1.4857

}}

==External links==
* [https://www.aihw.gov.au/reports/indigenous-australians/closing-the-gap-targets-key-findings-implications/contents/criminal-justice Closing the Gap targets: Key findings – Criminal justice] (Australian Institute of Health and Welfare)
* [https://www.myiacfp.org/the-relationship-between-justice-system-involvement-and-the-social-and-emotional-wellbeing-sewb-of-aboriginal-and-torres-strait-islander-youth/ The relationship between justice system involvement and the social and emotional wellbeing (SEWB) of Aboriginal and Torres Strait Islander youth] (IACFP)
* [https://bugmybarbook.org.au/chapters/imprisonment/ Imprisonment] (Bugmy Bar Book)
* [https://theconversation.com/excessive-strip-searching-shines-light-on-discrimination-of-aboriginal-women-in-the-criminal-justice-system-163969 Excessive strip searching shines light on discrimination of Aboriginal women in the criminal justice system] (The Conversation)
* [https://www.smh.com.au/national/nsw/aboriginal-girl-fights-to-exclude-men-from-seeing-strip-search-footage-20200310-p548pu.html Aboriginal girl fights to exclude men from seeing strip search footage] (Sydney Morning Herald)

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__TOC__

==Overview==
{{RoundBoxTop|theme=12}}
[[File:Kakadu (AU), Kakadu National Park, Anbangbang Rock Shelter -- 2019 -- 4106.jpg|thumb|250px|'''Figure 1'''. Emotional wellbeing for Indigenous Australians is viewed as health, connected with the land, culture, and community.]]

; Case study
In January of 2021, an unnamed incarcerated Aboriginal woman on remand at the [[w:Alexander Maconochie Centre|Alexander Maconochie Centre in the ACT]] was allegedly strip searched by four guards in riot gear, within view of male detainees (Larkin, 2021). The woman is a victim of a previous sexual assault.

This case, amongst others, has caused concern among health care professionals who work with Aboriginal women detainees (Larkin, 2021). For many First Nations communities, the showing of a woman's sensitive body parts is considered sacred to women's business (Thompson &amp; Archibald-Binge, 2020). This lore and culture has been practised for thousands of years. The separation of men's and women's business, and strict traditions and customs is central to many [[w:Australian Aboriginal culture|Aboriginal cultures]]. The conduct and nature of these traditions recognises and respects particular roles, ceremony and lore sacred to men and women (Sydney Nature Team, 2025). The customs and practices within men's and women's business are strict and if the rules are broken, harsh punishment is to follow. 

&quot;If women's business is conducted in front of males, cultural shame is likely to be the result. This is extremely distressing and would stay with the woman for a long time,&quot; (Thompson &amp; Archibald-Binge, 2020).

This local case, alongside many others, acknowledges how the absence of cultural safety within institutional practice can undermine Indigenous wellbeing. This chapter explores the social and emotional wellbeing model and the emotional effects of incarceration on Indigenous Australians. 

{{RoundBoxBottom}}

* Introduction to the problem: Indigenous Australians are incarcerated at a disproportionately high rate, accounting for 37% of all persons in custody as of March 2025 (ABS, 2025).
* &quot;Research shows that imprisonment has negative impacts on the physical and mental health of incarcerated individuals, and these impacts persist after release.&quot; - (Impacts of Imprisonment | Bugmy Bar Book, 2023) {{ic|Include page numbers for quotes (APA style)}}
* Incarceration significantly implicates{{huh}} the cultural and relational connections to land and kin which are directly correlational with wellbeing for many Indigenous Australians. 
* Introduction to the model/theory: Social and Emotional Wellbeing (SEWB) model was developed to support and strengthen Indigenous mental health --&gt; The SEWB model is a holistic, multi-dimensional concept of wellbeing which takes into account the impacts of the history of colonisation (Dudgeon, 2026).
* How incarceration negatively impacts Indigenous emotional wellbeing --&gt; which also affects mental health. 
* The SEWB model recognises that connection to land, sea, culture, and spirituality contribute to wellbeing.
* Incarceration affects SEWB domains --&gt; physical separation from family members, restricted cultural practice, removal from country. 
* Why does this matter? ...Access to culturally safe, responsive, and person-centred services is essential to improving the emotional wellbeing of Indigenous Australians in custody (Department of the Prime Minister and Cabinet, 2017). --&gt; Essential that psychological science be informed by Indigenous understandings of wellbeing.

{{RoundBoxTop|theme=11}}
'''Focus questions'''

* What is the relationship between incarceration and the emotional wellbeing of Indigenous Australians?
* What broader factors are affected by high rates of offending and imprisonment among First Nations people?
* What is the Social and Emotional Wellbeing (SEWB) model? 
* How does incarceration affect the domains of social and emotional wellbeing?
* What does the Social and Emotional Wellbeing model contribute that westernised frameworks don't?
{{RoundBoxBottom}}

==Incarceration and emotional wellbeing==
'''Focus question:''' ''What is the relationship between incarceration and the emotional wellbeing of Indigenous Australians?''

The relationship between incarceration and the emotional wellbeing of Indigenous Australians is bidirectional. Targeted discrimination and intergenerational trauma have undermined the health and wellbeing of Australia’s Aboriginal and Torres Strait Islander population, which directly leads to significantly poorer health status, social impoverishment and inequity resulting in the over-representation of Aboriginal people in Australian prisons” (Kendall et al., 2020). The relationship between poor mental health and contact with the criminal justice system is well established, and systemic issues in the criminal justice system can intensify mental health problems (Harrison et al., 2024). In 2021, the census-based estimated resident population of Aboriginal and Torres Strait Islander peoples was 3.8% of the total Australian population (ABS). In the June quarter of 2026, there were 18,396 Aboriginal and Torres Strait Islander prisoners, which accounts for 37% of the custodial population in Australia (Australian Bureau of Statistics [ABS], 2026). 

People in prison are disproportionately affected by poorer physical, mental, and social outcomes, with greater healthcare needs than the broader Australian population. They have higher rates of mental health conditions, chronic conditions, communicable disease, acquired brain injury, tobacco smoking, high-risk alcohol consumption, recent illicit drug use, and recent injecting drug use than the general population (AIHW 2026). As described by Haney (2003), the implication of incarceration on the individual often causes long-term consequences due to experiencing pain, deprivation, and extremely atypical patterns and norms of living and interacting with others, which is dysfunctional in periods post-incarceration. He argues that individuals are forced to quickly adapt to the institutional routine, where they are deprived of privacy and liberty, subjected to a diminished, stigmatised status, and live in sparse material conditions which overall are stressful and unpleasant for the individual (Haney, 2003). 

===Mental disorder and incarceration===
The relationship between poor mental health and engagement with the justice system is well established (Harrison et al., 2024). The prevalence of mental disorder among the general prison population is much higher than in the community, but there are complex links between incarceration, social adversity and poor mental health for Indigenous people (Shepherd et al., 2016). Indigenous Australians are incarcerated at a disproportionately high rate compared to non-indigenous Australians (ABS, 2026). In Hefferen et al.,’s (2012) study estimating the prevalence of mental disorder in a representative sample of Aboriginal and Torres Strait Islander people in Queensland prisons, the 12 month prevalence of mental disorder was 73% among men and 86% among women. Anxiety, depression, and psychosis, are particularly high in women (Heffernan et al., 2012). Research shows that individuals who experience several forms of disadvantage such as racism and gender discrimination, are more likely to experience poor health (Bastos et al., 2018).

===Trauma and PTSD===

==What contributes to high offending rates and imprisonment among First Nations people?==
'''Focus question:''' ''What broader factors are affected by high rates of offending and imprisonment among First Nations people?''
===Modifiable factors===
====Education====
====Employment====
====Housing====
====Removal from family====
====Living in a single-parent family====
====Experience of physical harm====
====Physical and mental health====
====Financial stress====
====Alcohol and drug use====
====Adverse childhood experiences====

==Social and Emotional Wellbeing==
'''Focus question:''' ''What is the Social and Emotional Wellbeing (SEWB) model?'' 
Social and Emotional Wellbeing (SEWB) is a stepped care model which is dedicated to focalising Aboriginal and Torres Strait Islander social and emotional wellbeing and mental health. The term social and emotional wellbeing (SEWB) is used by many Aboriginal and Torres Strait Islander people to describe the social, emotional, spiritual, and cultural wellbeing of a person (Gee et al., 2014). 
According to Gee et al., (2014), SEWB is the preferred term used to describe an individual's wellbeing as it corresponds with a holistic view of health, compared to using terms such as mental health and mental illness as it is perceived as medical terms that focalise on problems, and do not properly describe all the factors that make up and influence wellbeing.  

The SEWB framework has nine principles that define the concept of SEWB:
# Aboriginal and Torres Strait Islander health is viewed in a holistic context that encompasses mental, physical, cultural, and spiritual health. Land is central to wellbeing. The disruption of these interrelations will result in Aboriginal and Torres Strait Islander ill health (Dudgeon et al., 2014, p. xxiv). 
# Self-determination is central to the provision of Aboriginal and Torres Strait Islander health services (Dudgeon et al., 2014, p. xxiv).
# Culturally valid understandings must inform the provision of services and must guide assessment, care, and management of Aboriginal and Torres Strait Islander peoples health problems generally, and mental health problems in particular (Dudgeon et al., 2014, p. xxiv). 
# Trauma and loss which has been present since European invasion are a direct outcome of the disruption to cultural wellbeing. Trauma and loss of this magnitude continue to have intergenerational effects. This concept must be recognised (Dudgeon et al., 2014, p. xxiv). 
# The human rights of Aboriginal and Torres Strait Islander peoples must be recognised and respected. Human rights relevant to mental illness must be specifically addressed (Dudgeon et al., 2014, p. xxiv). 
# Racism, stigma, environmental adversity and social disadvantage constitute ongoing stressors and have negative impacts on Aboriginal and Torres Strait Islander people's mental health and wellbeing (Dudgeon et al., 2014, p. xxiv). 
# Recognition of the centrality of Aboriginal and Torres Strait Islander family and kinship must be recognised as well as the broader concepts of family and the bonds of reciprocal affection, responsibility and sharing (Dudgeon et al., 2014, p. xxiv). 
# Aboriginal or Torres Strait Islander culture or groups are not singular, but rather hundreds of groupings, languages, kinships, tribes, and ways of living and being. Aboriginal or Torres Strait Islander peoples may currently live in urban, rural, or remote settings, in urbanised, traditional, or other lifestyles and frequently move between these ways of living (Dudgeon et al., 2014, p. xxiv).
# Aboriginal and Torres Strait Islander peoples have great strengths, creativity, and endurance and a deep understanding of the relationships between human beings and their environment (Dudgeon et al., 2014, p. xxiv).

[[File:Determinants of social and emotional wellbeing.png|thumb|300px|'''Figure 1'''. Determinants of social and emotional wellbeing. Adapted from [Dudgeon &amp; Walker, 2015].]]

Figure 1, displays that the SEWB of individuals, families and communities are shaped by connections to body, mind and emotions, family and kinship, community, culture, land, and spirituality. ‘Connection’ refers to the diverse ways in which people experience and express these various domains of SEWB throughout the course of their lives. The nature of these connections are affected by the differentiation of needs across the lifespan (childhood, youth, adulthood, and old age) (Gee et al., 2014, p. 57). The disruption of these connections can result in higher likeliness of experiencing poorer SEWB (Gee at l., 2014, p. 58). 

==How incarceration affects SEWB domains==
'''Focus question:''' ''How does incarceration affect the domains of social and emotional wellbeing?''
* colonial impact (colonisation) --&gt; cultural, economic, and social bases of Indigenous lives and health has been significantly impacted by colonialism (&quot;through disease, massacre, dispossession of lands, relocation, forced labor, removal of children, and enforced cultural assimilation.&quot;)(Battams et al., 2021)

==Connection to community==
* Separation
* Limited/restrictive nature of visitation

==Connection to country==
* Removal from country
* Inability to participate or attend (in/to) cultural practices (ceremonies, obligations etc).
* Reference to opening case study, not only is incarceration and the criminal justice system preventing cultural agency for Indigenous Australians, but it is complicit in the cultural discrimination of Aboriginal lore and culture (Larkin, 2021). This point is quite direct; further elaborate.
* Identity within country and within the land.

==Emotional and mental wellbeing==
* Direct implications on wellbeing due to incarceration.

===Emotional resilience, and protective factors===
'''Focus Question:''' ''What factors improve/support emotional resilience during and after incarceration?''
===Why the Social and Emotional Wellbeing model?===
'''Focus Question:''' ''What does the Social and Emotional Wellbeing model contribute that Westernised frameworks don't?''
* Western definitions of mental health do not align with Aboriginal perspectives of health and wellbeing which endorse a more holistic approach to their conceptualisation (Harrison, 2021).

==Figures==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]]

* For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure; this can be the figure in the scenario
* For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples
* Images must be embedded from [[commons:|Wikimedia Commons]] which hosts free-to-use media such as photos, diagrams, graphs, video, and audio
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text)
* Cite each figure at least once in the main text (e.g., see Figure 2)

==Learning features==
;Quizzes
* One or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=simple&gt;
{The purpose of quizzes is to provide an interactive learning feature:
|type=&quot;()&quot;}
+ True
- False

{Long and complex quiz questions are recommended:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

==Future directions/recommendations==
Note: this section could be added to discuss future directions, and ways to improve the emotional wellbeing of Indigenous Australians in custody.

==Conclusion==
* Arguably the most important section
* Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking
* For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
* [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity)
* [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021)
* [[w:Self determination theory|Self determination theory]] (Wikipedia)
* [[Motivation and emotion/Assessment/Topic/Checklist|Topic development - Checklist]] (Wikiversity)
* [https://en.wikipedia.org/wiki/Indigenous_Australians_and_crime Indigenous incarceration]
* [https://en.wikipedia.org/wiki/Closing_the_Gap Closing the gap]

==References==
{{Hanging indent|1=

Australian Bureau of Statistics. (2025). ''Corrective services, Australia, March quarter 2025''. https://www.abs.gov.au/statistics/people/crime-and-justice/corrective-services-australia/latest-release

Australian Institute of Health and Welfare. (2025). ''Social and emotional wellbeing''. https://www.aihw.gov.au/reports/indigenous-mental-health-suicide-prevention/social-emotional-wellbeing

Battams, S., Delany-Crowe, T., Fisher, M., Wright, L., Krieg, A., McDermott, D., &amp; Baum, F. (2021). Applying crime prevention and health promotion frameworks to the problem of high incarceration rates for Aboriginal and Torres Strait Islander populations: Lessons from a case study from Victoria. ''International Indigenous Policy Journal'', ''12''(2), 1–29. https://doi.org/10.18584/iipj.2021.12.2.10208

Department of the Prime Minister and Cabinet. (2017, April 4). ''National strategic framework for Aboriginal and Torres Strait Islander peoples' mental health and social and emotional wellbeing 2017–2023''. Australian Indigenous HealthInfoNet. https://healthinfonet.ecu.edu.au/key-resources/policies-and-strategies/33834/

Dudgeon, P. (2026, May 26). ''Pat Dudgeon AM FAPS on developing the social and emotional wellbeing model to support Indigenous communities''. Australian Psychological Society. https://psychology.org.au/insights/pat-dudgeon-am-sewb-model

Dudgeon, P., &amp; Walker, R. (2015). Decolonising Australian psychology: Discourses, strategies, and practice. ''Journal of Social and Political Psychology'', ''3''(1). https://doi.org/10.5964/jspp.v3i1.4857

}}

==External links==
* [https://www.aihw.gov.au/reports/indigenous-australians/closing-the-gap-targets-key-findings-implications/contents/criminal-justice Closing the Gap targets: Key findings – Criminal justice] (Australian Institute of Health and Welfare)
* [https://www.myiacfp.org/the-relationship-between-justice-system-involvement-and-the-social-and-emotional-wellbeing-sewb-of-aboriginal-and-torres-strait-islander-youth/ The relationship between justice system involvement and the social and emotional wellbeing (SEWB) of Aboriginal and Torres Strait Islander youth] (IACFP)
* [https://bugmybarbook.org.au/chapters/imprisonment/ Imprisonment] (Bugmy Bar Book)
* [https://theconversation.com/excessive-strip-searching-shines-light-on-discrimination-of-aboriginal-women-in-the-criminal-justice-system-163969 Excessive strip searching shines light on discrimination of Aboriginal women in the criminal justice system] (The Conversation)
* [https://www.smh.com.au/national/nsw/aboriginal-girl-fights-to-exclude-men-from-seeing-strip-search-footage-20200310-p548pu.html Aboriginal girl fights to exclude men from seeing strip search footage] (Sydney Morning Herald)

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__TOC__

==Overview==
{{RoundBoxTop|theme=7}}

[[File:Begging man Harmony Lot 27 Elliot Street downtown Brattleboro VT July 2025 02.jpg|right|thumb|150px|'''Figure 1'''. Homeless man begging]]

;Scenario

Imagine that you are doing your weekly shopping and you come across a homeless person who is asking for food or money. The person present in an unkempt state and initially you make sure you walk past, your stomach drops, and subconsciously wrinkle your nose and you decide to take a longer path to the shops in order to avoid them. When paying for your groceries, you realise that you don’t have quite enough to pay the full amount, instantly, your face gets hot as there is a line of people waiting behind you and it seems they are all staring at you, judging your error. Whilst you are talking to the register assistant, asking for some time to go through your groceries to determine which items are a priority, the person behind you offers to make up the difference. Suddenly, the hot feeling in your face becomes a warm feeling in your chest and you start profusely thanking the person and ask if there is anything you can do to make it up to them, they respond with “when you are in a position to pay it forward to some else, please do so.”

{{RoundBoxBottom}}
[[w:Moral_emotions|Moral emotions]] potentially sets humans apart from other animals, and assist in reacting to social events that do not directly affect the self that are linked to the interests or welfare either of society as a whole or at least of persons other than the self (''Haidt, 2003).'' They arise when individuals evaluate actions, intentions, or social situations in terms of right or wrong, in accordance with social norms and moral standards, helping guide behaviours that support cooperation, fairness and social harmony. This is the key distinction between moral emotions and [[Motivation and emotion/Lectures/Individual emotions|basic emotions]], which are a person's response to a situation. Basic emotions come first or are primary, whilst moral emotions align with secondary emotions (Guy-Evans, 2026). They motivate people to heal others, repair harm, standup against injustice, or avoid behvaiours that could damage relationships.

There are 2 groups or families of moral emotion, with 4 quadrants and understanding them is essential to link how they motivate ethical and prosocial action. [[w:Self-conscious_emotions|Self-conscious moral emotions]] - such as guilt, shame, embarrassment, and authentic pride - occur when people evaluate their own behaviour against internalised moral standards. These emotions regulate the moral self by motivating reparative action, rule compliance, or withdrawal (Tangney, Tracy, &amp; Robins, 2007). Importantly [[Motivation and emotion/Book/2018/Guilt and shame|guilt and shame]] differ in their internalised state and motivation urge resulting in different behaviours; guilt‑proneness predicts empathy, apology, and reparative behaviour, whereas shame‑proneness predicts avoidance, defensiveness, and increased risk of antisocial behaviour (Tangney, Stuewig, &amp; Mashek, 2007). Other‑evaluative moral emotions—including compassion, gratitude, elevation/ awe, along with contempt, disgust and moral outrage—arise when people respond to the experiences or actions of others. These emotions generate intuitive impulses to help, reciprocate kindness, emulate moral exemplars, confront wrongdoing or avoid social violations (Haidt, 2003).

By examining the psychological mechanisms behind these emotions, this chapter explains how moral appraisals transform into behavioural tendencies. It also considers the biological responses and expressive behaviours that prepare the body for action, the social functions that support group living, and the contextual factors that strengthen or weaken moral motivation. Together, these insights show how moral emotions serve as powerful motivational systems that shape ethical and prosocial behaviour in everyday life.{{RoundBoxTop|theme=5}}
'''Focus questions'''

{{ic|Use bullet points as shown in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]}}

1.	What are the key moral emotions? &lt;br&gt;
2.     How are moral emotions felt?&lt;br&gt;
3.	How do moral emotions influence ethical and prosocial action?&lt;br&gt;
4.	What environmental factors can alter the influence of moral emotions?&lt;br&gt;
5.     How is positive psychology and the light triad effective at counteracting the moral  disengagement?{{RoundBoxBottom}}

==Moral emotions==
* General introduction into what moral emotions are; moral emotions are linked to a person's moral compass and conscious and help establish the development of an individual's learning of the difference between right and wrong. Explain the different types of moral emotions of shame, guilt, sympathy, empathy, contempt, anger and disgust (Turner, J.H., Stets, J.E. (2006). Each emotion elicits a specific bodily response. Refer to table 1
* Self- conscious emotions - [[Motivation and emotion/Book/2018/Guilt and shame|Shame, guilt]], [[Motivation and emotion/Book/2022/Embarrassment|embarrassment]], and [[Motivation and emotion/Book/2017/Pride|pride]] ([[doi:10.1146/annurev.psych.56.091103.070145|Tangney, Stuewig, &amp; Mashek. 2007]]) {{ic|Use APA style for citations with 3 or more authors}} {{ic|Move citation links into the References section}}
** Shame and guilt are, whilst similar [https://pmc.ncbi.nlm.nih.gov/articles/PMC12385681/ Santoro. G,et al (2025)] has defined shame as being deeply engrained self-conscious emotions linked to identity formation and guilt arising around specific events or behaviours. ''Needs further development*'' 
* other-focused moral emotions - [https://biblehub.com/topical/u/understanding_righteous_anger.htm Righteous anger], [[w:Contempt|Contempt]], [[w:Disgust|Disgust]], [[w:Awe|awe]] [[w:Elevation_(emotion)|elevation]] and [[Motivation and emotion/Book/2021/Gratitude|gratitude]]
Explain the difference between self- conscious and other focused emotion and the ways in which people cope with them [http://www.rpforschools.net/articles/ASP/Tangney,%20Tracy%20&amp;%20Robins%202007%20The%20self-conscious%20emotions%20-%20Theory%20and%20Research.pdf The self-counscious emotions]  (Tangle et al., 2007; pdf)

=== Background ===

* Plato [[w:Moral_psychology|moral psychology]]
* Kant
* Adam Smith
* David Hume

=== Modern theories ===

* Piaget
* Kohlberg
* Adler

=== Environmental influences ===

* Adverse Childhood experiences - (Katharine D. Wojcik, Daniel W. Cox, David Kealy, Adverse childhood experiences and shame- and guilt-proneness: Examining the mediating roles of interpersonal problems in a community sample, Child Abuse &amp; Neglect, Volume 98, 2019, 104233, ISSN 0145-2134, &lt;nowiki&gt;https://doi.org/10.1016/j.chiabu.2019.104233&lt;/nowiki&gt; .)
*positive environmental influence

== Moral emotions and influence on motivation and behaviours ==
{{ic|Include an introductory paragraph before branching into sub-sections}}

=== Elevation/ Gratitude - ===
Discuss how positive moral emotions (Elevation and gratitude) can contribute to moral flourishing and improve patient care, (linking back to the scenario). (Bai,C., Liu, R., and Zhang, H. 2026) 

{{RoundBoxTop|theme=7}}
;Let's look back at the scenario

You walk back to the car and are amazed at the kindness of strangers and so grateful that when you come across the person who was asking for money again. This time, you decide that even though you don’t have much in the way of money, you want to offer the person one of the ready meals in your shopping and wish the person a good day. Walking away, you feel a warm sensation in your chest and your back straightened and you find you are smiling to yourself.
{{RoundBoxBottom}}

=== Guilt ===
Explore the following ''&quot;Guilt is recognized as a social and moral emotion that drives prosocial behaviour, typically through actions to repair relationships with victims, often at a personal cost&quot; .('' Kinosada, Y., et al, 2026, p.1)

=== Shame ===
Traditionally shame has been used to punish and reform behaviour, but does it actually reduce criminality? Discuss. **one reference still waiting on88 cannot confirm if it is applicable. 

Is shame an effective emotion now or redundant and causes more harm than good? evolutionary, it was esentail for survival, in a modern society is it causing prevalence of mental health disorders. [https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2013.00310/full#S7 Frontiers | The Role of Self-Blaming Moral Emotions in Major Depression and Their Impact on Social-Economical Decision Making] 

Punishment and Shame: A Philosophical Study - a North Carolina Agricultural and Technical State University, Greensboro, NC, United States

=== Moral disengagement ===
Explore the way unethical acts are reasoned due to moral disengagement  

== Mitigating maladaptive moral affect ==
{{ic|Include an introductory paragraph before branching into sub-sections}}

=== Altruism ===
[[w:Altruism|Altruism]]

=== Light Triad ===
[[Motivation and emotion/Book/2021/Light triad|Light triad]] 

=== Self-determination theory ===
[[w:Self determination theory|Self determination theory]] 

==Figures==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]]

* For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples
* For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure
* Figures can show any kind of media such as photos, diagrams, graphs, video, audio, and so on
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text)
* Images must be embedded from [[commons:|Wikimedia Commons]]
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Cite each figure at least once in the main text (e.g., see Figure 2)

==Learning features==
Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options:

{{anchor|Scenarios}}
;Scenarios
* Scenarios, case studies, or examples that illustrate concepts in action
* Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages)
* Can be real or fictional; if real, provide citation(s)

{{anchor|Feature box}}
;Feature boxes
* Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect
* Consider using feature boxes for:
** [[#Scenarios|Scenarios]], case studies, or examples
** Focus questions
** Tips
** Quiz questions
** Take-home messages

;Embedded links
* When key words are introduced, use [[Help:Links|interwiki links]] to:
** Wikipedia articles (e.g., &quot;An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]&quot;) or
** Related book chapters (e.g., &quot;If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]&quot;)
*[[w:Moral_emotions|Moral emotions]] include [[Motivation and emotion/Book/2018/Guilt and shame|guilt, shame]], embarrassment, 

{{anchor|Tables}}
;Tables
* Use tables to organise and summarise information
* Cite each table at least once in the main text (e.g., see Table 1)
* Tables should be captioned
* [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted

'''Table 1''' 

''Bodily Responses to Moral emotions'' 
{| class=&quot;wikitable&quot;
!Strategy
!Bodily responses
|-
|Embarrassment 
|
|-
|Guilt
|
|-
|Shame
|
|-
|Pride
|
|-
|Righteous anger
|
|-
|Comptempt
|
|-
|Disgust
|
|-
|Elevation
|
|-
|Gratitude
|
|}

;Quizzes
* One or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=&quot;simple&quot;&gt;
{Unlike guilt, which pertains to specific actions, shame involves a global negative evaluation of the self.
|type=&quot;()&quot;}
+ True
- False

{Self-conscious emotions include righteous anger, contempt, disgust, elevation and gratitude
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

==Conclusion==
* Moral emotions motivate ethical decision and behaviour
* Childhood trauma can disrupt the development of moral emotions,
* All is not lost - protective factors can mitigate the negative impact of shame. 
* Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking
* For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
[[Help:Contents/Links#Interwiki_links|Internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity)
*

{{tip|Suggestions for this section:
* Link to the most relevant internal resources about the topic
* Include the source in parentheses
}}

==References==
Provide the references for all citations in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. Alternatively, you can use wiki style (as used on Wikipedia), as long as the information is complete and the formatting is consistent.

{{Hanging indent|1=

Bai,C., Liu, R., and Zhang, H. (2026) Moral elevation, gratitude, and meaning in nurses’ positive mental health. ''Nursing Ethics'' Vol. 33(4) 1078–1093 [https://journals.sagepub.com/doi/10.1177/09697330261424358 https://doi.org/10.1177/09697330261424358]

Kinosada, Y., Furukawa, Y., Wakai, T., &amp; Nakashima, K. (2026). Does guilt motivate prosocial behaviour at the expense of others? Preregistered replications and exploratory statistical modelling. ''Asian Journal of Social Psychology'', 29, e70099. https://doi-org.ezproxy.canberra.edu.au/10.1111/ajsp.70099 

Santoro, G., Sideli, L., Musetti, A., &amp; Schimmenti, A. (2025) The Relationship Between Childhood Trauma and Shame: The Mediating Role of Dissociation. ''European Journal of Investigation in Health, Psychology and Education''. ;15(8):151. [[doi:10.3390/ejihpe15080151|http://doi.org/10.3390/ejihpe15080151]]

Romera EM, Ortega-Ruiz R, Rodríguez-Barbero S and Falla D (2019) How Do You Think the Victims of Bullying Feel? A Study of Moral Emotions in Primary School. ''Frontiers in Psychology, Educational Psychology.'' 10:1753. https://doi.org/10.3389/fpsyg.2019.01753 [https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2019.01753/full l]

Tangney, J. P., Stuewig, J., &amp; Mashek, D., J., (2007). Moral Emotions and Moral Behavior. ''Annual Review of Psychology'' 58:345-372. https://doi.org/10.1146/annurev.psych.56.091103.070145 [https://doi.org/10.1146/annurev.psych.56.091103.070145]

Turner, J., H., &amp; Stets, J., E (2006). Moral Emotions. In ''Handbook of the Sociology of Emotions (''pp.544 - 566). Spinger. [https://link.springer.com/book/10.1007/978-0-387-30715-2 https://doi.org/10.1007/978-0-387-30715-2] . 

Tillman CJ, Gonzalez K, Whitman MV, Crawford WS and Hood AC (2018) A Multi-Functional View of Moral Disengagement: Exploring the Effects of Learning the Consequences. ''Frontiers in Psychology, Personality and Social Psychology''. 8:2286. [https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2017.02286/full#F2 doi: 10.3389/fpsyg.2017.02286]

Wojcik, K., D., Cox, D., W., &amp; Kealy,D. (2019) Adverse childhood experiences and shame- and guilt-proneness: Examining the mediating roles of interpersonal problems in a community sample, ''Child Abuse &amp; Neglec''t, Volume 98, 2019, 104233, ISSN 0145-2134, https://doi.org/10.1016/j.chiabu.2019.104233

}} 


APA style example:
{{Hanging indent|1=

Rosenberg, B. D., &amp; Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091

Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper &amp; Row.

}}

{{tip|Suggestions for this section:
* Important aspects of APA referencing style
** Author surname, followed by a comma, then the author initials separated by full stops and spaces
** Year of publication in parentheses
** Title of work in lower case (except first letter and proper names), ending in a full-stop
** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop
** doi as a URL which is a working hyperlink (i.e., clickable)
** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]:
Use &quot;Edit source&quot;
&lt;nowiki&gt;{{Hanging indent|1= the full list of references}}&lt;/nowiki&gt;
* The most common mistakes include:
** Incorrect capitalisation
** Incorrect italicisation
** dois which aren't clickable as working hyperlinks
** Citing sources that haven't been consulted
}}

==External links==
[https://www.ted.com/talks/asha_curran_how_acts_of_kindness_sparked_a_global_movement Ideas change everything] (TED)

[https://www.youtube.com/watch?v=b4CfyLe0IlQ Prosocial Behavior | Ethics Defined] (Youtube)


[[Help:Contents/Links#External_links|External links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)

{{tip|Suggestions for this section:
* Link to the most relevant external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotion]]
[[Category:Motivation and emotion/Book/Morality]]</text>
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__TOC__

==Overview==
{{RoundBoxTop|theme=7}}

[[File:Begging man Harmony Lot 27 Elliot Street downtown Brattleboro VT July 2025 02.jpg|right|thumb|150px|'''Figure 1'''. Homeless man begging]]

;Scenario

Imagine that you are doing your weekly shopping and you come across a homeless person who is asking for food or money. The person present in an unkempt state and initially you make sure you walk past, your stomach drops, and subconsciously wrinkle your nose and you decide to take a longer path to the shops in order to avoid them. When paying for your groceries, you realise that you don’t have quite enough to pay the full amount, instantly, your face gets hot as there is a line of people waiting behind you and it seems they are all staring at you, judging your error. Whilst you are talking to the register assistant, asking for some time to go through your groceries to determine which items are a priority, the person behind you offers to make up the difference. Suddenly, the hot feeling in your face becomes a warm feeling in your chest and you start profusely thanking the person and ask if there is anything you can do to make it up to them, they respond with “when you are in a position to pay it forward to some else, please do so.”

{{RoundBoxBottom}}
[[w:Moral_emotions|Moral emotions]] potentially sets humans apart from other animals, and assist in reacting to social events that do not directly affect the self that are linked to the interests or welfare either of society as a whole or at least of persons other than the self (''Haidt, 2003).'' They arise when individuals evaluate actions, intentions, or social situations in terms of right or wrong, in accordance with social norms and moral standards, helping guide behaviours that support cooperation, fairness and social harmony. This is the key distinction between moral emotions and [[Motivation and emotion/Lectures/Individual emotions|basic emotions]], which are a person's response to a situation. Basic emotions come first or are primary, whilst moral emotions align with secondary emotions (Guy-Evans, 2026). 

There are 2 groups or families of moral emotion, with 4 quadrants and understanding them is essential to link how they motivate ethical and prosocial action. [[w:Self-conscious_emotions|Self-conscious moral emotions]] - such as guilt, shame, embarrassment, and authentic pride - occur when people evaluate their own behaviour against internalised moral standards. These emotions regulate the moral self by motivating reparative action, helping others, rule compliance, or withdrawal (Tangney, Tracy, &amp; Robins, 2007). Importantly [[Motivation and emotion/Book/2018/Guilt and shame|guilt and shame]] differ in their internalised state and motivation urge resulting in different behaviours; guilt‑proneness predicts empathy, apology, and reparative behaviour, whereas shame‑proneness predicts avoidance, defensiveness, and increased risk of antisocial behaviour (Tangney, Stuewig, &amp; Mashek, 2007). Other‑evaluative moral emotions—including compassion, gratitude, elevation/ awe, along with contempt, disgust and moral outrage—arise when people respond to the experiences or actions of others. These emotions generate intuitive impulses to help, reciprocate kindness, emulate moral exemplars, confront wrongdoing or avoid social violations (Haidt, 2003).

By examining the psychological mechanisms behind these emotions, this chapter explains how moral appraisals transform into behavioural tendencies. It also considers the biological responses and expressive behaviours that prepare the body for action, the social functions that support group living, and the contextual factors that strengthen or weaken moral motivation. Together, these insights show how moral emotions serve as powerful motivational systems that shape ethical and prosocial behaviour in everyday life.{{RoundBoxTop|theme=5}}
'''Focus questions'''

{{ic|Use bullet points as shown in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]}}

1.	What are the key moral emotions? &lt;br&gt;
2.     How are moral emotions felt?&lt;br&gt;
3.	How do moral emotions influence ethical and prosocial action?&lt;br&gt;
4.	What environmental factors can alter the influence of moral emotions?&lt;br&gt;
5.     How is positive psychology and the light triad effective at counteracting the moral  disengagement?{{RoundBoxBottom}}

==Moral emotions==
* General introduction into what moral emotions are; moral emotions are linked to a person's moral compass and conscious and help establish the development of an individual's learning of the difference between right and wrong. Explain the different types of moral emotions of shame, guilt, sympathy, empathy, contempt, anger and disgust (Turner, J.H., Stets, J.E. (2006). Each emotion elicits a specific bodily response. Refer to table 1
* Self- conscious emotions - [[Motivation and emotion/Book/2018/Guilt and shame|Shame, guilt]], [[Motivation and emotion/Book/2022/Embarrassment|embarrassment]], and [[Motivation and emotion/Book/2017/Pride|pride]] ([[doi:10.1146/annurev.psych.56.091103.070145|Tangney, Stuewig, &amp; Mashek. 2007]]) {{ic|Use APA style for citations with 3 or more authors}} {{ic|Move citation links into the References section}}
** Shame and guilt are, whilst similar [https://pmc.ncbi.nlm.nih.gov/articles/PMC12385681/ Santoro. G,et al (2025)] has defined shame as being deeply engrained self-conscious emotions linked to identity formation and guilt arising around specific events or behaviours. ''Needs further development*'' 
* other-focused moral emotions - [https://biblehub.com/topical/u/understanding_righteous_anger.htm Righteous anger], [[w:Contempt|Contempt]], [[w:Disgust|Disgust]], [[w:Awe|awe]] [[w:Elevation_(emotion)|elevation]] and [[Motivation and emotion/Book/2021/Gratitude|gratitude]]
Explain the difference between self- conscious and other focused emotion and the ways in which people cope with them [http://www.rpforschools.net/articles/ASP/Tangney,%20Tracy%20&amp;%20Robins%202007%20The%20self-conscious%20emotions%20-%20Theory%20and%20Research.pdf The self-counscious emotions]  (Tangle et al., 2007; pdf)

=== Background ===

* Plato [[w:Moral_psychology|moral psychology]]
* Kant
* Adam Smith
* David Hume

=== Modern theories ===

* Piaget
* Kohlberg
* Adler

=== Environmental influences ===

* Adverse Childhood experiences - (Katharine D. Wojcik, Daniel W. Cox, David Kealy, Adverse childhood experiences and shame- and guilt-proneness: Examining the mediating roles of interpersonal problems in a community sample, Child Abuse &amp; Neglect, Volume 98, 2019, 104233, ISSN 0145-2134, &lt;nowiki&gt;https://doi.org/10.1016/j.chiabu.2019.104233&lt;/nowiki&gt; .)
*positive environmental influence

== Moral emotions and influence on motivation and behaviours ==
{{ic|Include an introductory paragraph before branching into sub-sections}}

=== Elevation/ Gratitude - ===
Discuss how positive moral emotions (Elevation and gratitude) can contribute to moral flourishing and improve patient care, (linking back to the scenario). (Bai,C., Liu, R., and Zhang, H. 2026) 

{{RoundBoxTop|theme=7}}
;Let's look back at the scenario

You walk back to the car and are amazed at the kindness of strangers and so grateful that when you come across the person who was asking for money again. This time, you decide that even though you don’t have much in the way of money, you want to offer the person one of the ready meals in your shopping and wish the person a good day. Walking away, you feel a warm sensation in your chest and your back straightened and you find you are smiling to yourself.
{{RoundBoxBottom}}

=== Guilt ===
Explore the following ''&quot;Guilt is recognized as a social and moral emotion that drives prosocial behaviour, typically through actions to repair relationships with victims, often at a personal cost&quot; .('' Kinosada, Y., et al, 2026, p.1)

=== Shame ===
Traditionally shame has been used to punish and reform behaviour, but does it actually reduce criminality? Discuss. **one reference still waiting on88 cannot confirm if it is applicable. 

Is shame an effective emotion now or redundant and causes more harm than good? evolutionary, it was esentail for survival, in a modern society is it causing prevalence of mental health disorders. [https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2013.00310/full#S7 Frontiers | The Role of Self-Blaming Moral Emotions in Major Depression and Their Impact on Social-Economical Decision Making] 

Punishment and Shame: A Philosophical Study - a North Carolina Agricultural and Technical State University, Greensboro, NC, United States

=== Moral disengagement ===
Explore the way unethical acts are reasoned due to moral disengagement  

== Mitigating maladaptive moral affect ==
{{ic|Include an introductory paragraph before branching into sub-sections}}

=== Altruism ===
[[w:Altruism|Altruism]]

=== Light Triad ===
[[Motivation and emotion/Book/2021/Light triad|Light triad]] 

=== Self-determination theory ===
[[w:Self determination theory|Self determination theory]] 

==Figures==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]]

* For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples
* For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure
* Figures can show any kind of media such as photos, diagrams, graphs, video, audio, and so on
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text)
* Images must be embedded from [[commons:|Wikimedia Commons]]
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Cite each figure at least once in the main text (e.g., see Figure 2)

==Learning features==
Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options:

{{anchor|Scenarios}}
;Scenarios
* Scenarios, case studies, or examples that illustrate concepts in action
* Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages)
* Can be real or fictional; if real, provide citation(s)

{{anchor|Feature box}}
;Feature boxes
* Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect
* Consider using feature boxes for:
** [[#Scenarios|Scenarios]], case studies, or examples
** Focus questions
** Tips
** Quiz questions
** Take-home messages

;Embedded links
* When key words are introduced, use [[Help:Links|interwiki links]] to:
** Wikipedia articles (e.g., &quot;An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]&quot;) or
** Related book chapters (e.g., &quot;If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]&quot;)
*[[w:Moral_emotions|Moral emotions]] include [[Motivation and emotion/Book/2018/Guilt and shame|guilt, shame]], embarrassment, 

{{anchor|Tables}}
;Tables
* Use tables to organise and summarise information
* Cite each table at least once in the main text (e.g., see Table 1)
* Tables should be captioned
* [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted

'''Table 1''' 

''Bodily Responses to Moral emotions'' 
{| class=&quot;wikitable&quot;
!Strategy
!Bodily responses
|-
|Embarrassment 
|
|-
|Guilt
|
|-
|Shame
|
|-
|Pride
|
|-
|Righteous anger
|
|-
|Comptempt
|
|-
|Disgust
|
|-
|Elevation
|
|-
|Gratitude
|
|}

;Quizzes
* One or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=&quot;simple&quot;&gt;
{Unlike guilt, which pertains to specific actions, shame involves a global negative evaluation of the self.
|type=&quot;()&quot;}
+ True
- False

{Self-conscious emotions include righteous anger, contempt, disgust, elevation and gratitude
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

==Conclusion==
* Moral emotions motivate ethical decision and behaviour
* Childhood trauma can disrupt the development of moral emotions,
* All is not lost - protective factors can mitigate the negative impact of shame. 
* Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking
* For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
[[Help:Contents/Links#Interwiki_links|Internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity)
*

{{tip|Suggestions for this section:
* Link to the most relevant internal resources about the topic
* Include the source in parentheses
}}

==References==
Provide the references for all citations in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. Alternatively, you can use wiki style (as used on Wikipedia), as long as the information is complete and the formatting is consistent.

{{Hanging indent|1=

Bai,C., Liu, R., and Zhang, H. (2026) Moral elevation, gratitude, and meaning in nurses’ positive mental health. ''Nursing Ethics'' Vol. 33(4) 1078–1093 [https://journals.sagepub.com/doi/10.1177/09697330261424358 https://doi.org/10.1177/09697330261424358]

Kinosada, Y., Furukawa, Y., Wakai, T., &amp; Nakashima, K. (2026). Does guilt motivate prosocial behaviour at the expense of others? Preregistered replications and exploratory statistical modelling. ''Asian Journal of Social Psychology'', 29, e70099. https://doi-org.ezproxy.canberra.edu.au/10.1111/ajsp.70099 

Santoro, G., Sideli, L., Musetti, A., &amp; Schimmenti, A. (2025) The Relationship Between Childhood Trauma and Shame: The Mediating Role of Dissociation. ''European Journal of Investigation in Health, Psychology and Education''. ;15(8):151. [[doi:10.3390/ejihpe15080151|http://doi.org/10.3390/ejihpe15080151]]

Romera EM, Ortega-Ruiz R, Rodríguez-Barbero S and Falla D (2019) How Do You Think the Victims of Bullying Feel? A Study of Moral Emotions in Primary School. ''Frontiers in Psychology, Educational Psychology.'' 10:1753. https://doi.org/10.3389/fpsyg.2019.01753 [https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2019.01753/full l]

Tangney, J. P., Stuewig, J., &amp; Mashek, D., J., (2007). Moral Emotions and Moral Behavior. ''Annual Review of Psychology'' 58:345-372. https://doi.org/10.1146/annurev.psych.56.091103.070145 [https://doi.org/10.1146/annurev.psych.56.091103.070145]

Turner, J., H., &amp; Stets, J., E (2006). Moral Emotions. In ''Handbook of the Sociology of Emotions (''pp.544 - 566). Spinger. [https://link.springer.com/book/10.1007/978-0-387-30715-2 https://doi.org/10.1007/978-0-387-30715-2] . 

Tillman CJ, Gonzalez K, Whitman MV, Crawford WS and Hood AC (2018) A Multi-Functional View of Moral Disengagement: Exploring the Effects of Learning the Consequences. ''Frontiers in Psychology, Personality and Social Psychology''. 8:2286. [https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2017.02286/full#F2 doi: 10.3389/fpsyg.2017.02286]

Wojcik, K., D., Cox, D., W., &amp; Kealy,D. (2019) Adverse childhood experiences and shame- and guilt-proneness: Examining the mediating roles of interpersonal problems in a community sample, ''Child Abuse &amp; Neglec''t, Volume 98, 2019, 104233, ISSN 0145-2134, https://doi.org/10.1016/j.chiabu.2019.104233

}} 


APA style example:
{{Hanging indent|1=

Rosenberg, B. D., &amp; Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091

Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper &amp; Row.

}}

{{tip|Suggestions for this section:
* Important aspects of APA referencing style
** Author surname, followed by a comma, then the author initials separated by full stops and spaces
** Year of publication in parentheses
** Title of work in lower case (except first letter and proper names), ending in a full-stop
** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop
** doi as a URL which is a working hyperlink (i.e., clickable)
** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]:
Use &quot;Edit source&quot;
&lt;nowiki&gt;{{Hanging indent|1= the full list of references}}&lt;/nowiki&gt;
* The most common mistakes include:
** Incorrect capitalisation
** Incorrect italicisation
** dois which aren't clickable as working hyperlinks
** Citing sources that haven't been consulted
}}

==External links==
[https://www.ted.com/talks/asha_curran_how_acts_of_kindness_sparked_a_global_movement Ideas change everything] (TED)

[https://www.youtube.com/watch?v=b4CfyLe0IlQ Prosocial Behavior | Ethics Defined] (Youtube)


[[Help:Contents/Links#External_links|External links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)

{{tip|Suggestions for this section:
* Link to the most relevant external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotion]]
[[Category:Motivation and emotion/Book/Morality]]</text>
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__TOC__

==Overview==
{{RoundBoxTop|theme=7}}

[[File:Begging man Harmony Lot 27 Elliot Street downtown Brattleboro VT July 2025 02.jpg|right|thumb|150px|'''Figure 1'''. Homeless man begging]]

;Scenario

Imagine that you are doing your weekly shopping and you come across a homeless person who is asking for food or money. The person present in an unkempt state and initially you make sure you walk past, your stomach drops, and subconsciously wrinkle your nose and you decide to take a longer path to the shops in order to avoid them. When paying for your groceries, you realise that you don’t have quite enough to pay the full amount, instantly, your face gets hot as there is a line of people waiting behind you and it seems they are all staring at you, judging your error. Whilst you are talking to the register assistant, asking for some time to go through your groceries to determine which items are a priority, the person behind you offers to make up the difference. Suddenly, the hot feeling in your face becomes a warm feeling in your chest and you start profusely thanking the person and ask if there is anything you can do to make it up to them, they respond with “when you are in a position to pay it forward to some else, please do so.”

{{RoundBoxBottom}}
[[w:Moral_emotions|Moral emotions]] potentially set humans apart from other animals, by enabaling people to react to social events that do not directly affect the self but concern the interests or welfare either of others and society as a whole (''Haidt, 2003).'' They arise when individuals evaluate actions, intentions, or social situations in terms of right or wrong, in accordance with social norms and moral standards. This guides behaviours that support cooperation, fairness and social harmony. This distinguishes moral emotions from [[Motivation and emotion/Lectures/Individual emotions|basic emotions]], which are a person's primary response to a situation. Basic emotions fast, short lived, whilst moral emotions align with secondary emotions that require a cognitive evaluation of the self from learned social meaning (Guy-Evans, 2026). 

To understand how moral emotions motivate behaviour, examination of the psychological/ psychological mechanisms behind these emotions is required. Moral emotions involve appraisals of responsibility and social meaning, biological responses that prepare the body for action, and expressive behaviours that communicate intentions. These mechanisms create ''action readiness'', transforming moral evaluations into behavioural tendencies such as helping, repairing harm, confronting wrongdoing, or avoiding social violations (Reeve, 2023).

Understanding moral emotions is essential to link how they motivate ethical and prosocial action. [[w:Self-conscious_emotions|Self-conscious moral emotions]] - such as guilt, shame, embarrassment, and authentic pride - occur when people evaluate their own behaviour against internalised moral standards. These emotions regulate the moral self by motivating reparative action, helping others, rule compliance, or withdrawal (Tangney, Tracy, &amp; Robins, 2007). Importantly [[Motivation and emotion/Book/2018/Guilt and shame|guilt and shame]] differ in their internalised state and motivation urge resulting in different behaviours; guilt‑proneness predicts empathy, apology, and reparative behaviour, whereas shame‑proneness predicts avoidance, defensiveness, and increased risk of antisocial behaviour (Tangney, Stuewig, &amp; Mashek, 2007). 

Other‑evaluative moral emotions—including compassion, gratitude, elevation/ awe, along with contempt, disgust and moral outrage—arise when people respond to the experiences or actions of others. These emotions generate intuitive impulses to help, reciprocate kindness, emulate moral exemplars, confront wrongdoing or avoid social violations (Haidt, 2003). Together, these insights show how moral emotions serve as powerful motivational systems that shape ethical and prosocial behaviour in everyday life.

{{RoundBoxTop|theme=5}}
'''Focus questions'''

{{ic|Use bullet points as shown in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]}}

1.	What are the key moral emotions? &lt;br&gt;
2.     How are moral emotions felt?&lt;br&gt;
3.	How do moral emotions influence ethical and prosocial action?&lt;br&gt;
4.	What environmental factors can alter the influence of moral emotions?&lt;br&gt;
5.     How is positive psychology and the light triad effective at counteracting the moral  disengagement?{{RoundBoxBottom}}

==Moral emotions==
* General introduction into what moral emotions are; moral emotions are linked to a person's moral compass and conscious and help establish the development of an individual's learning of the difference between right and wrong. Explain the different types of moral emotions of shame, guilt, sympathy, empathy, contempt, anger and disgust (Turner, J.H., Stets, J.E. (2006). Each emotion elicits a specific bodily response. Refer to table 1
* Self- conscious emotions - [[Motivation and emotion/Book/2018/Guilt and shame|Shame, guilt]], [[Motivation and emotion/Book/2022/Embarrassment|embarrassment]], and [[Motivation and emotion/Book/2017/Pride|pride]] ([[doi:10.1146/annurev.psych.56.091103.070145|Tangney, Stuewig, &amp; Mashek. 2007]]) {{ic|Use APA style for citations with 3 or more authors}} {{ic|Move citation links into the References section}}
** Shame and guilt are, whilst similar [https://pmc.ncbi.nlm.nih.gov/articles/PMC12385681/ Santoro. G,et al (2025)] has defined shame as being deeply engrained self-conscious emotions linked to identity formation and guilt arising around specific events or behaviours. ''Needs further development*'' 
* other-focused moral emotions - [https://biblehub.com/topical/u/understanding_righteous_anger.htm Righteous anger], [[w:Contempt|Contempt]], [[w:Disgust|Disgust]], [[w:Awe|awe]] [[w:Elevation_(emotion)|elevation]] and [[Motivation and emotion/Book/2021/Gratitude|gratitude]]
Explain the difference between self- conscious and other focused emotion and the ways in which people cope with them [http://www.rpforschools.net/articles/ASP/Tangney,%20Tracy%20&amp;%20Robins%202007%20The%20self-conscious%20emotions%20-%20Theory%20and%20Research.pdf The self-counscious emotions]  (Tangle et al., 2007; pdf)

=== Background ===

* Plato [[w:Moral_psychology|moral psychology]]
* Kant
* Adam Smith
* David Hume

=== Modern theories ===

* Piaget
* Kohlberg
* Adler

=== Environmental influences ===

* Adverse Childhood experiences - (Katharine D. Wojcik, Daniel W. Cox, David Kealy, Adverse childhood experiences and shame- and guilt-proneness: Examining the mediating roles of interpersonal problems in a community sample, Child Abuse &amp; Neglect, Volume 98, 2019, 104233, ISSN 0145-2134, &lt;nowiki&gt;https://doi.org/10.1016/j.chiabu.2019.104233&lt;/nowiki&gt; .)
*positive environmental influence

== Moral emotions and influence on motivation and behaviours ==
{{ic|Include an introductory paragraph before branching into sub-sections}}

=== Elevation/ Gratitude - ===
Discuss how positive moral emotions (Elevation and gratitude) can contribute to moral flourishing and improve patient care, (linking back to the scenario). (Bai,C., Liu, R., and Zhang, H. 2026) 

{{RoundBoxTop|theme=7}}
;Let's look back at the scenario

You walk back to the car and are amazed at the kindness of strangers and so grateful that when you come across the person who was asking for money again. This time, you decide that even though you don’t have much in the way of money, you want to offer the person one of the ready meals in your shopping and wish the person a good day. Walking away, you feel a warm sensation in your chest and your back straightened and you find you are smiling to yourself.
{{RoundBoxBottom}}

=== Guilt ===
Explore the following ''&quot;Guilt is recognized as a social and moral emotion that drives prosocial behaviour, typically through actions to repair relationships with victims, often at a personal cost&quot; .('' Kinosada, Y., et al, 2026, p.1)

=== Shame ===
Traditionally shame has been used to punish and reform behaviour, but does it actually reduce criminality? Discuss. **one reference still waiting on88 cannot confirm if it is applicable. 

Is shame an effective emotion now or redundant and causes more harm than good? evolutionary, it was esentail for survival, in a modern society is it causing prevalence of mental health disorders. [https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2013.00310/full#S7 Frontiers | The Role of Self-Blaming Moral Emotions in Major Depression and Their Impact on Social-Economical Decision Making] 

Punishment and Shame: A Philosophical Study - a North Carolina Agricultural and Technical State University, Greensboro, NC, United States

=== Moral disengagement ===
Explore the way unethical acts are reasoned due to moral disengagement  

== Mitigating maladaptive moral affect ==
{{ic|Include an introductory paragraph before branching into sub-sections}}

=== Altruism ===
[[w:Altruism|Altruism]]

=== Light Triad ===
[[Motivation and emotion/Book/2021/Light triad|Light triad]] 

=== Self-determination theory ===
[[w:Self determination theory|Self determination theory]] 

==Figures==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]]

* For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples
* For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure
* Figures can show any kind of media such as photos, diagrams, graphs, video, audio, and so on
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text)
* Images must be embedded from [[commons:|Wikimedia Commons]]
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Cite each figure at least once in the main text (e.g., see Figure 2)

==Learning features==
Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options:

{{anchor|Scenarios}}
;Scenarios
* Scenarios, case studies, or examples that illustrate concepts in action
* Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages)
* Can be real or fictional; if real, provide citation(s)

{{anchor|Feature box}}
;Feature boxes
* Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect
* Consider using feature boxes for:
** [[#Scenarios|Scenarios]], case studies, or examples
** Focus questions
** Tips
** Quiz questions
** Take-home messages

;Embedded links
* When key words are introduced, use [[Help:Links|interwiki links]] to:
** Wikipedia articles (e.g., &quot;An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]&quot;) or
** Related book chapters (e.g., &quot;If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]&quot;)
*[[w:Moral_emotions|Moral emotions]] include [[Motivation and emotion/Book/2018/Guilt and shame|guilt, shame]], embarrassment, 

{{anchor|Tables}}
;Tables
* Use tables to organise and summarise information
* Cite each table at least once in the main text (e.g., see Table 1)
* Tables should be captioned
* [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted

'''Table 1''' 

''Bodily Responses to Moral emotions'' 
{| class=&quot;wikitable&quot;
!Strategy
!Bodily responses
|-
|Embarrassment 
|
|-
|Guilt
|
|-
|Shame
|
|-
|Pride
|
|-
|Righteous anger
|
|-
|Comptempt
|
|-
|Disgust
|
|-
|Elevation
|
|-
|Gratitude
|
|}

;Quizzes
* One or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=&quot;simple&quot;&gt;
{Unlike guilt, which pertains to specific actions, shame involves a global negative evaluation of the self.
|type=&quot;()&quot;}
+ True
- False

{Self-conscious emotions include righteous anger, contempt, disgust, elevation and gratitude
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

==Conclusion==
* Moral emotions motivate ethical decision and behaviour
* Childhood trauma can disrupt the development of moral emotions,
* All is not lost - protective factors can mitigate the negative impact of shame. 
* Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking
* For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
[[Help:Contents/Links#Interwiki_links|Internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity)
*

{{tip|Suggestions for this section:
* Link to the most relevant internal resources about the topic
* Include the source in parentheses
}}

==References==
Provide the references for all citations in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. Alternatively, you can use wiki style (as used on Wikipedia), as long as the information is complete and the formatting is consistent.

{{Hanging indent|1=

Bai,C., Liu, R., and Zhang, H. (2026) Moral elevation, gratitude, and meaning in nurses’ positive mental health. ''Nursing Ethics'' Vol. 33(4) 1078–1093 [https://journals.sagepub.com/doi/10.1177/09697330261424358 https://doi.org/10.1177/09697330261424358]

Kinosada, Y., Furukawa, Y., Wakai, T., &amp; Nakashima, K. (2026). Does guilt motivate prosocial behaviour at the expense of others? Preregistered replications and exploratory statistical modelling. ''Asian Journal of Social Psychology'', 29, e70099. https://doi-org.ezproxy.canberra.edu.au/10.1111/ajsp.70099 

Santoro, G., Sideli, L., Musetti, A., &amp; Schimmenti, A. (2025) The Relationship Between Childhood Trauma and Shame: The Mediating Role of Dissociation. ''European Journal of Investigation in Health, Psychology and Education''. ;15(8):151. [[doi:10.3390/ejihpe15080151|http://doi.org/10.3390/ejihpe15080151]]

Romera EM, Ortega-Ruiz R, Rodríguez-Barbero S and Falla D (2019) How Do You Think the Victims of Bullying Feel? A Study of Moral Emotions in Primary School. ''Frontiers in Psychology, Educational Psychology.'' 10:1753. https://doi.org/10.3389/fpsyg.2019.01753 [https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2019.01753/full l]

Tangney, J. P., Stuewig, J., &amp; Mashek, D., J., (2007). Moral Emotions and Moral Behavior. ''Annual Review of Psychology'' 58:345-372. https://doi.org/10.1146/annurev.psych.56.091103.070145 [https://doi.org/10.1146/annurev.psych.56.091103.070145]

Turner, J., H., &amp; Stets, J., E (2006). Moral Emotions. In ''Handbook of the Sociology of Emotions (''pp.544 - 566). Spinger. [https://link.springer.com/book/10.1007/978-0-387-30715-2 https://doi.org/10.1007/978-0-387-30715-2] . 

Tillman CJ, Gonzalez K, Whitman MV, Crawford WS and Hood AC (2018) A Multi-Functional View of Moral Disengagement: Exploring the Effects of Learning the Consequences. ''Frontiers in Psychology, Personality and Social Psychology''. 8:2286. [https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2017.02286/full#F2 doi: 10.3389/fpsyg.2017.02286]

Wojcik, K., D., Cox, D., W., &amp; Kealy,D. (2019) Adverse childhood experiences and shame- and guilt-proneness: Examining the mediating roles of interpersonal problems in a community sample, ''Child Abuse &amp; Neglec''t, Volume 98, 2019, 104233, ISSN 0145-2134, https://doi.org/10.1016/j.chiabu.2019.104233

}} 


APA style example:
{{Hanging indent|1=

Rosenberg, B. D., &amp; Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091

Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper &amp; Row.

}}

{{tip|Suggestions for this section:
* Important aspects of APA referencing style
** Author surname, followed by a comma, then the author initials separated by full stops and spaces
** Year of publication in parentheses
** Title of work in lower case (except first letter and proper names), ending in a full-stop
** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop
** doi as a URL which is a working hyperlink (i.e., clickable)
** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]:
Use &quot;Edit source&quot;
&lt;nowiki&gt;{{Hanging indent|1= the full list of references}}&lt;/nowiki&gt;
* The most common mistakes include:
** Incorrect capitalisation
** Incorrect italicisation
** dois which aren't clickable as working hyperlinks
** Citing sources that haven't been consulted
}}

==External links==
[https://www.ted.com/talks/asha_curran_how_acts_of_kindness_sparked_a_global_movement Ideas change everything] (TED)

[https://www.youtube.com/watch?v=b4CfyLe0IlQ Prosocial Behavior | Ethics Defined] (Youtube)


[[Help:Contents/Links#External_links|External links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)

{{tip|Suggestions for this section:
* Link to the most relevant external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotion]]
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__TOC__

==Overview==
{{RoundBoxTop|theme=7}}

[[File:Begging man Harmony Lot 27 Elliot Street downtown Brattleboro VT July 2025 02.jpg|right|thumb|150px|'''Figure 1'''. Homeless man begging]]

;Scenario

Imagine that you are doing your weekly shopping and you come across a homeless person who is asking for food or money. The person present in an unkempt state and initially you make sure you walk past, your stomach drops, and subconsciously wrinkle your nose and you decide to take a longer path to the shops in order to avoid them. When paying for your groceries, you realise that you don’t have quite enough to pay the full amount, instantly, your face gets hot as there is a line of people waiting behind you and it seems they are all staring at you, judging your error. Whilst you are talking to the register assistant, asking for some time to go through your groceries to determine which items are a priority, the person behind you offers to make up the difference. Suddenly, the hot feeling in your face becomes a warm feeling in your chest and you start profusely thanking the person and ask if there is anything you can do to make it up to them, they respond with “when you are in a position to pay it forward to some else, please do so.”

{{RoundBoxBottom}}
[[w:Moral_emotions|Moral emotions]] potentially set humans apart from other animals, by enabaling people to react to social events that do not directly affect the self but concern the interests or welfare either of others and society as a whole (''Haidt, 2003).'' They arise when individuals evaluate actions, intentions, or social situations in terms of right or wrong, in accordance with social norms and moral standards. This guides behaviours that support cooperation, fairness and social harmony. This distinguishes moral emotions from [[Motivation and emotion/Lectures/Individual emotions|basic emotions]], which are a person's primary response to a situation. Basic emotions fast, short lived, whilst moral emotions align with secondary emotions that require a cognitive evaluation of the self from learned social meaning (''Guy-Evans'', 2026). 

To understand how moral emotions motivate behaviour, examination of the psychological/ psychological mechanisms behind these emotions is required. Moral emotions involve appraisals of responsibility and social meaning, biological responses that prepare the body for action, and expressive behaviours that communicate intentions. These mechanisms create ''action readiness'', transforming moral evaluations into behavioural tendencies such as helping, repairing harm, confronting wrongdoing, or avoiding social violations (''Reeve'', 2023).

Understanding moral emotions is essential to link how they motivate ethical and prosocial action. [[w:Self-conscious_emotions|Self-conscious moral emotions]] - such as guilt, shame, embarrassment, and authentic pride - occur when people evaluate their own behaviour against internalised moral standards. These emotions regulate the moral self by motivating reparative action, helping others, rule compliance, or withdrawal (''Tangney, Tracy, &amp; Robins'', 2007). Importantly [[Motivation and emotion/Book/2018/Guilt and shame|guilt and shame]] differ in their internalised state, appraisal of self and motivation urge resulting in different behaviours (''Tangney, Stuewig, &amp; Mashek'', 2007). 

Other‑evaluative moral emotions—including compassion, gratitude, elevation/ awe, along with contempt, disgust and moral outrage—arise when people respond to the experiences or actions of others. These emotions generate intuitive impulses to help, reciprocate kindness, emulate moral exemplars, confront wrongdoing or avoid social violations (''Haidt'', 2003). Together, these insights show how moral emotions serve as powerful motivational systems that shape ethical and prosocial behaviour in everyday life.

{{RoundBoxTop|theme=5}}'''Focus questions'''
{{ic|}}
*     What moral emotions and how do they differ from basic emotions? &lt;br&gt;
*     How are moral emotions felt and motivate action?&lt;br&gt;
*     How do self-conscious moral emotions influence ethical behaviour?
*     How to other-evaluating emotions motivate prosocial behaviour?{{RoundBoxBottom}}

==Moral emotions==
* General introduction into what moral emotions are; moral emotions are linked to a person's moral compass and conscious and help establish the development of an individual's learning of the difference between right and wrong. Explain the different types of moral emotions of shame, guilt, sympathy, empathy, contempt, anger and disgust (Turner, J.H., Stets, J.E. (2006). Each emotion elicits a specific bodily response. Refer to table 1
* Self- conscious emotions - [[Motivation and emotion/Book/2018/Guilt and shame|Shame, guilt]], [[Motivation and emotion/Book/2022/Embarrassment|embarrassment]], and [[Motivation and emotion/Book/2017/Pride|pride]] ([[doi:10.1146/annurev.psych.56.091103.070145|Tangney, Stuewig, &amp; Mashek. 2007]]) {{ic|Use APA style for citations with 3 or more authors}} {{ic|Move citation links into the References section}}
** Shame and guilt are, whilst similar [https://pmc.ncbi.nlm.nih.gov/articles/PMC12385681/ Santoro. G,et al (2025)] has defined shame as being deeply engrained self-conscious emotions linked to identity formation and guilt arising around specific events or behaviours. ''Needs further development*'' 
* other-focused moral emotions - [https://biblehub.com/topical/u/understanding_righteous_anger.htm Righteous anger], [[w:Contempt|Contempt]], [[w:Disgust|Disgust]], [[w:Awe|awe]] [[w:Elevation_(emotion)|elevation]] and [[Motivation and emotion/Book/2021/Gratitude|gratitude]]
Explain the difference between self- conscious and other focused emotion and the ways in which people cope with them [http://www.rpforschools.net/articles/ASP/Tangney,%20Tracy%20&amp;%20Robins%202007%20The%20self-conscious%20emotions%20-%20Theory%20and%20Research.pdf The self-counscious emotions]  (Tangle et al., 2007; pdf)

=== Background ===

* Plato [[w:Moral_psychology|moral psychology]]
* Kant
* Adam Smith
* David Hume

=== Modern theories ===

* Piaget
* Kohlberg
* Adler

=== Environmental influences ===

* Adverse Childhood experiences - (Katharine D. Wojcik, Daniel W. Cox, David Kealy, Adverse childhood experiences and shame- and guilt-proneness: Examining the mediating roles of interpersonal problems in a community sample, Child Abuse &amp; Neglect, Volume 98, 2019, 104233, ISSN 0145-2134, &lt;nowiki&gt;https://doi.org/10.1016/j.chiabu.2019.104233&lt;/nowiki&gt; .)
*positive environmental influence

== Moral emotions and influence on motivation and behaviours ==
{{ic|Include an introductory paragraph before branching into sub-sections}}

=== Elevation/ Gratitude - ===
Discuss how positive moral emotions (Elevation and gratitude) can contribute to moral flourishing and improve patient care, (linking back to the scenario). (Bai,C., Liu, R., and Zhang, H. 2026) 

{{RoundBoxTop|theme=7}}
;Let's look back at the scenario

You walk back to the car and are amazed at the kindness of strangers and so grateful that when you come across the person who was asking for money again. This time, you decide that even though you don’t have much in the way of money, you want to offer the person one of the ready meals in your shopping and wish the person a good day. Walking away, you feel a warm sensation in your chest and your back straightened and you find you are smiling to yourself.
{{RoundBoxBottom}}

=== Guilt ===
Explore the following ''&quot;Guilt is recognized as a social and moral emotion that drives prosocial behaviour, typically through actions to repair relationships with victims, often at a personal cost&quot; .('' Kinosada, Y., et al, 2026, p.1)

=== Shame ===
Traditionally shame has been used to punish and reform behaviour, but does it actually reduce criminality? Discuss. **one reference still waiting on88 cannot confirm if it is applicable. 

Is shame an effective emotion now or redundant and causes more harm than good? evolutionary, it was esentail for survival, in a modern society is it causing prevalence of mental health disorders. [https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2013.00310/full#S7 Frontiers | The Role of Self-Blaming Moral Emotions in Major Depression and Their Impact on Social-Economical Decision Making] 

Punishment and Shame: A Philosophical Study - a North Carolina Agricultural and Technical State University, Greensboro, NC, United States

=== Moral disengagement ===
Explore the way unethical acts are reasoned due to moral disengagement  

== Mitigating maladaptive moral affect ==
{{ic|Include an introductory paragraph before branching into sub-sections}}

=== Altruism ===
[[w:Altruism|Altruism]]

=== Light Triad ===
[[Motivation and emotion/Book/2021/Light triad|Light triad]] 

=== Self-determination theory ===
[[w:Self determination theory|Self determination theory]] 

==Figures==
[[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]]

* For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples
* For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure
* Figures can show any kind of media such as photos, diagrams, graphs, video, audio, and so on
* Embed figures throughout the chapter, starting with the scenario in the Overview section
* Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text)
* Images must be embedded from [[commons:|Wikimedia Commons]]
* Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed
* Cite each figure at least once in the main text (e.g., see Figure 2)

==Learning features==
Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options:

{{anchor|Scenarios}}
;Scenarios
* Scenarios, case studies, or examples that illustrate concepts in action
* Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages)
* Can be real or fictional; if real, provide citation(s)

{{anchor|Feature box}}
;Feature boxes
* Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect
* Consider using feature boxes for:
** [[#Scenarios|Scenarios]], case studies, or examples
** Focus questions
** Tips
** Quiz questions
** Take-home messages

;Embedded links
* When key words are introduced, use [[Help:Links|interwiki links]] to:
** Wikipedia articles (e.g., &quot;An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]&quot;) or
** Related book chapters (e.g., &quot;If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]&quot;)
*[[w:Moral_emotions|Moral emotions]] include [[Motivation and emotion/Book/2018/Guilt and shame|guilt, shame]], embarrassment, 

{{anchor|Tables}}
;Tables
* Use tables to organise and summarise information
* Cite each table at least once in the main text (e.g., see Table 1)
* Tables should be captioned
* [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted

'''Table 1''' 

''Bodily Responses to Moral emotions'' 
{| class=&quot;wikitable&quot;
!Strategy
!Bodily responses
|-
|Embarrassment 
|
|-
|Guilt
|
|-
|Shame
|
|-
|Pride
|
|-
|Righteous anger
|
|-
|Comptempt
|
|-
|Disgust
|
|-
|Elevation
|
|-
|Gratitude
|
|}

;Quizzes
* One or two quiz questions for each main section is better than a long quiz at the end
* Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages
* Ask easy rather than hard questions
* Different types of quiz questions are possible; see [[Help:Quiz|Quiz]]

Example simple quiz questions. Choose your answers and click &quot;Submit&quot;:
&lt;quiz display=&quot;simple&quot;&gt;
{Unlike guilt, which pertains to specific actions, shame involves a global negative evaluation of the self.
|type=&quot;()&quot;}
+ True
- False

{Self-conscious emotions include righteous anger, contempt, disgust, elevation and gratitude
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

==Conclusion==
* Moral emotions motivate ethical decision and behaviour
* Childhood trauma can disrupt the development of moral emotions,
* All is not lost - protective factors can mitigate the negative impact of shame. 
* Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking
* For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research
* Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem
* Recommended length: 150 to 330 words

{{tip|Suggestions for this section:
* What is the answer to the sub-title question based on psychological theory and research?
* What are the answers to the focus questions?
* What are the practical, take-home messages?
}}

==See also==
[[Help:Contents/Links#Interwiki_links|Internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity)
*

{{tip|Suggestions for this section:
* Link to the most relevant internal resources about the topic
* Include the source in parentheses
}}

==References==
Provide the references for all citations in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. Alternatively, you can use wiki style (as used on Wikipedia), as long as the information is complete and the formatting is consistent.

{{Hanging indent|1=

Bai,C., Liu, R., and Zhang, H. (2026) Moral elevation, gratitude, and meaning in nurses’ positive mental health. ''Nursing Ethics'' Vol. 33(4) 1078–1093 [https://journals.sagepub.com/doi/10.1177/09697330261424358 https://doi.org/10.1177/09697330261424358]

Kinosada, Y., Furukawa, Y., Wakai, T., &amp; Nakashima, K. (2026). Does guilt motivate prosocial behaviour at the expense of others? Preregistered replications and exploratory statistical modelling. ''Asian Journal of Social Psychology'', 29, e70099. https://doi-org.ezproxy.canberra.edu.au/10.1111/ajsp.70099 

Santoro, G., Sideli, L., Musetti, A., &amp; Schimmenti, A. (2025) The Relationship Between Childhood Trauma and Shame: The Mediating Role of Dissociation. ''European Journal of Investigation in Health, Psychology and Education''. ;15(8):151. [[doi:10.3390/ejihpe15080151|http://doi.org/10.3390/ejihpe15080151]]

Romera EM, Ortega-Ruiz R, Rodríguez-Barbero S and Falla D (2019) How Do You Think the Victims of Bullying Feel? A Study of Moral Emotions in Primary School. ''Frontiers in Psychology, Educational Psychology.'' 10:1753. https://doi.org/10.3389/fpsyg.2019.01753 [https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2019.01753/full l]

Tangney, J. P., Stuewig, J., &amp; Mashek, D., J., (2007). Moral Emotions and Moral Behavior. ''Annual Review of Psychology'' 58:345-372. https://doi.org/10.1146/annurev.psych.56.091103.070145 [https://doi.org/10.1146/annurev.psych.56.091103.070145]

Turner, J., H., &amp; Stets, J., E (2006). Moral Emotions. In ''Handbook of the Sociology of Emotions (''pp.544 - 566). Spinger. [https://link.springer.com/book/10.1007/978-0-387-30715-2 https://doi.org/10.1007/978-0-387-30715-2] . 

Tillman CJ, Gonzalez K, Whitman MV, Crawford WS and Hood AC (2018) A Multi-Functional View of Moral Disengagement: Exploring the Effects of Learning the Consequences. ''Frontiers in Psychology, Personality and Social Psychology''. 8:2286. [https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2017.02286/full#F2 doi: 10.3389/fpsyg.2017.02286]

Wojcik, K., D., Cox, D., W., &amp; Kealy,D. (2019) Adverse childhood experiences and shame- and guilt-proneness: Examining the mediating roles of interpersonal problems in a community sample, ''Child Abuse &amp; Neglec''t, Volume 98, 2019, 104233, ISSN 0145-2134, https://doi.org/10.1016/j.chiabu.2019.104233

}} 


APA style example:
{{Hanging indent|1=

Rosenberg, B. D., &amp; Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091

Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper &amp; Row.

}}

{{tip|Suggestions for this section:
* Important aspects of APA referencing style
** Author surname, followed by a comma, then the author initials separated by full stops and spaces
** Year of publication in parentheses
** Title of work in lower case (except first letter and proper names), ending in a full-stop
** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop
** doi as a URL which is a working hyperlink (i.e., clickable)
** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]:
Use &quot;Edit source&quot;
&lt;nowiki&gt;{{Hanging indent|1= the full list of references}}&lt;/nowiki&gt;
* The most common mistakes include:
** Incorrect capitalisation
** Incorrect italicisation
** dois which aren't clickable as working hyperlinks
** Citing sources that haven't been consulted
}}

==External links==
[https://www.ted.com/talks/asha_curran_how_acts_of_kindness_sparked_a_global_movement Ideas change everything] (TED)

[https://www.youtube.com/watch?v=b4CfyLe0IlQ Prosocial Behavior | Ethics Defined] (Youtube)


[[Help:Contents/Links#External_links|External links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:
* [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne)
* [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com)

{{tip|Suggestions for this section:
* Link to the most relevant external resources about the topic
* Include the source in parentheses after the link
}}

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
[[Category:Motivation and emotion/Book/Emotion]]
[[Category:Motivation and emotion/Book/Morality]]</text>
      <sha1>r3ux07f8ween747mm1yo2omf4fepgwa</sha1>
    </revision>
  </page>
  <page>
    <title>Talk:Motivation and emotion/Book/2026/Adolescent risk-taking and reward-system development</title>
    <ns>1</ns>
    <id>331270</id>
    <revision>
      <id>2841493</id>
      <parentid>2840073</parentid>
      <timestamp>2026-10-19T10:33:32Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <comment>Book chapter feedback</comment>
      <origin>2841493</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="23750" sha1="igvjh1ocecme7ml3r05jeqc0t62c95i" xml:space="preserve">== Discussion on chapter ==
Hey! I'm doing dopamine and sensation-seeking and id just love to say that this chapter is amazing with demonstrating young adolescents and risk-taking as I have had to dabble in that area, I think your structure is well thought out and I enjoy the emoji's in the quick revision. Super easy to read for someone seeking knowledge in risk-taking in adolescents and the reward system! The only thing id suggest is to check whether the sub-headings are meant to be capitalised because form last years chapters quite a bit of the high star ones seem to have them under cased except for the first letter   - Paige [[User:U3262868|U3262868]] ([[User talk:U3262868|discuss]] • [[Special:Contributions/U3262868|contribs]]) 21:33, 11 October 2026 (UTC)

==When does adolescent risk-taking peak?==
I'd be curious to know if its possible to say when risk-taking peaks in adolescence?
Sincerely, James

---- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:07, 19 August 2026 (UTC)

== Changes made  ==

hello, I changed the casing of your fist heading to make all the letters lower case expect for the first letter. I believe this is the format our teacher wants us to follow but just double check  [[User:Ella Kay244|Ella Kay244]] ([[User talk:Ella Kay244|discuss]] • [[Special:Contributions/Ella Kay244|contribs]]) 04:24, 25 August 2026 (UTC)

== Discussion comment: Adolescent risk-taking ==
Hi! I really liked the example of Mia at the start, I think works really well because it shows how quickly a situation can change when friends are involved. I also think it would be interesting to see whether reward-seeking is always negative, or whether some of these behaviours could be beneficial, e.g., independence or trying new things. I hadn’t really thought about the positive side of risk-taking before, so I think that will be an interesting part of your chapter!--[[User:U3275908|U3275908]] ([[User talk:U3275908|discuss]] • [[Special:Contributions/U3275908|contribs]]) 11:09, 26 August 2026 (UTC)

== How is reward classified for an adolescent? ==

I'd be super interested in what classified as a reward for adolescents. It's a really cool topic you've got, you covered social rewards briefly but other more general areas you talked about weren't so clear cut. Nothing on you its just the nature of how some of these things are laid out.  
Well done!! :) [[User:Revial76|Revial76]] ([[User talk:Revial76|discuss]] • [[Special:Contributions/Revial76|contribs]]) 15:23, 27 August 2026 (UTC)

&lt;!-- Official topic development feedback --&gt;
{{METF/2026
|1=
&lt;!-- Title --&gt;
# Title and subtitle are correctly worded and use [[w:Letter case#Sentence casing|sentence casing]]
|2=
&lt;!-- Heading structure --&gt;
&lt;!-- 2-level --&gt;
# Excellent – Well developed [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]]. Meaningful headings clearly relate directly to the core topic.
# Be careful that the structure isn't overly ambitious because the word count might blow out; be prepared to concentrate on core topics only
# The subtitle in the sub-headings should probably have the first letters capitalised
&lt;!-- Alignment with focus questions --&gt;
# Insufficient alignment between sub-title, focus questions, and top-level headings
|3=
&lt;!-- Overview--&gt;
# Very good
&lt;!-- Scenario --&gt;
# A scenario or case study is presented in a feature box with an image at the start of this section
&lt;!-- Description --&gt;
# A promising description of the problem/topic is planned or presented
# Consider making this more user-friendly, shifting most or all of the citations into subsequent sections
# Move external links into the references or external links
&lt;!-- Focus questions --&gt;
# Develop closer alignment between the sub-title, focus questions, and top-level headings
|4=
&lt;!-- Key points--&gt;
&lt;!-- Overall --&gt;
# Excellent – key points are well developed for each section
&lt;!-- Conclusion --&gt;
# Conclusion is well developed
|5=
&lt;!-- Figure --&gt;
# Figure(s) are presented and captioned
&lt;!-- Cite --&gt;
# Cite each figure at least once in the main text using APA style (e.g., see Figure 1)
&lt;!-- Size --&gt;
# Consider increasing image size(s)
|6=
&lt;!-- Learning feature --&gt;
&lt;!-- Interwiki links ---&gt;
# Add in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]] (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
&lt;!-- Scenarios/examples/case studies --&gt;
# Consider use of more scenarios/examples/case studies 
&lt;!-- Quiz --&gt;
# Promising use of quiz question(s)
&lt;!-- Tables --&gt;
# Also consider using tables to summarise key information
|7=
&lt;!-- References --&gt;
&lt;!-- Overall --&gt;
# Very good
&lt;!-- Systematic reviews --&gt;
# What are the most relevant systematic reviews/meta-analyses about this topic?
&lt;!-- APA style --&gt;
# Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]:
## capitalisation
|8=
&lt;!-- Resources --&gt;
&lt;!-- See also --&gt;
# See also
## Excellent
&lt;!-- External links --&gt;
# External links
## Excellent
|9=
&lt;!-- User page --&gt;
# Excellent
|10=
&lt;!-- Social contribution --&gt;
# Excellent – at least three different types of contributions with direct link(s) to evidence
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:37, 30 August 2026 (UTC)

== Suggestion for a related source ==
Hey there! This chapter seems to be coming along nicely, and I'm interested in how you'll expand upon it as you go. I'm doing a related chapter [[Motivation and emotion/Book/2026/Game of dice task and decision-making|here]] about the Game of Dice Task and how it relates to risk-based decision making. I've found a source in my own research that I think could be useful for your chapter, especially to the point of how executive functions develop over adolescence and the effect this has on decision-making. [https://www-tandfonline-com.ezproxy.canberra.edu.au/doi/full/10.1080/09297049.2014.934216 The study by Schiebener et al. (2014)] highlights cognitive differences between executive functions and reasoning, and makes a compelling case that in situtations of explicit numerical risk, the development of executive functions, not reasoning capability, is important for advantageous choices.

Hope this is helpful and best of luck with finalising your chapter. - Ryan [[User:U3216724|U3216724]] ([[User talk:U3216724|discuss]] • [[Special:Contributions/U3216724|contribs]]) 03:45, 5 October 2026 (UTC)

:This may also be a useful source for addressing James' initial comment about addressing when risk-taking peaks in adolescence. :) [[User:U3216724|U3216724]] ([[User talk:U3216724|discuss]] • [[Special:Contributions/U3216724|contribs]]) 03:46, 5 October 2026 (UTC)

== Social contribution: suggested additions on peer influence, young drivers and interventions ==
Hi! I really enjoyed reading your chapter - it overlaps with an area I studied in my Graduate Certificate in Adolescent Health and Wellbeing (2023), where my assessment focused on adolescent risk-taking and young Australian drivers.The Mia scenario is a great hook!

'''What did I do?'''

I've added some material to the chapter for your consideration. I initially wrote them as bullet points with references but then figured it'd probably be much easier for you to review in paragraphs (given the time constraints) so you can rework it into your own structure and voice. Here's what I did, noting you can also find it in the edit summaries section:

- Overview: replaced &quot;(add citation)&quot; with Duell et al. (2018) and Steinberg (2007).

- Social context and risk-taking: added a paragraph after your bullet points on real-world driving evidence (Simons-Morton et al., 2011) and an Australian study of Queensland learner and provisional drivers (Scott-Parker et al., 2012), linking these to peer-enhanced reward processing (Chein et al., 2011).

- Psychological implications: added two paragraphs, one on positive risk-taking and reward sensitivity as a strength (Romer et al., 2017; Duell &amp; Steinberg, 2019; Telzer, 2016), and one on reward-sensitive approaches to intervention (Yeager et al., 2018; Masten et al., 2015; Simons-Morton &amp; Ouimet, 2006).

- References: added the 10 new sources in APA style. '''One small thing I noticed: World Health Organisation (2026) is cited in &quot;What is adolescent risk-taking?&quot; but doesn't appear in the reference list yet.'''

'''My recommendations, based on my earlier study and this literature, are:'''

# Link the Mia scenario back to the real-world driving evidence so it carries through the chapter
# frame interventions around status, respect and peer norms rather than warnings or adult authority
# note that parental involvement and graduated driver licensing reduce exposure to high-reward, high-risk situations while self-regulation is still developing.

I hope these are okay - it works in my favour as well for social contributions because I hadn't done them yet, while ''hopefully'' in your view I've added value to your work while trying to keep your ''voice'' in the chapter. Please feel free to revise, move or remove anything that doesn't fit your direction. 

If there's any issues (e.g., you want to remove something or go back to your original work), please send me an email (u3284454@uni.canberra.edu.au) and I'll immediately do it for you. Happy to share my number via email as well.

Good luck with the chapter.

Cheers :)

Joel [[User:Jshottt|Jshottt]] ([[User talk:Jshottt|discuss]] • [[Special:Contributions/Jshottt|contribs]]) 23:35, 9 October 2026 (UTC)

== Social contribution: suggested adjustments to meet marking criteria ==

Hey, I think you have a great basis to work off on your chapter, and it seems like you already have some great additions from your peers. 

I have made some minor edits for spelling and sourcing in your chapter. 

A few suggestions that may help you as you fill out your chapter over today and tomorrow. 

Discussion surrounding Suicide
# the AIFS release you reference in your paragraph about suicide was published in 2025, but the data was gathered in 2018, so you might want to seek some more contemporary data on this point. 
# I would also recommend seeking some seperate evidence on your claims of healthier activities reducing suicidal thoughts and behaviours as this is not strictly explained in the AIFS data. 
# I would also consider how this paragraph could be made to answer the focus questions you have listed. 

Referencing discrepancies 
# There were some issues with the spelling of references included (particularly around accent marks on names). I have updated these where I found them 

Style suggestion 
# I agree with the above suggestion to link examples back to Mia throughout the chapter, this helps to explain concepts. 

Good luck on the rest of your chapter. 

Thanks 

--[[User:U3216851|U3216851]] ([[User talk:U3216851|discuss]] • [[Special:Contributions/U3216851|contribs]]) 02:22, 10 October 2026 (UTC)

== Recommendations :) ==
Hi there!

This chapter has an engaging scenario and a strong theoretical foundation through the Dual Systems and Maturational Imbalance models. I especially liked the discussion of positive risk-taking because it avoids presenting adolescent reward sensitivity solely as a deficit. Some sections still contain planning questions and bullet points, so converting these into connected paragraphs would improve the chapter’s flow and depth. It would also help to explain the difference between sensation-seeking and impulsivity, integrate the research more critically, remove the template instructions from the conclusion, and complete a final check of grammar, APA citations and the reference list. [[User:U3275909|U3275909]] ([[User talk:U3275909|discuss]] • [[Special:Contributions/U3275909|contribs]]) 23:48, 10 October 2026 (UTC)

== Social Context and Risk-Taking ==
Heya!
Love the book chapter and your description for figure 2. was so matter-a-fact it got a laugh out of me. I just had one question regarding the social context and risk taking section. You found risky driving changed based on who was in the car. What makes the motivation for social reward differ from conforming to social expectation? Moreso what examples could you provide to strengthen your arguement? (e.g. Driving safely when on a date might make your date feel safe improve their opinion of you during the date. Or the same driver could think driving recklessly might be more exciting and use that to chase the reward of wanting to appear more exciting to their date.) 

All in all well done!! [[User:Revial76|Revial76]] ([[User talk:Revial76|discuss]] • [[Special:Contributions/Revial76|contribs]]) 20:52, 13 October 2026 (UTC)

== Heading casing ==
{| style=&quot;float: center; background:transparent;color:inherit;&quot;
|-
| [[File:Crystal Clear app ktip.svg|48px|left]]
| {{#if:|Hi [[User:{{{1}}}|{{{1}}}]].|}} FYI, the recommended [[Wikiversity]] heading style uses [[w:Letter case#Sentence_case|sentence casing]]. For example:&lt;br&gt;
&lt;big&gt;&lt;big&gt;Self-determination theory&lt;/big&gt;&lt;/big&gt;
rather than
&lt;big&gt;&lt;big&gt;Self-Determination Theory&lt;/big&gt;&lt;/big&gt;

Here's an example chapter with correct heading casing: [[Motivation and emotion/Book/2019/Growth mindset development|Growth mindset development]]

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:33, 19 October 2026 (UTC)
|}

&lt;!-- Official book chapter feedback --&gt;
{{MEBF/2026
|1=
&lt;!-- Overall comments... --&gt;
# This is a reasonably good chapter that makes very good use of psychological theory and basic use of research to address a real-world phenomenon or problem
# The main area(s) for potential improvement:
#* more detailed review of the best psychological research about the topic
#* quality of written expression
#* integrate more strongly with other chapters by using embedded links to related topics
#* overuse of unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] (watch out for [[w:AI slop|AI slop]])—express more in your own words
&lt;!-- Overall - Edit summaries --&gt;
#* Use more specific [[w:Help:Edit summary|edit summaries]] to clearly communicate the changes made in each edit
&lt;!-- Overall - GenAI --&gt;
#* In some places, there is overreliance on genAI
#* There is insufficient acknowledgement in edit summaries when adding [[Motivation and emotion/Assessment/Using generative AI|genAI output]]; this violates academic integrity principles
&lt;!-- Overall – Citations --&gt;
# Insufficient use of academic, peer-reviewed citations to support claims
&lt;!-- Overall – Copyedits --&gt;
# For additional feedback, see the following comments and [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FAdolescent_risk-taking_and_reward-system_development&amp;diff=2841492&amp;oldid=2841484 these copyedits]
|2=
&lt;!-- Overview – Comments... --&gt;
# Excellent/Very good/Good/Reasonably good/Basic/Underdeveloped
&lt;!-- Overview – Scenario --&gt;
&lt;!-- Overview – Scenario - Description --&gt;
# Engaging scenario or case study
&lt;!-- Overview – Scenario - Figure --&gt;
# Figure 1 is relevant to the scenario
&lt;!-- Overview – Scenario - Feature box --&gt;
# The scenario uses an appropriate feature box
&lt;!-- Overview – Explains problem --&gt;
# Clearly explains the psychological problem or phenomenon
&lt;!-- Overview – Focus questions --&gt;
# The focus questions are excellent (clear and relevant)
|3=
&lt;!-- Theory comments... --&gt;
&lt;!-- Theory – Breadth --&gt;
# Very good—key theories are well explained and applied; minor areas for improvements
&lt;!-- Theory – Builds on --&gt;
# Builds on one [[w:|Wikipedia]] article and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
&lt;!-- Theory – Depth --&gt;
# Good depth is provided about key theory(ies)
&lt;!-- Theory – Tables/Figures/Lists --&gt;
# Insufficient/No use of tables, figures, and/or lists to clearly convey key theoretical information
&lt;!-- Theory – Citations --&gt;
# In many places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic.
&lt;!-- Theory – Examples --&gt;
# Good use of examples to illustrate theoretical concepts
|4=
&lt;!-- Research comments... --&gt;
&lt;!-- Research – Key findings --&gt;
# Insufficient review of relevant research
# Greater emphasis on systematic reviews and/or meta-analyses would be ideal
# More detail about key studies would be ideal
# In some places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic.
&lt;!-- Research – Critical thinking --&gt;
# Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident
# [[w:Critical thinking|Critical thinking]] about research could be further evidenced by:
## describing the methodology (e.g., sample, measures) in important studies
## considering the strength of relationships
## acknowledging limitations
## pointing out critiques/counterarguments
## suggesting ''specific'' directions for future research
|5=
&lt;!-- Integration comments... --&gt;
# Basic integration between the most relevant theory(ies) and the best research
# The chapter places more emphasis on theory than on research; strive for an integrated balance
# The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links
|6=
&lt;!-- Conclusion comments... --&gt;
# Reasonably good summary and conclusion
# Overly long paragraph; I've split into several paragraphs
# Move citations into main body text (keep the conclusion simple and uncluttered)
&lt;!-- Conclusion – Focus questions --&gt;
# Address the focus questions
&lt;!-- Conclusion – Take-home messages --&gt;
# Add practical, take-home message(s)
|7=
&lt;!-- Written expression – Style comments... --&gt;
&lt;!-- Written expression – Written expression --&gt;
# Written expression
## The quality of written expression is reasonably good
## Likely over-reliance on unacknowledged use of genAI
## The target audience is international, not domestic. [http://www.worldometers.info/world-population/australia-population/ Only 0.3% of the world human population lives in Australia].
&lt;!-- Written expression – Paragraphs --&gt;
## Some paragraphs are overly long. Communicate one key idea per paragraph in three to five sentences.
&lt;!-- Written expression – Language --&gt;
## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., &quot;it&quot;) instead of 1st (e.g., &quot;we&quot;) or 2nd person (e.g., &quot;you&quot;) in the main text. 1st or 2nd person can work well for case studies or feature boxes.
&lt;!-- Written expression – Layout --&gt;
# Layout
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-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:33, 19 October 2026 (UTC)</text>
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      <text bytes="1458" sha1="ilq3ua3v8xyk13hm3b6r7wjzo5wdowq" xml:space="preserve">== About Me ==
Hi, im [https://www.linkedin.com/in/noorah-chami-03542b444?utm_source=share_via&amp;utm_content=profile&amp;utm_medium=member_ios Noorah]. I am a current student at the University of Canberra, studying a double degree in [https://www.canberra.edu.au/course/SCSC01/2/2026 psychology and law.] I am in my third year, working towards becoming hopefully a lawyer, i chose to do psychology to gain more knowledge in human behaviour.  

I am currently employed as FOH cafe worker, i have been working in hospitality since i was 15. I'm eager and excited to start a new work journey that's more targeted to my future plans, and immerse myself in new experiences and lessons.   

== Hobbies ==

*Running
*Art
*Plant enthusiast

== Book Chapter Topic ==
I will be writing a book chapter on the emotion of [[Motivation and emotion/Book/2026/Awe and nature|awe and its relationship with nature.]] Im super excited to do research in this topic, as it's something i've never really read into, and as someone who wants to travel understanding how nature can induce Awe is very captivating. 

== Social Contributions ==

# Added a [[Motivation and emotion/Book/2025/Thirst regulation|discussion]] point about referencing. 
# Added to [[Motivation and emotion/Book/2025/Grit and academic achievement|discussion]] about captioning figures. 
# Added to [[Motivation and emotion/Book/2025/Exteroception and emotion|discussion]] about correct APA subheading requirements.</text>
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      <text bytes="23123" sha1="tdhq1h3s59vyx6ig8931ywm2udcvwl4" xml:space="preserve">{{title|Awe and nature:&lt;br&gt;How do nature-based experiences affect awe?}}
__TOC__

==Overview==
{{RoundBoxTop|theme=5}}
[[File:Valley View Yosemite August 2013 002.jpg|right|thumb|220px|'''Figure 1'''. Yosemite Mountains]]

'''Case Study: Feeling small in Yosemite '''

Imagine standing at Yosemite National Park, you see vast landscapes of mountains, immersed in green forests and the sky (see Figure 1). But what [[TESOL/Emotions|emotions]] do you think you might feel? You might feel physically smaller than the mountains, and you might suddenly feel as if your worries and fears feel less consuming. This complex emotional experience is called awe. 

Researchers investigated this experience by asking visitors at Yosemite to draw a picture of themselves after viewing the parks landscape, the participants had a tendency to draw themselves significantly smaller to the mountains. They compared these drawings to those of tourists at Fisherman’s Wharf, a more urban setting, who drew big portraits. This identified the idea of the small self, further research revealed that on the day individuals experienced awe, they were also more likely to perceive themselves as smaller (Monroy &amp; Kelter, 2023).

{{RoundBoxBottom}}

This chapter examines the characteristics of nature that elicits awe, the cognitive and emotional mechanisms underlying the experience, and how nature induced awe influences attention  
* The Yosemite findings raise a fundamental question. What is it about vast natural environments that can transform the way we think of individual experiences and the world around us? 
* Understanding this relationship through psychology can help investigate the cognitive and emotional processes involved in awe, and how this emotion can influence mental wellbeing. 
* Psychological research has revealed why certain natural experiences may evoke awe, and how awe changes attention and sense of self, and ultimately if these changes contribute to wellbeing. 
* Understanding the relationship between awe and nature, can help explain the impacts of nature on an individual.

{{RoundBoxTop|theme=2}}
;Focus questions
* What is Awe ?
* What is Awe connection to physiology?
* Can Awe be identified through facial expressions?
* What psychological processes explain the experience of awe in nature?  
* How does nature-induced awe influence the sense of self and psychological wellbeing? 
{{RoundBoxBottom}}

== The Emotion of Awe: More than just an emotion ==
Awe in a complex emotion and our minds response to vast stimuli that transcends current frames of reference, people typically experience awe to stimuli like wonders and panoramic views (Piff et al., 2015). Keltner and Haidt (2003) suggested a conceptualization of awe that consists of two aspects vastness and need for accommodation. [[Emotion|Emotionally]] Awe can trigger us to rethink our place in the world through self reflection, inducing positive wellbeing and less stress. Unlike other emotions Awe can be positive or negative as an emotion it generates feelings, arousal, purpose, and expression. Awe is a profound feeling of sense of self; people often feel a sense of awe towards things like nature, Awe can be explained as a distinct self-transcending emotion, awe is proposed to shift people’s perspective from an egocentric focus to a broader view of the self (Jiang et al., 2024). Awe if often experienced with encounters to music, visual art, collective movement like dance and rituals (Keltner and Monroy 2026). 

=== Origins of Awe ===
Historically Awe was associated with religious fear originating from an old word ''Agi'' meaning fright or terror. This suggests that awe was not originally conceptualised as a positive emotion, in 1757 Edmund Burke recognised that awe could arise from experiences such as thunder, art and music (Tix, 2015). Over history Awe has been conceptualised as many different facets this is particularly significant to how we measure Awe through psychology, cause we know it can be both a negative or positive emotion.  

=== The Five flavors of Awe ===

* Beauty 
* Threat
* Ability 
* Virtue 
* Supernatural

=== Awe as a basic emotion ===
In basic emotion theory (BET) emotions are brief states involving experiential, cognitive, physiological and expressive process that enables humans to respond to environmental stimuli, BET is the foundation of our six emotions anger, disgust, fear, sadness, surprise, and joy. Traditionally these six emotions are the basic emotions but Keltner and Monroy (2026) argue that awe may be a basic distinct emotion, it may not just be a mixture of surprise and happiness but have its own psychological and evolutionary functions. 

=== Vastness ===
Vastness refers to perceiving stimuli as being significantly larger than the usual frame of reference (Keltner &amp; Haidt, 2003), Keltner and Haidt idea of vastness goes beyond literal size and it includes stimuli that is perceptually or conceptually vast. This could be why the Yosemite can inflict Awe as it is physically a large mountain but conceptually it might be hard to understand. Any stimuli that goes beyond a normal individual's personal experience, can make them feel as if they are apart of something larger. 

=== Accomodation ===
The need for accommodation according to Keltner and Haidt (2003) refers to psychologist Jean Piaget process of adjusting mental structures that cannot assimilate a new experience. &quot;The success of one's attempt at accomodation may partially explain why awe can be both terrifying (when one fails to understand) and enlightening (when one succeeds)&quot; (Keltner &amp; Haidt 2003).  

== Physiological and Psychological effects of Awe ==

=== Physiological effects ===
Awe changes nervous system activity, Shiota et al. (2011) found that positive awe was generally associated with increased parasympathetic activity and reduced sympathetic activity, but interestingly found that breathing rate increased. This suggests why Awe is associated with relaxed mental states. However in a study by Gordon et al. (2017) found that threatening Awe experiences increased sympathetic activity, including heart rate. For example seeing a severe storm could induce threat based awe, a negative feeling of Awe. Awe can inhibit the response of goosebumps and chills Schurtz et al. (2012) found that awe was a common emotional trigger, this established that goosebumps may be a physical expression of awe and highlighting how deep Awe can make humans feel. 

=== The small self and perspective ===
One of the most recognised psychological effects of awe is the &quot;small self&quot;, where an individual experiences a reduced sense of self in relation to perceiving something much larger (Monroy &amp; Keltner, 2023). This concept can be seen in the Yosemite study introduced earlier, where the study highlighted the small self, being exposed to the mountains made the participants feel small. However feeling physically small does not mean feeling insignificant. Jiang et al., (2024) distinguishes that we may feel physically smaller but awe cannot make us feel insignificant instead it shifts our attention away from an egocentric perspective to broader view of the world. This broader perspective can explain why everyday worries can temporarily feel less consuming during awe. The source of stress has not been changed or fixed but instead a shift in perspective has changed. Büssing et al., (2025) found that awe and gratitude mediated the relationship between experiences of nature and wellbeing, suggesting that meaningful engagement with nature may matter more beyond simply being present in a natural environment.

The small self is further demonstrated where researchers developed a visual measurement consisting of seven drawings of a stick figure beside a sun, with each figure progressively increasing in size. Participants were to select the drawing that best represented their perceived sense of self, allowing researchers to examine how awe influences the perception of self (Bai et al., 2017). 

==Measurements of Awe==

=== Facial expressions of Awe ===
[[File:Rstb.2025.0148.f001.webp|thumb|'''Figure 3.''' Facial expressions ]]
Nature based Awe may induce recognisable facial expressions like raised eyebrows, widened eyes, and an open mouth. For example imagine looking at the night sky in rural Australia your facial expressions might show widen eyes, brows, and dropped jaw reflecting the emotion of awe and taking in the visual information. In a study by Keltner and Monroy in 2026, they observed patterns of facial expressions induced by awe across China, India, South Korea, Japan and the United States and found that approximately 63% of the elements of awe expressions overlapped.  Further research in Cowen and Keltner (2019, as cited in Keltner &amp; Monroy, 2026) examined more than 1,500 naturalistic photographs of facial expressions (see Figure 3), the analysis identified 28 distinguishable categories of emotional expressions including awe. In figure 3 Awe appears beside related emotions like surprise, fear and interest however it forms its own recognisable category suggesting that awe can include other basic emotions but cannot be reduced to those basic emotions. Furthermore the research in facial expression in Awe is limited in this specific studies participants were asked to imagine awe inspiring experiences rather than an actual response to natural stimuli. 

{{RoundBoxTop|theme=5}}
;Can Awe be measured in EEG
Awe is a complex emotion that is relatively hard to measure psychologically, but can we observe the feeling of Awe through brain activity? The Awe Experiment, developed by Brisbane based artists (Counterpilot) in collaboration with the Queensland Brain Institute, explored this question through an interactive performance at the World Science Festival. To measure brain activity participants were fitted with an EEG and participants listened to awe evoking narratives, Brain activity were translated in colourful lights. Although no scientific results came from this experiment, it is an interesting concept for future research.{{RoundBoxBottom}}

== Awe in everyday life ==

=== Attention and everyday awe ===
Although traditional theories emphasize vastness, awe does not only occur during rare encounters with dramatic landscape. More recent research has introduced this concept of wondering awe, a gentler more accessible experience that can emerge through attentive engagement with ordinary aspects of nature (Büssing et al., 2025). Rather than the exposure of Yosemite mountains, wondering awe emphasises an individual who pauses to notice the warmth of sunlight or the movement of leaves and feels a sense of awe. This contradicts the traditional explanation of awe, if perceived vastness is central to the experience how can something so small like sunlight evoke it? One possibility is that awe is influenced by the meaning and attention given to the stimuli. Slowing down and becoming engulfed in &quot;normal&quot; nature to notice complexity and beauty, establishes this idea of wondering awe. Furthermore the warmth of sunlight is still a complex idea and could extend beyond an individual's mental structure, which still highlights need for accommodation. Büssing et al., (2025) suggests nature exposure alone may not actively improve psychological wellbeing, instead the argument is that wondering awe may help explain how an individual's engagement with nature can inflict awe.

=== Changing nature and awe ===
{{RoundBoxTop|theme=5}}
;Imagine this ...
You walk the same route home every day after work, most days you barely notice the sky. But today the sky is filled with a vivid sunset (see Figure 2), you stop look up and take a brief moment to appreciate the sky, the location has not changed, but why are you experiencing a sense of awe in a familiar environment?
{{RoundBoxBottom}}

[[File:Sunset may 2006 panorama.jpg|thumb|'''Figure 2''': A sunset]]The ability of nature to evoke awe is also influenced by the context in which it is experienced. Natural environments are not static, the same location can appear ordinary in one moment than extraordinary in another moment. Smalley and White (2023), highlighted the concept of ephemeral phenomena such as sunsets, rainbows and storms, and found that these temporary changes influenced the connection of awe towards nature. Their findings suggest that a landscape does not have fixed awe value, instead its capacity to evoke awe may shift with changes in weather, light and time of day (Smalley &amp; White, 2023).

=== Awe in the digital world ===
Traditionally awe in nature has been studied with an individual who physically encounters vast natural environments, but what if we could feel awe through technology? 

Developments in digital technology challenge the idea of foundational awe, and question weather individuals need to be present in nature to experience awe. Virtual technology can recreate digital environments with the same characteristics such as spaciousness, scale and sensory immersion. This idea allows research into whether psychological experience of awe can also occur through simulated nature. Van Houwelingen-Snippe et al., (2020) found that spacious digital nature can make an individual experience awe especially when viewed alone suggesting the idea of perception scale. Similarly, virtual reality can create immersive environments that increase feelings of presence and perceived vastness, providing another method for eliciting awe (Jiang et al., 2024). These findings raise an interesting question, if awe depends on vastness does the nature producing it need to be real? Digital nature can be a useful tool in understanding the psychological process of awe more clearly, and achieve clinical based wellbeing treatments so everyone can feel awe.

== Awe and psychological wellbeing ==
Experiencing Awe in nature can influence an individual's immediate emotional state, it may also change how people perceive themselves and others. Research has associated awe with change in self focus, perspective, social connection and wellbeing (Jiang et al.,2024; Monroy &amp; Keltner, 2023). Understanding these effects may help explain why certain encounter with nature can change our perspectives.

Awe can help explain why some experiences in nature have positive psychological effects, ultimately it is how an individual responds to nature. The experience of awe may also extend beyond personal wellbeing by changing individual perspectives. Awe has been associated with greater prosocial behaviour and social connection (Jiang et al., 2024), while sublime experiences in nature can involve feelings of vitality, freedom and unity with the natural world (Bethelmy &amp; Corraliza, 2019). Awe and wellbeing is complex, because awe directly is not always a positive emotion. Awe can occur alongside negative emotions such as fear or even mixed emotional states (Jiang et al., 2024). Awe and fear can arise when vast powerful aspects of nature are perceived as a threat, such as a bushfire or flood the psychological impacts would probably not be beneficial. This demonstrates that the psychological benefits of nature induced awe may depend on how the experience is emotionally interpreted, particularly whether it is perceived as positive or threatening.

Quiz&lt;quiz display=&quot;simple&quot;&gt;
{Awe is an easy emotion to understand and is the same distinct emotion as Joy:
|type=&quot;()&quot;}
- True
+ False

{Spaciousness in a digital natural enviroment can contribute to the feeling of awe:
|type=&quot;()&quot;}
+ True
- False
&lt;/quiz&gt;

== Space and Awe ==
{{RoundBoxTop|theme=5}}
;Imagine this ...
Seeing Earth from space, surrounded by the vast darkness of the universe and the unknown, an experience you have never conceptualised. 
{{RoundBoxBottom}}&lt;gallery widths=&quot;250&quot; heights=&quot;250&quot;&gt;
File:The Earth seen from Apollo 17.jpg|'''Figure 4.''' Earth from space
&lt;/gallery&gt;This experience of seeing [[Earth]] from space is an extraordinary experience and is known as the overview effect, where astronauts report intense feelings of awe, wonder and connectedness from viewing earth from a completely different perspective (Yaden et al., 2016). Yaden et al. (2016) analysed that the overview effect involves both perceived vastness and cognitive accommodation, seeing an entire planet you thought you knew from a different perspective like this can challenge individuals mental frames. More interestingly astronauts have reported experiencing self transcendence, describing it as individual concerns becoming less significant and developing a stronger sense to humanity and the planet. More so some even commented that it changed self values and environmental awareness. 

==Conclusion==
* Nature induced awe must include vastness and need for accommodation rather than nature exposure alone. The two appraisal provide a foundational understanding of awe. 
* Wondering awe and ephemeral phenomena demonstrate that extraordinary experiences can emerge from ordinary or changing aspects in nature. 
* Awe can change how individuals perceive themselves and their experiences, rather than feeling insignificance its the shrinking of egocentric self focus that encourages a broader thinking. 
* The psychological effects of awe are not universally positive, natural environment can evoke happiness, social connection. But awe can coexist with threat and fear. Therefore, how an individual emotionally interprets awe, the certain interpretation may influence if it contributes to psychological wellbeing. 
* Digital and virtual environments can recreate characteristics of nature, suggesting that psychological perception may be as important as physical presence in nature.

==See also==
List [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:

* [[Motivation and emotion/Book/2016/Awe as an emotion|Awe as an emotion]] (Book chapter, 2016)
* [[Motivation and emotion/Book/2026/Awe and the diminished self|Awe and the diminished self]] (Book chapter, 2026)
* [[Motivation and emotion/Book/2017/Awe and well-being|Awe and Wellbeing]] (Book chapter, 2017)
* [[Motivation and emotion/Book/2024/Nature connection and emotional well-being|Nature connection and emotional well-being]] (Book chapter, 2024)
* [[Psychological well-being]] (Wikipedia) 

==References==
{{Hanging indent|1=

ReferencesAndy Tix Ph.D. (2015, October 12). The complexity of awe is revealed in how it has been conceptualized across time. Psychology Today. 
https://www.psychologytoday.com/au/blog/the-pursuit-peace/201510/brief-history-awe

Bai, Y., Maruskin, L. A., Chen, S., Gordon, A. M., Stellar, J. E., McNeil, G. D., Peng, K., &amp; Keltner, D. (2017). Awe, the diminished self, and collective engagement: Universals and cultural variations in the small self. Journal of Personality and Social Psychology, 113(2), 185–209. https://doi.org/10.1037/pspa0000087Bonnell, M. (2026, March 4). 

Nature, awe and mental health: Why we feel better outdoors. Peaceful Mind. https://peacefulmind.com.au/2026/03/04/the-role-of-nature-and-awe-in-creating-a-calmer-mind/

Büssing, A., Wilhelm, J., &amp; Rodrigues Recchia, D. (2025). Wondering awe is the mediator of the link between experience of nature and psychological wellbeing—Relevance for public health. International Journal of Environmental Research and Public Health, 22(11), 1679. https://doi.org/10.3390/ijerph22111679

Gordon, A. M., Stellar, J. E., Anderson, C. L., McNeil, G. D., Loew, D., &amp; Keltner, D. (2017). The dark side of the sublime: Distinguishing a threat-based variant of awe. Journal of Personality and Social Psychology, 113(2), 310–328. https://doi.org/10.1037/pspp0000120

Jiang, T., Hicks, J. A., Yuan, W., Yin, Y., Needy, L., &amp; Vess, M. (2024). The unique nature and psychosocial implications of awe. Nature Reviews Psychology, 3(7), 475–488. https://doi.org/10.1038/s44159-024-00322-z

Keltner, D., &amp; Haidt, J. (2003). Approaching awe, a moral, spiritual, and aesthetic emotion. Cognition and Emotion, 17(2), 297–314. https://doi.org/10.1080/02699930302297

Keltner, D., &amp; Monroy, M. (2026). The expression of awe: Evolutionary origins and cultural elaborations of a basic emotion. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 381(1959), 20250148. PubMed Central. https://doi.org/10.1098/rstb.2025.0148

Monroy, M., &amp; Keltner, D. (2022). Awe as a pathway to mental and physical health. Perspectives on Psychological Science, 18(2), 174569162210948. https://doi.org/10.1177/17456916221094856

Piff, P. K., Dietze, P., Feinberg, M., Stancato, D. M., &amp; Keltner, D. (2015). Awe, the small self, and prosocial behavior. Journal of Personality and Social Psychology, 108(6), 883–899. https://doi.org/10.1037/pspi0000018

Rogers, K. (2010, October 4). Biophilia hypothesis {{!}} description, nature, &amp; human behavior. Encyclopedia Britannica. https://www.britannica.com/science/biophilia-hypothesis

Schurtz, D. R., Blincoe, S., Smith, R. H., Powell, C. A. J., Combs, D. J. Y., &amp; Kim, S. H. (2011). Exploring the social aspects of goose bumps and their role in awe and envy. Motivation and Emotion, 36(2), 205–217. https://doi.org/10.1007/s11031-011-9243-8

Shiota, M. N., Neufeld, S. L., Yeung, W. H., Moser, S. E., &amp; Perea, E. F. (2011). Feeling good: Autonomic nervous system responding in five positive emotions. Emotion, 11(6), 1368–1378. https://doi.org/10.1037/a0024278

Smalley, A. J., &amp; White, M. P. (2023). Beyond blue-sky thinking: Diurnal patterns and ephemeral meteorological phenomena impact appraisals of beauty, awe, and value in urban and natural landscapes. Journal of Environmental Psychology, 86, 101955. https://doi.org/10.1016/j.jenvp.2023.101955

van Houwelingen-Snippe, J., van Rompay, T. J. L., de Jong, M. D. T., &amp; Ben Allouch, S. (2020). Does digital nature enhance social aspirations? An experimental study. International Journal of Environmental Research and Public Health, 17(4), 1454. https://doi.org/10.3390/ijerph17041454

Webb, D. (2025, March). Nature imagery and mental well-being. All About Psychology. Substack.Com. https://allaboutpsychology.substack.com/p/nature-imagery-and-mental-well-being

}}

==External links==
* [https://greatergood.berkeley.edu/video/item/how_scientists_measure_awe_in_the_wild How Scientists Measure Awe in the Wild] (Greater Good Magazine)
* [https://mindfulforestbathing.com.au/the-transformative-power-of-awe-in-nature/ The Transformative Power of Awe in Nature] (Mindful in nature)
* [https://www.psychologytoday.com/au/blog/finding-new-home/201807/the-psychology-awe-awe-in-nature The Psychology of Awe: Awe in Nature] (PsychologyToday)
* [https://ggsc.berkeley.edu/images/uploads/GGSC-JTF_White_Paper-Awe_FINAL.pdf The science of Awe.] (Greater Good Science Centre) 

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==Overview==
{{RoundBoxTop|theme=5}}
[[File:Valley View Yosemite August 2013 002.jpg|right|thumb|220px|'''Figure 1'''. Yosemite Mountains]]

'''Case Study: Feeling small in Yosemite '''

Imagine standing at Yosemite National Park, you see vast landscapes of mountains, immersed in green forests and the sky (see Figure 1). But what [[TESOL/Emotions|emotions]] do you think you might feel? You might feel physically smaller than the mountains, and you might suddenly feel as if your worries and fears feel less consuming. This complex emotional experience is called awe. 

Researchers investigated this experience by asking visitors at Yosemite to draw a picture of themselves after viewing the parks landscape, the participants had a tendency to draw themselves significantly smaller to the mountains. They compared these drawings to those of tourists at Fisherman’s Wharf, a more urban setting, who drew big portraits. This identified the idea of the small self, further research revealed that on the day individuals experienced awe, they were also more likely to perceive themselves as smaller (Monroy &amp; Kelter, 2023).

{{RoundBoxBottom}}

This chapter examines the characteristics of nature that elicits awe, the cognitive and emotional mechanisms underlying the experience, and how nature induced awe influences attention  
* The Yosemite findings raise a fundamental question. What is it about vast natural environments that can transform the way we think of individual experiences and the world around us? 
* Understanding this relationship through psychology can help investigate the cognitive and emotional processes involved in awe, and how this emotion can influence mental wellbeing. 
* Psychological research has revealed why certain natural experiences may evoke awe, and how awe changes attention and sense of self, and ultimately if these changes contribute to wellbeing. 
* Understanding the relationship between awe and nature, can help explain the impacts of nature on an individual.

{{RoundBoxTop|theme=2}}
;Focus questions
* What is Awe ?
* What is Awe connection to physiology?
* Can Awe be identified through facial expressions?
* What psychological processes explain the experience of awe in nature?  
* How does nature-induced awe influence the sense of self and psychological wellbeing? 
{{RoundBoxBottom}}

== The Emotion of Awe: More than just an emotion ==
Awe in a complex emotion and our minds response to vast stimuli that transcends current frames of reference, people typically experience awe to stimuli like wonders and panoramic views (Piff et al., 2015). Keltner and Haidt (2003) suggested a conceptualization of awe that consists of two aspects vastness and need for accommodation. [[Emotion|Emotionally]] Awe can trigger us to rethink our place in the world through self reflection, inducing positive wellbeing and less stress. Unlike other emotions Awe can be positive or negative as an emotion it generates feelings, arousal, purpose, and expression. Awe is a profound feeling of sense of self; people often feel a sense of awe towards things like nature, Awe can be explained as a distinct self-transcending emotion, awe is proposed to shift people’s perspective from an egocentric focus to a broader view of the self (Jiang et al., 2024). Awe if often experienced with encounters to music, visual art, collective movement like dance and rituals (Keltner and Monroy 2026). 

=== Origins of Awe ===
Historically Awe was associated with religious fear originating from an old word ''Agi'' meaning fright or terror. This suggests that awe was not originally conceptualised as a positive emotion, in 1757 Edmund Burke recognised that awe could arise from experiences such as thunder, art and music (Tix, 2015). Over history Awe has been conceptualised as many different facets this is particularly significant to how we measure Awe through psychology, cause we know it can be both a negative or positive emotion.  

=== The Five flavors of Awe ===

* Beauty 
* Threat
* Ability 
* Virtue 
* Supernatural

=== Awe as a basic emotion ===
In basic emotion theory (BET) emotions are brief states involving experiential, cognitive, physiological and expressive process that enables humans to respond to environmental stimuli, BET is the foundation of our six emotions anger, disgust, fear, sadness, surprise, and joy. Traditionally these six emotions are the basic emotions but Keltner and Monroy (2026) argue that awe may be a basic distinct emotion, it may not just be a mixture of surprise and happiness but have its own psychological and evolutionary functions. 

=== Vastness ===
Vastness refers to perceiving stimuli as being significantly larger than the usual frame of reference (Keltner &amp; Haidt, 2003), Keltner and Haidt idea of vastness goes beyond literal size and it includes stimuli that is perceptually or conceptually vast. This could be why the Yosemite can inflict Awe as it is physically a large mountain but conceptually it might be hard to understand. Any stimuli that goes beyond a normal individual's personal experience, can make them feel as if they are apart of something larger. 

=== Accomodation ===
The need for accommodation according to Keltner and Haidt (2003) refers to psychologist Jean Piaget process of adjusting mental structures that cannot assimilate a new experience. &quot;The success of one's attempt at accomodation may partially explain why awe can be both terrifying (when one fails to understand) and enlightening (when one succeeds)&quot; (Keltner &amp; Haidt 2003).  

== Physiological and Psychological effects of Awe ==

=== Physiological effects ===
Awe changes nervous system activity, Shiota et al. (2011) found that positive awe was generally associated with increased parasympathetic activity and reduced sympathetic activity, but interestingly found that breathing rate increased. This suggests why Awe is associated with relaxed mental states. However in a study by Gordon et al. (2017) found that threatening Awe experiences increased sympathetic activity, including heart rate. For example seeing a severe storm could induce threat based awe, a negative feeling of Awe. Awe can inhibit the response of goosebumps and chills Schurtz et al. (2012) found that awe was a common emotional trigger, this established that goosebumps may be a physical expression of awe and highlighting how deep Awe can make humans feel. 

=== The small self and perspective ===
One of the most recognised psychological effects of awe is the &quot;small self&quot;, where an individual experiences a reduced sense of self in relation to perceiving something much larger (Monroy &amp; Keltner, 2023). This concept can be seen in the Yosemite study introduced earlier, where the study highlighted the small self, being exposed to the mountains made the participants feel small. However feeling physically small does not mean feeling insignificant. Jiang et al., (2024) distinguishes that we may feel physically smaller but awe cannot make us feel insignificant instead it shifts our attention away from an egocentric perspective to broader view of the world. This broader perspective can explain why everyday worries can temporarily feel less consuming during awe. The source of stress has not been changed or fixed but instead a shift in perspective has changed. Büssing et al., (2025) found that awe and gratitude mediated the relationship between experiences of nature and wellbeing, suggesting that meaningful engagement with nature may matter more beyond simply being present in a natural environment.

The small self is further demonstrated where researchers developed a visual measurement consisting of seven drawings of a stick figure beside a sun, with each figure progressively increasing in size. Participants were to select the drawing that best represented their perceived sense of self, allowing researchers to examine how awe influences the perception of self (Bai et al., 2017). 

==Measurements of Awe==

=== Facial expressions of Awe ===
[[File:Rstb.2025.0148.f001.webp|thumb|'''Figure 3.''' Facial expressions ]]
Nature based Awe may induce recognisable facial expressions like raised eyebrows, widened eyes, and an open mouth. For example imagine looking at the night sky in rural Australia your facial expressions might show widen eyes, brows, and dropped jaw reflecting the emotion of awe and taking in the visual information. In a study by Keltner and Monroy in 2026, they observed patterns of facial expressions induced by awe across China, India, South Korea, Japan and the United States and found that approximately 63% of the elements of awe expressions overlapped.  Further research in Cowen and Keltner (2019, as cited in Keltner &amp; Monroy, 2026) examined more than 1,500 naturalistic photographs of facial expressions (see Figure 3), the analysis identified 28 distinguishable categories of emotional expressions including awe. In figure 3 Awe appears beside related emotions like surprise, fear and interest however it forms its own recognisable category suggesting that awe can include other basic emotions but cannot be reduced to those basic emotions. Furthermore the research in facial expression in Awe is limited in this specific studies participants were asked to imagine awe inspiring experiences rather than an actual response to natural stimuli. 

{{RoundBoxTop|theme=5}}
;Can Awe be measured in EEG
Awe is a complex emotion that is relatively hard to measure psychologically, but can we observe the feeling of Awe through brain activity? The Awe Experiment, developed by Brisbane based artists (Counterpilot) in collaboration with the Queensland Brain Institute, explored this question through an interactive performance at the World Science Festival. To measure brain activity participants were fitted with an EEG and participants listened to awe evoking narratives, Brain activity were translated in colourful lights. Although no scientific results came from this experiment, it is an interesting concept for future research.{{RoundBoxBottom}}

== Awe in everyday life ==

=== Attention and everyday awe ===
Although traditional theories emphasize vastness, awe does not only occur during rare encounters with dramatic landscape. More recent research has introduced this concept of wondering awe, a gentler more accessible experience that can emerge through attentive engagement with ordinary aspects of nature (Büssing et al., 2025). Rather than the exposure of Yosemite mountains, wondering awe emphasises an individual who pauses to notice the warmth of sunlight or the movement of leaves and feels a sense of awe. This contradicts the traditional explanation of awe, if perceived vastness is central to the experience how can something so small like sunlight evoke it? One possibility is that awe is influenced by the meaning and attention given to the stimuli. Slowing down and becoming engulfed in &quot;normal&quot; nature to notice complexity and beauty, establishes this idea of wondering awe. Furthermore the warmth of sunlight is still a complex idea and could extend beyond an individual's mental structure, which still highlights need for accommodation. Büssing et al., (2025) suggests nature exposure alone may not actively improve psychological wellbeing, instead the argument is that wondering awe may help explain how an individual's engagement with nature can inflict awe.

=== Changing nature and awe ===
{{RoundBoxTop|theme=5}}
;Imagine this ...
You walk the same route home every day after work, most days you barely notice the sky. But today the sky is filled with a vivid sunset (see Figure 2), you stop look up and take a brief moment to appreciate the sky, the location has not changed, but why are you experiencing a sense of awe in a familiar environment?
{{RoundBoxBottom}}

[[File:Sunset may 2006 panorama.jpg|thumb|'''Figure 2''': A sunset]]The ability of nature to evoke awe is also influenced by the context in which it is experienced. Natural environments are not static, the same location can appear ordinary in one moment than extraordinary in another moment. Smalley and White (2023), highlighted the concept of ephemeral phenomena such as sunsets, rainbows and storms, and found that these temporary changes influenced the connection of awe towards nature. Their findings suggest that a landscape does not have fixed awe value, instead its capacity to evoke awe may shift with changes in weather, light and time of day (Smalley &amp; White, 2023).

=== Awe in the digital world ===
Traditionally awe in nature has been studied with an individual who physically encounters vast natural environments, but what if we could feel awe through technology? 

Developments in digital technology challenge the idea of foundational awe, and question weather individuals need to be present in nature to experience awe. Virtual technology can recreate digital environments with the same characteristics such as spaciousness, scale and sensory immersion. This idea allows research into whether psychological experience of awe can also occur through simulated nature. Van Houwelingen-Snippe et al., (2020) found that spacious digital nature can make an individual experience awe especially when viewed alone suggesting the idea of perception scale. Similarly, virtual reality can create immersive environments that increase feelings of presence and perceived vastness, providing another method for eliciting awe (Jiang et al., 2024). These findings raise an interesting question, if awe depends on vastness does the nature producing it need to be real? Digital nature can be a useful tool in understanding the psychological process of awe more clearly, and achieve clinical based wellbeing treatments so everyone can feel awe.

== Awe and psychological wellbeing ==
Experiencing Awe in nature can influence an individual's immediate emotional state, it may also change how people perceive themselves and others. Research has associated awe with change in self focus, perspective, social connection and wellbeing (Jiang et al.,2024; Monroy &amp; Keltner, 2023). Understanding these effects may help explain why certain encounter with nature can change our perspectives.

Awe can help explain why some experiences in nature have positive psychological effects, ultimately it is how an individual responds to nature. The experience of awe may also extend beyond personal wellbeing by changing individual perspectives. Awe has been associated with greater prosocial behaviour and social connection (Jiang et al., 2024), while sublime experiences in nature can involve feelings of vitality, freedom and unity with the natural world (Bethelmy &amp; Corraliza, 2019). Awe and wellbeing is complex, because awe directly is not always a positive emotion. Awe can occur alongside negative emotions such as fear or even mixed emotional states (Jiang et al., 2024). Awe and fear can arise when vast powerful aspects of nature are perceived as a threat, such as a bushfire or flood the psychological impacts would probably not be beneficial. This demonstrates that the psychological benefits of nature induced awe may depend on how the experience is emotionally interpreted, particularly whether it is perceived as positive or threatening.

Quiz&lt;quiz display=&quot;simple&quot;&gt;
{Awe is an easy emotion to understand and is the same distinct emotion as Joy:
|type=&quot;()&quot;}
- True
+ False

{Spaciousness in a digital natural enviroment can contribute to the feeling of awe:
|type=&quot;()&quot;}
+ True
- False
&lt;/quiz&gt;

== Space and Awe ==
{{RoundBoxTop|theme=5}}
;Imagine this ...
Seeing Earth from space, surrounded by the vast darkness of the universe and the unknown, an experience you have never conceptualised. 
{{RoundBoxBottom}}&lt;gallery widths=&quot;250&quot; heights=&quot;250&quot;&gt;
File:The Earth seen from Apollo 17.jpg|'''Figure 4.''' Earth from space
&lt;/gallery&gt;This experience of seeing [[Earth]] from space is an extraordinary experience and is known as the overview effect, where astronauts report intense feelings of awe, wonder and connectedness from viewing earth from a completely different perspective (Yaden et al., 2016). Yaden et al. (2016) analysed that the overview effect involves both perceived vastness and cognitive accommodation, seeing an entire planet you thought you knew from a different perspective like this can challenge individuals mental frames. More interestingly astronauts have reported experiencing self transcendence, describing it as individual concerns becoming less significant and developing a stronger sense to humanity and the planet. More so some even commented that it changed self values and environmental awareness. 

==Conclusion==
* Nature induced awe must include vastness and need for accommodation rather than nature exposure alone. The two appraisal provide a foundational understanding of awe. 
* Wondering awe and ephemeral phenomena demonstrate that extraordinary experiences can emerge from ordinary or changing aspects in nature. 
* Awe can change how individuals perceive themselves and their experiences, rather than feeling insignificance its the shrinking of egocentric self focus that encourages a broader thinking. 
* The psychological effects of awe are not universally positive, natural environment can evoke happiness, social connection. But awe can coexist with threat and fear. Therefore, how an individual emotionally interprets awe, the certain interpretation may influence if it contributes to psychological wellbeing. 
* Digital and virtual environments can recreate characteristics of nature, suggesting that psychological perception may be as important as physical presence in nature.

==See also==
List [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:

* [[Motivation and emotion/Book/2016/Awe as an emotion|Awe as an emotion]] (Book chapter, 2016)
* [[Motivation and emotion/Book/2026/Awe and the diminished self|Awe and the diminished self]] (Book chapter, 2026)
* [[Motivation and emotion/Book/2017/Awe and well-being|Awe and Wellbeing]] (Book chapter, 2017)
* [[Motivation and emotion/Book/2024/Nature connection and emotional well-being|Nature connection and emotional well-being]] (Book chapter, 2024)
* [[Psychological well-being]] (Wikipedia) 

==References==
{{Hanging indent|1=

ReferencesAndy Tix Ph.D. (2015, October 12). The complexity of awe is revealed in how it has been conceptualized across time. Psychology Today. 
https://www.psychologytoday.com/au/blog/the-pursuit-peace/201510/brief-history-awe

Bai, Y., Maruskin, L. A., Chen, S., Gordon, A. M., Stellar, J. E., McNeil, G. D., Peng, K., &amp; Keltner, D. (2017). Awe, the diminished self, and collective engagement: Universals and cultural variations in the small self. Journal of Personality and Social Psychology, 113(2), 185–209. https://doi.org/10.1037/pspa0000087Bonnell, M. (2026, March 4). 

Nature, awe and mental health: Why we feel better outdoors. Peaceful Mind. https://peacefulmind.com.au/2026/03/04/the-role-of-nature-and-awe-in-creating-a-calmer-mind/

Büssing, A., Wilhelm, J., &amp; Rodrigues Recchia, D. (2025). Wondering awe is the mediator of the link between experience of nature and psychological wellbeing—Relevance for public health. International Journal of Environmental Research and Public Health, 22(11), 1679. https://doi.org/10.3390/ijerph22111679

Gordon, A. M., Stellar, J. E., Anderson, C. L., McNeil, G. D., Loew, D., &amp; Keltner, D. (2017). The dark side of the sublime: Distinguishing a threat-based variant of awe. Journal of Personality and Social Psychology, 113(2), 310–328. https://doi.org/10.1037/pspp0000120

Jiang, T., Hicks, J. A., Yuan, W., Yin, Y., Needy, L., &amp; Vess, M. (2024). The unique nature and psychosocial implications of awe. Nature Reviews Psychology, 3(7), 475–488. https://doi.org/10.1038/s44159-024-00322-z

Keltner, D., &amp; Haidt, J. (2003). Approaching awe, a moral, spiritual, and aesthetic emotion. Cognition and Emotion, 17(2), 297–314. https://doi.org/10.1080/02699930302297

Keltner, D., &amp; Monroy, M. (2026). The expression of awe: Evolutionary origins and cultural elaborations of a basic emotion. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 381(1959), 20250148. PubMed Central. https://doi.org/10.1098/rstb.2025.0148

Monroy, M., &amp; Keltner, D. (2022). Awe as a pathway to mental and physical health. Perspectives on Psychological Science, 18(2), 174569162210948. https://doi.org/10.1177/17456916221094856

Piff, P. K., Dietze, P., Feinberg, M., Stancato, D. M., &amp; Keltner, D. (2015). Awe, the small self, and prosocial behavior. Journal of Personality and Social Psychology, 108(6), 883–899. https://doi.org/10.1037/pspi0000018

Rogers, K. (2010, October 4). Biophilia hypothesis {{!}} description, nature, &amp; human behavior. Encyclopedia Britannica. https://www.britannica.com/science/biophilia-hypothesis

Schurtz, D. R., Blincoe, S., Smith, R. H., Powell, C. A. J., Combs, D. J. Y., &amp; Kim, S. H. (2011). Exploring the social aspects of goose bumps and their role in awe and envy. Motivation and Emotion, 36(2), 205–217. https://doi.org/10.1007/s11031-011-9243-8

Shiota, M. N., Neufeld, S. L., Yeung, W. H., Moser, S. E., &amp; Perea, E. F. (2011). Feeling good: Autonomic nervous system responding in five positive emotions. Emotion, 11(6), 1368–1378. https://doi.org/10.1037/a0024278

Smalley, A. J., &amp; White, M. P. (2023). Beyond blue-sky thinking: Diurnal patterns and ephemeral meteorological phenomena impact appraisals of beauty, awe, and value in urban and natural landscapes. Journal of Environmental Psychology, 86, 101955. https://doi.org/10.1016/j.jenvp.2023.101955

The AWE experiment — Counterpilot. (2025). Counterpilot. https://www.counterpilot.com.au/aweexperiment

van Houwelingen-Snippe, J., van Rompay, T. J. L., de Jong, M. D. T., &amp; Ben Allouch, S. (2020). Does digital nature enhance social aspirations? An experimental study. International Journal of Environmental Research and Public Health, 17(4), 1454. https://doi.org/10.3390/ijerph17041454

Webb, D. (2025, March). Nature imagery and mental well-being. All About Psychology. Substack.Com. https://allaboutpsychology.substack.com/p/nature-imagery-and-mental-well-being

Yaden, D. B., Iwry, J., Slack, K. J., Eichstaedt, J. C., Zhao, Y., Vaillant, G. E., &amp; Newberg, A. B. (2016). The overview effect: Awe and self-transcendent experience in space flight. Psychology of Consciousness: Theory, Research, and Practice, 3(1), 1–11. https://doi.org/10.1037/cns0000086

}}

==External links==
* [https://greatergood.berkeley.edu/video/item/how_scientists_measure_awe_in_the_wild How Scientists Measure Awe in the Wild] (Greater Good Magazine)
* [https://mindfulforestbathing.com.au/the-transformative-power-of-awe-in-nature/ The Transformative Power of Awe in Nature] (Mindful in nature)
* [https://www.psychologytoday.com/au/blog/finding-new-home/201807/the-psychology-awe-awe-in-nature The Psychology of Awe: Awe in Nature] (PsychologyToday)
* [https://ggsc.berkeley.edu/images/uploads/GGSC-JTF_White_Paper-Awe_FINAL.pdf The science of Awe.] (Greater Good Science Centre)
* [https://read.wiley.com/books/9781394219018/page/6/section/top-of-page Understanding Motivation and Emotion] (Wiley)
* [https://allaboutpsychology.substack.com/p/nature-imagery-and-mental-well-being Nature Imagery and Mental Well Being] (David Webb)
* [https://qbi.uq.edu.au/blog/2025/04/what-does-awe-do-our-brains What does awe do to our brains?] (Queensland Brain Institute)
* [https://www.frontiersin.org/journals/virtual-reality/articles/10.3389/frvir.2025.1532991/full Immersive videos of natural and urban environments can enhance awe and psychological well-being] (Frontiers Barth et al., 2025) 

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__TOC__

==Overview==
{{RoundBoxTop|theme=5}}
[[File:Valley View Yosemite August 2013 002.jpg|right|thumb|220px|'''Figure 1'''. Yosemite Mountains]]

'''Case Study: Feeling small in Yosemite '''

Imagine standing at Yosemite National Park, you see vast landscapes of mountains, immersed in green forests and the sky (see Figure 1). But what [[TESOL/Emotions|emotions]] do you think you might feel? You might feel physically smaller than the mountains, and you might suddenly feel as if your worries and fears feel less consuming. This complex emotional experience is called awe. 

Researchers investigated this experience by asking visitors at Yosemite to draw a picture of themselves after viewing the parks landscape, the participants had a tendency to draw themselves significantly smaller to the mountains. They compared these drawings to those of tourists at Fisherman’s Wharf, a more urban setting, who drew big portraits. This identified the idea of the small self, further research revealed that on the day individuals experienced awe, they were also more likely to perceive themselves as smaller (Monroy &amp; Kelter, 2023).

{{RoundBoxBottom}}

This chapter examines the characteristics of nature that elicits awe, the cognitive and emotional mechanisms underlying the experience, and how nature induced awe influences an individuals mind.  
* The Yosemite findings raise a fundamental question. What is it about vast natural environments that can transform the way we think of individual experiences and the world around us? 
* Understanding this relationship through psychology can help investigate the cognitive and emotional processes involved in awe, and how this emotion can influence mental wellbeing. 
* Psychological research has revealed why certain natural experiences may evoke awe, and how awe changes attention and sense of self, and ultimately if these changes contribute to wellbeing. 
* Understanding the relationship between awe and nature, can help explain the impacts of nature on an individual.

{{RoundBoxTop|theme=2}}
;Focus questions
* What is Awe ?
* What is Awe connection to physiology?
* Can Awe be identified through facial expressions?
* What psychological processes explain the experience of awe in nature?  
* How does nature-induced awe influence the sense of self and psychological wellbeing? 
{{RoundBoxBottom}}

== The Emotion of Awe: More than just an emotion ==
Awe in a complex emotion and our minds response to vast stimuli that transcends current frames of reference, people typically experience awe to stimuli like wonders and panoramic views (Piff et al., 2015). Keltner and Haidt (2003) suggested a conceptualization of awe that consists of two aspects vastness and need for accommodation. [[Emotion|Emotionally]] Awe can trigger us to rethink our place in the world through self reflection, inducing positive wellbeing and less stress. Unlike other emotions Awe can be positive or negative as an emotion it generates feelings, arousal, purpose, and expression. Awe is a profound feeling of sense of self; people often feel a sense of awe towards things like nature, Awe can be explained as a distinct self-transcending emotion, awe is proposed to shift people’s perspective from an egocentric focus to a broader view of the self (Jiang et al., 2024). Awe if often experienced with encounters to music, visual art, collective movement like dance and rituals (Keltner and Monroy 2026). 

=== Origins of Awe ===
Historically Awe was associated with religious fear originating from an old word ''Agi'' meaning fright or terror. This suggests that awe was not originally conceptualised as a positive emotion, in 1757 Edmund Burke recognised that awe could arise from experiences such as thunder, art and music (Tix, 2015). Over history Awe has been conceptualised as many different facets this is particularly significant to how we measure Awe through psychology, cause we know it can be both a negative or positive emotion.  

=== The Five flavors of Awe ===

* Beauty 
* Threat
* Ability 
* Virtue 
* Supernatural

=== Awe as a basic emotion ===
In basic emotion theory (BET) emotions are brief states involving experiential, cognitive, physiological and expressive process that enables humans to respond to environmental stimuli, BET is the foundation of our six emotions anger, disgust, fear, sadness, surprise, and joy. Traditionally these six emotions are the basic emotions but Keltner and Monroy (2026) argue that awe may be a basic distinct emotion, it may not just be a mixture of surprise and happiness but have its own psychological and evolutionary functions. 

=== Vastness ===
Vastness refers to perceiving stimuli as being significantly larger than the usual frame of reference (Keltner &amp; Haidt, 2003), Keltner and Haidt idea of vastness goes beyond literal size and it includes stimuli that is perceptually or conceptually vast. This could be why the Yosemite can inflict Awe as it is physically a large mountain but conceptually it might be hard to understand. Any stimuli that goes beyond a normal individual's personal experience, can make them feel as if they are apart of something larger. 

=== Accomodation ===
The need for accommodation according to Keltner and Haidt (2003) refers to psychologist Jean Piaget process of adjusting mental structures that cannot assimilate a new experience. &quot;The success of one's attempt at accomodation may partially explain why awe can be both terrifying (when one fails to understand) and enlightening (when one succeeds)&quot; (Keltner &amp; Haidt 2003).  

== Physiological and Psychological effects of Awe ==

=== Physiological effects ===
Awe changes nervous system activity, Shiota et al. (2011) found that positive awe was generally associated with increased parasympathetic activity and reduced sympathetic activity, but interestingly found that breathing rate increased. This suggests why Awe is associated with relaxed mental states. However in a study by Gordon et al. (2017) found that threatening Awe experiences increased sympathetic activity, including heart rate. For example seeing a severe storm could induce threat based awe, a negative feeling of Awe. Awe can inhibit the response of goosebumps and chills Schurtz et al. (2012) found that awe was a common emotional trigger, this established that goosebumps may be a physical expression of awe and highlighting how deep Awe can make humans feel. 

=== The small self and perspective ===
One of the most recognised psychological effects of awe is the &quot;small self&quot;, where an individual experiences a reduced sense of self in relation to perceiving something much larger (Monroy &amp; Keltner, 2023). This concept can be seen in the Yosemite study introduced earlier, where the study highlighted the small self, being exposed to the mountains made the participants feel small. However feeling physically small does not mean feeling insignificant. Jiang et al., (2024) distinguishes that we may feel physically smaller but awe cannot make us feel insignificant instead it shifts our attention away from an egocentric perspective to broader view of the world. This broader perspective can explain why everyday worries can temporarily feel less consuming during awe. The source of stress has not been changed or fixed but instead a shift in perspective has changed. Büssing et al., (2025) found that awe and gratitude mediated the relationship between experiences of nature and wellbeing, suggesting that meaningful engagement with nature may matter more beyond simply being present in a natural environment.

The small self is further demonstrated where researchers developed a visual measurement consisting of seven drawings of a stick figure beside a sun, with each figure progressively increasing in size. Participants were to select the drawing that best represented their perceived sense of self, allowing researchers to examine how awe influences the perception of self (Bai et al., 2017). 

==Measurements of Awe==

=== Facial expressions of Awe ===
[[File:Rstb.2025.0148.f001.webp|thumb|'''Figure 3.''' Facial expressions ]]
Nature based Awe may induce recognisable facial expressions like raised eyebrows, widened eyes, and an open mouth. For example imagine looking at the night sky in rural Australia your facial expressions might show widen eyes, brows, and dropped jaw reflecting the emotion of awe and taking in the visual information. In a study by Keltner and Monroy in 2026, they observed patterns of facial expressions induced by awe across China, India, South Korea, Japan and the United States and found that approximately 63% of the elements of awe expressions overlapped.  Further research in Cowen and Keltner (2019, as cited in Keltner &amp; Monroy, 2026) examined more than 1,500 naturalistic photographs of facial expressions (see Figure 3), the analysis identified 28 distinguishable categories of emotional expressions including awe. In figure 3 Awe appears beside related emotions like surprise, fear and interest however it forms its own recognisable category suggesting that awe can include other basic emotions but cannot be reduced to those basic emotions. Furthermore the research in facial expression in Awe is limited in this specific studies participants were asked to imagine awe inspiring experiences rather than an actual response to natural stimuli. 

{{RoundBoxTop|theme=5}}
;Can Awe be measured in EEG
Awe is a complex emotion that is relatively hard to measure psychologically, but can we observe the feeling of Awe through brain activity? The Awe Experiment, developed by Brisbane based artists (Counterpilot) in collaboration with the Queensland Brain Institute, explored this question through an interactive performance at the World Science Festival. To measure brain activity participants were fitted with an EEG and participants listened to awe evoking narratives, Brain activity were translated in colourful lights. Although no scientific results came from this experiment, it is an interesting concept for future research.{{RoundBoxBottom}}

== Awe in everyday life ==

=== Attention and everyday awe ===
Although traditional theories emphasize vastness, awe does not only occur during rare encounters with dramatic landscape. More recent research has introduced this concept of wondering awe, a gentler more accessible experience that can emerge through attentive engagement with ordinary aspects of nature (Büssing et al., 2025). Rather than the exposure of Yosemite mountains, wondering awe emphasises an individual who pauses to notice the warmth of sunlight or the movement of leaves and feels a sense of awe. This contradicts the traditional explanation of awe, if perceived vastness is central to the experience how can something so small like sunlight evoke it? One possibility is that awe is influenced by the meaning and attention given to the stimuli. Slowing down and becoming engulfed in &quot;normal&quot; nature to notice complexity and beauty, establishes this idea of wondering awe. Furthermore the warmth of sunlight is still a complex idea and could extend beyond an individual's mental structure, which still highlights need for accommodation. Büssing et al., (2025) suggests nature exposure alone may not actively improve psychological wellbeing, instead the argument is that wondering awe may help explain how an individual's engagement with nature can inflict awe.

=== Changing nature and awe ===
{{RoundBoxTop|theme=5}}
;Imagine this ...
You walk the same route home every day after work, most days you barely notice the sky. But today the sky is filled with a vivid sunset (see Figure 2), you stop look up and take a brief moment to appreciate the sky, the location has not changed, but why are you experiencing a sense of awe in a familiar environment?
{{RoundBoxBottom}}

[[File:Sunset may 2006 panorama.jpg|thumb|'''Figure 2''': A sunset]]The ability of nature to evoke awe is also influenced by the context in which it is experienced. Natural environments are not static, the same location can appear ordinary in one moment than extraordinary in another moment. Smalley and White (2023), highlighted the concept of ephemeral phenomena such as sunsets, rainbows and storms, and found that these temporary changes influenced the connection of awe towards nature. Their findings suggest that a landscape does not have fixed awe value, instead its capacity to evoke awe may shift with changes in weather, light and time of day (Smalley &amp; White, 2023).

=== Awe in the digital world ===
Traditionally awe in nature has been studied with an individual who physically encounters vast natural environments, but what if we could feel awe through technology? 

Developments in digital technology challenge the idea of foundational awe, and question weather individuals need to be present in nature to experience awe. Virtual technology can recreate digital environments with the same characteristics such as spaciousness, scale and sensory immersion. This idea allows research into whether psychological experience of awe can also occur through simulated nature. Van Houwelingen-Snippe et al., (2020) found that spacious digital nature can make an individual experience awe especially when viewed alone suggesting the idea of perception scale. Similarly, virtual reality can create immersive environments that increase feelings of presence and perceived vastness, providing another method for eliciting awe (Jiang et al., 2024). These findings raise an interesting question, if awe depends on vastness does the nature producing it need to be real? Digital nature can be a useful tool in understanding the psychological process of awe more clearly, and achieve clinical based wellbeing treatments so everyone can feel awe.

== Awe and psychological wellbeing ==
Experiencing Awe in nature can influence an individual's immediate emotional state, it may also change how people perceive themselves and others. Research has associated awe with change in self focus, perspective, social connection and wellbeing (Jiang et al.,2024; Monroy &amp; Keltner, 2023). Understanding these effects may help explain why certain encounter with nature can change our perspectives.

Awe can help explain why some experiences in nature have positive psychological effects, ultimately it is how an individual responds to nature. The experience of awe may also extend beyond personal wellbeing by changing individual perspectives. Awe has been associated with greater prosocial behaviour and social connection (Jiang et al., 2024), while sublime experiences in nature can involve feelings of vitality, freedom and unity with the natural world (Bethelmy &amp; Corraliza, 2019). Awe and wellbeing is complex, because awe directly is not always a positive emotion. Awe can occur alongside negative emotions such as fear or even mixed emotional states (Jiang et al., 2024). Awe and fear can arise when vast powerful aspects of nature are perceived as a threat, such as a bushfire or flood the psychological impacts would probably not be beneficial. This demonstrates that the psychological benefits of nature induced awe may depend on how the experience is emotionally interpreted, particularly whether it is perceived as positive or threatening.

Quiz&lt;quiz display=&quot;simple&quot;&gt;
{Awe is an easy emotion to understand and is the same distinct emotion as Joy:
|type=&quot;()&quot;}
- True
+ False

{Spaciousness in a digital natural enviroment can contribute to the feeling of awe:
|type=&quot;()&quot;}
+ True
- False
&lt;/quiz&gt;

== Space and Awe ==
{{RoundBoxTop|theme=5}}
;Imagine this ...
Seeing Earth from space, surrounded by the vast darkness of the universe and the unknown, an experience you have never conceptualised. 
{{RoundBoxBottom}}&lt;gallery widths=&quot;250&quot; heights=&quot;250&quot;&gt;
File:The Earth seen from Apollo 17.jpg|'''Figure 4.''' Earth from space
&lt;/gallery&gt;This experience of seeing [[Earth]] from space is an extraordinary experience and is known as the overview effect, where astronauts report intense feelings of awe, wonder and connectedness from viewing earth from a completely different perspective (Yaden et al., 2016). Yaden et al. (2016) analysed that the overview effect involves both perceived vastness and cognitive accommodation, seeing an entire planet you thought you knew from a different perspective like this can challenge individuals mental frames. More interestingly astronauts have reported experiencing self transcendence, describing it as individual concerns becoming less significant and developing a stronger sense to humanity and the planet. More so some even commented that it changed self values and environmental awareness.  

== Conclusion ==
Awe has evolved from an emotion seen as god fearing to an emotion that can be positive and self transcending, Awe demonstrates that our experiences in nature involve more than appreciating beautiful stimuli. From standing beneath mountains, noticing sunsets, the sun on our skin, nature can challenge our understanding of the world and interfere with our mental frameworks. Awe should be seen as it's own distinct emotion, it has attributes of other emotions like joy but should not be limited to other emotions due to its complexities, Nature induced awe must include vastness and need for accommodation, exposure alone cannot elicit awe these two pillars provide as a foundation for understanding awe. The feeling of Awe may appear as positive or negative making it complex and hard to measure in psychology, an interesting form of measurement would be EEG, although the study mentioned in this chapter had no scientific results, it would be interesting to continue future research into brain activity when feeling awe. Wondering awe and ephemeral phenomenon demonstrates that this idea of vastness is not literal size of the stimuli but the conceptual vastness the stimuli holds, and enhances the idea that extraordinary experiences can emerge from ordinary or changing aspects in nature. It can be the most simple aspects like wind moving leaves, rainbows appearing after rain these small things can elicit awe. When we feel awe it can make individuals perceive themselves as different looking at your life from a different lens, encourages a broader thinking and to think less of the self. All of a sudden worries that feel intense in our small lives, don't seem to matter anymore it shifts mental thinking. However although Awe can produce such great moving emotions, it can also inhibit negative feelings it coexists with threat and fear. Originally Awe was associated with the fear of god, fear in Awe although evolved is still prevalent and in nature can appear after events like storms, or seeing a dangerous waterfall. Stimuli like this can influence and activate our sympathetic system and raise heart rate, and can include goosebumps. The emotion of Awe has intense physical and mental changes, so how can we not group an emotion like Awe as its own distinct emotion. Furthermore with rising technologies and with the known physical 
* Digital and virtual environments can recreate characteristics of nature, suggesting that psychological perception may be as important as physical presence in nature.

==See also==
List [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:

* [[Motivation and emotion/Book/2016/Awe as an emotion|Awe as an emotion]] (Book chapter, 2016)
* [[Motivation and emotion/Book/2026/Awe and the diminished self|Awe and the diminished self]] (Book chapter, 2026)
* [[Motivation and emotion/Book/2017/Awe and well-being|Awe and Wellbeing]] (Book chapter, 2017)
* [[Motivation and emotion/Book/2024/Nature connection and emotional well-being|Nature connection and emotional well-being]] (Book chapter, 2024)
* [[Psychological well-being]] (Wikipedia) 

==References==
{{Hanging indent|1=

ReferencesAndy Tix Ph.D. (2015, October 12). The complexity of awe is revealed in how it has been conceptualized across time. Psychology Today. 
https://www.psychologytoday.com/au/blog/the-pursuit-peace/201510/brief-history-awe

Bai, Y., Maruskin, L. A., Chen, S., Gordon, A. M., Stellar, J. E., McNeil, G. D., Peng, K., &amp; Keltner, D. (2017). Awe, the diminished self, and collective engagement: Universals and cultural variations in the small self. Journal of Personality and Social Psychology, 113(2), 185–209. https://doi.org/10.1037/pspa0000087Bonnell, M. (2026, March 4). 

Nature, awe and mental health: Why we feel better outdoors. Peaceful Mind. https://peacefulmind.com.au/2026/03/04/the-role-of-nature-and-awe-in-creating-a-calmer-mind/

Büssing, A., Wilhelm, J., &amp; Rodrigues Recchia, D. (2025). Wondering awe is the mediator of the link between experience of nature and psychological wellbeing—Relevance for public health. International Journal of Environmental Research and Public Health, 22(11), 1679. https://doi.org/10.3390/ijerph22111679

Gordon, A. M., Stellar, J. E., Anderson, C. L., McNeil, G. D., Loew, D., &amp; Keltner, D. (2017). The dark side of the sublime: Distinguishing a threat-based variant of awe. Journal of Personality and Social Psychology, 113(2), 310–328. https://doi.org/10.1037/pspp0000120

Jiang, T., Hicks, J. A., Yuan, W., Yin, Y., Needy, L., &amp; Vess, M. (2024). The unique nature and psychosocial implications of awe. Nature Reviews Psychology, 3(7), 475–488. https://doi.org/10.1038/s44159-024-00322-z

Keltner, D., &amp; Haidt, J. (2003). Approaching awe, a moral, spiritual, and aesthetic emotion. Cognition and Emotion, 17(2), 297–314. https://doi.org/10.1080/02699930302297

Keltner, D., &amp; Monroy, M. (2026). The expression of awe: Evolutionary origins and cultural elaborations of a basic emotion. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 381(1959), 20250148. PubMed Central. https://doi.org/10.1098/rstb.2025.0148

Monroy, M., &amp; Keltner, D. (2022). Awe as a pathway to mental and physical health. Perspectives on Psychological Science, 18(2), 174569162210948. https://doi.org/10.1177/17456916221094856

Piff, P. K., Dietze, P., Feinberg, M., Stancato, D. M., &amp; Keltner, D. (2015). Awe, the small self, and prosocial behavior. Journal of Personality and Social Psychology, 108(6), 883–899. https://doi.org/10.1037/pspi0000018

Rogers, K. (2010, October 4). Biophilia hypothesis {{!}} description, nature, &amp; human behavior. Encyclopedia Britannica. https://www.britannica.com/science/biophilia-hypothesis

Schurtz, D. R., Blincoe, S., Smith, R. H., Powell, C. A. J., Combs, D. J. Y., &amp; Kim, S. H. (2011). Exploring the social aspects of goose bumps and their role in awe and envy. Motivation and Emotion, 36(2), 205–217. https://doi.org/10.1007/s11031-011-9243-8

Shiota, M. N., Neufeld, S. L., Yeung, W. H., Moser, S. E., &amp; Perea, E. F. (2011). Feeling good: Autonomic nervous system responding in five positive emotions. Emotion, 11(6), 1368–1378. https://doi.org/10.1037/a0024278

Smalley, A. J., &amp; White, M. P. (2023). Beyond blue-sky thinking: Diurnal patterns and ephemeral meteorological phenomena impact appraisals of beauty, awe, and value in urban and natural landscapes. Journal of Environmental Psychology, 86, 101955. https://doi.org/10.1016/j.jenvp.2023.101955

The AWE experiment — Counterpilot. (2025). Counterpilot. https://www.counterpilot.com.au/aweexperiment

van Houwelingen-Snippe, J., van Rompay, T. J. L., de Jong, M. D. T., &amp; Ben Allouch, S. (2020). Does digital nature enhance social aspirations? An experimental study. International Journal of Environmental Research and Public Health, 17(4), 1454. https://doi.org/10.3390/ijerph17041454

Webb, D. (2025, March). Nature imagery and mental well-being. All About Psychology. Substack.Com. https://allaboutpsychology.substack.com/p/nature-imagery-and-mental-well-being

Yaden, D. B., Iwry, J., Slack, K. J., Eichstaedt, J. C., Zhao, Y., Vaillant, G. E., &amp; Newberg, A. B. (2016). The overview effect: Awe and self-transcendent experience in space flight. Psychology of Consciousness: Theory, Research, and Practice, 3(1), 1–11. https://doi.org/10.1037/cns0000086

}}

==External links==
* [https://greatergood.berkeley.edu/video/item/how_scientists_measure_awe_in_the_wild How Scientists Measure Awe in the Wild] (Greater Good Magazine)
* [https://mindfulforestbathing.com.au/the-transformative-power-of-awe-in-nature/ The Transformative Power of Awe in Nature] (Mindful in nature)
* [https://www.psychologytoday.com/au/blog/finding-new-home/201807/the-psychology-awe-awe-in-nature The Psychology of Awe: Awe in Nature] (PsychologyToday)
* [https://ggsc.berkeley.edu/images/uploads/GGSC-JTF_White_Paper-Awe_FINAL.pdf The science of Awe.] (Greater Good Science Centre)
* [https://read.wiley.com/books/9781394219018/page/6/section/top-of-page Understanding Motivation and Emotion] (Wiley)
* [https://allaboutpsychology.substack.com/p/nature-imagery-and-mental-well-being Nature Imagery and Mental Well Being] (David Webb)
* [https://qbi.uq.edu.au/blog/2025/04/what-does-awe-do-our-brains What does awe do to our brains?] (Queensland Brain Institute)
* [https://www.frontiersin.org/journals/virtual-reality/articles/10.3389/frvir.2025.1532991/full Immersive videos of natural and urban environments can enhance awe and psychological well-being] (Frontiers Barth et al., 2025) 

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[[Category:Motivation and emotion/Book/Awe]]
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__TOC__

==Overview==
{{RoundBoxTop|theme=5}}
[[File:Valley View Yosemite August 2013 002.jpg|right|thumb|220px|'''Figure 1'''. Yosemite Mountains]]

'''Case Study: Feeling small in Yosemite '''

Imagine standing at Yosemite National Park, you see vast landscapes of mountains, immersed in green forests and the sky (see Figure 1). But what [[TESOL/Emotions|emotions]] do you think you might feel? You might feel physically smaller than the mountains, and you might suddenly feel as if your worries and fears feel less consuming. This complex emotional experience is called awe. 

Researchers investigated this experience by asking visitors at Yosemite to draw a picture of themselves after viewing the parks landscape, the participants had a tendency to draw themselves significantly smaller to the mountains. They compared these drawings to those of tourists at Fisherman’s Wharf, a more urban setting, who drew big portraits. This identified the idea of the small self, further research revealed that on the day individuals experienced awe, they were also more likely to perceive themselves as smaller (Monroy &amp; Kelter, 2023).

{{RoundBoxBottom}}

This chapter examines the characteristics of nature that elicits awe, the cognitive and emotional mechanisms underlying the experience, and how nature induced awe influences an individuals mind.  
* The Yosemite findings raise a fundamental question. What is it about vast natural environments that can transform the way we think of individual experiences and the world around us? 
* Understanding this relationship through psychology can help investigate the cognitive and emotional processes involved in awe, and how this emotion can influence mental wellbeing. 
* Psychological research has revealed why certain natural experiences may evoke awe, and how awe changes attention and sense of self, and ultimately if these changes contribute to wellbeing. 
* Understanding the relationship between awe and nature, can help explain the impacts of nature on an individual.

{{RoundBoxTop|theme=2}}
;Focus questions
* What is Awe ?
* What is Awe connection to physiology?
* Can Awe be identified through facial expressions?
* What psychological processes explain the experience of awe in nature?  
* How does nature-induced awe influence the sense of self and psychological wellbeing? 
{{RoundBoxBottom}}

== The Emotion of Awe: More than just an emotion ==
Awe in a complex emotion and our minds response to vast stimuli that transcends current frames of reference, people typically experience awe to stimuli like wonders and panoramic views (Piff et al., 2015). Keltner and Haidt (2003) suggested a conceptualization of awe that consists of two aspects vastness and need for accommodation. [[Emotion|Emotionally]] Awe can trigger us to rethink our place in the world through self reflection, inducing positive wellbeing and less stress. Unlike other emotions Awe can be positive or negative as an emotion it generates feelings, arousal, purpose, and expression. Awe is a profound feeling of sense of self; people often feel a sense of awe towards things like nature, Awe can be explained as a distinct self-transcending emotion, awe is proposed to shift people’s perspective from an egocentric focus to a broader view of the self (Jiang et al., 2024). Awe if often experienced with encounters to music, visual art, collective movement like dance and rituals (Keltner and Monroy 2026). 

=== Origins of Awe ===
Historically Awe was associated with religious fear originating from an old word ''Agi'' meaning fright or terror. This suggests that awe was not originally conceptualised as a positive emotion, in 1757 Edmund Burke recognised that awe could arise from experiences such as thunder, art and music (Tix, 2015). Over history Awe has been conceptualised as many different facets this is particularly significant to how we measure Awe through psychology, cause we know it can be both a negative or positive emotion.  

=== The Five flavors of Awe ===

* Beauty 
* Threat
* Ability 
* Virtue 
* Supernatural

=== Awe as a basic emotion ===
In basic emotion theory (BET) emotions are brief states involving experiential, cognitive, physiological and expressive process that enables humans to respond to environmental stimuli, BET is the foundation of our six emotions anger, disgust, fear, sadness, surprise, and joy. Traditionally these six emotions are the basic emotions but Keltner and Monroy (2026) argue that awe may be a basic distinct emotion, it may not just be a mixture of surprise and happiness but have its own psychological and evolutionary functions. 

=== Vastness ===
Vastness refers to perceiving stimuli as being significantly larger than the usual frame of reference (Keltner &amp; Haidt, 2003), Keltner and Haidt idea of vastness goes beyond literal size and it includes stimuli that is perceptually or conceptually vast. This could be why the Yosemite can inflict Awe as it is physically a large mountain but conceptually it might be hard to understand. Any stimuli that goes beyond a normal individual's personal experience, can make them feel as if they are apart of something larger. 

=== Accomodation ===
The need for accommodation according to Keltner and Haidt (2003) refers to psychologist Jean Piaget process of adjusting mental structures that cannot assimilate a new experience. &quot;The success of one's attempt at accomodation may partially explain why awe can be both terrifying (when one fails to understand) and enlightening (when one succeeds)&quot; (Keltner &amp; Haidt 2003).  

== Physiological and Psychological effects of Awe ==

=== Physiological effects ===
Awe changes nervous system activity, Shiota et al. (2011) found that positive awe was generally associated with increased parasympathetic activity and reduced sympathetic activity, but interestingly found that breathing rate increased. This suggests why Awe is associated with relaxed mental states. However in a study by Gordon et al. (2017) found that threatening Awe experiences increased sympathetic activity, including heart rate. For example seeing a severe storm could induce threat based awe, a negative feeling of Awe. Awe can inhibit the response of goosebumps and chills Schurtz et al. (2012) found that awe was a common emotional trigger, this established that goosebumps may be a physical expression of awe and highlighting how deep Awe can make humans feel. 

=== The small self and perspective ===
One of the most recognised psychological effects of awe is the &quot;small self&quot;, where an individual experiences a reduced sense of self in relation to perceiving something much larger (Monroy &amp; Keltner, 2023). This concept can be seen in the Yosemite study introduced earlier, where the study highlighted the small self, being exposed to the mountains made the participants feel small. However feeling physically small does not mean feeling insignificant. Jiang et al., (2024) distinguishes that we may feel physically smaller but awe cannot make us feel insignificant instead it shifts our attention away from an egocentric perspective to broader view of the world. This broader perspective can explain why everyday worries can temporarily feel less consuming during awe. The source of stress has not been changed or fixed but instead a shift in perspective has changed. Büssing et al., (2025) found that awe and gratitude mediated the relationship between experiences of nature and wellbeing, suggesting that meaningful engagement with nature may matter more beyond simply being present in a natural environment.

The small self is further demonstrated where researchers developed a visual measurement consisting of seven drawings of a stick figure beside a sun, with each figure progressively increasing in size. Participants were to select the drawing that best represented their perceived sense of self, allowing researchers to examine how awe influences the perception of self (Bai et al., 2017). 

==Measurements of Awe==

=== Facial expressions of Awe ===
[[File:Rstb.2025.0148.f001.webp|thumb|'''Figure 3.''' Facial expressions ]]
Nature based Awe may induce recognisable facial expressions like raised eyebrows, widened eyes, and an open mouth. For example imagine looking at the night sky in rural Australia your facial expressions might show widen eyes, brows, and dropped jaw reflecting the emotion of awe and taking in the visual information. In a study by Keltner and Monroy in 2026, they observed patterns of facial expressions induced by awe across China, India, South Korea, Japan and the United States and found that approximately 63% of the elements of awe expressions overlapped.  Further research in Cowen and Keltner (2019, as cited in Keltner &amp; Monroy, 2026) examined more than 1,500 naturalistic photographs of facial expressions (see Figure 3), the analysis identified 28 distinguishable categories of emotional expressions including awe. In figure 3 Awe appears beside related emotions like surprise, fear and interest however it forms its own recognisable category suggesting that awe can include other basic emotions but cannot be reduced to those basic emotions. Furthermore the research in facial expression in Awe is limited in this specific studies participants were asked to imagine awe inspiring experiences rather than an actual response to natural stimuli. 

{{RoundBoxTop|theme=5}}
;Can Awe be measured in EEG
Awe is a complex emotion that is relatively hard to measure psychologically, but can we observe the feeling of Awe through brain activity? The Awe Experiment, developed by Brisbane based artists (Counterpilot) in collaboration with the Queensland Brain Institute, explored this question through an interactive performance at the World Science Festival. To measure brain activity participants were fitted with an EEG and participants listened to awe evoking narratives, Brain activity were translated in colourful lights. Although no scientific results came from this experiment, it is an interesting concept for future research.{{RoundBoxBottom}}

== Awe in everyday life ==

=== Attention and everyday awe ===
Although traditional theories emphasize vastness, awe does not only occur during rare encounters with dramatic landscape. More recent research has introduced this concept of wondering awe, a gentler more accessible experience that can emerge through attentive engagement with ordinary aspects of nature (Büssing et al., 2025). Rather than the exposure of Yosemite mountains, wondering awe emphasises an individual who pauses to notice the warmth of sunlight or the movement of leaves and feels a sense of awe. This contradicts the traditional explanation of awe, if perceived vastness is central to the experience how can something so small like sunlight evoke it? One possibility is that awe is influenced by the meaning and attention given to the stimuli. Slowing down and becoming engulfed in &quot;normal&quot; nature to notice complexity and beauty, establishes this idea of wondering awe. Furthermore the warmth of sunlight is still a complex idea and could extend beyond an individual's mental structure, which still highlights need for accommodation. Büssing et al., (2025) suggests nature exposure alone may not actively improve psychological wellbeing, instead the argument is that wondering awe may help explain how an individual's engagement with nature can inflict awe.

=== Changing nature and awe ===
{{RoundBoxTop|theme=5}}
;Imagine this ...
You walk the same route home every day after work, most days you barely notice the sky. But today the sky is filled with a vivid sunset (see Figure 2), you stop look up and take a brief moment to appreciate the sky, the location has not changed, but why are you experiencing a sense of awe in a familiar environment?
{{RoundBoxBottom}}

[[File:Sunset may 2006 panorama.jpg|thumb|'''Figure 2''': A sunset]]The ability of nature to evoke awe is also influenced by the context in which it is experienced. Natural environments are not static, the same location can appear ordinary in one moment than extraordinary in another moment. Smalley and White (2023), highlighted the concept of ephemeral phenomena such as sunsets, rainbows and storms, and found that these temporary changes influenced the connection of awe towards nature. Their findings suggest that a landscape does not have fixed awe value, instead its capacity to evoke awe may shift with changes in weather, light and time of day (Smalley &amp; White, 2023).

=== Awe in the digital world ===
Traditionally awe in nature has been studied with an individual who physically encounters vast natural environments, but what if we could feel awe through technology? 

Developments in digital technology challenge the idea of foundational awe, and question weather individuals need to be present in nature to experience awe. Virtual technology can recreate digital environments with the same characteristics such as spaciousness, scale and sensory immersion. This idea allows research into whether psychological experience of awe can also occur through simulated nature. Van Houwelingen-Snippe et al., (2020) found that spacious digital nature can make an individual experience awe especially when viewed alone suggesting the idea of perception scale. Similarly, virtual reality can create immersive environments that increase feelings of presence and perceived vastness, providing another method for eliciting awe (Jiang et al., 2024). These findings raise an interesting question, if awe depends on vastness does the nature producing it need to be real? Digital nature can be a useful tool in understanding the psychological process of awe more clearly, and achieve clinical based wellbeing treatments so everyone can feel awe.

== Awe and psychological wellbeing ==
Experiencing Awe in nature can influence an individual's immediate emotional state, it may also change how people perceive themselves and others. Research has associated awe with change in self focus, perspective, social connection and wellbeing (Jiang et al.,2024; Monroy &amp; Keltner, 2023). Understanding these effects may help explain why certain encounter with nature can change our perspectives.

Awe can help explain why some experiences in nature have positive psychological effects, ultimately it is how an individual responds to nature. The experience of awe may also extend beyond personal wellbeing by changing individual perspectives. Awe has been associated with greater prosocial behaviour and social connection (Jiang et al., 2024), while sublime experiences in nature can involve feelings of vitality, freedom and unity with the natural world (Bethelmy &amp; Corraliza, 2019). Awe and wellbeing is complex, because awe directly is not always a positive emotion. Awe can occur alongside negative emotions such as fear or even mixed emotional states (Jiang et al., 2024). Awe and fear can arise when vast powerful aspects of nature are perceived as a threat, such as a bushfire or flood the psychological impacts would probably not be beneficial. This demonstrates that the psychological benefits of nature induced awe may depend on how the experience is emotionally interpreted, particularly whether it is perceived as positive or threatening.

Quiz&lt;quiz display=&quot;simple&quot;&gt;
{Awe is an easy emotion to understand and is the same distinct emotion as Joy:
|type=&quot;()&quot;}
- True
+ False

{Spaciousness in a digital natural enviroment can contribute to the feeling of awe:
|type=&quot;()&quot;}
+ True
- False
&lt;/quiz&gt;

== Space and Awe ==
{{RoundBoxTop|theme=5}}
;Imagine this ...
Seeing Earth from space, surrounded by the vast darkness of the universe and the unknown, an experience you have never conceptualised. 
{{RoundBoxBottom}}&lt;gallery widths=&quot;250&quot; heights=&quot;250&quot;&gt;
File:The Earth seen from Apollo 17.jpg|'''Figure 4.''' Earth from space
&lt;/gallery&gt;This experience of seeing [[Earth]] from space is an extraordinary experience and is known as the overview effect, where astronauts report intense feelings of awe, wonder and connectedness from viewing earth from a completely different perspective (Yaden et al., 2016). Yaden et al. (2016) analysed that the overview effect involves both perceived vastness and cognitive accommodation, seeing an entire planet you thought you knew from a different perspective like this can challenge individuals mental frames. More interestingly astronauts have reported experiencing self transcendence, describing it as individual concerns becoming less significant and developing a stronger sense to humanity and the planet. More so some even commented that it changed self values and environmental awareness.  

== Conclusion ==
Awe has evolved from an emotion seen as god fearing to an emotion that can be positive and self transcending, Awe demonstrates that our experiences in nature involve more than appreciating beautiful stimuli. From standing beneath mountains, noticing sunsets, the sun on our skin, nature can challenge our understanding of the world and interfere with our mental frameworks. Awe should be seen as it's own distinct emotion, it has attributes of other emotions like joy but should not be limited to other emotions due to its complexities, Nature induced awe must include vastness and need for accommodation, exposure alone cannot elicit awe these two pillars provide as a foundation for understanding awe. The feeling of Awe may appear as positive or negative making it complex and hard to measure in psychology, an interesting form of measurement would be EEG, although the study mentioned in this chapter had no scientific results, it would be interesting to continue future research into brain activity when feeling awe. Wondering awe and ephemeral phenomenon demonstrates that this idea of vastness is not literal size of the stimuli but the conceptual vastness the stimuli holds, and enhances the idea that extraordinary experiences can emerge from ordinary or changing aspects in nature. It can be the most simple aspects like wind moving leaves, rainbows appearing after rain these small things can elicit awe. When we feel awe it can make individuals perceive themselves as different looking at your life from a different lens, encourages a broader thinking and to think less of the self. All of a sudden worries that feel intense in our small lives, don't seem to matter anymore it shifts mental thinking. However although Awe can produce such great moving emotions, it can also inhibit negative feelings it coexists with threat and fear. Originally Awe was associated with the fear of god, fear in Awe although evolved is still prevalent and in nature can appear after events like storms, or seeing a dangerous waterfall. Stimuli like this can influence and activate our sympathetic system and raise heart rate, and can include goosebumps. The emotion of Awe has intense physical and mental changes, so how can we not group an emotion like Awe as its own distinct emotion. Furthermore with rising technologies and with the known physical benefits of Awe, an interesting future idea for research could be in the integration of VR in wellbeing. For elders or people who have to spend their entire lives in hospital, these people should be able to experience nature based awe. To promote connectedness to nature, relief from life stressors and higher life satisfaction. Understanding and being able to measure the psychology of Awe can be used as an important tool, as new tests for mental wellbeing.  
==See also==
List [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:

* [[Motivation and emotion/Book/2016/Awe as an emotion|Awe as an emotion]] (Book chapter, 2016)
* [[Motivation and emotion/Book/2026/Awe and the diminished self|Awe and the diminished self]] (Book chapter, 2026)
* [[Motivation and emotion/Book/2017/Awe and well-being|Awe and Wellbeing]] (Book chapter, 2017)
* [[Motivation and emotion/Book/2024/Nature connection and emotional well-being|Nature connection and emotional well-being]] (Book chapter, 2024)
* [[Psychological well-being]] (Wikipedia) 

==References==
{{Hanging indent|1=

ReferencesAndy Tix Ph.D. (2015, October 12). The complexity of awe is revealed in how it has been conceptualized across time. Psychology Today. 
https://www.psychologytoday.com/au/blog/the-pursuit-peace/201510/brief-history-awe

Bai, Y., Maruskin, L. A., Chen, S., Gordon, A. M., Stellar, J. E., McNeil, G. D., Peng, K., &amp; Keltner, D. (2017). Awe, the diminished self, and collective engagement: Universals and cultural variations in the small self. Journal of Personality and Social Psychology, 113(2), 185–209. https://doi.org/10.1037/pspa0000087Bonnell, M. (2026, March 4). 

Nature, awe and mental health: Why we feel better outdoors. Peaceful Mind. https://peacefulmind.com.au/2026/03/04/the-role-of-nature-and-awe-in-creating-a-calmer-mind/

Büssing, A., Wilhelm, J., &amp; Rodrigues Recchia, D. (2025). Wondering awe is the mediator of the link between experience of nature and psychological wellbeing—Relevance for public health. International Journal of Environmental Research and Public Health, 22(11), 1679. https://doi.org/10.3390/ijerph22111679

Gordon, A. M., Stellar, J. E., Anderson, C. L., McNeil, G. D., Loew, D., &amp; Keltner, D. (2017). The dark side of the sublime: Distinguishing a threat-based variant of awe. Journal of Personality and Social Psychology, 113(2), 310–328. https://doi.org/10.1037/pspp0000120

Jiang, T., Hicks, J. A., Yuan, W., Yin, Y., Needy, L., &amp; Vess, M. (2024). The unique nature and psychosocial implications of awe. Nature Reviews Psychology, 3(7), 475–488. https://doi.org/10.1038/s44159-024-00322-z

Keltner, D., &amp; Haidt, J. (2003). Approaching awe, a moral, spiritual, and aesthetic emotion. Cognition and Emotion, 17(2), 297–314. https://doi.org/10.1080/02699930302297

Keltner, D., &amp; Monroy, M. (2026). The expression of awe: Evolutionary origins and cultural elaborations of a basic emotion. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 381(1959), 20250148. PubMed Central. https://doi.org/10.1098/rstb.2025.0148

Monroy, M., &amp; Keltner, D. (2022). Awe as a pathway to mental and physical health. Perspectives on Psychological Science, 18(2), 174569162210948. https://doi.org/10.1177/17456916221094856

Piff, P. K., Dietze, P., Feinberg, M., Stancato, D. M., &amp; Keltner, D. (2015). Awe, the small self, and prosocial behavior. Journal of Personality and Social Psychology, 108(6), 883–899. https://doi.org/10.1037/pspi0000018

Rogers, K. (2010, October 4). Biophilia hypothesis {{!}} description, nature, &amp; human behavior. Encyclopedia Britannica. https://www.britannica.com/science/biophilia-hypothesis

Schurtz, D. R., Blincoe, S., Smith, R. H., Powell, C. A. J., Combs, D. J. Y., &amp; Kim, S. H. (2011). Exploring the social aspects of goose bumps and their role in awe and envy. Motivation and Emotion, 36(2), 205–217. https://doi.org/10.1007/s11031-011-9243-8

Shiota, M. N., Neufeld, S. L., Yeung, W. H., Moser, S. E., &amp; Perea, E. F. (2011). Feeling good: Autonomic nervous system responding in five positive emotions. Emotion, 11(6), 1368–1378. https://doi.org/10.1037/a0024278

Smalley, A. J., &amp; White, M. P. (2023). Beyond blue-sky thinking: Diurnal patterns and ephemeral meteorological phenomena impact appraisals of beauty, awe, and value in urban and natural landscapes. Journal of Environmental Psychology, 86, 101955. https://doi.org/10.1016/j.jenvp.2023.101955

The AWE experiment — Counterpilot. (2025). Counterpilot. https://www.counterpilot.com.au/aweexperiment

van Houwelingen-Snippe, J., van Rompay, T. J. L., de Jong, M. D. T., &amp; Ben Allouch, S. (2020). Does digital nature enhance social aspirations? An experimental study. International Journal of Environmental Research and Public Health, 17(4), 1454. https://doi.org/10.3390/ijerph17041454

Webb, D. (2025, March). Nature imagery and mental well-being. All About Psychology. Substack.Com. https://allaboutpsychology.substack.com/p/nature-imagery-and-mental-well-being

Yaden, D. B., Iwry, J., Slack, K. J., Eichstaedt, J. C., Zhao, Y., Vaillant, G. E., &amp; Newberg, A. B. (2016). The overview effect: Awe and self-transcendent experience in space flight. Psychology of Consciousness: Theory, Research, and Practice, 3(1), 1–11. https://doi.org/10.1037/cns0000086

}}

==External links==
* [https://greatergood.berkeley.edu/video/item/how_scientists_measure_awe_in_the_wild How Scientists Measure Awe in the Wild] (Greater Good Magazine)
* [https://mindfulforestbathing.com.au/the-transformative-power-of-awe-in-nature/ The Transformative Power of Awe in Nature] (Mindful in nature)
* [https://www.psychologytoday.com/au/blog/finding-new-home/201807/the-psychology-awe-awe-in-nature The Psychology of Awe: Awe in Nature] (PsychologyToday)
* [https://ggsc.berkeley.edu/images/uploads/GGSC-JTF_White_Paper-Awe_FINAL.pdf The science of Awe.] (Greater Good Science Centre)
* [https://read.wiley.com/books/9781394219018/page/6/section/top-of-page Understanding Motivation and Emotion] (Wiley)
* [https://allaboutpsychology.substack.com/p/nature-imagery-and-mental-well-being Nature Imagery and Mental Well Being] (David Webb)
* [https://qbi.uq.edu.au/blog/2025/04/what-does-awe-do-our-brains What does awe do to our brains?] (Queensland Brain Institute)
* [https://www.frontiersin.org/journals/virtual-reality/articles/10.3389/frvir.2025.1532991/full Immersive videos of natural and urban environments can enhance awe and psychological well-being] (Frontiers Barth et al., 2025) 

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==Overview==
{{RoundBoxTop|theme=5}}
[[File:Valley View Yosemite August 2013 002.jpg|right|thumb|220px|'''Figure 1'''. Yosemite Mountains]]

'''Case Study: Feeling small in Yosemite '''

Imagine standing at Yosemite National Park, you see vast landscapes of mountains, immersed in green forests and the sky (see Figure 1). But what [[TESOL/Emotions|emotions]] do you think you might feel? You might feel physically smaller than the mountains, and you might suddenly feel as if your worries and fears feel less consuming. This complex emotional experience is called awe. 

Researchers investigated this experience by asking visitors at Yosemite to draw a picture of themselves after viewing the parks landscape, the participants had a tendency to draw themselves significantly smaller to the mountains. They compared these drawings to those of tourists at Fisherman’s Wharf, a more urban setting, who drew big portraits. This identified the idea of the small self, further research revealed that on the day individuals experienced awe, they were also more likely to perceive themselves as smaller (Monroy &amp; Kelter, 2023).

{{RoundBoxBottom}}

This chapter examines the characteristics of nature that elicits awe, the cognitive and emotional mechanisms underlying the experience, and how nature induced awe influences an individuals mind.  
* The Yosemite findings raise a fundamental question. What is it about vast natural environments that can transform the way we think of individual experiences and the world around us? 
* Understanding this relationship through psychology can help investigate the cognitive and emotional processes involved in awe, and how this emotion can influence mental wellbeing. 
* Psychological research has revealed why certain natural experiences may evoke awe, and how awe changes attention and sense of self, and ultimately if these changes contribute to wellbeing. 
* Understanding the relationship between awe and nature, can help explain the impacts of nature on an individual.

{{RoundBoxTop|theme=2}}
;Focus questions
* What is Awe ?
* What is Awe connection to physiology?
* Can Awe be identified through facial expressions?
* What psychological processes explain the experience of awe in nature?  
* How does nature-induced awe influence the sense of self and psychological wellbeing? 
{{RoundBoxBottom}}

== The Emotion of Awe: More than just an emotion ==
Awe in a complex emotion and our minds response to vast stimuli that transcends current frames of reference, people typically experience awe to stimuli like wonders and panoramic views (Piff et al., 2015). Keltner and Haidt (2003) suggested a conceptualization of awe that consists of two aspects vastness and need for accommodation. [[Emotion|Emotionally]] Awe can trigger us to rethink our place in the world through self reflection, inducing positive wellbeing and less stress. Unlike other emotions Awe can be positive or negative as an emotion it generates feelings, arousal, purpose, and expression. Awe is a profound feeling of sense of self; people often feel a sense of awe towards things like nature, Awe can be explained as a distinct self-transcending emotion, awe is proposed to shift people’s perspective from an egocentric focus to a broader view of the self (Jiang et al., 2024). Awe if often experienced with encounters to music, visual art, collective movement like dance and rituals (Keltner and Monroy 2026). 

=== Origins of Awe ===
Historically Awe was associated with religious fear originating from an old word ''Agi'' meaning fright or terror. This suggests that awe was not originally conceptualised as a positive emotion, in 1757 Edmund Burke recognised that awe could arise from experiences such as thunder, art and music (Tix, 2015). Over history Awe has been conceptualised as many different facets this is particularly significant to how we measure Awe through psychology, cause we know it can be both a negative or positive emotion.  

=== The Five flavors of Awe ===

* Beauty 
* Threat
* Ability 
* Virtue 
* Supernatural

=== Awe as a basic emotion ===
In basic emotion theory (BET) emotions are brief states involving experiential, cognitive, physiological and expressive process that enables humans to respond to environmental stimuli, BET is the foundation of our six emotions anger, disgust, fear, sadness, surprise, and joy. Traditionally these six emotions are the basic emotions but Keltner and Monroy (2026) argue that awe may be a basic distinct emotion, it may not just be a mixture of surprise and happiness but have its own psychological and evolutionary functions. 

=== Vastness ===
Vastness refers to perceiving stimuli as being significantly larger than the usual frame of reference (Keltner &amp; Haidt, 2003), Keltner and Haidt idea of vastness goes beyond literal size and it includes stimuli that is perceptually or conceptually vast. This could be why the Yosemite can inflict Awe as it is physically a large mountain but conceptually it might be hard to understand. Any stimuli that goes beyond a normal individual's personal experience, can make them feel as if they are apart of something larger. 

=== Accomodation ===
The need for accommodation according to Keltner and Haidt (2003) refers to psychologist Jean Piaget process of adjusting mental structures that cannot assimilate a new experience. &quot;The success of one's attempt at accomodation may partially explain why awe can be both terrifying (when one fails to understand) and enlightening (when one succeeds)&quot; (Keltner &amp; Haidt 2003).  

== Physiological and Psychological effects of Awe ==

=== Physiological effects ===
Awe changes nervous system activity, Shiota et al. (2011) found that positive awe was generally associated with increased parasympathetic activity and reduced sympathetic activity, but interestingly found that breathing rate increased. This suggests why Awe is associated with relaxed mental states. However in a study by Gordon et al. (2017) found that threatening Awe experiences increased sympathetic activity, including heart rate. For example seeing a severe storm could induce threat based awe, a negative feeling of Awe. Awe can inhibit the response of goosebumps and chills Schurtz et al. (2012) found that awe was a common emotional trigger, this established that goosebumps may be a physical expression of awe and highlighting how deep Awe can make humans feel. 

=== The small self and perspective ===
One of the most recognised psychological effects of awe is the &quot;small self&quot;, where an individual experiences a reduced sense of self in relation to perceiving something much larger (Monroy &amp; Keltner, 2023). This concept can be seen in the Yosemite study introduced earlier, where the study highlighted the small self, being exposed to the mountains made the participants feel small. However feeling physically small does not mean feeling insignificant. Jiang et al., (2024) distinguishes that we may feel physically smaller but awe cannot make us feel insignificant instead it shifts our attention away from an egocentric perspective to broader view of the world. This broader perspective can explain why everyday worries can temporarily feel less consuming during awe. The source of stress has not been changed or fixed but instead a shift in perspective has changed. Büssing et al., (2025) found that awe and gratitude mediated the relationship between experiences of nature and wellbeing, suggesting that meaningful engagement with nature may matter more beyond simply being present in a natural environment.

The small self is further demonstrated where researchers developed a visual measurement consisting of seven drawings of a stick figure beside a sun, with each figure progressively increasing in size. Participants were to select the drawing that best represented their perceived sense of self, allowing researchers to examine how awe influences the perception of self (Bai et al., 2017). 

==Measurements of Awe==

=== Facial expressions of Awe ===
[[File:Rstb.2025.0148.f001.webp|thumb|'''Figure 3.''' Facial expressions ]]
Nature based Awe may induce recognisable facial expressions like raised eyebrows, widened eyes, and an open mouth. For example imagine looking at the night sky in rural Australia your facial expressions might show widen eyes, brows, and dropped jaw reflecting the emotion of awe and taking in the visual information. In a study by Keltner and Monroy in 2026, they observed patterns of facial expressions induced by awe across China, India, South Korea, Japan and the United States and found that approximately 63% of the elements of awe expressions overlapped.  Further research in Cowen and Keltner (2019, as cited in Keltner &amp; Monroy, 2026) examined more than 1,500 naturalistic photographs of facial expressions (see Figure 3), the analysis identified 28 distinguishable categories of emotional expressions including awe. In figure 3 Awe appears beside related emotions like surprise, fear and interest however it forms its own recognisable category suggesting that awe can include other basic emotions but cannot be reduced to those basic emotions. Furthermore the research in facial expression in Awe is limited in this specific studies participants were asked to imagine awe inspiring experiences rather than an actual response to natural stimuli. 

{{RoundBoxTop|theme=5}}
;Can Awe be measured in EEG
Awe is a complex emotion that is relatively hard to measure psychologically, but can we observe the feeling of Awe through brain activity? The Awe Experiment, developed by Brisbane based artists (Counterpilot) in collaboration with the Queensland Brain Institute, explored this question through an interactive performance at the World Science Festival. To measure brain activity participants were fitted with an EEG and participants listened to awe evoking narratives, Brain activity were translated in colourful lights. Although no scientific results came from this experiment, it is an interesting concept for future research.{{RoundBoxBottom}}

== Awe in everyday life ==

=== Attention and everyday awe ===
Although traditional theories emphasize vastness, awe does not only occur during rare encounters with dramatic landscape. More recent research has introduced this concept of wondering awe, a gentler more accessible experience that can emerge through attentive engagement with ordinary aspects of nature (Büssing et al., 2025). Rather than the exposure of Yosemite mountains, wondering awe emphasises an individual who pauses to notice the warmth of sunlight or the movement of leaves and feels a sense of awe. This contradicts the traditional explanation of awe, if perceived vastness is central to the experience how can something so small like sunlight evoke it? One possibility is that awe is influenced by the meaning and attention given to the stimuli. Slowing down and becoming engulfed in &quot;normal&quot; nature to notice complexity and beauty, establishes this idea of wondering awe. Furthermore the warmth of sunlight is still a complex idea and could extend beyond an individual's mental structure, which still highlights need for accommodation. Büssing et al., (2025) suggests nature exposure alone may not actively improve psychological wellbeing, instead the argument is that wondering awe may help explain how an individual's engagement with nature can inflict awe.

=== Changing nature and awe ===
{{RoundBoxTop|theme=5}}
;Imagine this ...
You walk the same route home every day after work, most days you barely notice the sky. But today the sky is filled with a vivid sunset (see Figure 2), you stop look up and take a brief moment to appreciate the sky, the location has not changed, but why are you experiencing a sense of awe in a familiar environment?
{{RoundBoxBottom}}

[[File:Sunset may 2006 panorama.jpg|thumb|'''Figure 2''': A sunset]]The ability of nature to evoke awe is also influenced by the context in which it is experienced. Natural environments are not static, the same location can appear ordinary in one moment than extraordinary in another moment. Smalley and White (2023), highlighted the concept of ephemeral phenomena such as sunsets, rainbows and storms, and found that these temporary changes influenced the connection of awe towards nature. Their findings suggest that a landscape does not have fixed awe value, instead its capacity to evoke awe may shift with changes in weather, light and time of day (Smalley &amp; White, 2023).

=== Awe in the digital world ===
Traditionally awe in nature has been studied with an individual who physically encounters vast natural environments, but what if we could feel awe through technology? 

Developments in digital technology challenge the idea of foundational awe, and question weather individuals need to be present in nature to experience awe. Virtual technology can recreate digital environments with the same characteristics such as spaciousness, scale and sensory immersion. This idea allows research into whether psychological experience of awe can also occur through simulated nature. Van Houwelingen-Snippe et al., (2020) found that spacious digital nature can make an individual experience awe especially when viewed alone suggesting the idea of perception scale. Similarly, virtual reality can create immersive environments that increase feelings of presence and perceived vastness, providing another method for eliciting awe (Jiang et al., 2024). These findings raise an interesting question, if awe depends on vastness does the nature producing it need to be real? Digital nature can be a useful tool in understanding the psychological process of awe more clearly, and achieve clinical based wellbeing treatments so everyone can feel awe.

== Awe and psychological wellbeing ==
Experiencing Awe in nature can influence an individual's immediate emotional state, it may also change how people perceive themselves and others. Research has associated awe with change in self focus, perspective, social connection and wellbeing (Jiang et al.,2024; Monroy &amp; Keltner, 2023). Understanding these effects may help explain why certain encounter with nature can change our perspectives.

Awe can help explain why some experiences in nature have positive psychological effects, ultimately it is how an individual responds to nature. The experience of awe may also extend beyond personal wellbeing by changing individual perspectives. Awe has been associated with greater prosocial behaviour and social connection (Jiang et al., 2024), while sublime experiences in nature can involve feelings of vitality, freedom and unity with the natural world (Bethelmy &amp; Corraliza, 2019). Awe and wellbeing is complex, because awe directly is not always a positive emotion. Awe can occur alongside negative emotions such as fear or even mixed emotional states (Jiang et al., 2024). Awe and fear can arise when vast powerful aspects of nature are perceived as a threat, such as a bushfire or flood the psychological impacts would probably not be beneficial. This demonstrates that the psychological benefits of nature induced awe may depend on how the experience is emotionally interpreted, particularly whether it is perceived as positive or threatening.

The psychological benefits of nature induced awe may depend on how individuals emotionally interpret their experiences. Liu et al. (2023) investigated this relationship through two experimental studies examining positive and threatening awe.  
{| class=&quot;wikitable&quot;
!Psychological Factor
!Positive Awe
!Negative Awe
|-
|Nature connectedness
|Increased feeling
|Increased Feeling
|-
|Stress releif
|Greater relief from previously stressful experience
|No significant improvement to stress. 
|-
|Life satisfaction
|Significantly improved
|No improvement 
|-
|Psychological Wellebing
|Higher Psychological wellbeing
|No improvement
|-
|Small Self
|Increased feeling of being small
|Increased feeling of being small
|-
|Power and Hope
|Lower feeling of powerlessness
|greater feeling of helplessness and loss of control.
|}

Other research has emphasised the small self effect, Liu et al. (2023) found that feeling small did not significantly explain improvements to satisfaction of life. This may suggest that how an individual perceives awe and its psychological benefits may be personal. 

Quiz&lt;quiz display=&quot;simple&quot;&gt;
{Awe is an easy emotion to understand and is the same distinct emotion as Joy:
|type=&quot;()&quot;}
- True
+ False

{Spaciousness in a digital natural enviroment can contribute to the feeling of awe:
|type=&quot;()&quot;}
+ True
- False
&lt;/quiz&gt;

== Space and Awe ==
{{RoundBoxTop|theme=5}}
;Imagine this ...
Seeing Earth from space, surrounded by the vast darkness of the universe and the unknown, an experience you have never conceptualised. 
{{RoundBoxBottom}}&lt;gallery widths=&quot;250&quot; heights=&quot;250&quot;&gt;
File:The Earth seen from Apollo 17.jpg|'''Figure 4.''' Earth from space
&lt;/gallery&gt;This experience of seeing [[Earth]] from space is an extraordinary experience and is known as the overview effect, where astronauts report intense feelings of awe, wonder and connectedness from viewing earth from a completely different perspective (Yaden et al., 2016). Yaden et al. (2016) analysed that the overview effect involves both perceived vastness and cognitive accommodation, seeing an entire planet you thought you knew from a different perspective like this can challenge individuals mental frames. More interestingly astronauts have reported experiencing self transcendence, describing it as individual concerns becoming less significant and developing a stronger sense to humanity and the planet. More so some even commented that it changed self values and environmental awareness.  

== Conclusion ==
Awe has evolved from an emotion seen as god fearing to an emotion that can be positive and self transcending, Awe demonstrates that our experiences in nature involve more than appreciating beautiful stimuli. From standing beneath mountains, noticing sunsets, the sun on our skin, nature can challenge our understanding of the world and interfere with our mental frameworks. Awe should be seen as it's own distinct emotion, it has attributes of other emotions like joy but should not be limited to other emotions due to its complexities, Nature induced awe must include vastness and need for accommodation, exposure alone cannot elicit awe these two pillars provide as a foundation for understanding awe. The feeling of Awe may appear as positive or negative making it complex and hard to measure in psychology, an interesting form of measurement would be EEG, although the study mentioned in this chapter had no scientific results, it would be interesting to continue future research into brain activity when feeling awe. Wondering awe and ephemeral phenomenon demonstrates that this idea of vastness is not literal size of the stimuli but the conceptual vastness the stimuli holds, and enhances the idea that extraordinary experiences can emerge from ordinary or changing aspects in nature. It can be the most simple aspects like wind moving leaves, rainbows appearing after rain these small things can elicit awe. When we feel awe it can make individuals perceive themselves as different looking at your life from a different lens, encourages a broader thinking and to think less of the self. All of a sudden worries that feel intense in our small lives, don't seem to matter anymore it shifts mental thinking. However although Awe can produce such great moving emotions, it can also inhibit negative feelings it coexists with threat and fear. Originally Awe was associated with the fear of god, fear in Awe although evolved is still prevalent and in nature can appear after events like storms, or seeing a dangerous waterfall. Stimuli like this can influence and activate our sympathetic system and raise heart rate, and can include goosebumps. The emotion of Awe has intense physical and mental changes, so how can we not group an emotion like Awe as its own distinct emotion. Furthermore with rising technologies and with the known physical benefits of Awe, an interesting future idea for research could be in the integration of VR in wellbeing. For elders or people who have to spend their entire lives in hospital, these people should be able to experience nature based awe. To promote connectedness to nature, relief from life stressors and higher life satisfaction. Understanding and being able to measure the psychology of Awe can be used as an important tool, as new tests for mental wellbeing.  
==See also==
List [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example:

* [[Motivation and emotion/Book/2016/Awe as an emotion|Awe as an emotion]] (Book chapter, 2016)
* [[Motivation and emotion/Book/2026/Awe and the diminished self|Awe and the diminished self]] (Book chapter, 2026)
* [[Motivation and emotion/Book/2017/Awe and well-being|Awe and Wellbeing]] (Book chapter, 2017)
* [[Motivation and emotion/Book/2024/Nature connection and emotional well-being|Nature connection and emotional well-being]] (Book chapter, 2024)
* [[Psychological well-being]] (Wikipedia) 

==References==
{{Hanging indent|1=

ReferencesAndy Tix Ph.D. (2015, October 12). The complexity of awe is revealed in how it has been conceptualized across time. Psychology Today. 
https://www.psychologytoday.com/au/blog/the-pursuit-peace/201510/brief-history-awe

Bai, Y., Maruskin, L. A., Chen, S., Gordon, A. M., Stellar, J. E., McNeil, G. D., Peng, K., &amp; Keltner, D. (2017). Awe, the diminished self, and collective engagement: Universals and cultural variations in the small self. Journal of Personality and Social Psychology, 113(2), 185–209. https://doi.org/10.1037/pspa0000087Bonnell, M. (2026, March 4). 

Nature, awe and mental health: Why we feel better outdoors. Peaceful Mind. https://peacefulmind.com.au/2026/03/04/the-role-of-nature-and-awe-in-creating-a-calmer-mind/

Büssing, A., Wilhelm, J., &amp; Rodrigues Recchia, D. (2025). Wondering awe is the mediator of the link between experience of nature and psychological wellbeing—Relevance for public health. International Journal of Environmental Research and Public Health, 22(11), 1679. https://doi.org/10.3390/ijerph22111679

Gordon, A. M., Stellar, J. E., Anderson, C. L., McNeil, G. D., Loew, D., &amp; Keltner, D. (2017). The dark side of the sublime: Distinguishing a threat-based variant of awe. Journal of Personality and Social Psychology, 113(2), 310–328. https://doi.org/10.1037/pspp0000120

Jia, L., Huo, Y., Jing, W., Bai, Y., Meng, Z., &amp; Di, M. (2023). Awe of nature and well-being: Roles of nature connectedness and powerlessness. Personality and Individual Differences, 201, 111946. https://doi.org/10.1016/j.paid.2022.111946

Jiang, T., Hicks, J. A., Yuan, W., Yin, Y., Needy, L., &amp; Vess, M. (2024). The unique nature and psychosocial implications of awe. Nature Reviews Psychology, 3(7), 475–488. https://doi.org/10.1038/s44159-024-00322-z

Keltner, D., &amp; Haidt, J. (2003). Approaching awe, a moral, spiritual, and aesthetic emotion. Cognition and Emotion, 17(2), 297–314. https://doi.org/10.1080/02699930302297

Keltner, D., &amp; Monroy, M. (2026). The expression of awe: Evolutionary origins and cultural elaborations of a basic emotion. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 381(1959), 20250148. PubMed Central. https://doi.org/10.1098/rstb.2025.0148

Monroy, M., &amp; Keltner, D. (2022). Awe as a pathway to mental and physical health. Perspectives on Psychological Science, 18(2), 174569162210948. https://doi.org/10.1177/17456916221094856

Piff, P. K., Dietze, P., Feinberg, M., Stancato, D. M., &amp; Keltner, D. (2015). Awe, the small self, and prosocial behavior. Journal of Personality and Social Psychology, 108(6), 883–899. https://doi.org/10.1037/pspi0000018

Rogers, K. (2010, October 4). Biophilia hypothesis {{!}} description, nature, &amp; human behavior. Encyclopedia Britannica. https://www.britannica.com/science/biophilia-hypothesis

Schurtz, D. R., Blincoe, S., Smith, R. H., Powell, C. A. J., Combs, D. J. Y., &amp; Kim, S. H. (2011). Exploring the social aspects of goose bumps and their role in awe and envy. Motivation and Emotion, 36(2), 205–217. https://doi.org/10.1007/s11031-011-9243-8

Shiota, M. N., Neufeld, S. L., Yeung, W. H., Moser, S. E., &amp; Perea, E. F. (2011). Feeling good: Autonomic nervous system responding in five positive emotions. Emotion, 11(6), 1368–1378. https://doi.org/10.1037/a0024278

Smalley, A. J., &amp; White, M. P. (2023). Beyond blue-sky thinking: Diurnal patterns and ephemeral meteorological phenomena impact appraisals of beauty, awe, and value in urban and natural landscapes. Journal of Environmental Psychology, 86, 101955. https://doi.org/10.1016/j.jenvp.2023.101955

The AWE experiment — Counterpilot. (2025). Counterpilot. https://www.counterpilot.com.au/aweexperiment

van Houwelingen-Snippe, J., van Rompay, T. J. L., de Jong, M. D. T., &amp; Ben Allouch, S. (2020). Does digital nature enhance social aspirations? An experimental study. International Journal of Environmental Research and Public Health, 17(4), 1454. https://doi.org/10.3390/ijerph17041454

Webb, D. (2025, March). Nature imagery and mental well-being. All About Psychology. Substack.Com. https://allaboutpsychology.substack.com/p/nature-imagery-and-mental-well-being

Yaden, D. B., Iwry, J., Slack, K. J., Eichstaedt, J. C., Zhao, Y., Vaillant, G. E., &amp; Newberg, A. B. (2016). The overview effect: Awe and self-transcendent experience in space flight. Psychology of Consciousness: Theory, Research, and Practice, 3(1), 1–11. https://doi.org/10.1037/cns0000086

}}

==External links==
* [https://greatergood.berkeley.edu/video/item/how_scientists_measure_awe_in_the_wild How Scientists Measure Awe in the Wild] (Greater Good Magazine)
* [https://mindfulforestbathing.com.au/the-transformative-power-of-awe-in-nature/ The Transformative Power of Awe in Nature] (Mindful in nature)
* [https://www.psychologytoday.com/au/blog/finding-new-home/201807/the-psychology-awe-awe-in-nature The Psychology of Awe: Awe in Nature] (PsychologyToday)
* [https://ggsc.berkeley.edu/images/uploads/GGSC-JTF_White_Paper-Awe_FINAL.pdf The science of Awe.] (Greater Good Science Centre)
* [https://read.wiley.com/books/9781394219018/page/6/section/top-of-page Understanding Motivation and Emotion] (Wiley)
* [https://allaboutpsychology.substack.com/p/nature-imagery-and-mental-well-being Nature Imagery and Mental Well Being] (David Webb)
* [https://qbi.uq.edu.au/blog/2025/04/what-does-awe-do-our-brains What does awe do to our brains?] (Queensland Brain Institute)
* [https://www.frontiersin.org/journals/virtual-reality/articles/10.3389/frvir.2025.1532991/full Immersive videos of natural and urban environments can enhance awe and psychological well-being] (Frontiers Barth et al., 2025) 

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I am '''James''', a 3rd year psychology student studying ''[[Motivation and emotion|Motivation and Emotion]]'' at the ''[https://www.canberra.edu.au/ University of Canberra]''.

Some of my hobbies are:

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* [[w:Photography|Photography]] and [[w:Videography|videography]]
* Travelling!

== Book chapter I'm working on ==
[[Motivation and emotion/Book/2026/Excitement as an emotion|Excitement as an emotion]]

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[[File:Hiking trails in Walyunga National Park, September 2024 02.jpg|thumb|'''Figure 1.''' Hiking trail in Walyunga National Park]]
I am '''James''', a 3rd year psychology student studying ''[[Motivation and emotion|Motivation and Emotion]]'' at the ''[https://www.canberra.edu.au/ University of Canberra]''.

Some of my hobbies are:

* [[w:Hiking|Hiking]] and nature
* [[w:Photography|Photography]] and [[w:Videography|videography]]
* Travelling!

== Book chapter I'm working on ==
[[Motivation and emotion/Book/2026/Excitement as an emotion|Excitement as an emotion]]

== Social Contributions ==

#[https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FBasal_ganglia_and_motivation&amp;diff=2823470&amp;oldid=2740812 03:46, 20 August 2026 U3292769 - Added title and subtitle (for book chapter: Basal ganglia and motivation)]
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__TOC__

==Overview==
{{RoundBoxTop|theme=3}} 
[[File:Holding hands by wall (Unsplash).jpg|thumb| '''Figure 1'''. Hands holding; representing friends comforting each other]] 

; Imagine this... 

Nathan has noticed his friend, Sam, becoming more distant over the last few months, loosing sleep and enjoyment in their hobbies. Knowing that Sam has a history of depression, Nathan becomes increasingly worried about their wellbeing. 

Uncertain about what to do, Nathan starts looking for ways to reach out to Sam; looking for advice for what to do and resources that they might be able to use. Eventually Nathan finds a course titled Mental Health First Aid and begins to feel empowered to help his friend (see Figure 1).

{{RoundBoxBottom}}
[[wikipedia:Mental_health|Mental health]] is an important determinant of [[wikipedia:Well-being|well-being]] and life satisfaction, is closely related to [[wikipedia:Mental_disorder|mental disorders]], impacts [[wikipedia:Interpersonal_relationship|interpersonal relationships]] and the overall wellbeing of a population (Hill et al., 2023, Gautam et al., 2024). [[wikipedia:Social_stigma|Social stigma]] is one of the largest deterrents from mental health support engagement, discouraging conversations around mental health struggles preventing those in need from finding informal social support and looking for professional help (Ahad et al., 2023).  

In an effort to promote mental health support [[wikipedia:Betty_Kitchener|Betty]] [[wikipedia:Betty_Kitchener|Ann Kitchener AM]] and [[wikipedia:Anthony_Jorm|Anthony Jorm]] developed the [[wikipedia:Mental_health_first_aid|mental health first aid]] (MHFA) program; an evidence-based course designed to equip trainees with skills to support others during times of mental distress or crisis and refer them to professional help when needed (Mental Health First Aid International, 2025). This course has continued to grow and develop into a program used on an international level (Mental Health First Aid International, 2025).  

By understanding the efficacy of the MHFA program and participant [[wikipedia:Motivation|motivation]] using [[wikipedia:Self-determination_theory|self-determination theory]] (SDT) it may be possible to promote engagement with MHFA courses and reduce stigma surrounding mental health on an international level.  {{RoundBoxTop|theme=3}} 
'''Focus questions''' 

* What is the importance of mental health?

* What is Mental Health First Aid?

* What is the impact and necessity of Mental Health First Aid? 

* How does Self-Determination Theory explain motivation to participate in Mental Health First Aid courses? {{RoundBoxBottom}}

== Mental health ==
[[File:Autism-Neurodiversity-or-Mental-health-symbol.svg|thumb|207x207px|'''Figure 2.''' Illustrated image of a brain in silhouetted head]]

Mental health describes a state of mental well-being that enables person’s ability to contribute to society, [[wikipedia:Coping|cope]] with [[wikipedia:Stress_(biology)|stress]], manage interpersonal relationships and [[wikipedia:Decision-making|decision-making]] (APA, 2026, WHO, 2026a, WHO, 2026b) and is one of the largest determinants of well-being and life satisfaction (Hill et al., 2023, Gautam et al., 2024). 

Mental health is informed by numerous factors, including biological predisposition, psychological conditions and social factors such as socio-economic status, social relationships and cultural context (Ahad et al., 2023, WHO, 2026b). Increased exposure to adverse life circumstances is closely related to decreased mental health and well-being whilst increasing chances of having a mental disorder (WHO, 2026a). Mental disorders affect 1/7th of the population, constituting 1.2 billion people internationally (WHO, 2026a), with the most common disorders experienced being [[wikipedia:Major_depressive_disorder|depression]] and [[wikipedia:Anxiety_disorder|anxiety]] (Auerbach et al., 2018, WHO, 2026a). 

Those who experience better mental health and well-being are more likely to have higher educational achievements, healthier lifestyles, increased productivity and decreased engagement with risky behaviours and antisocial behaviours such as crime, violence and substance use (Gautam et al., 2024). Well-being can be divided into eudemonic well-being, where a person experiences a sense of purpose and a desire to contribute to society, and hedonic well-being, where a person experiences more positive feelings (Hill et al., 2023). 

Given the importance of mental health at a societal and individual level, it is imperative that those who are struggling with their mental health have as few barriers preventing them from receiving treatment as possible. Social support and community based interventions are some of the most effective forms of mental health care (Ahad et al., 2023, Jorm et al., 2005, WHO, 2026b), even relatively small improvements to mental health can result in meaningful change to wellbeing. (Ahad et al., 2023). Whilst professional mental health treatment can effectively be provided at low costs (WHO, 2026b), mental health services are significantly under-resourced at an international level (WHO, 2026b). Additionally, social stigmas and cultural biases hinder engagement with mental health services and adherence to treatment plans (Ahad et al., 2023), decreasing the efficacy of existing resources and preventing informal social support amongst community members. An emphasis needs to be placed on the destigmatisation of mental disorders to improve reduce delay in accessing mental health treatment and the promotion of social support at a community level.

== Mental health first aid ==
MHFA is an evidenced-based training program that aims to reduce social stigma surrounding receiving mental health care, increase [[wikipedia:Mental_health_literacy|mental health literacy]] and equip trainees with the skills required to recognise and support those who might be struggling with their mental health; this support may include being a listening ear or redirecting the recipient of help to receiving professional assistance (Mental Health First Aid International, 2025). Three variations of the training program have been developed to specifically assist trainees across different age ranges with different target help groups. Two of the developed programs are designed for trainees to support young people, one of which is designed for teens, while the third program targets adult trainees supporting other adults (Mental Health First Aid International, 2025).  

MHFA introduces trainees to the ALGEE acronym; Assess and assist with crisis, Listen non-judgementally, Give reassurance and information, Encourage professional help, Encourage self-help and support strategies (Forthal et al., 2021, Mental Health First Aid International, 2025, Rodgers et al., 2019).  

Whilst MHFA originates from [[wikipedia:Australia|Australia]], the program has been applied at an international level; reaching over 50 countries and 9 million trainees (Mental Health First Aid International, 2025). The exact content, duration and linguistic phrasing of the program can be adapted to befit the cultural context the course is being used (Forthal et al., 2021), these alterations and studies showing the effects of the program to be consistent over multiple countries helps to support the cross-cultural validity of the program (Morgan et al., 2018).  

MHFA has consistently been found to increase trainees’ abilities to recognise mental disorders and crisis situations, beliefs in effective treatment and mental health literacy and knowledge whilst reducing stigma towards mental disorders (Forthal et al., 2021, Jorm et al., 2005, Morgan et al., 2018, Rodgers et al., 2019). Rodgers et al., (2019) highlights that, in addition to the effects above, trainees’ felt they had developed more [[wikipedia:Emotional_intelligence|emotional intelligence]] and [[wikipedia:Empathy|empathy]], strengthening their relationships and trust with people in their lives. 

Within a longitudinal study, Forthal et al. (2021) found that MHFA trainees who held more confidence in their ability to help others were more likely to report having used their training skills at follow up; this finding close aligns with Jorm et al’s (2005) suggestion that those who have more confidence in their skill feel more empowered to support others. Over multiple studies, majority of those who used their skills reported feeling that they had been helpful and were more likely to help friends and family over co-workers or strangers (Jorm et al., 2005, Rodgers et al., 2019). Providing information for and referring the recipient of help to appropriate professional help, listening without judgement and calming the recipient were the skills most often reported to have been used (Rodgers et al., 2019). Chan et al. (2024) found that trainees felt more confident and a sense of gratitude after using their skills and helping others. 

More research needs to be conducted into the effectiveness of trainee support on recipients (Forthal et al., 2021, Morgan et al., 2018), however, a number of trainees noted that the recipients of their help went on to seek professional assistance or felt that the environment when they started to use their skills (Jorm et al., 2005, Rodgers et al., 2019, Sibeoni et al., 2023). By empowering trainees to help others and removing stigma surrounding mental disorders or seeking mental healthcare is instrumental in creating settings that encourage preventative care, social support and healthy behaviours. 

== Motivation to help ==
By developing an understanding of what motivates MHFA trainees to help others it may be possible to identify other potential trainees and foster motivation to continue creating more supportive cultures around mental health.

=== Motivation to partake in MHFA courses ===
When interviewing MHFA trainees and officers about their motivations for partaking in the program a few common themes begin to emerge; motivation derived by career, motivation derived by a want to help others and motivation derived from experience (Carpini et al., 2024, Chan et al., 2024, Crawford &amp; Burns, 2020, Sibeoni et al., 2023).  

The most common motivator in MHFA participation was previous experience with mental health issues (Carpini et al., 2024, Chan et al., 2024, Crawford &amp; Burns, 2020, Sibeoni et al., 2023). These motivating experiences could range between being personal to being a shared experience with another person, or a combination of both (Carpini et al., 2024, Chan et al., 2024, Crawford &amp; Burns, 2020, Sibeoni et al., 2023). In Crawford &amp; Burn's (2020) study, it was the participants that had the most contact with others experiencing mental health issues that were most likely to have practiced the learnt skills and feel confident in their ability to help others. These initial experiences have been described as sparking participant interest in learning about mental health and wanting to support others. 

This motivation to help others was consistently listed as a factor in enrolling in MHFA courses (Carpini et al., 2024, Chan et al., 2024, Crawford &amp; Burns, 2020, Sibeoni et al., 2023) with participants often reporting a desire to develop skills to support other people in their lives, ranging from friends and family to coworkers (Chan et al., 2024, Crawford &amp; Burns, 2020, Sibeoni et al., 2023). This desire to learn and improve mental health literacy is further outlined by Crawford &amp; Burns (2020) as a motivating factor.  

Majority of research into MHFA training is derived from respondents working in or studying healthcare related fields such as [[wikipedia:Nursing|nursing]], [[wikipedia:Psychiatry|psychiatry]] or [[wikipedia:psychology|psychology]] (Chan et al., 2024, Crawford &amp; Burns, 2020, Sibeoni et al., 2023); this may be a factor in the number of responses referencing motivation to partake in MHFA programs for career purposes. Respondents would highlight wanting to be more prepared when going into practice and how the completion of the course would look good on a resume (Carpini et al., 2024, Crawford &amp; Burns, 2020, Sibeoni et al., 2023). One respondent from Chan and colleagues’ (2024) study reported being required to participate MHFA participation as a part of their job role. 

=== Contextualising MHFA motivation with SDT ===
SDT posits that humans have an inherent drive for self-improvement that can either be supported or impeded by social environments and the ways in which they impact psychological needs (Ryan &amp; Deci, 2020). According to SDT, basic psychological needs consist of competency, relatedness and autonomy and when satisfied positively contribute to well-being (Ryan &amp; Deci, 2017). [[wikipedia:Autonomy|Autonomy]] is a desire to act on one’s own accord and aligned with personal values and self-identity,[[wikipedia:Competence_(human_resources)|competency]] is a desire to feel competent in a task and [[wikipedia:Social_relation|relatedness]] is a desire to connect with others (Ryan &amp; Deci, 2017). SDT describes [[Intrinsic motivation|intrinsic]] motivation as occurring when a person has an inerrant interest in an action, is entirely autonomous and satisfies all basic psychological needs (Ryan &amp; Deci, 2020) whilst [[wikipedia:Motivation#Intrinsic_and_extrinsic|external]] motivation occurs when an additional incentive is required to want to complete an action (Ryan &amp; Deci, 2017).  

Of the explored motivations to partake in MHFA training, both previous experiences and wanting to help are intrinsic motivations whilst career driven participation is an external motivator. Both wanting to help and previous experiences are based on participant values and self-identity. Given desire to help and previous experiences are more significant motivators than career driven motivation, it is likely that participation in MHFA courses stems from an intrinsic motivation that coincides with careers that are also largely intrinsically motivated.  

=== Consequence and integration of intrinsic motivation on MHFA ===
Behaviour that is intrinsically motivated has been found to have positive effects on the wellbeing of the helper (Kelley et al., 2023, Weinstein &amp; Ryan, 2010, Zhang et al., 2024) and prolong satisfaction elicited from [[wikipedia:Prosocial_behavior|prosocial]] behaviours (Zhang et al., 2024) such as those exhibited in MHFA training.   

Those that engage with intrinsic prosocial behaviour are more likely to experience higher levels of mental health, feelings of happiness, well-being, and reduced feelings of depression (Weinstein &amp; Ryan, 2010, Zhang et al., 2024). Weinstein &amp; Ryan (2010) propose that this may be because intrinsic prosocial behaviour fulfils all aspects of basic psychological needs; competency is met by creating tangible changes in the world and utilising skills, relatedness is met by interacting and helping others and autonomy Is inherently met as the behaviour is volitional. This overall satisfaction of psychological needs feeds into itself and prolongs the feelings of happiness associated with the behaviours as seen in Zhang and colleagues' (2024) studies. 

Research has produced evidence of controlled motivation having adverse impacts on participant motivation, emotion and reflection on helping behaviour (Kelley et al., 2023, Weinstein &amp; Ryan, 2010, Zhang et al., 2024); this suggests that it is best to avoid forcing people to participate in MHFA training lest they reflect on their experiences and the program poorly. Instead, the best way to promote participants engaging with MHFA may be to increase their empathy and inherent interest in the subject matter (Pavey et al., 2012). Pavey et al., (2012) found that increasing empathy within participants using empathy-stimulating media increased intrinsic motivation to help and may possibly reinforce future prosocial behaviours. 

If potential participants can be identified and their interest fostered, it might be possible to encourage more people to partake in MHFA training to create positive and supportive environments for those struggling with their mental health.  

== Conclusion ==
Given the pervasiveness of mental health issues (WHO, 2026b) on an international scale, it is imperative that interventions are implemented to reduce the stigma placed on mental health and professional help is accessible. Mental health first aid aims to increase trainees’ confidence in intervening, increasing mental health literacy and social support, reducing stigma and empowering recipients of help to seek professional care (Mental Health First Aid International, 2025). Trainees are often intrinsically motivated, driven by experiences that spark personal prosocial values that encourage helping others (Carpini et al., 2024, Chan et al., 2024, Crawford &amp; Burns, 2020, Sibeoni et al., 2023). Given the impact intrinsically motivated prosocial behaviour has on both helper and recipient well-being (Kelley et al., 2023, Weinstein &amp; Ryan, 2010, Zhang et al., 2024), finding ways to promote intrinsic interests in mental health first aid may be beneficial in creating more friendly environments that facilitate mental health conversations.  

== See also ==

* [[wikipedia:Mental_health_first_aid|Mental health first aid]] (Wikipedia)
* [[Motivation and emotion/Book/2016/Mental health help-seeking motivation|Mental health help-seeking motivation]] (Book chapter, 2016)
* [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|Autonomy and intrinsic motivation in self-determination theory]] (Book chapter, 2025)

== References ==
{{hanging indent|1=

Ahad, A. A., Sanchez-Gonzalez, M., &amp; Junquera, P. (2023). Understanding and addressing mental health stigma across cultures for improving psychiatric care: A narrative review. Cureus, 15(5). https://doi.org/10.7759/cureus.39549

Auerbach, R. P., Mortier, P., Bruffaerts, R., Alonso, J., Benjet, C., Cuijpers, P., Demyttenaere, K., Ebert, D. D., Green, J. G., Hasking, P., Murray, E., Nock, M. K., Pinder-Amaker, S., Sampson, N. A., Stein, D. J., Vilagut, G., Zaslavsky, A. M., Kessler, R. C., &amp; WHO WMH-ICS Collaborators. (2018). WHO World Mental Health Surveys International College Student Project: Prevalence and distribution of mental disorders. Journal of Abnormal Psychology, 127(7), 623–638. https://doi.org/10.1037/abn0000362

American Psychological Association. (n.d.). Mental health. In APA dictionary of psychology. Retrieved October 8, 2026, from https://dictionary.apa.org/mental-health

Carpini, J. A., Booth, J., Johal, S., Odesnik, B., Soon, S., Boyne, E., Clifford, R., Ashoorian, D. (2024). Mental Health First Aid Officers in the Wild: A Qualitative Study of Role Formalisation, Motivation and Support Systems. Advances in Mental Health, 22(3), 249–267. https://doi.org/10.1080/18387357.2024.2320627

Chan, A. E., Kniola, E. T., &amp; Francis, R. (2024). Emotional Experiences of Mental Health First Aid Trainees: A Qualitative Study. Journal of Human Sciences and Extension, 12(2), 3. https://orcid.org/0000-0001-7607-8822 

Crawford, G., Burns, S. (2020). Confidence and motivation to help those with a mental health problem: experiences from a study of nursing students completing mental health first aid (MHFA) training. BMC Medical Education, 20(69). https://doi.org/10.1186/s12909-020-1983-2

Forthal, S., Sadowska, K., Pike, K. M., Balachander, M., Jacobsson, K., Hermosilla, S. (2021). Mental Health First Aid: A Systematic Review of Trainee Behavior and Recipient Mental Health Outcomes. Psychiatric Services, 73(4), 439–446. https://doi.org/10.1176/appi.ps.202100027

Gautam, S., Jain, A., Chaudhary, J., Gautam, M., Gaur, M., &amp; Grover, S. (2024). Concept of mental health and mental well-being, it's determinants and coping strategies. Indian journal of psychiatry, 66(2), 231-244. https://doi.org/10.4103/indianjpsychiatry.indianjpsychiatry_707_23

Hill, T.G., Mackinnon, S.P., Smale, B. (2023). Relative Importance of Individual and Community Predictors of Wellbeing. International Journal of Community Well-Being, 6, 279–299. https://doi.org/10.1007/s42413-023-00196-8

Jorm, A.F., Kitchener, B.A. Mugford, S.K. (2005). Experiences in applying skills learned in a mental health first aid training course: a qualitative study of participants' stories. BMC Psychiatry, 5(43). https://doi.org/10.1186/1471-244X-5-43

Kelley, N. J., Weinstein, N., Smith, E. E., Davis, W. E., Christy, A. G., Sedikides, C., &amp; Schlegel, R. J. (2023). Emotional, motivational and attitudinal consequences of autonomous prosocial behaviour. European Journal of Social Psychology, 53, 486–502. https://doi.org/10.1002/ejsp.2916

Mental Health First Aid Australia. (2025). Homepage {{!}} Mental Health First Aid. Mhfa.Com.Au. https://www.mhfa.com.au/

Morgan, A. J., Ross, A., &amp; Reavley, N. J. (2018). Systematic review and meta-analysis of Mental Health First Aid training: Effects on knowledge, stigma, and helping behaviour. PloS one, 13(5), e0197102. https://doi.org/10.1177/0146167211435940 https://doi.org/10.1371/journal.pone.0197102 

Pavey, L., Greitemeyer, T., &amp; Sparks, P. (2012). “I help because I want to, not because you tell me to” empathy increases autonomously motivated helping. Personality and Social Psychology Bulletin, 38(5), 681-689. https://doi.org/10.1177/0146167211435940

Rodgers, G., Burns, S., Crawford, G. (2021). “I was able to actually do something useful”: evaluating the experiences of university students after completing Mental Health First Aid: a mixed-methods study. Advances in Mental Health, 19(1), 40–62. https://doi.org/10.1080/18387357.2019.1663709

Ryan, R. M., &amp; Deci, E. L. (2017). Self-determination theory: Basic psychological needs in motivation, development, and wellness (pp. xii, 756). The Guilford Press. https://doi.org/10.1521/978.14625/28806 

Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. Contemporary Educational Psychology, 61, 1-11. https://doi.org/10.1016/j.cedpsych.2020.101860 

Sibeoni, J., Ellul, P., Bubola, T., Debiche, Y., Piot, M-A. (2023). Mental health first aid training among healthcare French students: a qualitative study, Frontiers in Medicine, 10. https://doi.org/10.3389/fmed.2023.1268277

Weinstein, N., &amp; Ryan, R. M. (2010). When helping helps: autonomous motivation for prosocial behavior and its influence on well-being for the helper and recipient. Journal of personality and social psychology, 98(2), 222-244. https://doi.org/10.1037/a0016984

World Health Organisation (2026). Mental health. World Health Organisation.https://www.who.int/news-room/fact-sheets/detail/mental-health-strengthening-our-response 

World Health Organisation (2026). Mental health. World Health Organisation.https://www.who.int/news-room/fact-sheets/detail/mental-health-strengthening-our-response 

Zhang, Z., Lv, J., Jiang, T., Chen, X., &amp; Luo, Y. (2024). Motivation matters: Autonomous motivation sustains the happiness from prosocial behavior. Motivation Science, 10(2), 100–109. https://doi.org/10.1037/mot0000319

}}

== External links ==

* [https://www.beyondblue.org.au/get-support/talk-to-a-counsellor Beyond blue] (Beyond Blue)
* [https://www.mhfa.com.au/ mental health first aid international information home page] (mental health first aid)

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__TOC__

==Overview== 
{{RoundBoxTop|theme=3}}
[[File:Finance Exam at the ATC.JPG|thumb|215px|'''Figure 1'''. Confidence doesn't mean you'll always get the answers right. ]]

'''Imagine this...'''

You're sitting in an exam feeling confident becuse {{sp}} the questions seem easy, so you quickly answer each one without second guessing yourself. You leave thinking you've done well, only to receive your result and realise you scored much lower than expected. How could you be so confident and still be so wrong? This is an example of overconfidence, which is the belief 'you are better than you are in reality.' (Johnson et al, 2011)
{{RoundBoxBottom}}

[[Biases in Human Reasoning/Unit 2: Common Biases|Overconfidence]] is an important concept to understand, as confidence can influence the way people make decisions. When people feel certain about their [[Knowing How You Know|judgement]] they may 'ignore or downplay potential risks, leading to poor deicison {{sp}} making.' (Vijaykumar et al, 2023). This points out the fact that confidence can sometimes be misleading when it is used as confirmation that a statement or answer is correct. (Hong et al, 2026) {{g}} conducted a study where participants were asked to remember medical terms and then answer questions regarding the terms. Results showed that most people were overconfident after a short period of exposure to the medical knowledge. These findings suggest that indivudals can feel a short window of knowledge which cause people to feel sufficently confident, even if they don't have accurate information {{rewrite}}.  

Psychological research can also help gauge the miscommunication being overconfidence and decision-making {{rewrite}}. Understanding the different forms of overconfidence, the cognitive processes that contribute to it, and its consequences can help people recognise when their confidence may be incorrect. It also highlights the importance of utilsiing {{sp}} evidence when making a claim, considering alternative options, and opening up to the chance of receving feedback when making decisions.  

{{RoundBoxTop|theme=3}}
'''Focus questions''' 

* What is overconfidence, and why does it occur? 
* How can overconfidence influence decision-making? 
* How can psychological strategies help reduce overconfidence?

{{RoundBoxBottom}} 

==Understanding Overconfidence ==
Overconfidence isn't simply defined as just one type of [[Living the Golden Rule/Working Through Common Misunderstandings|judgement error]] {{ic|instead, explain how it is defined}}. Overconfidence can be distinguished into sub-sections that help to uncover individual's beliefs and reality (Moore et al., 2008): '''overestimation, overplacement and overprecision'''. These forms are crucial to understand as they help explain why people become confident in their own judgements or abilities beyond what avaliable evidence supports.

'''Overestimation''' occurs when individuals overestimate 'their actual perfomance' (Moore et al., 2008). For example, a student may believe that they will acheive {{sp}} a 90% on an exam when their actual result is 70%. The student's confidence in their expected performance is therefore greater than their actual performance. When people face a difficult task, they will overestimate their execution of the task but also believe in a mistanked {{sp}} manner, that they are worse than others. Compared to an easy task however, people will underestimate their perfomance but will believe they are better than others at the task. {{f}}

'''Overplacement''' is 'characterized by the distorted belief that one is better than others.' (Vörös et al., 2025) For example, a student may assume that they perfomed better than most of their classmates because they felt confident in their abilities during an exam. This belief doesn't necessarily come from the assumption that an individual is better than others, but from the overconfidence in their own abilites and how they compare themselves with other people. Resarch has shown that people will place 'themselves as more succesful' {{sp}} than they actually are (Güner Gültekin et al., 2025) when positioned against others. 

'''Overprecision''' is 'the excessive certainity in one's judgement' (Moore, 2022). For example, a student might be extremely certain than an answer on an exam is correct even though they are uncertain about the information involved. Overprescision is important to note as a person can be confident without having enough evidence to justify that level of certainty. 

'''Table 1'''.

Types of overconfidence and how they affect judgement

{| class=&quot;wikitable&quot;
|+
!Types of overconfidence
!What it involves 
!Example
|-
|Overestimation
|Overestimating your own ability or perfomance 
|Believing you will score 90% on an exam when you actually score 70%
|-
|Overplacement
|Believing your ability or performance is better than other people's 
|Assuming you perfomed better than most students in an exam
|-
|Overprecision
|Being excessively certain that your judgement or estimate is correct.
|Being certian that an exam question is correct when there is actually an act of uncertainity
|}

Together, these forms demonstrate that overconfdence can occur in different ways. A person may overestimate their perfomance, have the belief they are more skilled than others or be overly certain that their judgement is accurate. Recognising these differences is important because the same person may experience different forms of overconfidence depending on the decision they are making. 

=== Cognitive processes underlying Overconfidence ===
One factor contributing to overconfidence is the way people assess and interpret information about themselves. A study conducted by (Güner Gültekin et al 2024) which focused on overconfidence in young decision makers concluded that particpants consistently overestimated their own perfomance, assuming they performed better than their peers. People may rely on information that supports their existing view of their abilities while giving less attention to information that challenges it. This demonstrates a 'fixed' level of intelligence in which people will avoid negative information ultimately showing 'significantly more overconfidence.'  (Ehrlinger et al, 2016).

The way people evaluate evidence can also influence their level of confidence. (Griffen et al, 1992) {{g}} distinguished between the '''strength and weight''' of evidence. [[Strength of materials|Strength]] is the 'extremeness of the available evidence' (Griffen et al, 1992) and [[Evaluating Evidence|weight]] refers to the credibility of the information. The study suggests that people's confidence is influenced by how strongly the evidence supports completing explantions, but they may not pay enough attention to the strength and weight of the task at hand. When evidence has high apparent strength but low weight, people may become more confident than the provided evidence. 

For example, imagine a student who remembers several occasons {{sp}} where they answered exam questions correctly. These experiences may feel convincing and lead the student to believe they have strong exam skills. However, they may {{missing}} less attention to previous mistakes where their confidence was inaccurate or where they made mistakes. In this situation, the student may focus on evidence that supports their confidence without fully considering how reliable the evidence is. 

[[Feedback]] is also another important component. People need information about the outcomes of their performance to recognise when their confidence does not match their actual performance. Without meaningful feedback, it can be difficult to identify errors and future judgements. A study conducted by (Lichtenstein et al, 1997) examined {{how}} the relationship between people's confidence and the accuracy of their answers to general-knowledge questions, concluding that people were consistenly {{sp}} overconfident and often expressed greater certainty than their actual accuracy justified.

This suggets that confidence should not be treated as a direct indicator of accuracy. A person can feel certain about a decision while still being unsure, meaning that recognising uncertainity {{sp}} and evaluating evidence are important parts of effective-decision making.

== Overconfidence in Decision-making ==
{{expand}}

=== Overconfidence and Risk-Taking ===
Overconfidence becomes significantly important when considering how people make decisions and the outcomes that follow. Confidence can influence how much information people consider, how willing they are to take risks, and whether they reconsider their initial judgement. As a result, overconfidence may influence decisions across areas such as education, finance, business and everday situations. {{f}}

One potential consequence of overconfidence is the inclincation to take risks. When individuals are overly confident in their skills or accuract, they may disregard the chance of negative circumstances. This can lead them to make decisions without fully considering risks involved {{g}} {{f}}

For example, a person who is highy confident in their ability to predict an investment's perfor {{sp}} may believe they are less likely to experience a loss. Research on finance professionals state 'that the risk they are willing to assume is positvley {{sp}} influenced by overconfidence and [[Optimisation|optimism]] and negatively influenced by [[Risk|risk perception]].' (Broihanne et al, 2014). This reduces the chance indviduals consider uncertainity {{sp}} in certain situations. 

This doesn't necessarliy {{sp}} mean that confidence always results to {{awkward}} risky behaviour. Research suggests that people can adjust their 'estimates less than they shuld {{sp}} have given their actual knowledge.' (Mannes et al, 2013). This is crucial because risk-taking decisions often involve certain outcomes, making accurate assessment of one's own knowledge particularly important. 

{{example}}

=== Consequences of Overconfidence ===
Overconfidence can also effect {{g}} the amount and type of information people use when making decisions. Research shows 'that the restriction of information leads to the processing of a greater proportion of diagnostically relevant information, even within biased processes.' (Rieu et al, 2024). If someone believes they already have the correct answer, they may have less reason to question their judgement.

This can create problems when new information is different to a person's initial belief. An overly confident person is less likely to rethink their decision and more inclined to lead with their original thought. This loops back to the theory (Griffen et al, 1992) that 'confidence is based on privleged access to the [[Evaluating Evidence|evidence]].' (Boldt et al, 2017). People focus heavily on information that appears convincing while overlooking its [[Reliability|reliability.]] {{f}}

Based on these factors {{g}} the consequences of overconfidence can stem beyond a single incorrect judgement. In education, a student may underestimate the amount of preperation for an exam. In business, an individual may become too confident in a predicition {{sp}} about future outcomes. In finance, excessive confidence may contribute to greater willingness to take risks.

{{RoundBoxTop|theme=3}} 
'''Scenario''' 

Jordan has always perfomed well in exams and feels confident about an upcoming psychology test. During the exam, Jordan finds most of the questions easy and quickly selects answers without checking them. Because Jordan feels certain about their knowledge, they decide not to review their answers or consider alternative options. After receving their results, Jordan discovers they scored much lower than expected. Jordan is suprised by the result because they were highly confident that their answers were correct 

{{RoundBoxBottom}}

{{RoundBoxTop|theme=3}} 
;Questions for readers
* Where can you see overconfidence in Jordan's decision-making? 
* What consequences did Jordan's overconfidence have?
* What could Jordan have done differently to make a more considered decision? 
Jordan's behaviour demonstrates '''overprecision''' because they were extremely certain that their answers were accurate. There is also a demonstration of elements of '''overestimation,''' due to Jordan expecting his overall perfomance to be higher than his actual result. Jordan's decision to not review his answers illustrates how high confidence may reduce the motivation to reconsider an initial judgement.

{{RoundBoxBottom}}

== Reducing Overconfidence ==
Although overconfidence can negatively affect [[Decision Making|decision-making]], psychological research suggests that its effects can be reduced by improving how people evaluate their judgements. This is recognised as a process called '''feedback''' which is 'defined as a regulatory mechanism where the effect of an action is fed back to modify and improve future action.' (Ramani et al, 2019 

People can also reduce overconfidence by considering alternative explanations and '''evaluating rather than relying on confidence alone'''. This connects to a thoery{{sp}} called [[Confirmation bias and conflict|confirmation bias]] which 'connotes the seeking or interepeting of evidence in ways that are partial to existing beliefs, expectations of a hypothesis in hand.' ( Nickerson et al, 1998). For important decisions slowing down can provide more time to consider information and uncertainity rather than immediately relying on an initial judgement.  

Together, strategies do not aim to eliminate confidence. Instead they encoruage{{sp}} peope{{sp}} to develop '''better-calibrated confidence,''' where their level of certainty more closley{{sp}} reflects the accuracy and strength of the avlaible{{sp}} evidence.

=== Strategies for Improving Decision-Making ===

&lt;quiz&gt; 
A student is very confident that they will achieve a high exam mark but receives a much lower result than expected. Which concept best describes this situation? 
|type=&quot;()&quot;} 
+ Overconfidence 
- Confirmation bias 
- Risk perception 
- Decision avoidance

{Which strategy could help a person recognise when their confidence is higher than their actual performance? 
|type=&quot;()&quot;} 
- Avoiding feedback 
+ Seeking accurate feedback 
- Making decisions more quickly 
- Relying only on intuition

{What does overprecision involve?
|type=&quot;()&quot;} 
- Believing you performed better than others 
- Overestimating your ability 
+ Being excessively certain that your judgement is correct 
- Avoiding decisions because of uncertainity
&lt;/quiz&gt;

==Conclusion==
Overconfidence can affect the way people make decisions by causing them to overestimate their abilities, believe they perform better than others, or become too certain that their judgements are correct. Although confidence can be helpful, it does not always mean a person is right. 

When people rely too heavily on their own judgement, they may overlook important information, underestimate risks, or miss opportunities to learn from their mistakes. Recognising overconfidence is important because it encoruages people to question their assumptions, consider different perspectives, and pay closer attention to the evidence. 

By learning from feedback and taking time to think decisions through, people can make more informed choices and develop a better understanding of when their confidence is justified. 

==See also==
* [[Biases in Human Reasoning/Unit 3: Biases in Decision-Making]] (Book Chapter, 2026)
* [https://en.wikipedia.org/wiki/Overconfidence_effect Overconfidence effect] (Wikipedia)
* [https://en.wikiversity.org/wiki/Seeking_True_Beliefs Seeking True Beliefs] (Book chapter, 2026)

==References==
{{Hanging indent|1=

Boldt, A., de Gardelle, V., &amp; Yeung, N. (2017). The impact of evidence reliability on sensitivity and bias in decision confidence. Journal of Experimental Psychology: Human Perception and Performance, 43(8), 1520–1531. https://doi.org/10.1037/xhp0000404

Broihanne, M. H., Merli, M., &amp; Roger, P. (2014). Overconfidence, risk perception and the risk-taking behavior of finance professionals. Finance Research Letters, 11(2), 64–73. https://doi.org/10.1016/j.frl.2013.11.002

Ehrlinger, J., Mitchum, A. L., &amp; Dweck, C. S. (2016). Understanding overconfidence: Theories of intelligence, preferential attention, and distorted self-assessment. Journal of Experimental Social Psychology, 63(1), 94–100. https://doi.org/10.1016/j.jesp.2015.11.001

Güner Gültekin, D., &amp; Akıncı, F. N. (2025c). Overestimating the self, outranking the group: An experimental study of overconfidence biases in young decision-makers. Behavioral Sciences, 15(12), 1671. https://doi.org/10.3390/bs15121671

Fischhoff, B., Slovic, P., &amp; Sarah, L. (1977). APA PsycNet. Psycnet.Apa.Org. https://psycnet.apa.org/record/1978-26658-001

Hong, S., Son, L. K., &amp; Kim, K. (2026). Metacognition and diagnostic decision-making: Short “blips” of knowledge and the consequences of overconfidence. Cognitive Research Principles and Implications, 11(1). https://doi.org/10.1186/s41235-026-00717-x

Johnson, D. D. P., &amp; Fowler, J. H. (2011). The evolution of overconfidence. Nature, 477(7364), 317–320. https://doi.org/10.1038/nature10384

Mannes, A. E., &amp; Moore, D. A. (2013). A behavioral demonstration of overconfidence in judgment. Psychological Science, 24(7), 1190–1197. https://doi.org/10.1177/0956797612470700

Moore, D. A. (2022). Overprecision is a property of thinking systems. Psychological Review. https://doi.org/10.1037/rev0000370

Nickerson, R. S. (1998). Confirmation bias: A ubiquitous phenomenon in many guises. Review of General Psychology, 2(2), 175–220. https://doi.org/https://doi.org/10.1037/1089-2680.2.2.175

Ramani, S., Könings, K. D., Ginsburg, S., &amp; van der Vleuten, C. PM. (2019). Feedback redefined: Principles and practice. Journal of General Internal Medicine, 34(5), 744–749. https://doi.org/10.1007/s11606-019-04874-2

Rieu, A., Loibl, K., &amp; Leuders, T. (2024). How context influences the processing of relevant information and judgment accuracy—The role of information restriction in judgment processes in diagnosing misconceptions. Frontiers in Psychology, 15. https://doi.org/10.3389/fpsyg.2024.1405756

Vijaykumar Dhannur, &amp; Shubham Kusane. (2023, June). Managing overconfidence bias in decision making: A review of the literature. unknown. ResearchGate. https://www.researchgate.net/publication/377781931_Managing_Overconfidence_Bias_in_Decision_Making_A_Review_of_the_Literature

Vörös, Z., Kovács, O. B., &amp; Tamás, P. (2025). Overplacement and market entry decisions: A modified market entry game to detect nascent entrepreneurs” goal‐motivated reasoning amid radical uncertainties. Strategic Change, 35(2), 163–175. https://doi.org/10.1002/jsc.2685

}}

== External Sources ==
* [https://www.sciencedirect.com/science/article/pii/S0022103115300135 Understanding overconfidence: Theories of intelligence, peferential attention, and distorted self-assessment] (ScienceDirect)
* [https://www.cogn-iq.org/learn/theory/overconfidence-bias/ Overconfidence Bias] (Cogn-IQ)
* [https://ideas.repec.org/a/ris/tecemp/2212.html&quot; Overconfidence, fear of failure, risk-taking and entrepreneurial intention: The behaviour of undergraduate students] (Ideas)

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      <text bytes="2675" sha1="97yfggny0l8p0qppel8tlgztcovx0jd" xml:space="preserve">== About me ==
Hi, 

My name is Zoe or Zo for short, and I work in the [https://www.aihr.com/blog/learning-and-development/ Learning and Development (L&amp;D) team] within my department in the Australian Public Service. I am currently in my third year, studying a Bachelor of Science in Psychology at the [https://www.canberra.edu.au/ University of Canberra] (UC) alongside working.  

I'm genuinely passionate about the intersection of Human Resource Management (HR) and psychology, much of the theory I've learnt whilst completing this degree feels directly transferable to my current role and to HR more broadly. My long-term career goal is to hopefully become an [[w:Industrial and organizational psychology|industrial psychologist]]. or a HR specialist. 

Within my studies, I have a particular interest in neurodiversity and how diverse considerations can be meaningfully applied across the field, as well as [[w:Emic and etic|emic and etic]] perspectives in understanding behaviour across cultural contexts.

And outside of my academic pursuits, I very much adore most animals and have a sweet spot for horses. As I have been horse riding nearly 10 years.
== Book chapter ==
The topic I have chosen for my book chapter is 

[[Motivation and emotion/Book/2026/Competence motivation in self-determination theory|Competence motivation in self-determination theory]]

I think this topic relates to almost everyone in some way, and it's more layered than it first appears particularly in how it connects back to diversity and individual differences. I'm keen to learn more about it and excited to share my findings with anyone who reads this chapter.

==Social contributions==
# '''04/09/2026''' – Corrected the title of a peer's chapter, ''Awe and the diminished self'', to match the book's formatting conventions. ([https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Awe_and_the_diminished_self&amp;oldid=2831066 see edit])
# '''04/09/2026''' – Posted on the UCLearn discussion board inviting peers to share article recommendations for my topic. ([https://uclearn.canberra.edu.au/courses/20143/discussion_topics/459237 see post])
# '''18/10/2026''' – Copyedited a peer's chapter, ''https://en.wikiversity.org/wiki/Motivation_and_emotion/Book/2026/Self-determination_theory_and_dementia_care'', fixing spelling, grammar and formatting to improve readability. ([PASTE-DIFF-LINK see edit])
# '''18/10/2026''' – Left constructive feedback on the talk page of ''Book Chapter Feedback – Students with Extensions'', with suggestions on referencing and clarity([https://uclearn.canberra.edu.au/courses/20143/discussion_topics/465940?entry_id=826057])</text>
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      <text bytes="2988" sha1="i607qqfz8org45gppsidc4xn1225mic" xml:space="preserve">== About me ==
Hi, 

My name is Zoe or Zo for short, and I work in the [https://www.aihr.com/blog/learning-and-development/ Learning and Development (L&amp;D) team] within my department in the Australian Public Service. I am currently in my third year, studying a Bachelor of Science in Psychology at the [https://www.canberra.edu.au/ University of Canberra] (UC) alongside working.  

I'm genuinely passionate about the intersection of Human Resource Management (HR) and psychology, much of the theory I've learnt whilst completing this degree feels directly transferable to my current role and to HR more broadly. My long-term career goal is to hopefully become an [[w:Industrial and organizational psychology|industrial psychologist]]. or a HR specialist. 

Within my studies, I have a particular interest in neurodiversity and how diverse considerations can be meaningfully applied across the field, as well as [[w:Emic and etic|emic and etic]] perspectives in understanding behaviour across cultural contexts.

And outside of my academic pursuits, I very much adore most animals and have a sweet spot for horses. As I have been horse riding nearly 10 years.
== Book chapter ==
The topic I have chosen for my book chapter is 

[[Motivation and emotion/Book/2026/Competence motivation in self-determination theory|Competence motivation in self-determination theory]]

I think this topic relates to almost everyone in some way, and it's more layered than it first appears particularly in how it connects back to diversity and individual differences. I'm keen to learn more about it and excited to share my findings with anyone who reads this chapter.

==Social contributions==
# '''04/09/2026''' – Corrected the title of a peer's chapter, ''Awe and the diminished self'', to match the book's formatting conventions. ([https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Awe_and_the_diminished_self&amp;oldid=2831066 see edit])
# '''04/09/2026''' – Posted on the UCLearn discussion board inviting peers to share article recommendations for my topic. ([https://uclearn.canberra.edu.au/courses/20143/discussion_topics/459237 see post])
# '''18/10/2026''' – Copyedited a peer's chapter, ''https://en.wikiversity.org/wiki/Motivation_and_emotion/Book/2026/Self-determination_theory_and_dementia_care'', fixing spelling, grammar and formatting to improve readability. (https://en.wikiversity.org/w/index.php?title=User:Zozo06&amp;oldid=2841392 see edits])
 '''18/10/2026'''– Fixed DOI links on a peers book chapter, ''https://en.wikiversity.org/wiki/Motivation_and_emotion/Book/2026/Self-determination_theory_and_dementia_care''(https://en.wikiversity.org/w/index.php?title=User:Zozo06&amp;oldid=2841392 see edits])
# '''18/10/2026''' – Left constructive feedback on the talk page of ''Book Chapter Feedback – Students with Extensions'', with suggestions on referencing and clarity([https://uclearn.canberra.edu.au/courses/20143/discussion_topics/465940?entry_id=826057])</text>
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      <text bytes="2990" sha1="hdp4hkjbfttd8irmu57fq01kgcbi8pj" xml:space="preserve">== About me ==
Hi, 

My name is Zoe or Zo for short, and I work in the [https://www.aihr.com/blog/learning-and-development/ Learning and Development (L&amp;D) team] within my department in the Australian Public Service. I am currently in my third year, studying a Bachelor of Science in Psychology at the [https://www.canberra.edu.au/ University of Canberra] (UC) alongside working.  

I'm genuinely passionate about the intersection of Human Resource Management (HR) and psychology, much of the theory I've learnt whilst completing this degree feels directly transferable to my current role and to HR more broadly. My long-term career goal is to hopefully become an [[w:Industrial and organizational psychology|industrial psychologist]]. or a HR specialist. 

Within my studies, I have a particular interest in neurodiversity and how diverse considerations can be meaningfully applied across the field, as well as [[w:Emic and etic|emic and etic]] perspectives in understanding behaviour across cultural contexts.

And outside of my academic pursuits, I very much adore most animals and have a sweet spot for horses. As I have been horse riding nearly 10 years.
== Book chapter ==
The topic I have chosen for my book chapter is 

[[Motivation and emotion/Book/2026/Competence motivation in self-determination theory|Competence motivation in self-determination theory]]

I think this topic relates to almost everyone in some way, and it's more layered than it first appears particularly in how it connects back to diversity and individual differences. I'm keen to learn more about it and excited to share my findings with anyone who reads this chapter.

==Social contributions==
# '''04/09/2026''' – Corrected the title of a peer's chapter, ''Awe and the diminished self'', to match the book's formatting conventions. ([https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2026/Awe_and_the_diminished_self&amp;oldid=2831066 see edit])
# '''04/09/2026''' – Posted on the UCLearn discussion board inviting peers to share article recommendations for my topic. ([https://uclearn.canberra.edu.au/courses/20143/discussion_topics/459237 see post])
# '''18/10/2026''' – Copyedited a peer's chapter, ''https://en.wikiversity.org/wiki/Motivation_and_emotion/Book/2026/Self-determination_theory_and_dementia_care'', fixing spelling, grammar and formatting to improve readability. (https://en.wikiversity.org/w/index.php?title=User:Zozo06&amp;oldid=2841392 see edits])

 '''18/10/2026'''– Fixed DOI links on a peers book chapter, ''https://en.wikiversity.org/wiki/Motivation_and_emotion/Book/2026/Self-determination_theory_and_dementia_care''(https://en.wikiversity.org/w/index.php?title=User:Zozo06&amp;oldid=2841392 see edits])

# '''18/10/2026''' – Left constructive feedback on the talk page of ''Book Chapter Feedback – Students with Extensions'', with suggestions on referencing and clarity([https://uclearn.canberra.edu.au/courses/20143/discussion_topics/465940?entry_id=826057])</text>
      <sha1>hdp4hkjbfttd8irmu57fq01kgcbi8pj</sha1>
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    <title>Motivation and emotion/Book/2026/Competence motivation in self-determination theory</title>
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      <timestamp>2026-10-18T12:25:07Z</timestamp>
      <contributor>
        <username>Zozo06</username>
        <id>3108967</id>
      </contributor>
      <comment>Removed leftover drafting notes and template text as well as trimmed some sentences to meet the word limit. Added some external links.</comment>
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      <text bytes="30269" sha1="cgwiizd6tpo3i1a6j252qmwq698wgj1" xml:space="preserve">{{title|Competence motivation in self-determination theory:&lt;br&gt;How does the need for competence function within self-determination theory to shape motivation and behaviour?}}
 
__TOC__

==Overview==
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study:'''
[[File:Woman Suffering from Stress at Work (cropped).jpg|thumb|right|260px|'''Figure 1'''. Facing a large, unstructured task without guidance or feedback can leave a person doubting their own ability.]]
 
Maya, a 24-year-old administrative officer, has not opened her biggest project in three days. Instead, she has answered every email and tidied a shared drive she built herself: familiar tasks she knows she can do well.
 
Two months ago, Maya was excited when her manager asked her to review and reorganise more than 500 folders in the team's records system (see Figure 1). But she received no guidance on where to start or what &quot;finished&quot; should look like. Each folder revealed new complexity, and nobody told her if her decisions were right. Some days she thinks, &quot;I just need clearer instructions.&quot; On other days her thoughts turn personal: &quot;I'm hopeless at this.&quot; The first thought sends her to ask for help; the second sends her back to her inbox.
 
''Why does the same task leave a person ready to improve on some days, and ready to give up on others?''
&lt;/div&gt;
 
 
According to [[w:Self-determination theory|self-determination theory]] (SDT), this difference often comes down to the need for [[Motivation and emotion/Book/2011/Self-determination theory|competence]]. Competence is the need to feel effective and capable (Ryan &amp; Deci, 2017). It is one of three basic psychological needs, alongside [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|autonomy]] and [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|relatedness]] (Ryan &amp; Deci, 2017). When competence is satisfied, people tend to show stronger [[Motivation and emotion/Book/2013/Intrinsic motivation|intrinsic motivation]], persistence, and wellbeing (Ryan &amp; Deci, 2020). When it is frustrated, as in Maya's case, people tend to avoid tasks and give up (Vansteenkiste et al., 2020).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Focus questions'''
* What is competence, according to self-determination theory?
* How does competence relate to intrinsic motivation?
* How does cognitive evaluation theory explain why feedback and rewards can strengthen or undermine motivation?
* What happens when the need for competence is frustrated?
* What does research show about how competence can be supported?
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Self-determination theory and competence==
 
===What is self-determination theory?===
SDT is a broad theory of human motivation. It proposes that people have three innate psychological needs: autonomy (feeling volitional), competence (feeling effective), as well as relatedness (feeling connected to others) (Deci &amp; Ryan, 1985; Ryan &amp; Deci, 2017). SDT is made up of six mini-theories, and two of these are central to this chapter. These are cognitive evaluation theory and basic psychological needs theory (Vansteenkiste et al., 2020). SDT is often compared with [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]]. Maslow (1943) proposed a hierarchy in which lower needs, such as physiological and safety needs, generally take priority over higher needs, such as esteem and self-actualisation. He placed mastery within esteem needs. SDT agrees that people strive to feel capable. However, SDT does not rank its needs and considers all three essential at all times (Ryan &amp; Deci, 2017).
 
[[File:MaslowsHierarchyOfNeeds.svg|thumb|right|300px|'''Figure 2'''. Maslow's hierarchy of needs places mastery within esteem needs, near the top of the hierarchy. SDT treats competence as essential at every level.]]
 
Tay and Diener (2011) tested these two views using Gallup World Poll data from 60,865 people in 123 countries. The countries were grouped into eight world regions: Africa, East and South Asia, the former Soviet Union, Latin America, the Middle East, Northern Europe and Anglo nations, Southeast Asia, and Southern Europe. Although people did tend to meet basic and safety needs first, which partly supports Maslow, each need, including mastery, contributed to wellbeing regardless of whether the other needs were met (Tay &amp; Diener, 2011; see Figure 2). The needs that mirror SDT, namely social relationships, autonomy, and mastery, were among the strongest predictors of everyday feelings in all eight regions. One limitation is that the data were cross-sectional. Each need was also measured with only two or three yes or no questions, so the study shows association, not cause. 
 
===What is competence within self-determination theory?===
The idea of competence as a motivational force dates back to White (1959), who challenged the drive theories of his time. He noticed that infants and young animals explore and play, as well as manipulate objects, even when they are fed and safe. He argued that this behaviour comes from a built-in need to have an effect on the environment, which he called effectance motivation. SDT builds on this idea and defines competence as the need to ''feel'' effective, not simply to possess a skill (Ryan &amp; Deci, 2017). This means that a highly skilled person can still feel incompetent if they receive no sign that their efforts are working.
 
According to SDT, competence is best satisfied in well-structured environments that offer ''optimal challenge'', positive feedback, and opportunities for growth (Ryan &amp; Deci, 2020). An optimally challenging task sits slightly beyond a person's current skill, but it comes with enough structure and support to close the gap (Reeve, 2024). Tasks that are too easy offer no sense of growth. Tasks that are too hard, especially without guidance, signal failure. Maya's difficulty illustrates how a lack of structure and feedback can make a manageable task feel too hard.
 
Basic psychological needs theory treats need satisfaction and need frustration as two separate experiences (Vansteenkiste &amp; Ryan, 2013). Need satisfaction is linked to a &quot;bright&quot; pathway of growth and engagement, as well as wellbeing (Vansteenkiste et al., 2020). Need frustration is linked to a &quot;dark&quot; pathway of defensiveness, avoidance, and ill-being (Vansteenkiste et al., 2020). This means that low satisfaction and active frustration are not the same thing. Receiving no feedback may leave a person unfulfilled, but being repeatedly made to feel ineffective actively harms wellbeing (Vansteenkiste &amp; Ryan, 2013). The case study shows this shift. Maya moves from low satisfaction in the early weeks to active frustration after her manager's review.
 
===Competence and self-efficacy===
Competence overlaps closely with [[w:Self-efficacy|self-efficacy]], which is a person's belief that they can successfully perform a specific behaviour (Bandura, 1977). Bandura separated two expectations that shape whether people act. An ''efficacy expectation'' asks &quot;Can I do it?&quot;, and an ''outcome expectation'' asks &quot;Will it work?&quot; Efficacy beliefs are built from four sources: personal mastery experiences, watching similar others succeed, verbal persuasion, and how people interpret their own stress (Bandura, 1977). Of these, mastery experiences are the most powerful.
 
In the case study, several of these sources are weakened. Without feedback, Maya cannot judge whether her decisions are effective, so her real progress is not experienced as mastery. Her manager's comments act as negative persuasion. Her anxiety before opening the project is also likely to be read as evidence that she is not capable. The key difference between the two concepts is that self-efficacy is a belief about a specific future task (Bandura, 1977). In contrast, SDT treats competence as a universal need that shapes motivation and wellbeing over time (Ryan &amp; Deci, 2017). In practice, however, the two are difficult to separate, because both are usually measured with similar self-report questions. Some &quot;competence&quot; findings may therefore simply reflect confidence.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Competence and intrinsic motivation==
 
SDT's central claim is that the ''quality'' of motivation matters as much as its quantity (Ryan &amp; Deci, 2020). Feeling competent affects where people sit on the motivation continuum, as well as how they respond to feedback and rewards (Deci et al., 1999; Ryan &amp; Deci, 2020).
 
===The motivation continuum===
SDT describes motivation as a continuum (Ryan &amp; Deci, 2020; see Figure 3). The continuum ranges from [[Motivation and emotion/Book/2014/Amotivation|amotivation]], meaning no intention to act, through several forms of extrinsic motivation, to intrinsic motivation, meaning acting for enjoyment or interest (Ryan &amp; Deci, 2020). A lack of competence is one of the main causes of amotivation (Ryan &amp; Deci, 2000). It shows in thoughts such as &quot;I can't do this&quot; or &quot;my effort won't make a difference&quot;. In contrast, feeling capable helps people [[w:Internalization (sociology)|internalise]] the value of a task, so the task feels self-endorsed instead of obligatory (Ryan &amp; Deci, 2020). In the case study, Maya's growing avoidance of her project suggests she is sliding toward amotivation.
 
[[File:Taxonomy of motivation.png|thumb|center|600px|'''Figure 3'''. The SDT motivation continuum, ranging from amotivation, through controlled and autonomous forms of extrinsic motivation, to intrinsic motivation.]]
 
===Cognitive evaluation theory===
[[Motivation and emotion/Book/2021/Cognitive evaluation theory and motivation|Cognitive evaluation theory]] (CET) explains how external events such as feedback and rewards affect intrinsic motivation (Ryan &amp; Deci, 2000). According to CET, every such event has a ''controlling'' aspect, which affects autonomy, and an ''informational'' aspect, which affects competence (Ryan &amp; Deci, 2000). Informational feedback increases perceived competence and intrinsic motivation (Deci et al., 1999). In contrast, rewards that feel like pressure tend to undermine intrinsic motivation, even when they signal success (Deci et al., 1999). CET therefore predicts that ''how'' feedback is delivered matters as much as ''what'' it says. Later versions of CET added a third, ''amotivating'' aspect (Ryan &amp; Deci, 2017). Events that signal incompetence, or that effort will not change the outcome, can push people toward amotivation. Criticism that offers no way forward, such as the feedback Maya receives, is likely to carry this amotivating message.
 
Research largely supports these predictions. In Deci's (1971) original experiment, students paid $1 for each puzzle they solved later spent less free time on the puzzles once payment stopped. However, the study had only 24 participants, and the result was only a trend (Deci, 1971). A later meta-analysis of 128 experiments, mostly with children and university students, found a clearer pattern (Deci et al., 1999). People who expected a tangible reward for an interesting task spent less free time on it afterwards. In studies with children, this effect was still present more than a week later. The most damaging rewards were those that signalled a person had fallen short (Deci et al., 1999). Feedback style also mattered. Informational praise increased intrinsic motivation, but the same praise with a controlling phrase such as &quot;just as you ''should''&quot; decreased it (Ryan et al., 1983, as cited in Deci et al., 1999). Negative feedback was less harmful when it included guidance on how to improve (Fong et al., 2019). Rewards did not undermine motivation for boring tasks or when they were unexpected (Deci et al., 1999).
 
CET assumes that these effects work ''through'' perceived competence (Ryan &amp; Deci, 2017). However, relatively few studies have measured perceived competence directly to test this (Deci et al., 1999). The results fit the theory, but the mechanism is more often assumed than demonstrated. Even so, the practical message is consistent. Feedback that identifies a problem, such as &quot;the scope needs to be better defined&quot;, without showing how to fix it is unlikely to support competence (Fong et al., 2019).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{According to cognitive evaluation theory, positive feedback is most likely to increase intrinsic motivation when it is:

|type=&quot;()&quot;}
- Given with a large financial reward
+ Informative and delivered in an autonomy-supportive way
- Delivered as a comparison with other people
- Given constantly, regardless of performance
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==When competence is frustrated==
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's first review'''
 
'''Week 6.''' Maya's manager reviews the project. She acknowledges some progress, then adds that the plan needs to be clearer and the scope better defined. She does not say what a clearer plan looks like or how to narrow the scope. Maya leaves the meeting feeling like a failure. She had enjoyed the first few folders, but now she dreads opening the system.
 
'''What is happening?''' The feedback identified a problem without giving Maya the information to solve it. Her effort no longer seems to lead anywhere, which is when a need starts to be actively frustrated, not just unmet.
&lt;/div&gt;
 
Research supports the distinction between low satisfaction and active frustration (Vansteenkiste &amp; Ryan, 2013). In studies with athletes, Bartholomew et al. (2011) found that controlling coaching led athletes to report need thwarting. Need thwarting, in turn, predicted burnout, depressive symptoms, and negative emotion (Bartholomew et al., 2011). Feeling actively undermined was more harmful than simply not feeling supported. This suggests that vague, critical feedback may be more harmful to Maya than no feedback at all.
 
When people repeatedly experience that their effort makes no difference, they may develop [[w:Learned helplessness|learned helplessness]] (Seligman &amp; Maier, 1967). In classic experiments, dogs exposed to inescapable shocks later failed to escape shocks they could have avoided (Seligman &amp; Maier, 1967). Dogs that had been given control earlier learned to escape. In humans, helplessness reduces effort and is linked to apathy and depression (Abramson et al., 1978). How people explain failure also matters. Explaining failure with stable, uncontrollable causes (&quot;I'm just bad at this&quot;) is more damaging than explaining it with changeable causes (&quot;I didn't have clear instructions&quot;) (Abramson et al., 1978). Maya's two thoughts reflect this difference. &quot;I just need clearer instructions&quot; is a changeable explanation that keeps her trying. &quot;I'm hopeless at this&quot; is a stable explanation that predicts giving up.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Maya thinks, &quot;I'm hopeless at this.&quot; According to research on explanatory style, why is this thought more harmful than &quot;I just need clearer instructions&quot;?

|type=&quot;()&quot;}
- It is less accurate
+ It explains failure with a stable cause she cannot change
- It blames her manager instead of herself
- It focuses on the task rather than on herself
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==What supports or undermines competence?==
 
In two workplace studies, Baard et al. (2004) found that employees' satisfaction of autonomy, competence, and relatedness predicted their wellbeing as well as their performance evaluations. Because supervisors rated performance, this finding is less affected by self-report bias. However, the design still cannot show which came first. A meta-analysis by Van den Broeck et al. (2016) found that competence predicted wellbeing, work attitudes, and behaviour, even after the other two needs were taken into account. This suggests that competence is not simply a by-product of feeling autonomous or connected. Leadership also matters. Managers' autonomy-supportive behaviour is associated with greater need satisfaction as well as more autonomous motivation in employees (Slemp et al., 2018). These findings suggest that the manager's feedback is central to Maya's difficulties.
 
Similar patterns appear in classrooms. Bureau et al. (2022) pooled studies of what predicts student motivation and found that, of the three needs, support for competence was the strongest predictor of autonomous motivation (Bureau et al., 2022). This is a notable finding, because SDT has historically given autonomy the most attention (Ryan &amp; Deci, 2017). It suggests that, at least in classrooms, feeling capable may matter as much as feeling free to choose. However, the meta-analysis draws mainly on correlational studies, so it shows which students do well, but it does not prove that supporting competence causes better outcomes.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==How strong is the evidence?==
The strength of the evidence depends on the methods used. The reward findings, for example, were contested. Cameron and Pierce (1994) found no overall undermining effect and called for &quot;abandoning cognitive evaluation theory&quot; (p. 396). Deci et al. (1999) argued that this result came from mixing boring and interesting tasks, as well as using inappropriate control groups. Laboratory studies also relied mostly on single sessions with children and students (Deci et al., 1999). Self-reported interest also showed much weaker effects than behaviour. Outside the laboratory, most studies are cross-sectional. This makes it unclear whether competence drives motivation or whether motivated people simply feel more competent (Van den Broeck et al., 2016).
 
Some critics have questioned whether basic needs are truly universal, because SDT was developed largely in Western contexts (Chen et al., 2015). However, a study of adults in Belgium, China, Peru, and the United States found that need satisfaction and need frustration predicted wellbeing and ill-being in all four cultures (Chen et al., 2015). Together with the overlap between competence and self-efficacy, these limitations point to the same gap noted in CET. SDT predicts outcomes well, but whether competence itself is the active ingredient remains less certain than the theory suggests (Deci et al., 1999).
 
Most competence research has also used neurotypical samples (Morsink et al., 2022). Morsink et al. (2022) noted that research on [[w:Attention deficit hyperactivity disorder|attention-deficit/hyperactivity disorder]] (ADHD) has mostly studied rewards and overlooked psychological needs. This is despite evidence that children with more ADHD symptoms report lower need satisfaction at school. Frequent correction may push teachers and parents toward controlling styles, which can further frustrate competence (Morsink et al., 2022). Whether supporting competence helps neurodivergent people in the same way remains largely untested.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Applying competence in practice==
The research reviewed so far points to a consistent set of conditions under which people feel capable. Table 1 contrasts environments that support competence with those that thwart it. Each feature is drawn from the evidence above.
 
{| class=&quot;wikitable&quot; style=&quot;margin:1em auto; border-radius:8px;&quot;
|+ '''Table 1'''&lt;br&gt;''Features of Competence-Supportive and Competence-Thwarting Environments''
|-
! style=&quot;background:#eaf3fc;&quot; | Competence-supportive !! style=&quot;background:#fff6e8;&quot; | Competence-thwarting
|-
| Clear expectations about how to succeed || Vague or missing guidance
|-
| Guidance and modelling of &quot;how-to&quot; skills || Being left to work it out alone
|-
| Optimal challenge matched to current skills || Tasks far too hard or too easy
|-
| Specific, informative feedback || Absent, harsh, or controlling feedback
|-
| Long-term goals broken into short-term goals || No sense of progress
|-
| Mistakes framed as learning || Mistakes criticised or punished
|}
 
These features reflect the four sources of competence support in SDT, which are clear expectations, optimal challenge, guidance, and constructive feedback (Reeve, 2024).
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's turnaround'''
 
'''Week 8.''' Maya's manager notices the slowing progress and changes approach. They agree on what &quot;finished&quot; looks like and break the project into stages, starting with the 50 most-used folders.
 
'''Week 12.''' After each stage, Maya receives specific feedback on what is working. She now makes decisions confidently and has started suggesting improvements herself.
 
'''What changed?''' Not the task, but the structure around it: clear expectations, achievable steps, and feedback that informed instead of judged. Each gave Maya evidence that she was effective.
&lt;/div&gt;
 
Breaking Maya's project into stages draws on [[w:Goal setting|goal-setting theory]] (Locke &amp; Latham, 2002). Locke and Latham (2002) reviewed 35 years of laboratory and field studies. They found that specific, challenging goals combined with regular feedback consistently outperform vague &quot;do your best&quot; goals. Specific goals work partly because they show people exactly what success looks like. Each completed stage also acts as a mastery experience, which is the strongest source of self-efficacy (Bandura, 1977). This helps explain why Maya's confidence returned once the work was divided into stages.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Which change would best support Maya's need for competence?

|type=&quot;()&quot;}
- Offering her a bonus if she finishes faster
+ Breaking the project into stages with clear goals and specific feedback
- Telling her she is doing a great job regardless of progress
- Comparing her progress with a colleague's
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Conclusion==
Competence is the need to ''feel'' effective, and SDT treats it as important at all times, not only once basic needs are met (Ryan &amp; Deci, 2017; Tay &amp; Diener, 2011). Feeling competent moves people toward more autonomous motivation (Ryan &amp; Deci, 2020). CET explains why the same feedback can either energise or deflate a person, depending on whether it informs or controls (Deci et al., 1999).
 
When competence is actively frustrated, the consequences are more severe than when it is simply unmet. These consequences range from burnout to the helpless thinking shown in the case study (Abramson et al., 1978; Bartholomew et al., 2011). Research across workplaces, classrooms, and sport suggests that clear expectations and informational feedback, as well as challenges broken into achievable steps, can reverse this pattern (Baard et al., 2004; Locke &amp; Latham, 2002). However, much of this evidence is correlational and rarely tests competence directly as the mechanism (Van den Broeck et al., 2016).
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==See also==
* [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|Autonomy and intrinsic motivation in self-determination theory]] (Book chapter, 2025)
* [[Motivation and emotion/Book/2011/Self-determination theory|Self-determination theory]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Book chapter, 2026)
* [[w:Self-determination theory|Self-determination theory]] (Wikipedia)
* [[w:Self-efficacy|Self-efficacy]] (Wikipedia)
* [[w:Learned helplessness|Learned helplessness]] (Wikipedia)
 
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==References==
{{Hanging indent|1=

Abramson, L. Y., Seligman, M. E., &amp; Teasdale, J. D. (1978). Learned helplessness in humans: Critique and reformulation. Journal of Abnormal Psychology (1965), 87(1), 49–74. https://doi.org/10.1037/0021-843X.87.1.49
 
Baard, P. P., Deci, E. L., &amp; Ryan, R. M. (2004). Intrinsic need satisfaction: a motivational basis of performance and well-being in two work settings. Journal of Applied Social Psychology, 34(10), 2045–2068. https://doi.org/10.1111/j.1559-1816.2004.tb02690.x

Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191–215. https://doi.org/10.1037/0033-295X.84.2.191
 
Bartholomew, K. J., Ntoumanis, N., Ryan, R. M., Bosch, J. A., &amp; Thøgersen-Ntoumani, C. (2011). Self-Determination Theory and Diminished Functioning: The Role of Interpersonal Control and Psychological Need Thwarting. Personality &amp; Social Psychology Bulletin, 37(11), 1459–1473. https://doi.org/10.1177/0146167211413125
 
Bureau, J. S., Howard, J. L., Chong, J. X. Y., &amp; Guay, F. (2022). Pathways to Student Motivation: A Meta-Analysis of Antecedents of Autonomous and Controlled Motivations. Review of Educational Research, 92(1), 46–72. https://doi.org/10.3102/00346543211042426
 
Cameron, J., &amp; Pierce, W. D. (1994). Reinforcement, Reward, and Intrinsic Motivation: A Meta-Analysis. Review of Educational Research, 64(3), 363–423. https://doi.org/10.3102/00346543064003363

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. Motivation and Emotion, 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1

Deci, E. L. (1971). Effects of externally mediated rewards on intrinsic motivation. Journal of Personality and Social Psychology, 18(1), 105–115. https://doi.org/10.1037/h0030644
 
Deci, E. L., Koestner, R., &amp; Ryan, R. M. (1999). A Meta-Analytic Review of Experiments Examining the Effects of Extrinsic Rewards on Intrinsic Motivation. Psychological Bulletin, 125(6), 627–668. https://doi.org/10.1037/0033-2909.125.6.627
 
Deci, E. L., &amp; Ryan, R. M. (1985). ''Intrinsic motivation and self-determination in human behavior''. Springer. https://doi.org/10.1016/j.cedpsych.2020.101860.

Fong, C. J., Patall, E. A., Vasquez, A. C., &amp; Stautberg, S. (2019). A Meta-Analysis of Negative Feedback on Intrinsic Motivation. Educational Psychology Review, 31(1), 121–162. https://doi.org/10.1007/s10648-018-9446-6
 
Locke, E. A., &amp; Latham, G. P. (2002). Building a practically useful theory of goal setting and task motivation: A 35-year odyssey. The American Psychologist, 57(9), 705–717. https://doi.org/10.1037/0003-066X.57.9.705

Maslow, A. H. (1943). A theory of human motivation. ''Psychological Review, 50''(4), 370–396. https://doi.org/10.1037/h0054346
 
Morsink, S., Van der Oord, S., Antrop, I., Danckaerts, M., &amp; Scheres, A. (2022). Studying motivation in ADHD: The role of internal motives and the relevance of self determination theory. ''Journal of Attention Disorders, 26''(8), 1139–1158. https://doi.org/10.1177/10870547211050948
 
Reeve, J. (2024). ''Understanding motivation and emotion'' (8th ed.). Wiley.
 
Ryan, R. M., &amp; Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. ''American Psychologist, 55''(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68
 
Ryan, R. M., &amp; Deci, E. L. (2017). ''Self-determination theory: Basic psychological needs in motivation, development, and wellness''. Guilford Press. https://doi.org/10.1521/978.14625/28806
 
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Slemp, G. R., Kern, M. L., Patrick, K. J., &amp; Ryan, R. M. (2018). Leader autonomy support in the workplace: A meta-analytic review. ''Motivation and Emotion, 42''(5), 706–724. https://doi.org/10.1007/s11031-018-9698-y
 
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Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A review of self-determination theory's basic psychological needs at work. ''Journal of Management, 42''(5), 1195–1229. https://doi.org/10.1177/0149206316632058
 
Vansteenkiste, M., &amp; Ryan, R. M. (2013). On psychological growth and vulnerability: Basic psychological need satisfaction and need frustration as a unifying principle. ''Journal of Psychotherapy Integration, 23''(3), 263–280. https://doi.org/10.1037/a0032359
 
Vansteenkiste, M., Ryan, R. M., &amp; Soenens, B. (2020). Basic psychological need theory: Advancements, critical themes, and future directions. ''Motivation and Emotion, 44''(1), 1–31. https://doi.org/10.1007/s11031-019-09818-1
 
White, R. W. (1959). Motivation reconsidered: The concept of competence. ''Psychological Review, 66''(5), 297–333. https://doi.org/10.1037/h0040934
}}


==External links==
* [https://open.ncl.ac.uk/theories/20/self-determination-theory/
* [https://www.apa.org/ed/schools/teaching-learning/top-twenty/motivation
* [https://positivepsychology.com/self-determination-theory/

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[[Category:Motivation and emotion/Book/Self-determination theory/Competence]]</text>
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      <text bytes="30181" sha1="evdwfoz3obgtmibw03u6ldczr9jeyvw" xml:space="preserve">{{title|Competence motivation in self-determination theory:&lt;br&gt;How does the need for competence function within self-determination theory to shape motivation and behaviour?}}
 
__TOC__

==Overview==
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study:'''
[[File:Woman Suffering from Stress at Work (cropped).jpg|thumb|right|260px|'''Figure 1'''. Facing a large, unstructured task without guidance or feedback can leave a person doubting their own ability.]]
 
Maya, a 24-year-old administrative officer, has not opened her biggest project in three days. Instead, she has answered every email and tidied a shared drive she built herself: familiar tasks she knows she can do well.
 
Two months ago, Maya was excited when her manager asked her to review and reorganise more than 500 folders in the team's records system (see Figure 1). But she received no guidance on where to start or what &quot;finished&quot; should look like. Each folder revealed new complexity, and nobody told her if her decisions were right. Some days she thinks, &quot;I just need clearer instructions.&quot; On other days her thoughts turn personal: &quot;I'm hopeless at this.&quot; The first thought sends her to ask for help; the second sends her back to her inbox.
 
''Why does the same task leave a person ready to improve on some days, and ready to give up on others?''
&lt;/div&gt;
 
 
According to [[w:Self-determination theory|self-determination theory]] (SDT), this difference often comes down to the need for [[Motivation and emotion/Book/2011/Self-determination theory|competence]]. Competence is the need to feel effective and capable (Ryan &amp; Deci, 2017). It is one of three basic psychological needs, alongside [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|autonomy]] and [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|relatedness]] (Ryan &amp; Deci, 2017). When competence is satisfied, people tend to show stronger [[Motivation and emotion/Book/2013/Intrinsic motivation|intrinsic motivation]], persistence, and wellbeing (Ryan &amp; Deci, 2020). When it is frustrated, as in Maya's case, people tend to avoid tasks and give up (Vansteenkiste et al., 2020).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Focus questions'''
* What is competence, according to self-determination theory?
* How does competence relate to intrinsic motivation?
* How does cognitive evaluation theory explain why feedback and rewards can strengthen or undermine motivation?
* What happens when the need for competence is frustrated?
* What does research show about how competence can be supported?
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Self-determination theory and competence==
 
===What is self-determination theory?===
SDT is a broad theory of human motivation. It proposes that people have three innate psychological needs: autonomy (feeling volitional), competence (feeling effective), as well as relatedness (feeling connected to others) (Deci &amp; Ryan, 1985; Ryan &amp; Deci, 2017). SDT is made up of six mini-theories, and two of these are central to this chapter. These are cognitive evaluation theory and basic psychological needs theory (Vansteenkiste et al., 2020). SDT is often compared with [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]]. Maslow (1943) proposed a hierarchy in which lower needs, such as physiological and safety needs, generally take priority over higher needs, such as esteem and self-actualisation. He placed mastery within esteem needs. SDT agrees that people strive to feel capable. However, SDT does not rank its needs and considers all three essential at all times (Ryan &amp; Deci, 2017).
 
[[File:MaslowsHierarchyOfNeeds.svg|thumb|right|300px|'''Figure 2'''. Maslow's hierarchy of needs places mastery within esteem needs, near the top of the hierarchy. SDT treats competence as essential at every level.]]
 
Tay and Diener (2011) tested these two views using Gallup World Poll data from 60,865 people in 123 countries. Although people did tend to meet basic and safety needs first, which partly supports Maslow, each need, including mastery, contributed to wellbeing regardless of whether the other needs were met (Tay &amp; Diener, 2011). The needs that mirror SDT, namely social relationships, autonomy, and mastery, were among the strongest predictors of everyday feelings across all eight world regions studied. One limitation is that the data were cross-sectional. Each need was also measured with only two or three yes or no questions, so the study shows association, not cause.
 
===What is competence within self-determination theory?===
The idea of competence as a motivational force dates back to White (1959), who challenged the drive theories of his time. He noticed that infants and young animals explore and play, as well as manipulate objects, even when they are fed and safe. He argued that this behaviour comes from a built-in need to have an effect on the environment, which he called effectance motivation. SDT builds on this idea and defines competence as the need to ''feel'' effective, not simply to possess a skill (Ryan &amp; Deci, 2017). This means that a highly skilled person can still feel incompetent if they receive no sign that their efforts are working.
 
According to SDT, competence is best satisfied in well-structured environments that offer ''optimal challenge'', positive feedback, and opportunities for growth (Ryan &amp; Deci, 2020). An optimally challenging task sits slightly beyond a person's current skill, but it comes with enough structure and support to close the gap. Tasks that are too easy offer no sense of growth, while tasks that are too hard, especially without guidance, signal failure (Reeve, 2024). Maya's difficulty illustrates how a lack of structure and feedback can make a manageable task feel too hard.
 
Basic psychological needs theory treats need satisfaction and need frustration as two separate experiences (Vansteenkiste &amp; Ryan, 2013). Need satisfaction is linked to a &quot;bright&quot; pathway of growth and engagement, as well as wellbeing (Vansteenkiste et al., 2020). Need frustration is linked to a &quot;dark&quot; pathway of defensiveness, avoidance, and ill-being (Vansteenkiste et al., 2020). Low satisfaction and active frustration are therefore not the same thing. Receiving no feedback may leave a person unfulfilled, but being repeatedly made to feel ineffective actively harms wellbeing (Vansteenkiste &amp; Ryan, 2013). The case study shows this shift. Maya moves from low satisfaction in the early weeks to active frustration after her manager's review, described later in the chapter.
 
===Competence and self-efficacy===
Competence overlaps closely with [[w:Self-efficacy|self-efficacy]], which is a person's belief that they can successfully perform a specific behaviour (Bandura, 1977). Bandura separated two expectations that shape whether people act. An ''efficacy expectation'' asks &quot;Can I do it?&quot;, and an ''outcome expectation'' asks &quot;Will it work?&quot; Efficacy beliefs are built from four sources: personal mastery experiences, watching similar others succeed, verbal persuasion, and how people interpret their own stress (Bandura, 1977). Of these, mastery experiences are the most powerful (Bandura, 1977).
 
In the case study, several of these sources are weakened. Without feedback, Maya cannot judge whether her decisions are effective, so her real progress is not experienced as mastery. As the case study later shows, her manager's comments act as negative persuasion. Her anxiety before opening the project is also likely to be read as evidence that she is not capable. The key difference between the two concepts is that self-efficacy is a belief about a specific future task (Bandura, 1977). In contrast, SDT treats competence as a universal need that shapes motivation and wellbeing over time (Ryan &amp; Deci, 2017). In practice, however, the two are difficult to separate, because both are usually measured with similar self-report questions. Some &quot;competence&quot; findings may therefore simply reflect confidence.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Competence and intrinsic motivation==
 
SDT's central claim is that the ''quality'' of motivation matters as much as its quantity (Ryan &amp; Deci, 2020). Feeling competent affects where people sit on the motivation continuum, as well as how they respond to feedback and rewards (Deci et al., 1999; Ryan &amp; Deci, 2020).
 
===The motivation continuum===
SDT describes motivation as a continuum (Ryan &amp; Deci, 2020; see Figure 3). The continuum ranges from [[Motivation and emotion/Book/2014/Amotivation|amotivation]], meaning no intention to act, through several forms of extrinsic motivation, to intrinsic motivation, meaning acting for enjoyment or interest (Ryan &amp; Deci, 2020). A lack of competence is one of the main causes of amotivation (Ryan &amp; Deci, 2000). It shows in thoughts such as &quot;I can't do this&quot; or &quot;my effort won't make a difference&quot;. In contrast, feeling capable helps people [[w:Internalization (sociology)|internalise]] the value of a task, so the task feels self-endorsed instead of obligatory (Ryan &amp; Deci, 2020). In the case study, Maya's growing avoidance of her project suggests she is sliding toward amotivation.
 
[[File:Taxonomy of motivation.png|thumb|center|600px|'''Figure 3'''. The SDT motivation continuum, ranging from amotivation, through controlled and autonomous forms of extrinsic motivation, to intrinsic motivation.]]
 
===Cognitive evaluation theory===
[[Motivation and emotion/Book/2021/Cognitive evaluation theory and motivation|Cognitive evaluation theory]] (CET) explains how external events such as feedback and rewards affect intrinsic motivation (Ryan &amp; Deci, 2000). According to CET, every such event has a ''controlling'' aspect, which affects autonomy, and an ''informational'' aspect, which affects competence (Ryan &amp; Deci, 2000). Informational feedback increases perceived competence and intrinsic motivation (Deci et al., 1999). In contrast, rewards that feel like pressure tend to undermine intrinsic motivation, even when they signal success (Deci et al., 1999). CET therefore predicts that ''how'' feedback is delivered matters as much as ''what'' it says. Later versions of CET added a third, ''amotivating'' aspect (Ryan &amp; Deci, 2017). Events that signal incompetence, or that effort will not change the outcome, can push people toward amotivation. Criticism that offers no way forward, such as the feedback Maya later receives, is likely to carry this amotivating message.
 
Research generally supports these predictions, although the earliest evidence was weak. RIn Deci's (1971) original experiment, students paid $1 for each puzzle they solved later spent less free time on the puzzles once payment stopped. However, the study had only 24 participants, and the result was only a trend (Deci, 1971). A later meta-analysis of 128 experiments, mostly with children and university students, found a clearer pattern (Deci et al., 1999). People who expected a tangible reward for an interesting task spent less free time on it afterwards. In studies with children, this effect was still present more than a week later. The most damaging rewards were those that signalled a person had fallen short (Deci et al., 1999). Feedback style also mattered. Informational praise increased intrinsic motivation, but the same praise with a controlling phrase such as &quot;just as you ''should''&quot; decreased it (Ryan et al., 1983, as cited in Deci et al., 1999). Negative feedback was less harmful when it included guidance on how to improve (Fong et al., 2019). Rewards did not undermine motivation for boring tasks or when they were unexpected (Deci et al., 1999).
 
CET assumes that these effects work ''through'' perceived competence (Ryan &amp; Deci, 2017). However, relatively few studies have measured perceived competence directly to test this (Deci et al., 1999). The results fit the theory, but the mechanism is more often assumed than demonstrated. Even so, the practical message is consistent. Feedback that identifies a problem, such as &quot;the scope needs to be better defined&quot;, without showing how to fix it is unlikely to support competence (Fong et al., 2019).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{According to cognitive evaluation theory, positive feedback is most likely to increase intrinsic motivation when it is:

|type=&quot;()&quot;}
- Given with a large financial reward
+ Informative and delivered in an autonomy-supportive way
- Delivered as a comparison with other people
- Given constantly, regardless of performance
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==When competence is frustrated==
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's first review'''
 
'''Week 6.''' Maya's manager reviews the project. She acknowledges some progress, then adds that the plan needs to be clearer and the scope better defined. She does not say what a clearer plan looks like or how to narrow the scope. Maya leaves the meeting feeling like a failure. She had enjoyed the first few folders, but now she dreads opening the system.
 
'''What is happening?''' The feedback identified a problem without giving Maya the information to solve it. Her effort no longer seems to lead anywhere, which is when a need starts to be actively frustrated, not just unmet.
&lt;/div&gt;
 
Research supports the distinction between low satisfaction and active frustration (Vansteenkiste &amp; Ryan, 2013). In studies with athletes, Bartholomew et al. (2011) found that controlling coaching led athletes to report need thwarting. Need thwarting, in turn, predicted burnout, depressive symptoms, and negative emotion (Bartholomew et al., 2011). Feeling actively undermined was more harmful than simply not feeling supported. This suggests that vague, critical feedback may be more harmful to Maya than no feedback at all.
 
When people repeatedly experience that their effort makes no difference, they may develop [[w:Learned helplessness|learned helplessness]] (Seligman &amp; Maier, 1967). In classic experiments, dogs exposed to inescapable shocks later failed to escape shocks they could have avoided (Seligman &amp; Maier, 1967). Dogs that had been given control earlier learned to escape. In humans, helplessness reduces effort and is linked to apathy and depression (Abramson et al., 1978). How people explain failure also matters. Explaining failure with stable, uncontrollable causes (&quot;I'm just bad at this&quot;) is more damaging than explaining it with changeable causes (&quot;I didn't have clear instructions&quot;) (Abramson et al., 1978). Maya's two thoughts reflect this difference. &quot;I just need clearer instructions&quot; is a changeable explanation that keeps her trying. &quot;I'm hopeless at this&quot; is a stable explanation that predicts giving up.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Maya thinks, &quot;I'm hopeless at this.&quot; According to research on explanatory style, why is this thought more harmful than &quot;I just need clearer instructions&quot;?

|type=&quot;()&quot;}
- It is less accurate
+ It explains failure with a stable cause she cannot change
- It blames her manager instead of herself
- It focuses on the task rather than on herself
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==What supports or undermines competence?==
 
In two workplace studies, Baard et al. (2004) found that employees' satisfaction of autonomy, competence, and relatedness predicted their wellbeing as well as their performance evaluations. Because supervisors rated performance, this finding is less affected by self-report bias. However, the design still cannot show which came first. A meta-analysis by Van den Broeck et al. (2016) found that competence predicted wellbeing, work attitudes, and behaviour, even after the other two needs were taken into account. This suggests that competence is not simply a by-product of feeling autonomous or connected. Leadership also matters. Managers' autonomy-supportive behaviour is associated with greater need satisfaction as well as more autonomous motivation in employees (Slemp et al., 2018). These findings suggest that the manager's feedback is central to Maya's difficulties.
 
Similar patterns appear in classrooms. Bureau et al. (2022) pooled studies of what predicts student motivation and found that, of the three needs, support for competence was the strongest predictor of autonomous motivation (Bureau et al., 2022). This is a notable finding, because SDT has historically given autonomy the most attention (Ryan &amp; Deci, 2017). It suggests that, at least in classrooms, feeling capable may matter as much as feeling free to choose. However, the meta-analysis draws mainly on correlational studies, so it shows which students do well, but it does not prove that supporting competence causes better outcomes.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
The strength of the evidence depends on the methods used. The reward findings, for example, were contested. Cameron and Pierce (1994) found no overall undermining effect and called for &quot;abandoning cognitive evaluation theory&quot; (p. 396). Deci et al. (1999) argued that this result came from mixing boring and interesting tasks, as well as using inappropriate control groups. Laboratory studies also relied mostly on single sessions with children and students (Deci et al., 1999). Self-reported interest also showed much weaker effects than behaviour. Outside the laboratory, most studies are cross-sectional. This makes it unclear whether competence drives motivation or whether motivated people simply feel more competent (Van den Broeck et al., 2016).
 
Some critics have questioned whether basic needs are truly universal, because SDT was developed largely in Western contexts (Chen et al., 2015). However, a study of adults in Belgium, China, Peru, and the United States found that need satisfaction and need frustration predicted wellbeing and ill-being in all four cultures (Chen et al., 2015). Together with the overlap between competence and self-efficacy, these limitations point to the same gap noted in CET. SDT predicts outcomes well, but whether competence itself is the active ingredient remains less certain than the theory suggests (Deci et al., 1999).
 
Most competence research has also used neurotypical samples (Morsink et al., 2022). Morsink et al. (2022) noted that research on [[w:Attention deficit hyperactivity disorder|attention-deficit/hyperactivity disorder]] (ADHD) has mostly studied rewards and overlooked psychological needs. This is despite evidence that children with more ADHD symptoms report lower need satisfaction at school. (Morsink et al., 2022) Frequent correction may push teachers and parents toward controlling styles, which can further frustrate competence (Morsink et al., 2022). Whether supporting competence helps neurodivergent people in the same way remains largely untested.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Applying competence in practice==
The research reviewed so far points to a consistent set of conditions under which people feel capable. Table 1 contrasts environments that support competence with those that thwart it. Each feature is drawn from the evidence above.
 
{| class=&quot;wikitable&quot; style=&quot;margin:1em auto; border-radius:8px;&quot;
|+ '''Table 1'''&lt;br&gt;''Features of Competence-Supportive and Competence-Thwarting Environments''
|-
! style=&quot;background:#eaf3fc;&quot; | Competence-supportive !! style=&quot;background:#fff6e8;&quot; | Competence-thwarting
|-
| Clear expectations about how to succeed || Vague or missing guidance
|-
| Guidance and modelling of &quot;how-to&quot; skills || Being left to work it out alone
|-
| Optimal challenge matched to current skills || Tasks far too hard or too easy
|-
| Specific, informative feedback || Absent, harsh, or controlling feedback
|-
| Long-term goals broken into short-term goals || No sense of progress
|-
| Mistakes framed as learning || Mistakes criticised or punished
|}
 
These features reflect the four sources of competence support in SDT, which are clear expectations, optimal challenge, guidance, and constructive feedback (Reeve, 2024).
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's turnaround'''
 
'''Week 8.''' Maya's manager notices the slowing progress and changes approach. They agree on what &quot;finished&quot; looks like and break the project into stages, starting with the 50 most-used folders.
 
'''Week 12.''' After each stage, Maya receives specific feedback on what is working. She now makes decisions confidently and has started suggesting improvements herself.
 
'''What changed?''' The structure around how the task would be completed: clear expectations, achievable steps, and feedback that informed instead of judged. Each gave Maya evidence that she was effective.
&lt;/div&gt;
 
Breaking Maya's project into stages draws on [[w:Goal setting|goal-setting theory]] (Locke &amp; Latham, 2002). Locke and Latham (2002) reviewed 35 years of laboratory and field studies. They found that specific, challenging goals combined with regular feedback consistently outperform vague &quot;do your best&quot; goals. Specific goals work partly because they show people exactly what success looks like. Each completed stage also acts as a mastery experience, which is the strongest source of self-efficacy (Bandura, 1977). This helps explain why Maya's confidence returned once the work was divided into stages.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Which change would best support Maya's need for competence?

|type=&quot;()&quot;}
- Offering her a bonus if she finishes faster
+ Breaking the project into stages with clear goals and specific feedback
- Telling her she is doing a great job regardless of progress
- Comparing her progress with a colleague's
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Conclusion==
Competence is the need to ''feel'' effective, and SDT treats it as important at all times, not only once basic needs are met (Ryan &amp; Deci, 2017; Tay &amp; Diener, 2011). Feeling competent moves people toward more autonomous motivation (Ryan &amp; Deci, 2020). CET explains why the same feedback can either energise or deflate a person, depending on whether it informs or controls (Deci et al., 1999).
 
When competence is actively frustrated, the consequences are more severe than when it is simply unmet. These consequences range from burnout to the helpless thinking shown in the case study (Abramson et al., 1978; Bartholomew et al., 2011). Research across workplaces, classrooms suggests that clear expectations and informational feedback, as well as challenges broken into achievable steps, can reverse this pattern (Baard et al., 2004; Locke &amp; Latham, 2002). However, much of this evidence is correlational and rarely tests competence directly as the mechanism (Van den Broeck et al., 2016).
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==See also==
* [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|Autonomy and intrinsic motivation in self-determination theory]] (Book chapter, 2025)
* [[Motivation and emotion/Book/2011/Self-determination theory|Self-determination theory]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Book chapter, 2026)
* [[w:Self-determination theory|Self-determination theory]] (Wikipedia)
* [[w:Self-efficacy|Self-efficacy]] (Wikipedia)
* [[w:Learned helplessness|Learned helplessness]] (Wikipedia)
 
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==References==
{{Hanging indent|1=

Abramson, L. Y., Seligman, M. E., &amp; Teasdale, J. D. (1978). Learned helplessness in humans: Critique and reformulation. Journal of Abnormal Psychology (1965), 87(1), 49–74. https://doi.org/10.1037/0021-843X.87.1.49
 
Baard, P. P., Deci, E. L., &amp; Ryan, R. M. (2004). Intrinsic need satisfaction: a motivational basis of performance and well-being in two work settings. Journal of Applied Social Psychology, 34(10), 2045–2068. https://doi.org/10.1111/j.1559-1816.2004.tb02690.x

Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191–215. https://doi.org/10.1037/0033-295X.84.2.191
 
Bartholomew, K. J., Ntoumanis, N., Ryan, R. M., Bosch, J. A., &amp; Thøgersen-Ntoumani, C. (2011). Self-Determination Theory and Diminished Functioning: The Role of Interpersonal Control and Psychological Need Thwarting. Personality &amp; Social Psychology Bulletin, 37(11), 1459–1473. https://doi.org/10.1177/0146167211413125
 
Bureau, J. S., Howard, J. L., Chong, J. X. Y., &amp; Guay, F. (2022). Pathways to Student Motivation: A Meta-Analysis of Antecedents of Autonomous and Controlled Motivations. Review of Educational Research, 92(1), 46–72. https://doi.org/10.3102/00346543211042426
 
Cameron, J., &amp; Pierce, W. D. (1994). Reinforcement, Reward, and Intrinsic Motivation: A Meta-Analysis. Review of Educational Research, 64(3), 363–423. https://doi.org/10.3102/00346543064003363

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. Motivation and Emotion, 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1

Deci, E. L. (1971). Effects of externally mediated rewards on intrinsic motivation. Journal of Personality and Social Psychology, 18(1), 105–115. https://doi.org/10.1037/h0030644
 
Deci, E. L., Koestner, R., &amp; Ryan, R. M. (1999). A Meta-Analytic Review of Experiments Examining the Effects of Extrinsic Rewards on Intrinsic Motivation. Psychological Bulletin, 125(6), 627–668. https://doi.org/10.1037/0033-2909.125.6.627
 
Deci, E. L., &amp; Ryan, R. M. (1985). ''Intrinsic motivation and self-determination in human behavior''. Springer. https://doi.org/10.1016/j.cedpsych.2020.101860.

Fong, C. J., Patall, E. A., Vasquez, A. C., &amp; Stautberg, S. (2019). A Meta-Analysis of Negative Feedback on Intrinsic Motivation. Educational Psychology Review, 31(1), 121–162. https://doi.org/10.1007/s10648-018-9446-6
 
Locke, E. A., &amp; Latham, G. P. (2002). Building a practically useful theory of goal setting and task motivation: A 35-year odyssey. The American Psychologist, 57(9), 705–717. https://doi.org/10.1037/0003-066X.57.9.705

Maslow, A. H. (1943). A theory of human motivation. ''Psychological Review, 50''(4), 370–396. https://doi.org/10.1037/h0054346
 
Morsink, S., Van der Oord, S., Antrop, I., Danckaerts, M., &amp; Scheres, A. (2022). Studying motivation in ADHD: The role of internal motives and the relevance of self determination theory. ''Journal of Attention Disorders, 26''(8), 1139–1158. https://doi.org/10.1177/10870547211050948
 
Reeve, J. (2024). ''Understanding motivation and emotion'' (8th ed.). Wiley.
 
Ryan, R. M., &amp; Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. ''American Psychologist, 55''(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68
 
Ryan, R. M., &amp; Deci, E. L. (2017). ''Self-determination theory: Basic psychological needs in motivation, development, and wellness''. Guilford Press. https://doi.org/10.1521/978.14625/28806
 
Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology, 61'', Article 101860. https://doi.org/10.1016/j.cedpsych.2020.101860
 
Seligman, M. E. P., &amp; Maier, S. F. (1967). Failure to escape traumatic shock. ''Journal of Experimental Psychology, 74''(1), 1–9. https://doi.org/10.1037/h0024514
 
Slemp, G. R., Kern, M. L., Patrick, K. J., &amp; Ryan, R. M. (2018). Leader autonomy support in the workplace: A meta-analytic review. ''Motivation and Emotion, 42''(5), 706–724. https://doi.org/10.1007/s11031-018-9698-y
 
Tay, L., &amp; Diener, E. (2011). Needs and subjective well-being around the world. ''Journal of Personality and Social Psychology, 101''(2), 354–365. https://doi.org/10.1037/a0023779
 
Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A review of self-determination theory's basic psychological needs at work. ''Journal of Management, 42''(5), 1195–1229. https://doi.org/10.1177/0149206316632058
 
Vansteenkiste, M., &amp; Ryan, R. M. (2013). On psychological growth and vulnerability: Basic psychological need satisfaction and need frustration as a unifying principle. ''Journal of Psychotherapy Integration, 23''(3), 263–280. https://doi.org/10.1037/a0032359
 
Vansteenkiste, M., Ryan, R. M., &amp; Soenens, B. (2020). Basic psychological need theory: Advancements, critical themes, and future directions. ''Motivation and Emotion, 44''(1), 1–31. https://doi.org/10.1007/s11031-019-09818-1
 
White, R. W. (1959). Motivation reconsidered: The concept of competence. ''Psychological Review, 66''(5), 297–333. https://doi.org/10.1037/h0040934
}}


==External links==
* [https://open.ncl.ac.uk/theories/20/self-determination-theory/
* [https://www.apa.org/ed/schools/teaching-learning/top-twenty/motivation
* [https://positivepsychology.com/self-determination-theory/

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      <text bytes="30178" sha1="4gla6vp8oozlb8jizplt8nvfvlkhu15" xml:space="preserve">{{title|Competence motivation in self-determination theory:&lt;br&gt;How does the need for competence function within self-determination theory to shape motivation and behaviour?}}
 
__TOC__

==Overview==
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study:'''
[[File:Woman Suffering from Stress at Work (cropped).jpg|thumb|right|260px|'''Figure 1'''. Facing a large, unstructured task without guidance or feedback can leave a person doubting their own ability.]]
 
Maya, a 24-year-old administrative officer, has not opened her biggest project in three days. Instead, she has answered every email and tidied a shared drive she built herself: familiar tasks she knows she can do well.
 
Two months ago, Maya was excited when her manager asked her to review and reorganise more than 500 folders in the team's records system (see Figure 1). But she received no guidance on where to start or what &quot;finished&quot; should look like. Each folder revealed new complexity, and nobody told her if her decisions were right. Some days she thinks, &quot;I just need clearer instructions.&quot; On other days her thoughts turn personal: &quot;I'm hopeless at this.&quot; The first thought sends her to ask for help; the second sends her back to her inbox.
 
''Why does the same task leave a person ready to improve on some days, and ready to give up on others?''
&lt;/div&gt;
 
 
According to [[w:Self-determination theory|self-determination theory]] (SDT), this difference often comes down to the need for [[Motivation and emotion/Book/2011/Self-determination theory|competence]]. Competence is the need to feel effective and capable (Ryan &amp; Deci, 2017). It is one of three basic psychological needs, alongside [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|autonomy]] and [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|relatedness]] (Ryan &amp; Deci, 2017). When competence is satisfied, people tend to show stronger [[Motivation and emotion/Book/2013/Intrinsic motivation|intrinsic motivation]], persistence, and wellbeing (Ryan &amp; Deci, 2020). When it is frustrated, as in Maya's case, people tend to avoid tasks and give up (Vansteenkiste et al., 2020).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Focus questions'''
* What is competence, according to self-determination theory?
* How does competence relate to intrinsic motivation?
* How does cognitive evaluation theory explain why feedback and rewards can strengthen or undermine motivation?
* What happens when the need for competence is frustrated?
* What does research show about how competence can be supported?
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Self-determination theory and competence==
 
===What is self-determination theory?===
SDT is a broad theory of human motivation. It proposes that people have three innate psychological needs: autonomy (feeling volitional), competence (feeling effective), as well as relatedness (feeling connected to others) (Deci &amp; Ryan, 1985; Ryan &amp; Deci, 2017). SDT is made up of six mini-theories, and two of these are central to this chapter. These are cognitive evaluation theory and basic psychological needs theory (Vansteenkiste et al., 2020). SDT is often compared with [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]]. Maslow (1943) proposed a hierarchy in which lower needs, such as physiological and safety needs, generally take priority over higher needs, such as esteem and self-actualisation. He placed mastery within esteem needs. SDT agrees that people strive to feel capable. However, SDT does not rank its needs and considers all three essential at all times (Ryan &amp; Deci, 2017).
 
[[File:MaslowsHierarchyOfNeeds.svg|thumb|right|300px|'''Figure 2'''. Maslow's hierarchy of needs places mastery within esteem needs, near the top of the hierarchy. SDT treats competence as essential at every level.]]
 
Tay and Diener (2011) tested these two views using Gallup World Poll data from 60,865 people in 123 countries. Although people did tend to meet basic and safety needs first, which partly supports Maslow, each need, including mastery, contributed to wellbeing regardless of whether the other needs were met (Tay &amp; Diener, 2011). The needs that mirror SDT, namely social relationships, autonomy, and mastery, were among the strongest predictors of everyday feelings across all eight world regions studied. One limitation is that the data were cross-sectional. Each need was also measured with only two or three yes or no questions, so the study shows association, not cause.
 
===What is competence within self-determination theory?===
The idea of competence as a motivational force dates back to White (1959), who challenged the drive theories of his time. He noticed that infants and young animals explore and play, as well as manipulate objects, even when they are fed and safe. He argued that this behaviour comes from a built-in need to have an effect on the environment, which he called effectance motivation. SDT builds on this idea and defines competence as the need to ''feel'' effective, not simply to possess a skill (Ryan &amp; Deci, 2017). This means that a highly skilled person can still feel incompetent if they receive no sign that their efforts are working.
 
According to SDT, competence is best satisfied in well-structured environments that offer ''optimal challenge'', positive feedback, and opportunities for growth (Ryan &amp; Deci, 2020). An optimally challenging task sits slightly beyond a person's current skill, but it comes with enough structure and support to close the gap. Tasks that are too easy offer no sense of growth, while tasks that are too hard, especially without guidance, signal failure (Reeve, 2024). Maya's difficulty illustrates how a lack of structure and feedback can make a manageable task feel too hard.
 
Basic psychological needs theory treats need satisfaction and need frustration as two separate experiences (Vansteenkiste &amp; Ryan, 2013). Need satisfaction is linked to a &quot;bright&quot; pathway of growth and engagement, as well as wellbeing (Vansteenkiste et al., 2020). Need frustration is linked to a &quot;dark&quot; pathway of defensiveness, avoidance, and ill-being (Vansteenkiste et al., 2020). Low satisfaction and active frustration are therefore not the same thing. Receiving no feedback may leave a person unfulfilled, but being repeatedly made to feel ineffective actively harms wellbeing (Vansteenkiste &amp; Ryan, 2013). The case study shows this shift. Maya moves from low satisfaction in the early weeks to active frustration after her manager's review, described later in the chapter.
 
===Competence and self-efficacy===
Competence overlaps closely with [[w:Self-efficacy|self-efficacy]], which is a person's belief that they can successfully perform a specific behaviour (Bandura, 1977). Bandura separated two expectations that shape whether people act. An ''efficacy expectation'' asks &quot;Can I do it?&quot;, and an ''outcome expectation'' asks &quot;Will it work?&quot; Efficacy beliefs are built from four sources: personal mastery experiences, watching similar others succeed, verbal persuasion, and how people interpret their own stress (Bandura, 1977). Of these, mastery experiences are the most powerful (Bandura, 1977).
 
In the case study, several of these sources are weakened. Without feedback, Maya cannot judge whether her decisions are effective, so her real progress is not experienced as mastery. As the case study later shows, her manager's comments act as negative persuasion. Her anxiety before opening the project is also likely to be read as evidence that she is not capable. The key difference between the two concepts is that self-efficacy is a belief about a specific future task (Bandura, 1977). In contrast, SDT treats competence as a universal need that shapes motivation and wellbeing over time (Ryan &amp; Deci, 2017). In practice, however, the two are difficult to separate, because both are usually measured with similar self-report questions. Some &quot;competence&quot; findings may therefore simply reflect confidence.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Competence and intrinsic motivation==
 
SDT's central claim is that the ''quality'' of motivation matters as much as its quantity (Ryan &amp; Deci, 2020). Feeling competent affects where people sit on the motivation continuum, as well as how they respond to feedback and rewards (Deci et al., 1999; Ryan &amp; Deci, 2020).
 
===The motivation continuum===
SDT describes motivation as a continuum (Ryan &amp; Deci, 2020; see Figure 3). The continuum ranges from [[Motivation and emotion/Book/2014/Amotivation|amotivation]], meaning no intention to act, through several forms of extrinsic motivation, to intrinsic motivation, meaning acting for enjoyment or interest (Ryan &amp; Deci, 2020). A lack of competence is one of the main causes of amotivation (Ryan &amp; Deci, 2000). It shows in thoughts such as &quot;I can't do this&quot; or &quot;my effort won't make a difference&quot;. In contrast, feeling capable helps people [[w:Internalization (sociology)|internalise]] the value of a task, so the task feels self-endorsed instead of obligatory (Ryan &amp; Deci, 2020). In the case study, Maya's growing avoidance of her project suggests she is sliding toward amotivation.
 
[[File:Taxonomy of motivation.png|thumb|center|600px|'''Figure 3'''. The SDT motivation continuum, ranging from amotivation, through controlled and autonomous forms of extrinsic motivation, to intrinsic motivation.]]
 
===Cognitive evaluation theory===
[[Motivation and emotion/Book/2021/Cognitive evaluation theory and motivation|Cognitive evaluation theory]] (CET) explains how external events such as feedback and rewards affect intrinsic motivation (Ryan &amp; Deci, 2000). According to CET, every such event has a ''controlling'' aspect, which affects autonomy, and an ''informational'' aspect, which affects competence (Ryan &amp; Deci, 2000). Informational feedback increases perceived competence and intrinsic motivation (Deci et al., 1999). In contrast, rewards that feel like pressure tend to undermine intrinsic motivation, even when they signal success (Deci et al., 1999). CET therefore predicts that ''how'' feedback is delivered matters as much as ''what'' it says. Later versions of CET added a third, ''amotivating'' aspect (Ryan &amp; Deci, 2017). Events that signal incompetence, or that effort will not change the outcome, can push people toward amotivation. Criticism that offers no way forward, such as the feedback Maya later receives, is likely to carry this amotivating message.
 
Research generally supports these predictions, although the earliest evidence was weak. RIn Deci's (1971) original experiment, students paid $1 for each puzzle they solved later spent less free time on the puzzles once payment stopped. However, the study had only 24 participants, and the result was only a trend (Deci, 1971). A later meta-analysis of 128 experiments, mostly with children and university students, found a clearer pattern (Deci et al., 1999). People who expected a tangible reward for an interesting task spent less free time on it afterwards. In studies with children, this effect was still present more than a week later. The most damaging rewards were those that signalled a person had fallen short (Deci et al., 1999). Feedback style also mattered. Informational praise increased intrinsic motivation, but the same praise with a controlling phrase such as &quot;just as you ''should''&quot; decreased it (Ryan et al., 1983, as cited in Deci et al., 1999). Negative feedback was less harmful when it included guidance on how to improve (Fong et al., 2019). Rewards did not undermine motivation for boring tasks or when they were unexpected (Deci et al., 1999).
 
CET assumes that these effects work ''through'' perceived competence (Ryan &amp; Deci, 2017). However, relatively few studies have measured perceived competence directly to test this (Deci et al., 1999). The results fit the theory, but the mechanism is more often assumed than demonstrated. Even so, the practical message is consistent. Feedback that identifies a problem, such as &quot;the scope needs to be better defined&quot;, without showing how to fix it is unlikely to support competence (Fong et al., 2019).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{According to cognitive evaluation theory, positive feedback is most likely to increase intrinsic motivation when it is:

|type=&quot;()&quot;}
- Given with a large financial reward
+ Informative and delivered in an autonomy-supportive way
- Delivered as a comparison with other people
- Given constantly, regardless of performance
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==When competence is frustrated==
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's first review'''
 
'''Week 6.''' Maya's manager reviews the project. She acknowledges some progress, then adds that the plan needs to be clearer and the scope better defined. She does not say what a clearer plan looks like or how to narrow the scope. Maya leaves the meeting feeling like a failure. She had enjoyed the first few folders, but now she dreads opening the system.
 
'''What is happening?''' The feedback identified a problem without giving Maya the information to solve it. Her effort no longer seems to lead anywhere, which is when a need starts to be actively frustrated, not just unmet.
&lt;/div&gt;
 
Research supports the distinction between low satisfaction and active frustration (Vansteenkiste &amp; Ryan, 2013). In studies with athletes, Bartholomew et al. (2011) found that controlling coaching led athletes to report need thwarting. Need thwarting, in turn, predicted burnout, depressive symptoms, and negative emotion (Bartholomew et al., 2011). Feeling actively undermined was more harmful than simply not feeling supported. This suggests that vague, critical feedback may be more harmful to Maya than no feedback at all.
 
When people repeatedly experience that their effort makes no difference, they may develop [[w:Learned helplessness|learned helplessness]] (Seligman &amp; Maier, 1967). In classic experiments, dogs exposed to inescapable shocks later failed to escape shocks they could have avoided (Seligman &amp; Maier, 1967). Dogs that had been given control earlier learned to escape. In humans, helplessness reduces effort and is linked to apathy and depression (Abramson et al., 1978). How people explain failure also matters. Explaining failure with stable, uncontrollable causes (&quot;I'm just bad at this&quot;) is more damaging than explaining it with changeable causes (&quot;I didn't have clear instructions&quot;) (Abramson et al., 1978). Maya's two thoughts reflect this difference. &quot;I just need clearer instructions&quot; is a changeable explanation that keeps her trying. &quot;I'm hopeless at this&quot; is a stable explanation that predicts giving up.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Maya thinks, &quot;I'm hopeless at this.&quot; According to research on explanatory style, why is this thought more harmful than &quot;I just need clearer instructions&quot;?

|type=&quot;()&quot;}
- It is less accurate
+ It explains failure with a stable cause she cannot change
- It blames her manager instead of herself
- It focuses on the task rather than on herself
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==What supports or undermines competence?==
 
In two workplace studies, Baard et al. (2004) found that employees' satisfaction of autonomy, competence, and relatedness predicted their wellbeing as well as their performance evaluations. Because supervisors rated performance, this finding is less affected by self-report bias. However, the design still cannot show which came first. A meta-analysis by Van den Broeck et al. (2016) found that competence predicted wellbeing, work attitudes, and behaviour, even after the other two needs were taken into account. This suggests that competence is not simply a by-product of feeling autonomous or connected. Leadership also matters. Managers' autonomy-supportive behaviour is associated with greater need satisfaction as well as more autonomous motivation in employees (Slemp et al., 2018). These findings suggest that the manager's feedback is central to Maya's difficulties.
 
Similar patterns appear in classrooms. Bureau et al. (2022) pooled studies of what predicts student motivation and found that, of the three needs, support for competence was the strongest predictor of autonomous motivation (Bureau et al., 2022). This is a notable finding, because SDT has historically given autonomy the most attention (Ryan &amp; Deci, 2017). It suggests that, at least in classrooms, feeling capable may matter as much as feeling free to choose. However, the meta-analysis draws mainly on correlational studies, so it shows which students do well, but it does not prove that supporting competence causes better outcomes.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
The strength of the evidence depends on the methods used. The reward findings, for example, were contested. Cameron and Pierce (1994) found no overall undermining effect and called for &quot;abandoning cognitive evaluation theory&quot; (p. 396). Deci et al. (1999) argued that this result came from mixing boring and interesting tasks, as well as using inappropriate control groups. Laboratory studies also relied mostly on single sessions with children and students (Deci et al., 1999). Self-reported interest also showed much weaker effects than behaviour. Outside the laboratory, most studies are cross-sectional. This makes it unclear whether competence drives motivation or whether motivated people simply feel more competent (Van den Broeck et al., 2016).
 
Some critics have questioned whether basic needs are truly universal, because SDT was developed largely in Western contexts (Chen et al., 2015). However, a study of adults in Belgium, China, Peru, and the United States found that need satisfaction and need frustration predicted wellbeing and ill-being in all four cultures (Chen et al., 2015). Together with the overlap between competence and self-efficacy, these limitations point to the same gap noted in CET. SDT predicts outcomes well, but whether competence itself is the active ingredient remains less certain than the theory suggests (Deci et al., 1999).
 
Most competence research has also used neurotypical samples (Morsink et al., 2022). Morsink et al. (2022) noted that research on [[w:Attention deficit hyperactivity disorder|attention-deficit/hyperactivity disorder]] (ADHD) has mostly studied rewards and overlooked psychological needs. This is despite evidence that children with more ADHD symptoms report lower need satisfaction at school. (Morsink et al., 2022) Frequent correction may push teachers and parents toward controlling styles, which can further frustrate competence (Morsink et al., 2022). Whether supporting competence helps neurodivergent people in the same way remains largely untested.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Applying competence in practice==
The research reviewed so far points to a consistent set of conditions under which people feel capable. Table 1 contrasts environments that support competence with those that thwart it. Each feature is drawn from the evidence above.
 
{| class=&quot;wikitable&quot; style=&quot;margin:1em auto; border-radius:8px;&quot;
|+ '''Table 1'''&lt;br&gt;''Features of Competence-Supportive and Competence-Thwarting Environments''
|-
! style=&quot;background:#eaf3fc;&quot; | Competence-supportive !! style=&quot;background:#fff6e8;&quot; | Competence-thwarting
|-
| Clear expectations about how to succeed || Vague or missing guidance
|-
| Guidance and modelling of &quot;how-to&quot; skills || Being left to work it out alone
|-
| Optimal challenge matched to current skills || Tasks far too hard or too easy
|-
| Specific, informative feedback || Absent, harsh, or controlling feedback
|-
| Long-term goals broken into short-term goals || No sense of progress
|-
| Mistakes framed as learning || Mistakes criticised or punished
|}
 
These features reflect the four sources of competence support in SDT, which are clear expectations, optimal challenge, guidance, and constructive feedback (Reeve, 2024).
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's turnaround'''
 
'''Week 8.''' Maya's manager notices the slowing progress and changes approach. They agree on what &quot;finished&quot; looks like and break the project into stages, starting with the 50 most-used folders.
 
'''Week 12.''' After each stage, Maya receives specific feedback on what is working. She now makes decisions confidently and has started suggesting improvements herself.
 
'''What changed?''' The structure around how the task would be completed: clear expectations, achievable steps, and feedback that informed instead of judged. Each gave Maya evidence that she was effective.
&lt;/div&gt;
 
Breaking Maya's project into stages draws on [[w:Goal setting|goal-setting theory]] (Locke &amp; Latham, 2002). Locke and Latham (2002) reviewed 35 years of laboratory and field studies. They found that specific, challenging goals combined with regular feedback consistently outperform vague &quot;do your best&quot; goals. Specific goals work partly because they show people exactly what success looks like. Each completed stage also acts as a mastery experience, which is the strongest source of self-efficacy (Bandura, 1977). This helps explain why Maya's confidence returned once the work was divided into stages.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Which change would best support Maya's need for competence?

|type=&quot;()&quot;}
- Offering her a bonus if she finishes faster
+ Breaking the project into stages with clear goals and specific feedback
- Telling her she is doing a great job regardless of progress
- Comparing her progress with a colleague's
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Conclusion==
Competence is the need to ''feel'' effective, and SDT treats it as important at all times, not only once basic needs are met (Ryan &amp; Deci, 2017; Tay &amp; Diener, 2011). Feeling competent moves people toward more autonomous motivation (Ryan &amp; Deci, 2020). CET explains why the same feedback can either energise or deflate a person, depending on whether it informs or controls (Deci et al., 1999).
 
When competence is actively frustrated, the consequences are more severe than when it is simply unmet. These consequences range from burnout to the helpless thinking shown in the case study (Abramson et al., 1978; Bartholomew et al., 2011). Research across workplaces, classrooms suggests that clear expectations and informational feedback, as well as challenges broken into achievable steps, can reverse this pattern (Baard et al., 2004; Locke &amp; Latham, 2002). However, much of this evidence is correlational and rarely tests competence directly as the mechanism (Van den Broeck et al., 2016).
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==See also==
* [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|Autonomy and intrinsic motivation in self-determination theory]] (Book chapter, 2025)
* [[Motivation and emotion/Book/2011/Self-determination theory|Self-determination theory]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Book chapter, 2026)
* [[w:Self-determination theory|Self-determination theory]] (Wikipedia)
* [[w:Self-efficacy|Self-efficacy]] (Wikipedia)
* [[w:Learned helplessness|Learned helplessness]] (Wikipedia)
 
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==References==
{{Hanging indent|1=

Abramson, L. Y., Seligman, M. E., &amp; Teasdale, J. D. (1978). Learned helplessness in humans: Critique and reformulation. Journal of Abnormal Psychology (1965), 87(1), 49–74. https://doi.org/10.1037/0021-843X.87.1.49
 
Baard, P. P., Deci, E. L., &amp; Ryan, R. M. (2004). Intrinsic need satisfaction: a motivational basis of performance and well-being in two work settings. Journal of Applied Social Psychology, 34(10), 2045–2068. https://doi.org/10.1111/j.1559-1816.2004.tb02690.x

Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191–215. https://doi.org/10.1037/0033-295X.84.2.191
 
Bartholomew, K. J., Ntoumanis, N., Ryan, R. M., Bosch, J. A., &amp; Thøgersen-Ntoumani, C. (2011). Self-Determination Theory and Diminished Functioning: The Role of Interpersonal Control and Psychological Need Thwarting. Personality &amp; Social Psychology Bulletin, 37(11), 1459–1473. https://doi.org/10.1177/0146167211413125
 
Bureau, J. S., Howard, J. L., Chong, J. X. Y., &amp; Guay, F. (2022). Pathways to Student Motivation: A Meta-Analysis of Antecedents of Autonomous and Controlled Motivations. Review of Educational Research, 92(1), 46–72. https://doi.org/10.3102/00346543211042426
 
Cameron, J., &amp; Pierce, W. D. (1994). Reinforcement, Reward, and Intrinsic Motivation: A Meta-Analysis. Review of Educational Research, 64(3), 363–423. https://doi.org/10.3102/00346543064003363

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. Motivation and Emotion, 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1

Deci, E. L. (1971). Effects of externally mediated rewards on intrinsic motivation. Journal of Personality and Social Psychology, 18(1), 105–115. https://doi.org/10.1037/h0030644
 
Deci, E. L., Koestner, R., &amp; Ryan, R. M. (1999). A Meta-Analytic Review of Experiments Examining the Effects of Extrinsic Rewards on Intrinsic Motivation. Psychological Bulletin, 125(6), 627–668. https://doi.org/10.1037/0033-2909.125.6.627
 
Deci, E. L., &amp; Ryan, R. M. (1985). ''Intrinsic motivation and self-determination in human behavior''. Springer. https://doi.org/10.1016/j.cedpsych.2020.101860.

Fong, C. J., Patall, E. A., Vasquez, A. C., &amp; Stautberg, S. (2019). A Meta-Analysis of Negative Feedback on Intrinsic Motivation. Educational Psychology Review, 31(1), 121–162. https://doi.org/10.1007/s10648-018-9446-6
 
Locke, E. A., &amp; Latham, G. P. (2002). Building a practically useful theory of goal setting and task motivation: A 35-year odyssey. The American Psychologist, 57(9), 705–717. https://doi.org/10.1037/0003-066X.57.9.705

Maslow, A. H. (1943). A theory of human motivation. ''Psychological Review, 50''(4), 370–396. https://doi.org/10.1037/h0054346
 
Morsink, S., Van der Oord, S., Antrop, I., Danckaerts, M., &amp; Scheres, A. (2022). Studying motivation in ADHD: The role of internal motives and the relevance of self determination theory. ''Journal of Attention Disorders, 26''(8), 1139–1158. https://doi.org/10.1177/10870547211050948
 
Reeve, J. (2024). ''Understanding motivation and emotion'' (8th ed.). Wiley.
 
Ryan, R. M., &amp; Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. ''American Psychologist, 55''(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68
 
Ryan, R. M., &amp; Deci, E. L. (2017). ''Self-determination theory: Basic psychological needs in motivation, development, and wellness''. Guilford Press. https://doi.org/10.1521/978.14625/28806
 
Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology, 61'', Article 101860. https://doi.org/10.1016/j.cedpsych.2020.101860
 
Seligman, M. E. P., &amp; Maier, S. F. (1967). Failure to escape traumatic shock. ''Journal of Experimental Psychology, 74''(1), 1–9. https://doi.org/10.1037/h0024514
 
Slemp, G. R., Kern, M. L., Patrick, K. J., &amp; Ryan, R. M. (2018). Leader autonomy support in the workplace: A meta-analytic review. ''Motivation and Emotion, 42''(5), 706–724. https://doi.org/10.1007/s11031-018-9698-y
 
Tay, L., &amp; Diener, E. (2011). Needs and subjective well-being around the world. ''Journal of Personality and Social Psychology, 101''(2), 354–365. https://doi.org/10.1037/a0023779
 
Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A review of self-determination theory's basic psychological needs at work. ''Journal of Management, 42''(5), 1195–1229. https://doi.org/10.1177/0149206316632058
 
Vansteenkiste, M., &amp; Ryan, R. M. (2013). On psychological growth and vulnerability: Basic psychological need satisfaction and need frustration as a unifying principle. ''Journal of Psychotherapy Integration, 23''(3), 263–280. https://doi.org/10.1037/a0032359
 
Vansteenkiste, M., Ryan, R. M., &amp; Soenens, B. (2020). Basic psychological need theory: Advancements, critical themes, and future directions. ''Motivation and Emotion, 44''(1), 1–31. https://doi.org/10.1007/s11031-019-09818-1
 
White, R. W. (1959). Motivation reconsidered: The concept of competence. ''Psychological Review, 66''(5), 297–333. https://doi.org/10.1037/h0040934
}}


==External links==
* https://open.ncl.ac.uk/theories/20/self-determination-theory/
* https://www.apa.org/ed/schools/teaching-learning/top-twenty/motivation
* https://positivepsychology.com/self-determination-theory/

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      <text bytes="30217" sha1="o4rsx9crv4cay41vo3qtijos1zh1row" xml:space="preserve">{{title|Competence motivation in self-determination theory:&lt;br&gt;How does the need for competence function within self-determination theory to shape motivation and behaviour?}}
 __TOC__

==Overview==
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study:'''
[[File:Woman Suffering from Stress at Work (cropped).jpg|thumb|right|260px|'''Figure 1'''. Facing a large, unstructured task without guidance or feedback can leave a person doubting their own ability.]]
 
Maya, a 24-year-old administrative officer, has not opened her biggest project in three days. Instead, she has answered every email and tidied a shared drive she built herself: familiar tasks she knows she can do well.
 
Two months ago, Maya was excited when her manager asked her to review and reorganise more than 500 folders in the team's records system (see Figure 1). But she received no guidance on where to start or what &quot;finished&quot; should look like. Each folder revealed new complexity, and nobody told her if her decisions were right. Some days she thinks, &quot;I just need clearer instructions.&quot; On other days her thoughts turn personal: &quot;I'm hopeless at this.&quot; The first thought sends her to ask for help; the second sends her back to her inbox.
 
''Why does the same task leave a person ready to improve on some days, and ready to give up on others?''
&lt;/div&gt;
 
 
According to [[w:Self-determination theory|self-determination theory]] (SDT), this difference often comes down to the need for [[Motivation and emotion/Book/2011/Self-determination theory|competence]]. Competence is the need to feel effective and capable (Ryan &amp; Deci, 2017). It is one of three basic psychological needs, alongside [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|autonomy]] and [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|relatedness]] (Ryan &amp; Deci, 2017). When competence is satisfied, people tend to show stronger [[Motivation and emotion/Book/2013/Intrinsic motivation|intrinsic motivation]], persistence, and wellbeing (Ryan &amp; Deci, 2020). When it is frustrated, as in Maya's case, people tend to avoid tasks and give up (Vansteenkiste et al., 2020).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Focus questions'''
* What is competence, according to self-determination theory?
* How does competence relate to intrinsic motivation?
* How does cognitive evaluation theory explain why feedback and rewards can strengthen or undermine motivation?
* What happens when the need for competence is frustrated?
* What does research show about how competence can be supported?
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Self-determination theory and competence==
 
===What is self-determination theory?===
SDT is a broad theory of human motivation. It proposes that people have three innate psychological needs: autonomy (feeling volitional), competence (feeling effective), as well as relatedness (feeling connected to others) (Deci &amp; Ryan, 1985; Ryan &amp; Deci, 2017). SDT is made up of six mini-theories, and two of these are central to this chapter. These are cognitive evaluation theory and basic psychological needs theory (Vansteenkiste et al., 2020). SDT is often compared with [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]]. Maslow (1943) proposed a hierarchy in which lower needs, such as physiological and safety needs, generally take priority over higher needs, such as esteem and self-actualisation. He placed mastery within esteem needs. SDT agrees that people strive to feel capable. However, SDT does not rank its needs and considers all three essential at all times (Ryan &amp; Deci, 2017).
 
[[File:MaslowsHierarchyOfNeeds.svg|thumb|right|300px|'''Figure 2'''. Maslow's hierarchy of needs places mastery within esteem needs, near the top of the hierarchy. SDT treats competence as essential at every level.]]
 
Tay and Diener (2011) tested these two views using Gallup World Poll data from 60,865 people in 123 countries. Although people did tend to meet basic and safety needs first, which partly supports Maslow, each need, including mastery, contributed to wellbeing regardless of whether the other needs were met (Tay &amp; Diener, 2011). The needs that mirror SDT, namely social relationships, autonomy, and mastery, were among the strongest predictors of everyday feelings across all eight world regions studied. One limitation is that the data were cross-sectional. Each need was also measured with only two or three yes or no questions, so the study shows association, not cause.
 
===What is competence within self-determination theory?===
The idea of competence as a motivational force dates back to White (1959), who challenged the drive theories of his time. He noticed that infants and young animals explore and play, as well as manipulate objects, even when they are fed and safe. He argued that this behaviour comes from a built-in need to have an effect on the environment, which he called effectance motivation. SDT builds on this idea and defines competence as the need to ''feel'' effective, not simply to possess a skill (Ryan &amp; Deci, 2017). This means that a highly skilled person can still feel incompetent if they receive no sign that their efforts are working.
 
According to SDT, competence is best satisfied in well-structured environments that offer ''[[wikipedia:Challenge_point_framework|optimal challenge]]'', positive feedback, and opportunities for growth (Ryan &amp; Deci, 2020). An optimally challenging task sits slightly beyond a person's current skill, but it comes with enough structure and support to close the gap. Tasks that are too easy offer no sense of growth, while tasks that are too hard, especially without guidance, signal failure (Reeve, 2024). Maya's difficulty illustrates how a lack of structure and feedback can make a manageable task feel too hard.
 
Basic psychological needs theory treats need satisfaction and need frustration as two separate experiences (Vansteenkiste &amp; Ryan, 2013). Need satisfaction is linked to a &quot;bright&quot; pathway of growth and engagement, as well as wellbeing (Vansteenkiste et al., 2020). Need frustration is linked to a &quot;dark&quot; pathway of defensiveness, avoidance, and ill-being (Vansteenkiste et al., 2020). Low satisfaction and active frustration are therefore not the same thing. Receiving no feedback may leave a person unfulfilled, but being repeatedly made to feel ineffective actively harms wellbeing (Vansteenkiste &amp; Ryan, 2013). The case study shows this shift. Maya moves from low satisfaction in the early weeks to active frustration after her manager's review, described later in the chapter.
 
===Competence and self-efficacy===
Competence overlaps closely with [[w:Self-efficacy|self-efficacy]], which is a person's belief that they can successfully perform a specific behaviour (Bandura, 1977). Bandura separated two expectations that shape whether people act. An ''efficacy expectation'' asks &quot;Can I do it?&quot;, and an ''outcome expectation'' asks &quot;Will it work?&quot; Efficacy beliefs are built from four sources: personal mastery experiences, watching similar others succeed, verbal persuasion, and how people interpret their own stress (Bandura, 1977). Of these, mastery experiences are the most powerful (Bandura, 1977).
 
In the case study, several of these sources are weakened. Without feedback, Maya cannot judge whether her decisions are effective, so her real progress is not experienced as mastery. As the case study later shows, her manager's comments act as negative persuasion. Her anxiety before opening the project is also likely to be read as evidence that she is not capable. The key difference between the two concepts is that self-efficacy is a belief about a specific future task (Bandura, 1977). In contrast, SDT treats competence as a universal need that shapes motivation and wellbeing over time (Ryan &amp; Deci, 2017). In practice, however, the two are difficult to separate, because both are usually measured with similar self-report questions. Some &quot;competence&quot; findings may therefore simply reflect confidence.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Competence and intrinsic motivation==
 
SDT's central claim is that the ''quality'' of motivation matters as much as its quantity (Ryan &amp; Deci, 2020). Feeling competent affects where people sit on the motivation continuum, as well as how they respond to feedback and rewards (Deci et al., 1999; Ryan &amp; Deci, 2020).
 
===The motivation continuum===
SDT describes motivation as a continuum (Ryan &amp; Deci, 2020; see Figure 3). The continuum ranges from [[Motivation and emotion/Book/2014/Amotivation|amotivation]], meaning no intention to act, through several forms of extrinsic motivation, to intrinsic motivation, meaning acting for enjoyment or interest (Ryan &amp; Deci, 2020). A lack of competence is one of the main causes of amotivation (Ryan &amp; Deci, 2000). It shows in thoughts such as &quot;I can't do this&quot; or &quot;my effort won't make a difference&quot;. In contrast, feeling capable helps people [[w:Internalization (sociology)|internalise]] the value of a task, so the task feels self-endorsed instead of obligatory (Ryan &amp; Deci, 2020). In the case study, Maya's growing avoidance of her project suggests she is sliding toward amotivation.
 
[[File:Taxonomy of motivation.png|thumb|center|600px|'''Figure 3'''. The SDT motivation continuum, ranging from amotivation, through controlled and autonomous forms of extrinsic motivation, to intrinsic motivation.]]
 
===Cognitive evaluation theory===
[[Motivation and emotion/Book/2021/Cognitive evaluation theory and motivation|Cognitive evaluation theory]] (CET) explains how external events such as feedback and rewards affect intrinsic motivation (Ryan &amp; Deci, 2000). According to CET, every such event has a ''controlling'' aspect, which affects autonomy, and an ''informational'' aspect, which affects competence (Ryan &amp; Deci, 2000). Informational feedback increases perceived competence and intrinsic motivation (Deci et al., 1999). In contrast, rewards that feel like pressure tend to undermine intrinsic motivation, even when they signal success (Deci et al., 1999). CET therefore predicts that ''how'' feedback is delivered matters as much as ''what'' it says. Later versions of CET added a third, ''amotivating'' aspect (Ryan &amp; Deci, 2017). Events that signal incompetence, or that effort will not change the outcome, can push people toward amotivation. Criticism that offers no way forward, such as the feedback Maya later receives, is likely to carry this amotivating message.
 
Research generally supports these predictions, although the earliest evidence was weak. RIn Deci's (1971) original experiment, students paid $1 for each puzzle they solved later spent less free time on the puzzles once payment stopped. However, the study had only 24 participants, and the result was only a trend (Deci, 1971). A later meta-analysis of 128 experiments, mostly with children and university students, found a clearer pattern (Deci et al., 1999). People who expected a tangible reward for an interesting task spent less free time on it afterwards. In studies with children, this effect was still present more than a week later. The most damaging rewards were those that signalled a person had fallen short (Deci et al., 1999). Feedback style also mattered. Informational praise increased intrinsic motivation, but the same praise with a controlling phrase such as &quot;just as you ''should''&quot; decreased it (Ryan et al., 1983, as cited in Deci et al., 1999). Negative feedback was less harmful when it included guidance on how to improve (Fong et al., 2019). Rewards did not undermine motivation for boring tasks or when they were unexpected (Deci et al., 1999).
 
CET assumes that these effects work ''through'' perceived competence (Ryan &amp; Deci, 2017). However, relatively few studies have measured perceived competence directly to test this (Deci et al., 1999). The results fit the theory, but the mechanism is more often assumed than demonstrated. Even so, the practical message is consistent. Feedback that identifies a problem, such as &quot;the scope needs to be better defined&quot;, without showing how to fix it is unlikely to support competence (Fong et al., 2019).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{According to cognitive evaluation theory, positive feedback is most likely to increase intrinsic motivation when it is:

|type=&quot;()&quot;}
- Given with a large financial reward
+ Informative and delivered in an autonomy-supportive way
- Delivered as a comparison with other people
- Given constantly, regardless of performance
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==When competence is frustrated==
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's first review'''
 
'''Week 6.''' Maya's manager reviews the project. She acknowledges some progress, then adds that the plan needs to be clearer and the scope better defined. She does not say what a clearer plan looks like or how to narrow the scope. Maya leaves the meeting feeling like a failure. She had enjoyed the first few folders, but now she dreads opening the system.
 
'''What is happening?''' The feedback identified a problem without giving Maya the information to solve it. Her effort no longer seems to lead anywhere, which is when a need starts to be actively frustrated, not just unmet.
&lt;/div&gt;
 
Research supports the distinction between low satisfaction and active frustration (Vansteenkiste &amp; Ryan, 2013). In studies with athletes, Bartholomew et al. (2011) found that controlling coaching led athletes to report need thwarting. Need thwarting, in turn, predicted burnout, depressive symptoms, and negative emotion (Bartholomew et al., 2011). Feeling actively undermined was more harmful than simply not feeling supported. This suggests that vague, critical feedback may be more harmful to Maya than no feedback at all.
 
When people repeatedly experience that their effort makes no difference, they may develop [[w:Learned helplessness|learned helplessness]] (Seligman &amp; Maier, 1967). In classic experiments, dogs exposed to inescapable shocks later failed to escape shocks they could have avoided (Seligman &amp; Maier, 1967). Dogs that had been given control earlier learned to escape. In humans, helplessness reduces effort and is linked to apathy and depression (Abramson et al., 1978). How people explain failure also matters. Explaining failure with stable, uncontrollable causes (&quot;I'm just bad at this&quot;) is more damaging than explaining it with changeable causes (&quot;I didn't have clear instructions&quot;) (Abramson et al., 1978). Maya's two thoughts reflect this difference. &quot;I just need clearer instructions&quot; is a changeable explanation that keeps her trying. &quot;I'm hopeless at this&quot; is a stable explanation that predicts giving up.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Maya thinks, &quot;I'm hopeless at this.&quot; According to research on explanatory style, why is this thought more harmful than &quot;I just need clearer instructions&quot;?

|type=&quot;()&quot;}
- It is less accurate
+ It explains failure with a stable cause she cannot change
- It blames her manager instead of herself
- It focuses on the task rather than on herself
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==What supports or undermines competence?==
 
In two workplace studies, Baard et al. (2004) found that employees' satisfaction of autonomy, competence, and relatedness predicted their wellbeing as well as their performance evaluations. Because supervisors rated performance, this finding is less affected by self-report bias. However, the design still cannot show which came first. A meta-analysis by Van den Broeck et al. (2016) found that competence predicted wellbeing, work attitudes, and behaviour, even after the other two needs were taken into account. This suggests that competence is not simply a by-product of feeling autonomous or connected. Leadership also matters. Managers' autonomy-supportive behaviour is associated with greater need satisfaction as well as more autonomous motivation in employees (Slemp et al., 2018). These findings suggest that the manager's feedback is central to Maya's difficulties.
 
Similar patterns appear in classrooms. Bureau et al. (2022) pooled studies of what predicts student motivation and found that, of the three needs, support for competence was the strongest predictor of autonomous motivation (Bureau et al., 2022). This is a notable finding, because SDT has historically given autonomy the most attention (Ryan &amp; Deci, 2017). It suggests that, at least in classrooms, feeling capable may matter as much as feeling free to choose. However, the meta-analysis draws mainly on correlational studies, so it shows which students do well, but it does not prove that supporting competence causes better outcomes.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
The strength of the evidence depends on the methods used. The reward findings, for example, were contested. Cameron and Pierce (1994) found no overall undermining effect and called for &quot;abandoning cognitive evaluation theory&quot; (p. 396). Deci et al. (1999) argued that this result came from mixing boring and interesting tasks, as well as using inappropriate control groups. Laboratory studies also relied mostly on single sessions with children and students (Deci et al., 1999). Self-reported interest also showed much weaker effects than behaviour. Outside the laboratory, most studies are cross-sectional. This makes it unclear whether competence drives motivation or whether motivated people simply feel more competent (Van den Broeck et al., 2016).
 
Some critics have questioned whether basic needs are truly universal, because SDT was developed largely in Western contexts (Chen et al., 2015). However, a study of adults in Belgium, China, Peru, and the United States found that need satisfaction and need frustration predicted wellbeing and ill-being in all four cultures (Chen et al., 2015). Together with the overlap between competence and self-efficacy, these limitations point to the same gap noted in CET. SDT predicts outcomes well, but whether competence itself is the active ingredient remains less certain than the theory suggests (Deci et al., 1999).
 
Most competence research has also used neurotypical samples (Morsink et al., 2022). Morsink et al. (2022) noted that research on [[w:Attention deficit hyperactivity disorder|attention-deficit/hyperactivity disorder]] (ADHD) has mostly studied rewards and overlooked psychological needs. This is despite evidence that children with more ADHD symptoms report lower need satisfaction at school. (Morsink et al., 2022) Frequent correction may push teachers and parents toward controlling styles, which can further frustrate competence (Morsink et al., 2022). Whether supporting competence helps neurodivergent people in the same way remains largely untested.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Applying competence in practice==
The research reviewed so far points to a consistent set of conditions under which people feel capable. Table 1 contrasts environments that support competence with those that thwart it. Each feature is drawn from the evidence above.
 
{| class=&quot;wikitable&quot; style=&quot;margin:1em auto; border-radius:8px;&quot;
|+ '''Table 1'''&lt;br&gt;''Features of Competence-Supportive and Competence-Thwarting Environments''
|-
! style=&quot;background:#eaf3fc;&quot; | Competence-supportive !! style=&quot;background:#fff6e8;&quot; | Competence-thwarting
|-
| Clear expectations about how to succeed || Vague or missing guidance
|-
| Guidance and modelling of &quot;how-to&quot; skills || Being left to work it out alone
|-
| Optimal challenge matched to current skills || Tasks far too hard or too easy
|-
| Specific, informative feedback || Absent, harsh, or controlling feedback
|-
| Long-term goals broken into short-term goals || No sense of progress
|-
| Mistakes framed as learning || Mistakes criticised or punished
|}
 
These features reflect the four sources of competence support in SDT, which are clear expectations, optimal challenge, guidance, and constructive feedback (Reeve, 2024).
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's turnaround'''
 
'''Week 8.''' Maya's manager notices the slowing progress and changes approach. They agree on what &quot;finished&quot; looks like and break the project into stages, starting with the 50 most-used folders.
 
'''Week 12.''' After each stage, Maya receives specific feedback on what is working. She now makes decisions confidently and has started suggesting improvements herself.
 
'''What changed?''' The structure around how the task would be completed: clear expectations, achievable steps, and feedback that informed instead of judged. Each gave Maya evidence that she was effective.
&lt;/div&gt;
 
Breaking Maya's project into stages draws on [[w:Goal setting|goal-setting theory]] (Locke &amp; Latham, 2002). Locke and Latham (2002) reviewed 35 years of laboratory and field studies. They found that specific, challenging goals combined with regular feedback consistently outperform vague &quot;do your best&quot; goals. Specific goals work partly because they show people exactly what success looks like. Each completed stage also acts as a mastery experience, which is the strongest source of self-efficacy (Bandura, 1977). This helps explain why Maya's confidence returned once the work was divided into stages.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Which change would best support Maya's need for competence?

|type=&quot;()&quot;}
- Offering her a bonus if she finishes faster
+ Breaking the project into stages with clear goals and specific feedback
- Telling her she is doing a great job regardless of progress
- Comparing her progress with a colleague's
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Conclusion==
Competence is the need to ''feel'' effective, and SDT treats it as important at all times, not only once basic needs are met (Ryan &amp; Deci, 2017; Tay &amp; Diener, 2011). Feeling competent moves people toward more autonomous motivation (Ryan &amp; Deci, 2020). CET explains why the same feedback can either energise or deflate a person, depending on whether it informs or controls (Deci et al., 1999).
 
When competence is actively frustrated, the consequences are more severe than when it is simply unmet. These consequences range from burnout to the helpless thinking shown in the case study (Abramson et al., 1978; Bartholomew et al., 2011). Research across workplaces, classrooms suggests that clear expectations and informational feedback, as well as challenges broken into achievable steps, can reverse this pattern (Baard et al., 2004; Locke &amp; Latham, 2002). However, much of this evidence is correlational and rarely tests competence directly as the mechanism (Van den Broeck et al., 2016).
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==See also==
* [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|Autonomy and intrinsic motivation in self-determination theory]] (Book chapter, 2025)
* [[Motivation and emotion/Book/2011/Self-determination theory|Self-determination theory]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Book chapter, 2026)
* [[w:Self-determination theory|Self-determination theory]] (Wikipedia)
* [[w:Self-efficacy|Self-efficacy]] (Wikipedia)
* [[w:Learned helplessness|Learned helplessness]] (Wikipedia)
 
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==References==
{{Hanging indent|1=

Abramson, L. Y., Seligman, M. E., &amp; Teasdale, J. D. (1978). Learned helplessness in humans: Critique and reformulation. Journal of Abnormal Psychology (1965), 87(1), 49–74. https://doi.org/10.1037/0021-843X.87.1.49
 
Baard, P. P., Deci, E. L., &amp; Ryan, R. M. (2004). Intrinsic need satisfaction: a motivational basis of performance and well-being in two work settings. Journal of Applied Social Psychology, 34(10), 2045–2068. https://doi.org/10.1111/j.1559-1816.2004.tb02690.x

Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191–215. https://doi.org/10.1037/0033-295X.84.2.191
 
Bartholomew, K. J., Ntoumanis, N., Ryan, R. M., Bosch, J. A., &amp; Thøgersen-Ntoumani, C. (2011). Self-Determination Theory and Diminished Functioning: The Role of Interpersonal Control and Psychological Need Thwarting. Personality &amp; Social Psychology Bulletin, 37(11), 1459–1473. https://doi.org/10.1177/0146167211413125
 
Bureau, J. S., Howard, J. L., Chong, J. X. Y., &amp; Guay, F. (2022). Pathways to Student Motivation: A Meta-Analysis of Antecedents of Autonomous and Controlled Motivations. Review of Educational Research, 92(1), 46–72. https://doi.org/10.3102/00346543211042426
 
Cameron, J., &amp; Pierce, W. D. (1994). Reinforcement, Reward, and Intrinsic Motivation: A Meta-Analysis. Review of Educational Research, 64(3), 363–423. https://doi.org/10.3102/00346543064003363

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. Motivation and Emotion, 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1

Deci, E. L. (1971). Effects of externally mediated rewards on intrinsic motivation. Journal of Personality and Social Psychology, 18(1), 105–115. https://doi.org/10.1037/h0030644
 
Deci, E. L., Koestner, R., &amp; Ryan, R. M. (1999). A Meta-Analytic Review of Experiments Examining the Effects of Extrinsic Rewards on Intrinsic Motivation. Psychological Bulletin, 125(6), 627–668. https://doi.org/10.1037/0033-2909.125.6.627
 
Deci, E. L., &amp; Ryan, R. M. (1985). ''Intrinsic motivation and self-determination in human behavior''. Springer. https://doi.org/10.1016/j.cedpsych.2020.101860.

Fong, C. J., Patall, E. A., Vasquez, A. C., &amp; Stautberg, S. (2019). A Meta-Analysis of Negative Feedback on Intrinsic Motivation. Educational Psychology Review, 31(1), 121–162. https://doi.org/10.1007/s10648-018-9446-6
 
Locke, E. A., &amp; Latham, G. P. (2002). Building a practically useful theory of goal setting and task motivation: A 35-year odyssey. The American Psychologist, 57(9), 705–717. https://doi.org/10.1037/0003-066X.57.9.705

Maslow, A. H. (1943). A theory of human motivation. ''Psychological Review, 50''(4), 370–396. https://doi.org/10.1037/h0054346
 
Morsink, S., Van der Oord, S., Antrop, I., Danckaerts, M., &amp; Scheres, A. (2022). Studying motivation in ADHD: The role of internal motives and the relevance of self determination theory. ''Journal of Attention Disorders, 26''(8), 1139–1158. https://doi.org/10.1177/10870547211050948
 
Reeve, J. (2024). ''Understanding motivation and emotion'' (8th ed.). Wiley.
 
Ryan, R. M., &amp; Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. ''American Psychologist, 55''(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68
 
Ryan, R. M., &amp; Deci, E. L. (2017). ''Self-determination theory: Basic psychological needs in motivation, development, and wellness''. Guilford Press. https://doi.org/10.1521/978.14625/28806
 
Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology, 61'', Article 101860. https://doi.org/10.1016/j.cedpsych.2020.101860
 
Seligman, M. E. P., &amp; Maier, S. F. (1967). Failure to escape traumatic shock. ''Journal of Experimental Psychology, 74''(1), 1–9. https://doi.org/10.1037/h0024514
 
Slemp, G. R., Kern, M. L., Patrick, K. J., &amp; Ryan, R. M. (2018). Leader autonomy support in the workplace: A meta-analytic review. ''Motivation and Emotion, 42''(5), 706–724. https://doi.org/10.1007/s11031-018-9698-y
 
Tay, L., &amp; Diener, E. (2011). Needs and subjective well-being around the world. ''Journal of Personality and Social Psychology, 101''(2), 354–365. https://doi.org/10.1037/a0023779
 
Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A review of self-determination theory's basic psychological needs at work. ''Journal of Management, 42''(5), 1195–1229. https://doi.org/10.1177/0149206316632058
 
Vansteenkiste, M., &amp; Ryan, R. M. (2013). On psychological growth and vulnerability: Basic psychological need satisfaction and need frustration as a unifying principle. ''Journal of Psychotherapy Integration, 23''(3), 263–280. https://doi.org/10.1037/a0032359
 
Vansteenkiste, M., Ryan, R. M., &amp; Soenens, B. (2020). Basic psychological need theory: Advancements, critical themes, and future directions. ''Motivation and Emotion, 44''(1), 1–31. https://doi.org/10.1007/s11031-019-09818-1
 
White, R. W. (1959). Motivation reconsidered: The concept of competence. ''Psychological Review, 66''(5), 297–333. https://doi.org/10.1037/h0040934
}}


==External links==
* https://open.ncl.ac.uk/theories/20/self-determination-theory/
* https://www.apa.org/ed/schools/teaching-learning/top-twenty/motivation
* https://positivepsychology.com/self-determination-theory/

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      <text bytes="30306" sha1="g35hpgpj2o6qy0cfjzhecanparvafhq" xml:space="preserve">{{title|Competence motivation in self-determination theory:&lt;br&gt;How does the need for competence function within self-determination theory to shape motivation and behaviour?}}
 __TOC__

==Overview==
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study:'''
[[File:Woman Suffering from Stress at Work (cropped).jpg|thumb|right|260px|'''Figure 1'''. Facing a large, unstructured task without guidance or feedback can leave a person doubting their own ability.]]
 
Maya, a 24-year-old administrative officer, has not opened her biggest project in three days. Instead, she has answered every email and tidied a shared drive she built herself: familiar tasks she knows she can do well.
 
Two months ago, Maya was excited when her manager asked her to review and reorganise more than 500 folders in the team's records system. But she received no guidance on where to start or what &quot;finished&quot; should look like. Each folder revealed new complexity, and nobody told her if her decisions were right. (see Figure 1). Some days she thinks, &quot;I just need clearer instructions.&quot; On other days her thoughts turn personal: &quot;I'm hopeless at this.&quot; The first thought sends her to ask for help; the second sends her back to her inbox.
 
''Why does the same task leave a person ready to improve on some days, and ready to give up on others?''
&lt;/div&gt;
 
 
According to [[w:Self-determination theory|self-determination theory]] (SDT), this difference often comes down to the need for [[Motivation and emotion/Book/2011/Self-determination theory|competence]]. Competence is the need to feel effective and capable (Ryan &amp; Deci, 2017). It is one of three basic psychological needs, alongside [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|autonomy]] and [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|relatedness]] (Ryan &amp; Deci, 2017). When competence is satisfied, people tend to show stronger [[Motivation and emotion/Book/2013/Intrinsic motivation|intrinsic motivation]], persistence, and wellbeing (Ryan &amp; Deci, 2020). When it is frustrated, as in Maya's case, people tend to avoid tasks and give up (Vansteenkiste et al., 2020).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Focus questions'''
* What is competence, according to self-determination theory?
* How does competence relate to intrinsic motivation?
* How does cognitive evaluation theory explain why feedback and rewards can strengthen or undermine motivation?
* What happens when the need for competence is frustrated?
* What does research show about how competence can be supported?
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Self-determination theory and competence==
 
===What is self-determination theory?===
SDT is a broad theory of human motivation. It proposes that people have three innate psychological needs: autonomy (feeling volitional), competence (feeling effective), as well as relatedness (feeling connected to others) (Deci &amp; Ryan, 1985; Ryan &amp; Deci, 2017). SDT is made up of six mini-theories, and two of these are central to this chapter. These are cognitive evaluation theory and basic psychological needs theory (Vansteenkiste et al., 2020). SDT is often compared with [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]]. Maslow (1943) proposed a hierarchy in which lower needs, such as physiological and safety needs, generally take priority over higher needs, such as esteem and self-actualisation. He placed mastery within esteem needs. SDT agrees that people strive to feel capable. However, SDT does not rank its needs and considers all three essential at all times (Ryan &amp; Deci, 2017).
 
[[File:MaslowsHierarchyOfNeeds.svg|thumb|right|300px|'''Figure 2'''. Maslow's hierarchy of needs places mastery within esteem needs, near the top of the hierarchy. SDT treats competence as essential at every level.]]
 
Tay and Diener (2011) tested these two views using Gallup World Poll data from 60,865 people in 123 countries. Although people did tend to meet basic and safety needs first, which partly supports Maslow, each need, including mastery, contributed to wellbeing regardless of whether the other needs were met (Tay &amp; Diener, 2011). The needs that mirror SDT, namely social relationships, autonomy, and mastery, were among the strongest predictors of everyday feelings across all eight world regions studied. One limitation is that the data were cross-sectional. Each need was also measured with only two or three yes or no questions, so the study shows association, not cause.
 
===What is competence within self-determination theory?===
The idea of competence as a motivational force dates back to White (1959), who challenged the drive theories of his time. He noticed that infants and young animals explore and play, as well as manipulate objects, even when they are fed and safe. He argued that this behaviour comes from a built-in need to have an effect on the environment, which he called effectance motivation. SDT builds on this idea and defines competence as the need to ''feel'' effective, not simply to possess a skill (Ryan &amp; Deci, 2017). This means that a highly skilled person can still feel incompetent if they receive no sign that their efforts are working.
 
According to SDT, competence is best satisfied in well-structured environments that offer ''[[wikipedia:Challenge_point_framework|optimal challenge]]'', positive feedback, and opportunities for growth (Ryan &amp; Deci, 2020). An optimally challenging task sits slightly beyond a person's current skill, but it comes with enough structure and support to close the gap. Tasks that are too easy offer no sense of growth, while tasks that are too hard, especially without guidance, signal failure (Reeve, 2024). Maya's difficulty illustrates how a lack of structure and feedback can make a manageable task feel too hard.
 
Basic psychological needs theory treats need satisfaction and need frustration as two separate experiences (Vansteenkiste &amp; Ryan, 2013). Need satisfaction is linked to a &quot;bright&quot; pathway of growth and engagement, as well as wellbeing (Vansteenkiste et al., 2020). Need frustration is linked to a &quot;dark&quot; pathway of defensiveness, avoidance, and ill-being (Vansteenkiste et al., 2020). Low satisfaction and active frustration are therefore not the same thing. Receiving no feedback may leave a person unfulfilled, but being repeatedly made to feel ineffective actively harms wellbeing (Vansteenkiste &amp; Ryan, 2013). The case study shows this shift. Maya moves from low satisfaction in the early weeks to active frustration after her manager's review, described later in the chapter.
 
===Competence and self-efficacy===
Competence overlaps closely with [[w:Self-efficacy|self-efficacy]], which is a person's belief that they can successfully perform a specific behaviour (Bandura, 1977). Bandura separated two expectations that shape whether people act. An ''efficacy expectation'' asks &quot;Can I do it?&quot;, and an ''outcome expectation'' asks &quot;Will it work?&quot; Efficacy beliefs are built from four sources: personal mastery experiences, watching similar others succeed, verbal persuasion, and how people interpret their own stress (Bandura, 1977). Of these, mastery experiences are the most powerful (Bandura, 1977).
 
In the case study, several of these sources are weakened. Without feedback, Maya cannot judge whether her decisions are effective, so her real progress is not experienced as mastery. As the case study later shows, her manager's comments act as negative persuasion. Her anxiety before opening the project is also likely to be read as evidence that she is not capable. The key difference between the two concepts is that self-efficacy is a belief about a specific future task (Bandura, 1977). In contrast, SDT treats competence as a universal need that shapes motivation and wellbeing over time (Ryan &amp; Deci, 2017). In practice, however, the two are difficult to separate, because both are usually measured with similar self-report questions. Some &quot;competence&quot; findings may therefore simply reflect confidence.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Competence and intrinsic motivation==
 
SDT's central claim is that the ''quality'' of motivation matters as much as its quantity (Ryan &amp; Deci, 2020). Feeling competent affects where people sit on the motivation continuum, as well as how they respond to feedback and rewards (Deci et al., 1999; Ryan &amp; Deci, 2020).
 
===The motivation continuum===
SDT describes motivation as a continuum (Ryan &amp; Deci, 2020; see Figure 3). The continuum ranges from [[Motivation and emotion/Book/2014/Amotivation|amotivation]], meaning no intention to act, through several forms of extrinsic motivation, to intrinsic motivation, meaning acting for enjoyment or interest (Ryan &amp; Deci, 2020). A lack of competence is one of the main causes of amotivation (Ryan &amp; Deci, 2000). It shows in thoughts such as &quot;I can't do this&quot; or &quot;my effort won't make a difference&quot;. In contrast, feeling capable helps people [[w:Internalization (sociology)|internalise]] the value of a task, so the task feels self-endorsed instead of obligatory (Ryan &amp; Deci, 2020). In the case study, Maya's growing avoidance of her project suggests she is sliding toward amotivation.
 
[[File:Taxonomy of motivation.png|thumb|center|600px|'''Figure 3'''. The SDT motivation continuum, ranging from amotivation, through controlled and autonomous forms of extrinsic motivation, to intrinsic motivation.]]
 
===Cognitive evaluation theory===
[[Motivation and emotion/Book/2021/Cognitive evaluation theory and motivation|Cognitive evaluation theory]] (CET) explains how external events such as feedback and rewards affect intrinsic motivation (Ryan &amp; Deci, 2000). According to CET, every such event has a ''controlling'' aspect, which affects autonomy, and an ''informational'' aspect, which affects competence (Ryan &amp; Deci, 2000). Informational feedback increases perceived competence and intrinsic motivation (Deci et al., 1999). In contrast, rewards that feel like pressure tend to undermine intrinsic motivation, even when they signal success (Deci et al., 1999). CET therefore predicts that ''how'' feedback is delivered matters as much as ''what'' it says. Later versions of CET added a third, ''amotivating'' aspect (Ryan &amp; Deci, 2017). Events that signal incompetence, or that effort will not change the outcome, can push people toward amotivation. Criticism that offers no way forward, such as the feedback Maya later receives, is likely to carry this amotivating message.
 
Research generally supports these predictions, although the earliest evidence was weak. RIn Deci's (1971) original experiment, students paid $1 for each puzzle they solved later spent less free time on the puzzles once payment stopped. However, the study had only 24 participants, and the result was only a trend (Deci, 1971). A later meta-analysis of 128 experiments, mostly with children and university students, found a clearer pattern (Deci et al., 1999). People who expected a tangible reward for an interesting task spent less free time on it afterwards. In studies with children, this effect was still present more than a week later. The most damaging rewards were those that signalled a person had fallen short (Deci et al., 1999). Feedback style also mattered. Informational praise increased intrinsic motivation, but the same praise with a controlling phrase such as &quot;just as you ''should''&quot; decreased it (Ryan et al., 1983, as cited in Deci et al., 1999). Negative feedback was less harmful when it included guidance on how to improve (Fong et al., 2019). Rewards did not undermine motivation for boring tasks or when they were unexpected (Deci et al., 1999).
 
CET assumes that these effects work ''through'' perceived competence (Ryan &amp; Deci, 2017). However, relatively few studies have measured perceived competence directly to test this (Deci et al., 1999). The results fit the theory, but the mechanism is more often assumed than demonstrated. Even so, the practical message is consistent. Feedback that identifies a problem, such as &quot;the scope needs to be better defined&quot;, without showing how to fix it is unlikely to support competence (Fong et al., 2019).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{According to cognitive evaluation theory, positive feedback is most likely to increase intrinsic motivation when it is:

|type=&quot;()&quot;}
- Given with a large financial reward
+ Informative and delivered in an autonomy-supportive way
- Delivered as a comparison with other people
- Given constantly, regardless of performance
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==When competence is frustrated==
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's first review'''
 
'''Week 6.''' Maya's manager reviews the project. She acknowledges some progress, then adds that the plan needs to be clearer and the scope better defined. She does not say what a clearer plan looks like or how to narrow the scope. Maya leaves the meeting feeling like a failure. She had enjoyed the first few folders, but now she dreads opening the system.
 
'''What is happening?''' The feedback identified a problem without giving Maya the information to solve it. Her effort no longer seems to lead anywhere, which is when a need starts to be actively frustrated, not just unmet.
&lt;/div&gt;
 
Research supports the distinction between low satisfaction and active frustration (Vansteenkiste &amp; Ryan, 2013). Bartholomew et al. (2011) found that athletes who saw their coach as controlling reported greater thwarting of all three needs. Need thwarting, in turn, predicted burnout, depressive symptoms, and negative emotion (Bartholomew et al., 2011). Feeling actively undermined was more harmful than simply not feeling supported. If the same pattern holds for competence, vague, critical feedback may harm Maya more than no feedback at all.
 
When people repeatedly experience that their effort makes no difference, they may develop [[w:Learned helplessness|learned helplessness]] (Seligman &amp; Maier, 1967). In classic experiments, dogs exposed to inescapable shocks later failed to escape shocks they could have avoided (Seligman &amp; Maier, 1967). Dogs that had been given control earlier learned to escape. In humans, helplessness reduces effort and is linked to apathy and depression (Abramson et al., 1978).How people explain failure also matters. The reformulated helplessness model proposes that explaining failure with internal, stable and global causes is more damaging than explaining it with external, unstable or specific causes (Abramson et al., 1978). Maya's two thoughts show this difference. &quot;I'm hopeless at this&quot; blames a lasting personal flaw and is more likely to lead to giving up, whereas &quot;I just need clearer instructions&quot; points to a specific, changeable cause that keeps her trying.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Maya thinks, &quot;I'm hopeless at this.&quot; According to research on explanatory style, why is this thought more harmful than &quot;I just need clearer instructions&quot;?

|type=&quot;()&quot;}
- It is less accurate
+ It explains failure with an internal, stable cause she cannot easily change
- It blames her manager instead of herself
- It focuses on the task rather than on herself
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==What supports or undermines competence?==
 
In two workplace studies, Baard et al. (2004) found that employees' satisfaction of autonomy, competence, and relatedness predicted their wellbeing as well as their performance evaluations. Because supervisors rated performance, this finding is less affected by self-report bias. However, the design still cannot show which came first. A meta-analysis by Van den Broeck et al. (2016) found that competence predicted wellbeing, work attitudes, and behaviour, even after the other two needs were taken into account. This suggests that competence is not simply a by-product of feeling autonomous or connected. Leadership also matters. Managers' autonomy-supportive behaviour is associated with greater need satisfaction as well as more autonomous motivation in employees (Slemp et al., 2018). These findings suggest that the manager's feedback is central to Maya's difficulties.
 
Similar patterns appear in classrooms. Bureau et al. (2022) pooled studies of what predicts student motivation and found that, of the three needs, support for competence was the strongest predictor of autonomous motivation (Bureau et al., 2022). This is a notable finding, because SDT has historically given autonomy the most attention (Ryan &amp; Deci, 2017). It suggests that, at least in classrooms, feeling capable may matter as much as feeling free to choose. However, the meta-analysis draws mainly on correlational studies, so it shows which students do well, but it does not prove that supporting competence causes better outcomes.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
The strength of the evidence depends on the methods used. The reward findings, for example, were contested. Cameron and Pierce (1994) found no overall undermining effect and called for &quot;abandoning cognitive evaluation theory&quot; (p. 396). Deci et al. (1999) argued that this result came from mixing boring and interesting tasks, as well as using inappropriate control groups. Laboratory studies also relied mostly on single sessions with children and students (Deci et al., 1999). Self-reported interest also showed much weaker effects than behaviour. Outside the laboratory, most studies are cross-sectional. This makes it unclear whether competence drives motivation or whether motivated people simply feel more competent (Van den Broeck et al., 2016).
 
Some critics have questioned whether basic needs are truly universal, because SDT was developed largely in Western contexts (Chen et al., 2015). However, a study of adults in Belgium, China, Peru, and the United States found that need satisfaction and need frustration predicted wellbeing and ill-being in all four cultures (Chen et al., 2015). Together with the overlap between competence and self-efficacy, these limitations point to the same gap noted in CET. SDT predicts outcomes well, but whether competence itself is the active ingredient remains less certain than the theory suggests (Deci et al., 1999).
 
Most competence research has also used neurotypical samples (Morsink et al., 2022). Morsink et al. (2022) noted that research on [[w:Attention deficit hyperactivity disorder|attention-deficit/hyperactivity disorder]] (ADHD) has mostly studied rewards and overlooked psychological needs. This is despite evidence that children with more ADHD symptoms report lower need satisfaction at school. (Morsink et al., 2022) Frequent correction may push teachers and parents toward controlling styles, which can further frustrate competence (Morsink et al., 2022). Whether supporting competence helps neurodivergent people in the same way remains largely untested.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Applying competence in practice==
The research reviewed so far points to a consistent set of conditions under which people feel capable. Table 1 contrasts environments that support competence with those that thwart it. Each feature is drawn from the evidence above.
 
{| class=&quot;wikitable&quot; style=&quot;margin:1em auto; border-radius:8px;&quot;
|+ '''Table 1'''&lt;br&gt;''Features of Competence-Supportive and Competence-Thwarting Environments''
|-
! style=&quot;background:#eaf3fc;&quot; | Competence-supportive !! style=&quot;background:#fff6e8;&quot; | Competence-thwarting
|-
| Clear expectations about how to succeed || Vague or missing guidance
|-
| Guidance and modelling of &quot;how-to&quot; skills || Being left to work it out alone
|-
| Optimal challenge matched to current skills || Tasks far too hard or too easy
|-
| Specific, informative feedback || Absent, harsh, or controlling feedback
|-
| Long-term goals broken into short-term goals || No sense of progress
|-
| Mistakes framed as learning || Mistakes criticised or punished
|}
 
These features reflect the four sources of competence support in SDT, which are clear expectations, optimal challenge, guidance, and constructive feedback (Reeve, 2024).
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's turnaround'''
 
'''Week 8.''' Maya's manager notices the slowing progress and changes approach. They agree on what &quot;finished&quot; looks like and break the project into stages, starting with the 50 most-used folders.
 
'''Week 12.''' After each stage, Maya receives specific feedback on what is working. She now makes decisions confidently and has started suggesting improvements herself.
 
'''What changed?''' The structure around how the task would be completed: clear expectations, achievable steps, and feedback that informed instead of judged. Each gave Maya evidence that she was effective.
&lt;/div&gt;
 
Breaking Maya's project into stages draws on [[w:Goal setting|goal-setting theory]] (Locke &amp; Latham, 2002). Locke and Latham (2002) reviewed 35 years of laboratory and field studies. They found that specific, challenging goals combined with regular feedback consistently outperform vague &quot;do your best&quot; goals. Specific goals work partly because they show people exactly what success looks like. Each completed stage also acts as a mastery experience, which is the strongest source of self-efficacy (Bandura, 1977). This helps explain why Maya's confidence returned once the work was divided into stages.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Which change would best support Maya's need for competence?

|type=&quot;()&quot;}
- Offering her a bonus if she finishes faster
+ Breaking the project into stages with clear goals and specific feedback
- Telling her she is doing a great job regardless of progress
- Comparing her progress with a colleague's
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Conclusion==
Competence is the need to ''feel'' effective, and SDT treats it as important at all times, not only once basic needs are met (Ryan &amp; Deci, 2017; Tay &amp; Diener, 2011). Feeling competent moves people toward more autonomous motivation (Ryan &amp; Deci, 2020). CET explains why the same feedback can either energise or deflate a person, depending on whether it informs or controls (Deci et al., 1999).
 
When competence is actively frustrated, the consequences are more severe than when it is simply unmet. These consequences range from burnout to the helpless thinking shown in the case study (Abramson et al., 1978; Bartholomew et al., 2011). Research across workplaces, classrooms suggests that clear expectations and informational feedback, as well as challenges broken into achievable steps, can reverse this pattern (Baard et al., 2004; Locke &amp; Latham, 2002). However, much of this evidence is correlational and rarely tests competence directly as the mechanism (Van den Broeck et al., 2016).
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==See also==
* [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|Autonomy and intrinsic motivation in self-determination theory]] (Book chapter, 2025)
* [[Motivation and emotion/Book/2011/Self-determination theory|Self-determination theory]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Book chapter, 2026)
* [[w:Self-determination theory|Self-determination theory]] (Wikipedia)
* [[w:Self-efficacy|Self-efficacy]] (Wikipedia)
* [[w:Learned helplessness|Learned helplessness]] (Wikipedia)
 
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==References==
{{Hanging indent|1=

Abramson, L. Y., Seligman, M. E., &amp; Teasdale, J. D. (1978). Learned helplessness in humans: Critique and reformulation. Journal of Abnormal Psychology (1965), 87(1), 49–74. https://doi.org/10.1037/0021-843X.87.1.49
 
Baard, P. P., Deci, E. L., &amp; Ryan, R. M. (2004). Intrinsic need satisfaction: a motivational basis of performance and well-being in two work settings. Journal of Applied Social Psychology, 34(10), 2045–2068. https://doi.org/10.1111/j.1559-1816.2004.tb02690.x

Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191–215. https://doi.org/10.1037/0033-295X.84.2.191
 
Bartholomew, K. J., Ntoumanis, N., Ryan, R. M., Bosch, J. A., &amp; Thøgersen-Ntoumani, C. (2011). Self-Determination Theory and Diminished Functioning: The Role of Interpersonal Control and Psychological Need Thwarting. Personality &amp; Social Psychology Bulletin, 37(11), 1459–1473. https://doi.org/10.1177/0146167211413125
 
Bureau, J. S., Howard, J. L., Chong, J. X. Y., &amp; Guay, F. (2022). Pathways to Student Motivation: A Meta-Analysis of Antecedents of Autonomous and Controlled Motivations. Review of Educational Research, 92(1), 46–72. https://doi.org/10.3102/00346543211042426
 
Cameron, J., &amp; Pierce, W. D. (1994). Reinforcement, Reward, and Intrinsic Motivation: A Meta-Analysis. Review of Educational Research, 64(3), 363–423. https://doi.org/10.3102/00346543064003363

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. Motivation and Emotion, 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1

Deci, E. L. (1971). Effects of externally mediated rewards on intrinsic motivation. Journal of Personality and Social Psychology, 18(1), 105–115. https://doi.org/10.1037/h0030644
 
Deci, E. L., Koestner, R., &amp; Ryan, R. M. (1999). A Meta-Analytic Review of Experiments Examining the Effects of Extrinsic Rewards on Intrinsic Motivation. Psychological Bulletin, 125(6), 627–668. https://doi.org/10.1037/0033-2909.125.6.627
 
Deci, E. L., &amp; Ryan, R. M. (1985). ''Intrinsic motivation and self-determination in human behavior''. Springer. https://doi.org/10.1016/j.cedpsych.2020.101860.

Fong, C. J., Patall, E. A., Vasquez, A. C., &amp; Stautberg, S. (2019). A Meta-Analysis of Negative Feedback on Intrinsic Motivation. Educational Psychology Review, 31(1), 121–162. https://doi.org/10.1007/s10648-018-9446-6
 
Locke, E. A., &amp; Latham, G. P. (2002). Building a practically useful theory of goal setting and task motivation: A 35-year odyssey. The American Psychologist, 57(9), 705–717. https://doi.org/10.1037/0003-066X.57.9.705

Maslow, A. H. (1943). A theory of human motivation. ''Psychological Review, 50''(4), 370–396. https://doi.org/10.1037/h0054346
 
Morsink, S., Van der Oord, S., Antrop, I., Danckaerts, M., &amp; Scheres, A. (2022). Studying motivation in ADHD: The role of internal motives and the relevance of self determination theory. ''Journal of Attention Disorders, 26''(8), 1139–1158. https://doi.org/10.1177/10870547211050948
 
Reeve, J. (2024). ''Understanding motivation and emotion'' (8th ed.). Wiley.
 
Ryan, R. M., &amp; Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. ''American Psychologist, 55''(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68
 
Ryan, R. M., &amp; Deci, E. L. (2017). ''Self-determination theory: Basic psychological needs in motivation, development, and wellness''. Guilford Press. https://doi.org/10.1521/978.14625/28806
 
Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology, 61'', Article 101860. https://doi.org/10.1016/j.cedpsych.2020.101860
 
Seligman, M. E. P., &amp; Maier, S. F. (1967). Failure to escape traumatic shock. ''Journal of Experimental Psychology, 74''(1), 1–9. https://doi.org/10.1037/h0024514
 
Slemp, G. R., Kern, M. L., Patrick, K. J., &amp; Ryan, R. M. (2018). Leader autonomy support in the workplace: A meta-analytic review. ''Motivation and Emotion, 42''(5), 706–724. https://doi.org/10.1007/s11031-018-9698-y
 
Tay, L., &amp; Diener, E. (2011). Needs and subjective well-being around the world. ''Journal of Personality and Social Psychology, 101''(2), 354–365. https://doi.org/10.1037/a0023779
 
Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A review of self-determination theory's basic psychological needs at work. ''Journal of Management, 42''(5), 1195–1229. https://doi.org/10.1177/0149206316632058
 
Vansteenkiste, M., &amp; Ryan, R. M. (2013). On psychological growth and vulnerability: Basic psychological need satisfaction and need frustration as a unifying principle. ''Journal of Psychotherapy Integration, 23''(3), 263–280. https://doi.org/10.1037/a0032359
 
Vansteenkiste, M., Ryan, R. M., &amp; Soenens, B. (2020). Basic psychological need theory: Advancements, critical themes, and future directions. ''Motivation and Emotion, 44''(1), 1–31. https://doi.org/10.1007/s11031-019-09818-1
 
White, R. W. (1959). Motivation reconsidered: The concept of competence. ''Psychological Review, 66''(5), 297–333. https://doi.org/10.1037/h0040934
}}


==External links==
* https://open.ncl.ac.uk/theories/20/self-determination-theory/
* https://www.apa.org/ed/schools/teaching-learning/top-twenty/motivation
* https://positivepsychology.com/self-determination-theory/

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      <text bytes="30340" sha1="1g1iah35aae7n5udvrwqrh86xbiko1f" xml:space="preserve">{{title|Competence motivation in self-determination theory:&lt;br&gt;How does the need for competence function within self-determination theory to shape motivation and behaviour?}}
 __TOC__

==Overview==
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study:'''
[[File:Woman Suffering from Stress at Work (cropped).jpg|thumb|right|260px|'''Figure 1'''. Facing a large, unstructured task without guidance or feedback can leave a person doubting their own ability.]]
 
Maya, a 24-year-old administrative officer, has not opened her biggest project in three days. Instead, she has answered every email and tidied a shared drive she built herself: familiar tasks she knows she can do well.
 
Two months ago, Maya was excited when her manager asked her to review and reorganise more than 500 folders in the team's records system. But she received no guidance on where to start or what &quot;finished&quot; should look like. Each folder revealed new complexity, and nobody told her if her decisions were right. (see Figure 1). Some days she thinks, &quot;I just need clearer instructions.&quot; On other days her thoughts turn personal: &quot;I'm hopeless at this.&quot; The first thought sends her to ask for help; the second sends her back to her inbox.
 
''Why does the same task leave a person ready to improve on some days, and ready to give up on others?''
&lt;/div&gt;
 
 
According to [[w:Self-determination theory|self-determination theory]] (SDT), this difference often comes down to the need for [[Motivation and emotion/Book/2011/Self-determination theory|competence]]. Competence is the need to feel effective and capable (Ryan &amp; Deci, 2017). It is one of three basic psychological needs, alongside [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|autonomy]] and [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|relatedness]] (Ryan &amp; Deci, 2017). When competence is satisfied, people tend to show stronger [[Motivation and emotion/Book/2013/Intrinsic motivation|intrinsic motivation]], persistence, and wellbeing (Ryan &amp; Deci, 2020). When it is frustrated, as in Maya's case, people tend to avoid tasks and give up (Vansteenkiste et al., 2020).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Focus questions'''
* What is competence, according to self-determination theory?
* How does competence relate to intrinsic motivation?
* How does cognitive evaluation theory explain why feedback and rewards can strengthen or undermine motivation?
* What happens when the need for competence is frustrated?
* What does research show about how competence can be supported?
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Self-determination theory and competence==
 
===What is self-determination theory?===
SDT is a broad theory of human motivation. It proposes that people have three innate psychological needs: autonomy (feeling volitional), competence (feeling effective), as well as relatedness (feeling connected to others) (Deci &amp; Ryan, 1985; Ryan &amp; Deci, 2017). SDT is made up of six mini-theories, and two of these are central to this chapter. These are cognitive evaluation theory and basic psychological needs theory (Vansteenkiste et al., 2020). SDT is often compared with [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]]. Maslow (1943) proposed a hierarchy in which lower needs, such as physiological and safety needs, generally take priority over higher needs, such as esteem and self-actualisation. He placed mastery within esteem needs. SDT agrees that people strive to feel capable. However, SDT does not rank its needs and considers all three essential at all times (Ryan &amp; Deci, 2017).
 
[[File:MaslowsHierarchyOfNeeds.svg|thumb|right|300px|'''Figure 2'''. Maslow's hierarchy of needs places mastery within esteem needs, near the top of the hierarchy. SDT treats competence as essential at every level.]]
 
Tay and Diener (2011) tested these two views using Gallup World Poll data from 60,865 people in 123 countries. Although people did tend to meet basic and safety needs first, which partly supports Maslow, each need, including mastery, contributed to wellbeing regardless of whether the other needs were met (Tay &amp; Diener, 2011). The needs that mirror SDT, namely social relationships, autonomy, and mastery, were among the strongest predictors of everyday feelings across all eight world regions studied. One limitation is that the data were cross-sectional. Each need was also measured with only two or three yes or no questions, so the study shows association, not cause.
 
===What is competence within self-determination theory?===
The idea of competence as a motivational force dates back to White (1959), who challenged the drive theories of his time. He noticed that infants and young animals explore and play, as well as manipulate objects, even when they are fed and safe. He argued that this behaviour comes from a built-in need to have an effect on the environment, which he called effectance motivation. SDT builds on this idea and defines competence as the need to ''feel'' effective, not simply to possess a skill (Ryan &amp; Deci, 2017). This means that a highly skilled person can still feel incompetent if they receive no sign that their efforts are working.
 
According to SDT, competence is best satisfied in well-structured environments that offer ''[[wikipedia:Challenge_point_framework|optimal challenge]]'', positive feedback, and opportunities for growth (Ryan &amp; Deci, 2020). An optimally challenging task sits slightly beyond a person's current skill, but it comes with enough structure and support to close the gap. Tasks that are too easy offer no sense of growth, while tasks that are too hard, especially without guidance, signal failure (Reeve, 2024). Maya's difficulty illustrates how a lack of structure and feedback can make a manageable task feel too hard.
 
Basic psychological needs theory treats need satisfaction and need frustration as two separate experiences (Vansteenkiste &amp; Ryan, 2013). Need satisfaction is linked to a &quot;bright&quot; pathway of growth and engagement, as well as wellbeing (Vansteenkiste et al., 2020). Need frustration is linked to a &quot;dark&quot; pathway of defensiveness, avoidance, and ill-being (Vansteenkiste et al., 2020). Low satisfaction and active frustration are therefore not the same thing. Receiving no feedback may leave a person unfulfilled, but being repeatedly made to feel ineffective actively harms wellbeing (Vansteenkiste &amp; Ryan, 2013). The case study shows this shift. Maya moves from low satisfaction in the early weeks to active frustration after her manager's review, described later in the chapter.
 
===Competence and self-efficacy===
Competence overlaps closely with [[w:Self-efficacy|self-efficacy]], which is a person's belief that they can successfully perform a specific behaviour (Bandura, 1977). Bandura separated two expectations that shape whether people act. An ''efficacy expectation'' asks &quot;Can I do it?&quot;, and an ''outcome expectation'' asks &quot;Will it work?&quot; Efficacy beliefs are built from four sources: personal mastery experiences, watching similar others succeed, verbal persuasion, and how people interpret their own stress (Bandura, 1977). Of these, mastery experiences are the most powerful (Bandura, 1977).
 
In the case study, several of these sources are weakened. Without feedback, Maya cannot judge whether her decisions are effective, so her real progress is not experienced as mastery. As the case study later shows, her manager's comments act as negative persuasion. Her anxiety before opening the project is also likely to be read as evidence that she is not capable. The key difference between the two concepts is that self-efficacy is a belief about a specific future task (Bandura, 1977). In contrast, SDT treats competence as a universal need that shapes motivation and wellbeing over time (Ryan &amp; Deci, 2017). In practice, however, the two are difficult to separate, because both are usually measured with similar self-report questions. Some &quot;competence&quot; findings may therefore simply reflect confidence.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Competence and intrinsic motivation==
 
SDT's central claim is that the ''quality'' of motivation matters as much as its quantity (Ryan &amp; Deci, 2020). Feeling competent affects where people sit on the motivation continuum, as well as how they respond to feedback and rewards (Deci et al., 1999; Ryan &amp; Deci, 2020).
 
===The motivation continuum===
SDT describes motivation as a continuum (Ryan &amp; Deci, 2020; see Figure 3). The continuum ranges from [[Motivation and emotion/Book/2014/Amotivation|amotivation]], meaning no intention to act, through several forms of extrinsic motivation, to intrinsic motivation, meaning acting for enjoyment or interest (Ryan &amp; Deci, 2020). A lack of competence is one of the main causes of amotivation (Ryan &amp; Deci, 2000). It shows in thoughts such as &quot;I can't do this&quot; or &quot;my effort won't make a difference&quot;. In contrast, feeling capable helps people [[w:Internalization (sociology)|internalise]] the value of a task, so the task feels self-endorsed instead of obligatory (Ryan &amp; Deci, 2020). In the case study, Maya's growing avoidance of her project suggests she is sliding toward amotivation.
 
[[File:Taxonomy of motivation.png|thumb|center|600px|'''Figure 3'''. The SDT motivation continuum, ranging from amotivation, through controlled and autonomous forms of extrinsic motivation, to intrinsic motivation.]]
 
===Cognitive evaluation theory===
[[Motivation and emotion/Book/2021/Cognitive evaluation theory and motivation|Cognitive evaluation theory]] (CET) explains how external events such as feedback and rewards affect intrinsic motivation (Ryan &amp; Deci, 2000). According to CET, every such event has a ''controlling'' aspect, which affects autonomy, and an ''informational'' aspect, which affects competence (Ryan &amp; Deci, 2000). Informational feedback increases perceived competence and intrinsic motivation (Deci et al., 1999). In contrast, rewards that feel like pressure tend to undermine intrinsic motivation, even when they signal success (Deci et al., 1999). CET therefore predicts that ''how'' feedback is delivered matters as much as ''what'' it says. Later versions of CET added a third, ''amotivating'' aspect (Ryan &amp; Deci, 2017). Events that signal incompetence, or that effort will not change the outcome, can push people toward amotivation. Criticism that offers no way forward, such as the feedback Maya later receives, is likely to carry this amotivating message.
 
Research generally supports these predictions, although the earliest evidence was weak. RIn Deci's (1971) original experiment, students paid $1 for each puzzle they solved later spent less free time on the puzzles once payment stopped. However, the study had only 24 participants, and the result was only a trend (Deci, 1971). A later meta-analysis of 128 experiments, mostly with children and university students, found a clearer pattern (Deci et al., 1999). People who expected a tangible reward for an interesting task spent less free time on it afterwards. In studies with children, this effect was still present more than a week later. The most damaging rewards were those that signalled a person had fallen short (Deci et al., 1999). Feedback style also mattered. Informational praise increased intrinsic motivation, but the same praise with a controlling phrase such as &quot;just as you ''should''&quot; decreased it (Ryan et al., 1983, as cited in Deci et al., 1999). Negative feedback was less harmful when it included guidance on how to improve (Fong et al., 2019). Rewards did not undermine motivation for boring tasks or when they were unexpected (Deci et al., 1999).
 
CET assumes that these effects work ''through'' perceived competence (Ryan &amp; Deci, 2017). However, relatively few studies have measured perceived competence directly to test this (Deci et al., 1999). The results fit the theory, but the mechanism is more often assumed than demonstrated. Even so, the practical message is consistent. Feedback that identifies a problem, such as &quot;the scope needs to be better defined&quot;, without showing how to fix it is unlikely to support competence (Fong et al., 2019).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{According to cognitive evaluation theory, positive feedback is most likely to increase intrinsic motivation when it is:

|type=&quot;()&quot;}
- Given with a large financial reward
+ Informative and delivered in an autonomy-supportive way
- Delivered as a comparison with other people
- Given constantly, regardless of performance
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==When competence is frustrated==
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's first review'''
 
'''Week 6.''' Maya's manager reviews the project. She acknowledges some progress, then adds that the plan needs to be clearer and the scope better defined. She does not say what a clearer plan looks like or how to narrow the scope. Maya leaves the meeting feeling like a failure. She had enjoyed the first few folders, but now she dreads opening the system.
 
'''What is happening?''' The feedback identified a problem without giving Maya the information to solve it. Her effort no longer seems to lead anywhere, which is when a need starts to be actively frustrated, not just unmet.
&lt;/div&gt;
 
Research supports the distinction between low satisfaction and active frustration (Vansteenkiste &amp; Ryan, 2013). Bartholomew et al. (2011) found that athletes who saw their coach as controlling reported greater thwarting of all three needs. Need thwarting, in turn, predicted burnout, depressive symptoms, and negative emotion (Bartholomew et al., 2011). Feeling actively undermined was more harmful than simply not feeling supported. If the same pattern holds for competence, vague, critical feedback may harm Maya more than no feedback at all.
 
When people repeatedly experience that their effort makes no difference, they may develop [[w:Learned helplessness|learned helplessness]] (Seligman &amp; Maier, 1967). In classic experiments, dogs exposed to inescapable shocks later failed to escape shocks they could have avoided (Seligman &amp; Maier, 1967). Dogs that had been given control earlier learned to escape. In humans, helplessness reduces effort and is linked to apathy and depression (Abramson et al., 1978).How people explain failure also matters. The reformulated helplessness model proposes that explaining failure with internal, stable and global causes is more damaging than explaining it with external, unstable or specific causes (Abramson et al., 1978). Maya's two thoughts show this difference. &quot;I'm hopeless at this&quot; blames a lasting personal flaw and is more likely to lead to giving up, whereas &quot;I just need clearer instructions&quot; points to a specific, changeable cause that keeps her trying.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Maya thinks, &quot;I'm hopeless at this.&quot; According to research on explanatory style, why is this thought more harmful than &quot;I just need clearer instructions&quot;?

|type=&quot;()&quot;}
- It is less accurate
+ It explains failure with an internal, stable cause she cannot easily change
- It blames her manager instead of herself
- It focuses on the task rather than on herself
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==What supports or undermines competence?==
 
In two workplace studies, Baard et al. (2004) found that employees' satisfaction of autonomy, competence, and relatedness predicted their wellbeing as well as their performance evaluations. Because supervisors rated performance, this finding is less affected by self-report bias. However, the design still cannot show which came first. A meta-analysis by Van den Broeck et al. (2016) found that competence predicted wellbeing, work attitudes, and behaviour, even after the other two needs were taken into account. This suggests that competence is not simply a by-product of feeling autonomous or connected. Leadership also matters. Managers' autonomy-supportive behaviour is associated with greater need satisfaction as well as more autonomous motivation in employees (Slemp et al., 2018). This suggests that how Maya's manager behaves may affect her need satisfaction, including her sense of competence.
 
Similar patterns appear in classrooms. Bureau et al. (2022) pooled studies of what predicts student motivation and found that, of the three needs, support for competence was the strongest predictor of autonomous motivation (Bureau et al., 2022). This is a notable finding, because SDT has historically given autonomy the most attention (Ryan &amp; Deci, 2017). It suggests that, at least in classrooms, feeling capable may matter as much as feeling free to choose. However, the meta-analysis draws mainly on correlational studies, so it shows which students do well, but it does not prove that supporting competence causes better outcomes.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
The strength of the evidence depends on the methods used. The reward findings, for example, were contested. Cameron and Pierce (1994, as cited in Deci et al., 1999) found no overall undermining effect and argued that CET should be abandoned. Deci et al. (1999) argued that this result came from mixing boring and interesting tasks, as well as using inappropriate control groups. Laboratory studies also relied mostly on single sessions with children and students (Deci et al., 1999). Self-reported interest also showed much weaker effects than behaviour. Outside the laboratory, most studies are cross-sectional. This makes it unclear whether competence drives motivation or whether motivated people simply feel more competent (Van den Broeck et al., 2016).
 
Some critics have questioned whether basic needs are truly universal, because SDT was developed largely in Western contexts (Chen et al., 2015). However, a study of adults in Belgium, China, Peru, and the United States found that need satisfaction and need frustration predicted wellbeing and ill-being in all four cultures (Chen et al., 2015). Together with the overlap between competence and self-efficacy, these limitations point to the same gap noted in CET. SDT predicts outcomes well, but whether competence itself is the active ingredient remains less certain than the theory suggests (Deci et al., 1999).
 
Most competence research has also used neurotypical samples (Morsink et al., 2022). Morsink et al. (2022) noted that research on [[w:Attention deficit hyperactivity disorder|attention-deficit/hyperactivity disorder]] (ADHD) has mostly studied rewards and overlooked psychological needs. This is despite evidence that children with more ADHD symptoms report lower need satisfaction at school.(Morsink et al., 2022) Frequent correction may push teachers and parents toward controlling styles, which can further frustrate competence (Morsink et al., 2022). Whether supporting competence helps neurodivergent people in the same way remains largely untested.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Applying competence in practice==
The research reviewed so far points to a consistent set of conditions under which people feel capable. Table 1 contrasts environments that support competence with those that thwart it. Each feature is drawn from the evidence above.
 
{| class=&quot;wikitable&quot; style=&quot;margin:1em auto; border-radius:8px;&quot;
|+ '''Table 1'''&lt;br&gt;''Features of Competence-Supportive and Competence-Thwarting Environments''
|-
! style=&quot;background:#eaf3fc;&quot; | Competence-supportive !! style=&quot;background:#fff6e8;&quot; | Competence-thwarting
|-
| Clear expectations about how to succeed || Vague or missing guidance
|-
| Guidance and modelling of &quot;how-to&quot; skills || Being left to work it out alone
|-
| Optimal challenge matched to current skills || Tasks far too hard or too easy
|-
| Specific, informative feedback || Absent, harsh, or controlling feedback
|-
| Long-term goals broken into short-term goals || No sense of progress
|-
| Mistakes framed as learning || Mistakes criticised or punished
|}
 
These features reflect the four sources of competence support in SDT, which are clear expectations, optimal challenge, guidance, and constructive feedback (Reeve, 2024).
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's turnaround'''
 
'''Week 8.''' Maya's manager notices the slowing progress and changes approach. They agree on what &quot;finished&quot; looks like and break the project into stages, starting with the 50 most-used folders.
 
'''Week 12.''' After each stage, Maya receives specific feedback on what is working. She now makes decisions confidently and has started suggesting improvements herself.
 
'''What changed?''' The structure around how the task would be completed: clear expectations, achievable steps, and feedback that informed instead of judged. Each gave Maya evidence that she was effective.
&lt;/div&gt;
 
Breaking Maya's project into stages draws on [[w:Goal setting|goal-setting theory]] (Locke &amp; Latham, 2002). Locke and Latham (2002) reviewed 35 years of laboratory and field studies. They found that specific, challenging goals combined with regular feedback consistently outperform vague &quot;do your best&quot; goals. Specific goals work partly because they show people exactly what success looks like. Each completed stage also acts as a mastery experience, which is the strongest source of self-efficacy (Bandura, 1977). This helps explain why Maya's confidence returned once the work was divided into stages.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Which change would best support Maya's need for competence?

|type=&quot;()&quot;}
- Offering her a bonus if she finishes faster
+ Breaking the project into stages with clear goals and specific feedback
- Telling her she is doing a great job regardless of progress
- Comparing her progress with a colleague's
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Conclusion==
Competence is the need to ''feel'' effective, and SDT treats it as important at all times, not only once basic needs are met (Ryan &amp; Deci, 2017; Tay &amp; Diener, 2011). Feeling competent moves people toward more autonomous motivation (Ryan &amp; Deci, 2020). CET explains why the same feedback can either energise or deflate a person, depending on whether it informs or controls (Deci et al., 1999).
 
When competence is actively frustrated, the consequences are more severe than when it is simply unmet. These consequences range from burnout to the helpless thinking shown in the case study (Abramson et al., 1978; Bartholomew et al., 2011). Research across workplaces, classrooms suggests that clear expectations and informational feedback, as well as challenges broken into achievable steps, can reverse this pattern (Baard et al., 2004; Locke &amp; Latham, 2002). However, much of this evidence is correlational and rarely tests competence directly as the mechanism (Van den Broeck et al., 2016).
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==See also==
* [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|Autonomy and intrinsic motivation in self-determination theory]] (Book chapter, 2025)
* [[Motivation and emotion/Book/2011/Self-determination theory|Self-determination theory]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Book chapter, 2026)
* [[w:Self-determination theory|Self-determination theory]] (Wikipedia)
* [[w:Self-efficacy|Self-efficacy]] (Wikipedia)
* [[w:Learned helplessness|Learned helplessness]] (Wikipedia)
 
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==References==
{{Hanging indent|1=

Abramson, L. Y., Seligman, M. E., &amp; Teasdale, J. D. (1978). Learned helplessness in humans: Critique and reformulation. Journal of Abnormal Psychology (1965), 87(1), 49–74. https://doi.org/10.1037/0021-843X.87.1.49
 
Baard, P. P., Deci, E. L., &amp; Ryan, R. M. (2004). Intrinsic need satisfaction: a motivational basis of performance and well-being in two work settings. Journal of Applied Social Psychology, 34(10), 2045–2068. https://doi.org/10.1111/j.1559-1816.2004.tb02690.x

Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191–215. https://doi.org/10.1037/0033-295X.84.2.191
 
Bartholomew, K. J., Ntoumanis, N., Ryan, R. M., Bosch, J. A., &amp; Thøgersen-Ntoumani, C. (2011). Self-Determination Theory and Diminished Functioning: The Role of Interpersonal Control and Psychological Need Thwarting. Personality &amp; Social Psychology Bulletin, 37(11), 1459–1473. https://doi.org/10.1177/0146167211413125
 
Bureau, J. S., Howard, J. L., Chong, J. X. Y., &amp; Guay, F. (2022). Pathways to Student Motivation: A Meta-Analysis of Antecedents of Autonomous and Controlled Motivations. Review of Educational Research, 92(1), 46–72. https://doi.org/10.3102/00346543211042426
 
Cameron, J., &amp; Pierce, W. D. (1994). Reinforcement, Reward, and Intrinsic Motivation: A Meta-Analysis. Review of Educational Research, 64(3), 363–423. https://doi.org/10.3102/00346543064003363

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. Motivation and Emotion, 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1

Deci, E. L. (1971). Effects of externally mediated rewards on intrinsic motivation. Journal of Personality and Social Psychology, 18(1), 105–115. https://doi.org/10.1037/h0030644
 
Deci, E. L., Koestner, R., &amp; Ryan, R. M. (1999). A Meta-Analytic Review of Experiments Examining the Effects of Extrinsic Rewards on Intrinsic Motivation. Psychological Bulletin, 125(6), 627–668. https://doi.org/10.1037/0033-2909.125.6.627
 
Deci, E. L., &amp; Ryan, R. M. (1985). ''Intrinsic motivation and self-determination in human behavior''. Springer. https://doi.org/10.1016/j.cedpsych.2020.101860.

Fong, C. J., Patall, E. A., Vasquez, A. C., &amp; Stautberg, S. (2019). A Meta-Analysis of Negative Feedback on Intrinsic Motivation. Educational Psychology Review, 31(1), 121–162. https://doi.org/10.1007/s10648-018-9446-6
 
Locke, E. A., &amp; Latham, G. P. (2002). Building a practically useful theory of goal setting and task motivation: A 35-year odyssey. The American Psychologist, 57(9), 705–717. https://doi.org/10.1037/0003-066X.57.9.705

Maslow, A. H. (1943). A theory of human motivation. ''Psychological Review, 50''(4), 370–396. https://doi.org/10.1037/h0054346
 
Morsink, S., Van der Oord, S., Antrop, I., Danckaerts, M., &amp; Scheres, A. (2022). Studying motivation in ADHD: The role of internal motives and the relevance of self determination theory. ''Journal of Attention Disorders, 26''(8), 1139–1158. https://doi.org/10.1177/10870547211050948
 
Reeve, J. (2024). ''Understanding motivation and emotion'' (8th ed.). Wiley.
 
Ryan, R. M., &amp; Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. ''American Psychologist, 55''(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68
 
Ryan, R. M., &amp; Deci, E. L. (2017). ''Self-determination theory: Basic psychological needs in motivation, development, and wellness''. Guilford Press. https://doi.org/10.1521/978.14625/28806
 
Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology, 61'', Article 101860. https://doi.org/10.1016/j.cedpsych.2020.101860
 
Seligman, M. E. P., &amp; Maier, S. F. (1967). Failure to escape traumatic shock. ''Journal of Experimental Psychology, 74''(1), 1–9. https://doi.org/10.1037/h0024514
 
Slemp, G. R., Kern, M. L., Patrick, K. J., &amp; Ryan, R. M. (2018). Leader autonomy support in the workplace: A meta-analytic review. ''Motivation and Emotion, 42''(5), 706–724. https://doi.org/10.1007/s11031-018-9698-y
 
Tay, L., &amp; Diener, E. (2011). Needs and subjective well-being around the world. ''Journal of Personality and Social Psychology, 101''(2), 354–365. https://doi.org/10.1037/a0023779
 
Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A review of self-determination theory's basic psychological needs at work. ''Journal of Management, 42''(5), 1195–1229. https://doi.org/10.1177/0149206316632058
 
Vansteenkiste, M., &amp; Ryan, R. M. (2013). On psychological growth and vulnerability: Basic psychological need satisfaction and need frustration as a unifying principle. ''Journal of Psychotherapy Integration, 23''(3), 263–280. https://doi.org/10.1037/a0032359
 
Vansteenkiste, M., Ryan, R. M., &amp; Soenens, B. (2020). Basic psychological need theory: Advancements, critical themes, and future directions. ''Motivation and Emotion, 44''(1), 1–31. https://doi.org/10.1007/s11031-019-09818-1
 
White, R. W. (1959). Motivation reconsidered: The concept of competence. ''Psychological Review, 66''(5), 297–333. https://doi.org/10.1037/h0040934
}}


==External links==
* https://open.ncl.ac.uk/theories/20/self-determination-theory/
* https://www.apa.org/ed/schools/teaching-learning/top-twenty/motivation
* https://positivepsychology.com/self-determination-theory/

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[[Category:Motivation and emotion/Book/Self-determination theory/Competence]]</text>
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      <text bytes="30292" sha1="8rqbxmwb1nde00ro8m4ht9t16fnzlkh" xml:space="preserve">{{title|Competence motivation in self-determination theory:&lt;br&gt;How does the need for competence function within self-determination theory to shape motivation and behaviour?}}
 __TOC__

==Overview==
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study:'''
[[File:Woman Suffering from Stress at Work (cropped).jpg|thumb|right|260px|'''Figure 1'''. Facing a large, unstructured task without guidance or feedback can leave a person doubting their own ability.]]
 
Maya, a 24-year-old administrative officer, has not opened her biggest project in three days. Instead, she has answered every email and tidied a shared drive she built herself: familiar tasks she knows she can do well.
 
Two months ago, Maya was excited when her manager asked her to review and reorganise more than 500 folders in the team's records system. But she received no guidance on where to start or what &quot;finished&quot; should look like. Each folder revealed new complexity, and nobody told her if her decisions were right. (see Figure 1). Some days she thinks, &quot;I just need clearer instructions.&quot; On other days her thoughts turn personal: &quot;I'm hopeless at this.&quot; The first thought sends her to ask for help; the second sends her back to her inbox.
 
''Why does the same task leave a person ready to improve on some days, and ready to give up on others?''
&lt;/div&gt;
 
 
According to [[w:Self-determination theory|self-determination theory]] (SDT), this difference often comes down to the need for [[Motivation and emotion/Book/2011/Self-determination theory|competence]]. Competence is the need to feel effective and capable (Ryan &amp; Deci, 2017). It is one of three basic psychological needs, alongside [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|autonomy]] and [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|relatedness]] (Ryan &amp; Deci, 2017). When competence is satisfied, people tend to show stronger [[Motivation and emotion/Book/2013/Intrinsic motivation|intrinsic motivation]], persistence, and wellbeing (Ryan &amp; Deci, 2020). When it is frustrated, as in Maya's case, people tend to avoid tasks and give up (Vansteenkiste et al., 2020).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Focus questions'''
* What is competence, according to self-determination theory?
* How does competence relate to intrinsic motivation?
* How does cognitive evaluation theory explain why feedback and rewards can strengthen or undermine motivation?
* What happens when the need for competence is frustrated?
* What does research show about how competence can be supported?
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Self-determination theory and competence==
 
===What is self-determination theory?===
SDT is a broad theory of human motivation. It proposes that people have three innate psychological needs: autonomy (feeling volitional), competence (feeling effective), as well as relatedness (feeling connected to others) (Deci &amp; Ryan, 1985; Ryan &amp; Deci, 2017). SDT is made up of six mini-theories, and two of these are central to this chapter. These are cognitive evaluation theory and basic psychological needs theory (Vansteenkiste et al., 2020). SDT is often compared with [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]]. Maslow (1943) proposed a hierarchy in which lower needs, such as physiological and safety needs, generally take priority over higher needs, such as esteem and self-actualisation. He placed mastery within esteem needs. SDT agrees that people strive to feel capable. However, SDT does not rank its needs and considers all three essential at all times (Ryan &amp; Deci, 2017).
 
[[File:MaslowsHierarchyOfNeeds.svg|thumb|right|300px|'''Figure 2'''. Maslow's hierarchy of needs places mastery within esteem needs, near the top of the hierarchy. SDT treats competence as essential at every level.]]
 
Tay and Diener (2011) tested these two views using Gallup World Poll data from 60,865 people in 123 countries. Although people did tend to meet basic and safety needs first, which partly supports Maslow, each need, including mastery, contributed to wellbeing regardless of whether the other needs were met (Tay &amp; Diener, 2011). The needs that mirror SDT, namely social relationships, autonomy, and mastery, were among the strongest predictors of everyday feelings across all eight world regions studied. One limitation is that the data were cross-sectional. Each need was also measured with only two or three yes or no questions, so the study shows association, not cause.
 
===What is competence within self-determination theory?===
The idea of competence as a motivational force dates back to White (1959), who challenged the drive theories of his time. He noticed that infants and young animals explore and play, as well as manipulate objects, even when they are fed and safe. He argued that this behaviour comes from a built-in need to have an effect on the environment, which he called effectance motivation. SDT builds on this idea and defines competence as the need to ''feel'' effective, not simply to possess a skill (Ryan &amp; Deci, 2017). This means that a highly skilled person can still feel incompetent if they receive no sign that their efforts are working.
 
According to SDT, competence is best satisfied in well-structured environments that offer ''[[wikipedia:Challenge_point_framework|optimal challenge]]'', positive feedback, and opportunities for growth (Ryan &amp; Deci, 2020). An optimally challenging task sits slightly beyond a person's current skill, but it comes with enough structure and support to close the gap. Tasks that are too easy offer no sense of growth, while tasks that are too hard, especially without guidance, signal failure (Reeve, 2024). Maya's difficulty illustrates how a lack of structure and feedback can make a manageable task feel too hard.
 
Basic psychological needs theory treats need satisfaction and need frustration as two separate experiences (Vansteenkiste &amp; Ryan, 2013). Need satisfaction is linked to a &quot;bright&quot; pathway of growth and engagement, as well as wellbeing (Vansteenkiste et al., 2020). Need frustration is linked to a &quot;dark&quot; pathway of defensiveness, avoidance, and ill-being (Vansteenkiste et al., 2020). Low satisfaction and active frustration are therefore not the same thing. Receiving no feedback may leave a person unfulfilled, but being repeatedly made to feel ineffective actively harms wellbeing (Vansteenkiste &amp; Ryan, 2013). The case study shows this shift. Maya moves from low satisfaction in the early weeks to active frustration after her manager's review, described later in the chapter.
 
===Competence and self-efficacy===
Competence overlaps closely with [[w:Self-efficacy|self-efficacy]], which is a person's belief that they can successfully perform a specific behaviour (Bandura, 1977). Bandura separated two expectations that shape whether people act. An ''efficacy expectation'' asks &quot;Can I do it?&quot;, and an ''outcome expectation'' asks &quot;Will it work?&quot; Efficacy beliefs are built from four sources: personal mastery experiences, watching similar others succeed, verbal persuasion, and how people interpret their own stress (Bandura, 1977). Of these, mastery experiences are the most powerful (Bandura, 1977).
 
In the case study, several of these sources are weakened. Without feedback, Maya cannot judge whether her decisions are effective, so her real progress is not experienced as mastery. As the case study later shows, her manager's comments act as negative persuasion. Her anxiety before opening the project is also likely to be read as evidence that she is not capable. The key difference between the two concepts is that self-efficacy is a belief about a specific future task (Bandura, 1977). In contrast, SDT treats competence as a universal need that shapes motivation and wellbeing over time (Ryan &amp; Deci, 2017). In practice, however, the two are difficult to separate, because both are usually measured with similar self-report questions. Some &quot;competence&quot; findings may therefore simply reflect confidence.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Competence and intrinsic motivation==
 
SDT's central claim is that the ''quality'' of motivation matters as much as its quantity (Ryan &amp; Deci, 2020). Feeling competent affects where people sit on the motivation continuum, as well as how they respond to feedback and rewards (Deci et al., 1999; Ryan &amp; Deci, 2020).
 
===The motivation continuum===
SDT describes motivation as a continuum (Ryan &amp; Deci, 2020; see Figure 3). The continuum ranges from [[Motivation and emotion/Book/2014/Amotivation|amotivation]], meaning no intention to act, through several forms of extrinsic motivation, to intrinsic motivation, meaning acting for enjoyment or interest (Ryan &amp; Deci, 2020). A lack of competence is one of the main causes of amotivation (Ryan &amp; Deci, 2000). It shows in thoughts such as &quot;I can't do this&quot; or &quot;my effort won't make a difference&quot;. In contrast, feeling capable helps people [[w:Internalization (sociology)|internalise]] the value of a task, so the task feels self-endorsed instead of obligatory (Ryan &amp; Deci, 2020). In the case study, Maya's growing avoidance of her project suggests she is sliding toward amotivation.
 
[[File:Taxonomy of motivation.png|thumb|center|600px|'''Figure 3'''. The SDT motivation continuum, ranging from amotivation, through controlled and autonomous forms of extrinsic motivation, to intrinsic motivation.]]
 
===Cognitive evaluation theory===
[[Motivation and emotion/Book/2021/Cognitive evaluation theory and motivation|Cognitive evaluation theory]] (CET) explains how external events such as feedback and rewards affect intrinsic motivation (Ryan &amp; Deci, 2000). According to CET, every such event has a ''controlling'' aspect, which affects autonomy, and an ''informational'' aspect, which affects competence (Ryan &amp; Deci, 2000). Informational feedback increases perceived competence and intrinsic motivation (Deci et al., 1999). In contrast, rewards that feel like pressure tend to undermine intrinsic motivation, even when they signal success (Deci et al., 1999). CET therefore predicts that ''how'' feedback is delivered matters as much as ''what'' it says. Later versions of CET added a third, ''amotivating'' aspect (Ryan &amp; Deci, 2017). Events that signal incompetence, or that effort will not change the outcome, can push people toward amotivation. Criticism that offers no way forward, such as the feedback Maya later receives, is likely to carry this amotivating message.
 
Research generally supports these predictions, although the earliest evidence was weak. RIn Deci's (1971) original experiment, students paid $1 for each puzzle they solved later spent less free time on the puzzles once payment stopped. However, the study had only 24 participants, and the result was only a trend (Deci, 1971). A later meta-analysis of 128 experiments, mostly with children and university students, found a clearer pattern (Deci et al., 1999). People who expected a tangible reward for an interesting task spent less free time on it afterwards. In studies with children, this effect was still present more than a week later. The most damaging rewards were those that signalled a person had fallen short (Deci et al., 1999). Feedback style also mattered. Informational praise increased intrinsic motivation, but the same praise with a controlling phrase such as &quot;just as you ''should''&quot; decreased it (Ryan et al., 1983, as cited in Deci et al., 1999). Negative feedback was less harmful when it included guidance on how to improve (Fong et al., 2019). Rewards did not undermine motivation for boring tasks or when they were unexpected (Deci et al., 1999).
 
CET assumes that these effects work ''through'' perceived competence (Ryan &amp; Deci, 2017). However, relatively few studies have measured perceived competence directly to test this (Deci et al., 1999). The results fit the theory, but the mechanism is more often assumed than demonstrated. Even so, the practical message is consistent. Feedback that identifies a problem, such as &quot;the scope needs to be better defined&quot;, without showing how to fix it is unlikely to support competence (Fong et al., 2019).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{According to cognitive evaluation theory, positive feedback is most likely to increase intrinsic motivation when it is:

|type=&quot;()&quot;}
- Given with a large financial reward
+ Informative and delivered in an autonomy-supportive way
- Delivered as a comparison with other people
- Given constantly, regardless of performance
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==When competence is frustrated==
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's first review'''
 
'''Week 6.''' Maya's manager reviews the project. She acknowledges some progress, then adds that the plan needs to be clearer and the scope better defined. She does not say what a clearer plan looks like or how to narrow the scope. Maya leaves the meeting feeling like a failure. She had enjoyed the first few folders, but now she dreads opening the system.
 
'''What is happening?''' The feedback identified a problem without giving Maya the information to solve it. Her effort no longer seems to lead anywhere, which is when a need starts to be actively frustrated, not just unmet.
&lt;/div&gt;
 
Research supports the distinction between low satisfaction and active frustration (Vansteenkiste &amp; Ryan, 2013). Bartholomew et al. (2011) found that athletes who saw their coach as controlling reported greater thwarting of all three needs. Need thwarting, in turn, predicted burnout, depressive symptoms, and negative emotion (Bartholomew et al., 2011). Feeling actively undermined was more harmful than simply not feeling supported. If the same pattern holds for competence, vague, critical feedback may harm Maya more than no feedback at all.
 
When people repeatedly experience that their effort makes no difference, they may develop [[w:Learned helplessness|learned helplessness]] (Seligman &amp; Maier, 1967). In classic experiments, dogs exposed to inescapable shocks later failed to escape shocks they could have avoided (Seligman &amp; Maier, 1967). Dogs that had been given control earlier learned to escape. In humans, helplessness reduces effort and is linked to apathy and depression (Abramson et al., 1978).How people explain failure also matters. The reformulated helplessness model proposes that explaining failure with internal, stable and global causes is more damaging than explaining it with external, unstable or specific causes (Abramson et al., 1978). Maya's two thoughts show this difference. &quot;I'm hopeless at this&quot; blames a lasting personal flaw and is more likely to lead to giving up, whereas &quot;I just need clearer instructions&quot; points to a specific, changeable cause that keeps her trying.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Maya thinks, &quot;I'm hopeless at this.&quot; According to research on explanatory style, why is this thought more harmful than &quot;I just need clearer instructions&quot;?

|type=&quot;()&quot;}
- It is less accurate
+ It explains failure with an internal, stable cause she cannot easily change
- It blames her manager instead of herself
- It focuses on the task rather than on herself
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==What supports or undermines competence?==
 
In two workplace studies, Baard et al. (2004) found that employees' satisfaction of autonomy, competence, and relatedness predicted their wellbeing as well as their performance evaluations. Because supervisors rated performance, this finding is less affected by self-report bias. However, the design still cannot show which came first. A meta-analysis by Van den Broeck et al. (2016) found that competence predicted wellbeing, work attitudes, and behaviour, even after the other two needs were taken into account. This suggests that competence is not simply a by-product of feeling autonomous or connected. Leadership also matters. Managers' autonomy-supportive behaviour is associated with greater need satisfaction as well as more autonomous motivation in employees (Slemp et al., 2018). This suggests that how Maya's manager behaves may affect her need satisfaction, including her sense of competence.
 
Similar patterns appear in classrooms. Bureau et al. (2022) pooled studies of what predicts student motivation and found that, of the three needs, support for competence was the strongest predictor of autonomous motivation (Bureau et al., 2022). This is a notable finding, because SDT has historically given autonomy the most attention (Ryan &amp; Deci, 2017). It suggests that, at least in classrooms, feeling capable may matter as much as feeling free to choose. However, the meta-analysis draws mainly on correlational studies, so it shows which students do well, but it does not prove that supporting competence causes better outcomes.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
The strength of the evidence depends on the methods used. The reward findings, for example, were contested. Cameron and Pierce (1994, as cited in Deci et al., 1999) found no overall undermining effect and argued that CET should be abandoned. Deci et al. (1999) argued that this result came from mixing boring and interesting tasks, as well as using inappropriate control groups. Laboratory studies also relied mostly on single sessions with children and students (Deci et al., 1999). Self-reported interest also showed much weaker effects than behaviour. Outside the laboratory, most studies are cross-sectional. This makes it unclear whether competence drives motivation or whether motivated people simply feel more competent (Van den Broeck et al., 2016).
 
Some critics have questioned whether basic needs are truly universal, because SDT was developed largely in Western contexts (Chen et al., 2015). However, a study of adults in Belgium, China, Peru, and the United States found that need satisfaction and need frustration predicted wellbeing and ill-being in all four cultures (Chen et al., 2015). Together with the overlap between competence and self-efficacy, these limitations point to the same gap noted in CET. SDT predicts outcomes well, but whether competence itself is the active ingredient remains less certain than the theory suggests (Deci et al., 1999).
 
Most competence research has also used neurotypical samples (Morsink et al., 2022). Morsink et al. (2022) noted that research on [[w:Attention deficit hyperactivity disorder|attention-deficit/hyperactivity disorder]] (ADHD) has mostly studied rewards and overlooked psychological needs. This is despite evidence that children with more ADHD symptoms report lower need satisfaction at school.(Morsink et al., 2022) Frequent correction may push teachers and parents toward controlling styles, which can further frustrate competence (Morsink et al., 2022). Whether supporting competence helps neurodivergent people in the same way remains largely untested.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Applying competence in practice==
The research reviewed so far points to a consistent set of conditions under which people feel capable. Table 1 contrasts environments that support competence with those that thwart it. These features reflect the four sources of competence support in SDT, which are clear expectations, optimal challenge, guidance, and constructive feedback (Reeve, 2024).
 
{| class=&quot;wikitable&quot; style=&quot;margin:1em auto; border-radius:8px;&quot;
|+ '''Table 1'''&lt;br&gt;''Features of Competence-Supportive and Competence-Thwarting Environments''
|-
! style=&quot;background:#eaf3fc;&quot; | Competence-supportive !! style=&quot;background:#fff6e8;&quot; | Competence-thwarting
|-
| Clear expectations about how to succeed || Vague or missing guidance
|-
| Guidance and modelling of &quot;how-to&quot; skills || Being left to work it out alone
|-
| Optimal challenge matched to current skills || Tasks far too hard or too easy
|-
| Specific, informative feedback || Absent, harsh, or controlling feedback
|-
| Long-term goals broken into short-term goals || No sense of progress
|-
| Mistakes framed as learning || Mistakes criticised or punished
|}

 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's turnaround'''
 
'''Week 8.''' Maya's manager notices the slowing progress and changes approach. They agree on what &quot;finished&quot; looks like and break the project into stages, starting with the 50 most-used folders.
 
'''Week 12.''' After each stage, Maya receives specific feedback on what is working. She now makes decisions confidently and has started suggesting improvements herself.
 
'''What changed?''' The structure around how the task would be completed: clear expectations, achievable steps, and feedback that informed instead of judged. Each gave Maya evidence that she was effective.
&lt;/div&gt;
 
Breaking Maya's project into stages draws on [[w:Goal setting|goal-setting theory]] (Locke &amp; Latham, 2002). Locke and Latham (2002) reviewed 35 years of laboratory and field studies. They found that specific, challenging goals combined with regular feedback consistently outperform vague &quot;do your best&quot; goals. Specific goals work partly because they show people exactly what success looks like. Each completed stage also acts as a mastery experience, which is the strongest source of self-efficacy (Bandura, 1977). This helps explain why Maya's confidence returned once the work was divided into stages.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Which change would best support Maya's need for competence?

|type=&quot;()&quot;}
- Offering her a bonus if she finishes faster
+ Breaking the project into stages with clear goals and specific feedback
- Telling her she is doing a great job regardless of progress
- Comparing her progress with a colleague's
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Conclusion==
Competence is the need to ''feel'' effective, and SDT treats it as important at all times, not only once basic needs are met (Ryan &amp; Deci, 2017; Tay &amp; Diener, 2011). Feeling competent moves people toward more autonomous motivation (Ryan &amp; Deci, 2020). CET explains why the same feedback can either energise or deflate a person, depending on whether it informs or controls (Deci et al., 1999).
 
When competence is actively frustrated, the consequences are more severe than when it is simply unmet. These consequences range from burnout to the helpless thinking shown in the case study (Abramson et al., 1978; Bartholomew et al., 2011). Research across workplaces, classrooms suggests that clear expectations and informational feedback, as well as challenges broken into achievable steps, can reverse this pattern (Baard et al., 2004; Locke &amp; Latham, 2002). However, much of this evidence is correlational and rarely tests competence directly as the mechanism (Van den Broeck et al., 2016).
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==See also==
* [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|Autonomy and intrinsic motivation in self-determination theory]] (Book chapter, 2025)
* [[Motivation and emotion/Book/2011/Self-determination theory|Self-determination theory]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Book chapter, 2026)
* [[w:Self-determination theory|Self-determination theory]] (Wikipedia)
* [[w:Self-efficacy|Self-efficacy]] (Wikipedia)
* [[w:Learned helplessness|Learned helplessness]] (Wikipedia)
 
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==References==
{{Hanging indent|1=

Abramson, L. Y., Seligman, M. E., &amp; Teasdale, J. D. (1978). Learned helplessness in humans: Critique and reformulation. Journal of Abnormal Psychology (1965), 87(1), 49–74. https://doi.org/10.1037/0021-843X.87.1.49
 
Baard, P. P., Deci, E. L., &amp; Ryan, R. M. (2004). Intrinsic need satisfaction: a motivational basis of performance and well-being in two work settings. Journal of Applied Social Psychology, 34(10), 2045–2068. https://doi.org/10.1111/j.1559-1816.2004.tb02690.x

Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191–215. https://doi.org/10.1037/0033-295X.84.2.191
 
Bartholomew, K. J., Ntoumanis, N., Ryan, R. M., Bosch, J. A., &amp; Thøgersen-Ntoumani, C. (2011). Self-Determination Theory and Diminished Functioning: The Role of Interpersonal Control and Psychological Need Thwarting. Personality &amp; Social Psychology Bulletin, 37(11), 1459–1473. https://doi.org/10.1177/0146167211413125
 
Bureau, J. S., Howard, J. L., Chong, J. X. Y., &amp; Guay, F. (2022). Pathways to Student Motivation: A Meta-Analysis of Antecedents of Autonomous and Controlled Motivations. Review of Educational Research, 92(1), 46–72. https://doi.org/10.3102/00346543211042426
 
Cameron, J., &amp; Pierce, W. D. (1994). Reinforcement, Reward, and Intrinsic Motivation: A Meta-Analysis. Review of Educational Research, 64(3), 363–423. https://doi.org/10.3102/00346543064003363

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. Motivation and Emotion, 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1

Deci, E. L. (1971). Effects of externally mediated rewards on intrinsic motivation. Journal of Personality and Social Psychology, 18(1), 105–115. https://doi.org/10.1037/h0030644
 
Deci, E. L., Koestner, R., &amp; Ryan, R. M. (1999). A Meta-Analytic Review of Experiments Examining the Effects of Extrinsic Rewards on Intrinsic Motivation. Psychological Bulletin, 125(6), 627–668. https://doi.org/10.1037/0033-2909.125.6.627
 
Deci, E. L., &amp; Ryan, R. M. (1985). ''Intrinsic motivation and self-determination in human behavior''. Springer. https://doi.org/10.1016/j.cedpsych.2020.101860.

Fong, C. J., Patall, E. A., Vasquez, A. C., &amp; Stautberg, S. (2019). A Meta-Analysis of Negative Feedback on Intrinsic Motivation. Educational Psychology Review, 31(1), 121–162. https://doi.org/10.1007/s10648-018-9446-6
 
Locke, E. A., &amp; Latham, G. P. (2002). Building a practically useful theory of goal setting and task motivation: A 35-year odyssey. The American Psychologist, 57(9), 705–717. https://doi.org/10.1037/0003-066X.57.9.705

Maslow, A. H. (1943). A theory of human motivation. ''Psychological Review, 50''(4), 370–396. https://doi.org/10.1037/h0054346
 
Morsink, S., Van der Oord, S., Antrop, I., Danckaerts, M., &amp; Scheres, A. (2022). Studying motivation in ADHD: The role of internal motives and the relevance of self determination theory. ''Journal of Attention Disorders, 26''(8), 1139–1158. https://doi.org/10.1177/10870547211050948
 
Reeve, J. (2024). ''Understanding motivation and emotion'' (8th ed.). Wiley.
 
Ryan, R. M., &amp; Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. ''American Psychologist, 55''(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68
 
Ryan, R. M., &amp; Deci, E. L. (2017). ''Self-determination theory: Basic psychological needs in motivation, development, and wellness''. Guilford Press. https://doi.org/10.1521/978.14625/28806
 
Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology, 61'', Article 101860. https://doi.org/10.1016/j.cedpsych.2020.101860
 
Seligman, M. E. P., &amp; Maier, S. F. (1967). Failure to escape traumatic shock. ''Journal of Experimental Psychology, 74''(1), 1–9. https://doi.org/10.1037/h0024514
 
Slemp, G. R., Kern, M. L., Patrick, K. J., &amp; Ryan, R. M. (2018). Leader autonomy support in the workplace: A meta-analytic review. ''Motivation and Emotion, 42''(5), 706–724. https://doi.org/10.1007/s11031-018-9698-y
 
Tay, L., &amp; Diener, E. (2011). Needs and subjective well-being around the world. ''Journal of Personality and Social Psychology, 101''(2), 354–365. https://doi.org/10.1037/a0023779
 
Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A review of self-determination theory's basic psychological needs at work. ''Journal of Management, 42''(5), 1195–1229. https://doi.org/10.1177/0149206316632058
 
Vansteenkiste, M., &amp; Ryan, R. M. (2013). On psychological growth and vulnerability: Basic psychological need satisfaction and need frustration as a unifying principle. ''Journal of Psychotherapy Integration, 23''(3), 263–280. https://doi.org/10.1037/a0032359
 
Vansteenkiste, M., Ryan, R. M., &amp; Soenens, B. (2020). Basic psychological need theory: Advancements, critical themes, and future directions. ''Motivation and Emotion, 44''(1), 1–31. https://doi.org/10.1007/s11031-019-09818-1
 
White, R. W. (1959). Motivation reconsidered: The concept of competence. ''Psychological Review, 66''(5), 297–333. https://doi.org/10.1037/h0040934
}}


==External links==
* https://open.ncl.ac.uk/theories/20/self-determination-theory/
* https://www.apa.org/ed/schools/teaching-learning/top-twenty/motivation
* https://positivepsychology.com/self-determination-theory/

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      <text bytes="30340" sha1="igyke24oywycd5yz8d7boaahgijzrvm" xml:space="preserve">{{title|Competence motivation in self-determination theory:&lt;br&gt;How does the need for competence function within self-determination theory to shape motivation and behaviour?}}
 __TOC__

==Overview==
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study:'''
[[File:Woman Suffering from Stress at Work (cropped).jpg|thumb|right|260px|'''Figure 1'''. Facing a large, unstructured task without guidance or feedback can leave a person doubting their own ability.]]
 
Maya, a 24-year-old administrative officer, has not opened her biggest project in three days. Instead, she has answered every email and tidied a shared drive she built herself: familiar tasks she knows she can do well.
 
Two months ago, Maya was excited when her manager asked her to review and reorganise more than 500 folders in the team's records system. But she received no guidance on where to start or what &quot;finished&quot; should look like. Each folder revealed new complexity, and nobody told her if her decisions were right. (see Figure 1). Some days she thinks, &quot;I just need clearer instructions.&quot; On other days her thoughts turn personal: &quot;I'm hopeless at this.&quot; The first thought sends her to ask for help; the second sends her back to her inbox.
 
''Why does the same task leave a person ready to improve on some days, and ready to give up on others?''
&lt;/div&gt;
 
 
According to [[w:Self-determination theory|self-determination theory]] (SDT), this difference often comes down to the need for [[Motivation and emotion/Book/2011/Self-determination theory|competence]]. Competence is the need to feel effective and capable (Ryan &amp; Deci, 2017). It is one of three basic psychological needs, alongside [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|autonomy]] and [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|relatedness]] (Ryan &amp; Deci, 2017). When competence is satisfied, people tend to show stronger [[Motivation and emotion/Book/2013/Intrinsic motivation|intrinsic motivation]], persistence, and wellbeing (Ryan &amp; Deci, 2020). When it is frustrated, as in Maya's case, people tend to avoid tasks and give up (Vansteenkiste et al., 2020).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Focus questions'''
* What is competence, according to self-determination theory?
* How does competence relate to intrinsic motivation?
* How does cognitive evaluation theory explain why feedback and rewards can strengthen or undermine motivation?
* What happens when the need for competence is frustrated?
* What does research show about how competence can be supported?
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Self-determination theory and competence==
 
===What is self-determination theory?===
SDT is a broad theory of human motivation. It proposes that people have three innate psychological needs: autonomy (feeling volitional), competence (feeling effective), as well as relatedness (feeling connected to others) (Deci &amp; Ryan, 1985; Ryan &amp; Deci, 2017). SDT is made up of six mini-theories, and two of these are central to this chapter. These are cognitive evaluation theory and basic psychological needs theory (Vansteenkiste et al., 2020). SDT is often compared with [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]]. Maslow (1943) proposed a hierarchy in which lower needs, such as physiological and safety needs, generally take priority over higher needs, such as esteem and self-actualisation. He placed mastery within esteem needs. SDT agrees that people strive to feel capable. However, SDT does not rank its needs and considers all three essential at all times (Ryan &amp; Deci, 2017).
 
[[File:MaslowsHierarchyOfNeeds.svg|thumb|right|300px|'''Figure 2'''. Maslow's hierarchy of needs places mastery within esteem needs, near the top of the hierarchy. SDT treats competence as essential at every level.]]
 
Tay and Diener (2011) tested these two views using Gallup World Poll data from 60,865 people in 123 countries. Although people did tend to meet basic and safety needs first, which partly supports Maslow, each need, including mastery, contributed to wellbeing regardless of whether the other needs were met (Tay &amp; Diener, 2011). The needs that mirror SDT, namely social relationships, autonomy, and mastery, were among the strongest predictors of everyday feelings across all eight world regions studied. One limitation is that the data were cross-sectional. Each need was also measured with only two or three yes or no questions, so the study shows association, not cause.
 
===What is competence within self-determination theory?===
The idea of competence as a motivational force dates back to White (1959), who challenged the drive theories of his time. He noticed that infants and young animals explore and play, as well as manipulate objects, even when they are fed and safe. He argued that this behaviour comes from a built-in need to have an effect on the environment, which he called effectance motivation. SDT builds on this idea and defines competence as the need to ''feel'' effective, not simply to possess a skill (Ryan &amp; Deci, 2017). This means that a highly skilled person can still feel incompetent if they receive no sign that their efforts are working.
 
According to SDT, competence is best satisfied in well-structured environments that offer ''[[wikipedia:Challenge_point_framework|optimal challenge]]'', positive feedback, and opportunities for growth (Ryan &amp; Deci, 2020). An optimally challenging task sits slightly beyond a person's current skill, but it comes with enough structure and support to close the gap. Tasks that are too easy offer no sense of growth, while tasks that are too hard, especially without guidance, signal failure (Reeve, 2024). Maya's difficulty illustrates how a lack of structure and feedback can make a manageable task feel too hard.
 
Basic psychological needs theory treats need satisfaction and need frustration as two separate experiences (Vansteenkiste &amp; Ryan, 2013). Need satisfaction is linked to a &quot;bright&quot; pathway of growth and engagement, as well as wellbeing (Vansteenkiste et al., 2020). Need frustration is linked to a &quot;dark&quot; pathway of defensiveness, avoidance, and ill-being (Vansteenkiste et al., 2020). Low satisfaction and active frustration are therefore not the same thing. Receiving no feedback may leave a person unfulfilled, but being repeatedly made to feel ineffective actively harms wellbeing (Vansteenkiste &amp; Ryan, 2013). The case study shows this shift. Maya moves from low satisfaction in the early weeks to active frustration after her manager's review, described later in the chapter.
 
===Competence and self-efficacy===
Competence overlaps closely with [[w:Self-efficacy|self-efficacy]], which is a person's belief that they can successfully perform a specific behaviour (Bandura, 1977). Bandura separated two expectations that shape whether people act. An ''efficacy expectation'' asks &quot;Can I do it?&quot;, and an ''outcome expectation'' asks &quot;Will it work?&quot; Efficacy beliefs are built from four sources: personal mastery experiences, watching similar others succeed, verbal persuasion, and how people interpret their own stress (Bandura, 1977). Of these, mastery experiences are the most powerful (Bandura, 1977).
 
In the case study, several of these sources are weakened. Without feedback, Maya cannot judge whether her decisions are effective, so her real progress is not experienced as mastery. As the case study later shows, her manager's comments act as negative persuasion. Her anxiety before opening the project is also likely to be read as evidence that she is not capable. The key difference between the two concepts is that self-efficacy is a belief about a specific future task (Bandura, 1977). In contrast, SDT treats competence as a universal need that shapes motivation and wellbeing over time (Ryan &amp; Deci, 2017). In practice, however, the two are difficult to separate, because both are usually measured with similar self-report questions. Some &quot;competence&quot; findings may therefore simply reflect confidence.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Competence and intrinsic motivation==
 
SDT's central claim is that the ''quality'' of motivation matters as much as its quantity (Ryan &amp; Deci, 2020). Feeling competent affects where people sit on the motivation continuum, as well as how they respond to feedback and rewards (Deci et al., 1999; Ryan &amp; Deci, 2020).
 
===The motivation continuum===
SDT describes [[motivation as a continuum]] (Ryan &amp; Deci, 2020; see Figure 3). The continuum ranges from [[Motivation and emotion/Book/2014/Amotivation|amotivation]], meaning no intention to act, through several forms of extrinsic motivation, to intrinsic motivation, meaning acting for enjoyment or interest (Ryan &amp; Deci, 2020). A lack of competence is one of the main causes of amotivation (Ryan &amp; Deci, 2000). It shows in thoughts such as &quot;I can't do this&quot; or &quot;my effort won't make a difference&quot;. In contrast, feeling capable helps people [[w:Internalization (sociology)|internalise]] the value of a task, so the task feels self-endorsed instead of obligatory (Ryan &amp; Deci, 2020). In the case study, Maya's growing avoidance of her project suggests she is sliding toward amotivation.
 
[[File:Taxonomy of motivation.png|thumb|center|600px|'''Figure 3'''. The SDT motivation continuum, ranging from amotivation, through controlled and autonomous forms of extrinsic motivation, to intrinsic motivation.]]
 
===Cognitive evaluation theory===
[[Motivation and emotion/Book/2021/Cognitive evaluation theory and motivation|Cognitive evaluation theory]] (CET) explains how external events such as feedback and rewards affect intrinsic motivation (Ryan &amp; Deci, 2000). According to CET, every such event has a ''controlling'' aspect, which affects autonomy, and an ''informational'' aspect, which affects competence (Ryan &amp; Deci, 2000). Informational feedback increases perceived competence and intrinsic motivation (Deci et al., 1999). In contrast, rewards that feel like pressure tend to undermine intrinsic motivation, even when they signal success (Deci et al., 1999). CET therefore predicts that ''how'' feedback is delivered matters as much as ''what'' it says. Later versions of CET added a third, ''amotivating'' aspect (Ryan &amp; Deci, 2017). Events that signal incompetence, or that effort will not change the outcome, can push people toward amotivation. Criticism that offers no way forward, such as the feedback Maya later receives, is likely to carry this amotivating message.
 
Research generally supports these predictions, although the earliest evidence was weak. RIn Deci's (1971) original experiment, students paid $1 for each puzzle they solved later spent less free time on the puzzles once payment stopped. However, the study had only 24 participants, and the result was only a trend (Deci, 1971). A later meta-analysis of 128 experiments, mostly with children and university students, found a clearer pattern (Deci et al., 1999). People who expected a tangible reward for an interesting task spent less free time on it afterwards. In studies with children, this effect was still present more than a week later. The most damaging rewards were those that signalled a person had fallen short (Deci et al., 1999). Feedback style also mattered. Informational praise increased intrinsic motivation, but the same praise with a controlling phrase such as &quot;just as you ''should''&quot; decreased it (Ryan et al., 1983, as cited in Deci et al., 1999). Negative feedback was less harmful when it included guidance on how to improve (Fong et al., 2019). Rewards did not undermine motivation for boring tasks or when they were unexpected (Deci et al., 1999).
 
CET assumes that these effects work ''through'' perceived competence (Ryan &amp; Deci, 2017). However, relatively few studies have measured perceived competence directly to test this (Deci et al., 1999). The results fit the theory, but the mechanism is more often assumed than demonstrated. Even so, the practical message is consistent. Feedback that identifies a problem, such as &quot;the scope needs to be better defined&quot;, without showing how to fix it is unlikely to support competence (Fong et al., 2019).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{According to cognitive evaluation theory, positive feedback is most likely to increase intrinsic motivation when it is:

|type=&quot;()&quot;}
- Given with a large financial reward
+ Informative and delivered in an autonomy-supportive way
- Delivered as a comparison with other people
- Given constantly, regardless of performance
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==When competence is frustrated==
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's first review'''
 
'''Week 6.''' Maya's manager reviews the project. She acknowledges some progress, then adds that the plan needs to be clearer and the scope better defined. She does not say what a clearer plan looks like or how to narrow the scope. Maya leaves the meeting feeling like a failure. She had enjoyed the first few folders, but now she dreads opening the system.
 
'''What is happening?''' The feedback identified a problem without giving Maya the information to solve it. Her effort no longer seems to lead anywhere, which is when a need starts to be actively frustrated, not just unmet.
&lt;/div&gt;
 
Research supports the distinction between low satisfaction and active frustration (Vansteenkiste &amp; Ryan, 2013). Bartholomew et al. (2011) found that athletes who saw their coach as controlling reported greater thwarting of all three needs. Need thwarting, in turn, predicted burnout, depressive symptoms, and negative emotion (Bartholomew et al., 2011). Feeling actively undermined was more harmful than simply not feeling supported. If the same pattern holds for competence, vague, critical feedback may harm Maya more than no feedback at all.
 
When people repeatedly experience that their effort makes no difference, they may develop [[w:Learned helplessness|learned helplessness]] (Seligman &amp; Maier, 1967). In classic experiments, dogs exposed to inescapable shocks later failed to escape shocks they could have avoided (Seligman &amp; Maier, 1967). Dogs that had been given control earlier learned to escape. In humans, helplessness reduces effort and is linked to apathy and depression (Abramson et al., 1978).How people explain failure also matters. The reformulated helplessness model proposes that explaining failure with internal, stable and global causes is more damaging than explaining it with external, unstable or specific causes (Abramson et al., 1978). Maya's two thoughts show this difference. &quot;I'm hopeless at this&quot; blames a lasting personal flaw and is more likely to lead to giving up, whereas &quot;I just need clearer instructions&quot; points to a specific, changeable cause that keeps her trying.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Maya thinks, &quot;I'm hopeless at this.&quot; According to research on explanatory style, why is this thought more harmful than &quot;I just need clearer instructions&quot;?

|type=&quot;()&quot;}
- It is less accurate
+ It explains failure with an internal, stable cause she cannot easily change
- It blames her manager instead of herself
- It focuses on the task rather than on herself
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==What supports or undermines competence?==
 
In two workplace studies, Baard et al. (2004) found that employees' satisfaction of autonomy, competence, and relatedness predicted their wellbeing as well as their performance evaluations. Because supervisors rated performance, this finding is less affected by self-report bias. However, the design still cannot show which came first. A meta-analysis by Van den Broeck et al. (2016) found that competence predicted wellbeing, work attitudes, and behaviour, even after the other two needs were taken into account. This suggests that competence is not simply a by-product of feeling autonomous or connected. Leadership also matters. Managers' autonomy-supportive behaviour is associated with greater need satisfaction as well as more autonomous motivation in employees (Slemp et al., 2018). This suggests that how Maya's manager behaves may affect her need satisfaction, including her sense of competence.
 
Similar patterns appear in classrooms. Bureau et al. (2022) pooled studies of what predicts student motivation and found that, of the three needs, support for competence was the strongest predictor of autonomous motivation (Bureau et al., 2022). This is a notable finding, because SDT has historically given autonomy the most attention (Ryan &amp; Deci, 2017). It suggests that, at least in classrooms, feeling capable may matter as much as feeling free to choose. However, the meta-analysis draws mainly on correlational studies, so it shows which students do well, but it does not prove that supporting competence causes better outcomes.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
The strength of the evidence depends on the methods used. The reward findings, for example, were contested. Cameron and Pierce (1994, as cited in Deci et al., 1999) found no overall undermining effect and argued that CET should be abandoned. Deci et al. (1999) argued that this result came from mixing boring and interesting tasks, as well as using inappropriate control groups. Laboratory studies also relied mostly on single sessions with children and students (Deci et al., 1999). Self-reported interest also showed much weaker effects than behaviour. Outside the laboratory, most studies are cross-sectional. This makes it unclear whether competence drives motivation or whether motivated people simply feel more competent (Van den Broeck et al., 2016).
 
Some critics have questioned whether basic needs are truly universal, because SDT was developed largely in Western contexts (Chen et al., 2015). However, a study of adults in Belgium, China, Peru, and the United States found that need satisfaction and need frustration predicted wellbeing and ill-being in all four cultures (Chen et al., 2015). Together with the overlap between competence and self-efficacy, these limitations point to the same gap noted in CET. SDT predicts outcomes well, but whether competence itself is the active ingredient remains less certain than the theory suggests (Deci et al., 1999).
 
Most competence research has also used neurotypical samples (Morsink et al., 2022). Morsink et al. (2022) noted that research on [[w:Attention deficit hyperactivity disorder|attention-deficit/hyperactivity disorder]] (ADHD) has mostly studied rewards and overlooked psychological needs. This is despite evidence that children with more ADHD symptoms report lower need satisfaction at school.(Morsink et al., 2022) Frequent correction may push teachers and parents toward controlling styles, which can further frustrate competence (Morsink et al., 2022). Whether supporting competence helps neurodivergent people in the same way remains largely untested.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Applying competence in practice==
The research reviewed so far points to a consistent set of conditions under which people feel capable. Table 1 contrasts environments that support competence with those that thwart it. These features reflect the four sources of competence support in SDT, which are clear expectations, optimal challenge, guidance, and constructive feedback (Reeve, 2024).
 
{| class=&quot;wikitable&quot; style=&quot;margin:1em auto; border-radius:8px;&quot;
|+ '''Table 1'''&lt;br&gt;''Features of Competence-Supportive and Competence-Thwarting Environments''
|-
! style=&quot;background:#eaf3fc;&quot; | Competence-supportive !! style=&quot;background:#fff6e8;&quot; | Competence-thwarting
|-
| Clear expectations about how to succeed || Vague or missing guidance
|-
| Guidance and modelling of &quot;how-to&quot; skills || Being left to work it out alone
|-
| Optimal challenge matched to current skills || Tasks far too hard or too easy
|-
| Specific, informative feedback || Absent, harsh, or controlling feedback
|-
| Long-term goals broken into short-term goals || No sense of progress
|-
| Mistakes framed as learning || Mistakes criticised or punished
|}

 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's turnaround'''
 
'''Week 8.''' Maya's manager notices the slowing progress and changes approach. They agree on what &quot;finished&quot; looks like and break the project into stages, starting with the 50 most-used folders.
 
'''Week 12.''' After each stage, Maya receives specific feedback on what is working. She now makes decisions confidently and has started suggesting improvements herself.
 
'''What changed?''' The structure around how the task would be completed: clear expectations, achievable steps, and feedback that informed instead of judged. Each gave Maya evidence that she was effective.
&lt;/div&gt;
 
Breaking Maya's project into stages draws on [[w:Goal setting|goal-setting theory]] (Locke &amp; Latham, 2002). Locke and Latham (2002) reviewed 35 years of laboratory and field studies. They found that specific, challenging goals combined with regular feedback consistently outperform vague &quot;do your best&quot; goals. Specific goals work partly because they show people exactly what success looks like. Each completed stage also acts as a mastery experience, which is the strongest source of self-efficacy (Bandura, 1977). This helps explain why Maya's confidence returned once the work was divided into stages.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Which change would best support Maya's need for competence?

|type=&quot;()&quot;}
- Offering her a bonus if she finishes faster
+ Breaking the project into stages with clear goals and specific feedback
- Telling her she is doing a great job regardless of progress
- Comparing her progress with a colleague's
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Conclusion==
Competence is the need to ''feel'' effective, and SDT treats it as important at all times, not only once basic needs are met (Ryan &amp; Deci, 2017; Tay &amp; Diener, 2011). Feeling competent moves people toward more autonomous motivation (Ryan &amp; Deci, 2020). CET explains why the same feedback can either energise or deflate a person, depending on whether it informs or controls (Deci et al., 1999).
 
When competence is actively frustrated, the consequences are more severe than when it is simply unmet. These consequences range from burnout to the helpless thinking shown in the case study (Abramson et al., 1978; Bartholomew et al., 2011). Research across workplaces, classrooms suggests that clear expectations and informational feedback, as well as challenges broken into achievable steps, can reverse this pattern (Baard et al., 2004; Locke &amp; Latham, 2002). However, much of this evidence is correlational and rarely tests competence directly as the mechanism (Van den Broeck et al., 2016).
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==See also==
* [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|Autonomy and intrinsic motivation in self-determination theory]] (Book chapter, 2025)
* [[Motivation and emotion/Book/2011/Self-determination theory|Self-determination theory]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Book chapter, 2026)
* [[w:Self-determination theory|Self-determination theory]] (Wikipedia)
* [[w:Self-efficacy|Self-efficacy]] (Wikipedia)
* [[w:Learned helplessness|Learned helplessness]] (Wikipedia)
 
 
==References==
{{Hanging indent|1=

Abramson, L. Y., Seligman, M. E., &amp; Teasdale, J. D. (1978). Learned helplessness in humans: Critique and reformulation. Journal of Abnormal Psychology (1965), 87(1), 49–74. https://doi.org/10.1037/0021-843X.87.1.49
 
Baard, P. P., Deci, E. L., &amp; Ryan, R. M. (2004). Intrinsic need satisfaction: a motivational basis of performance and well-being in two work settings. Journal of Applied Social Psychology, 34(10), 2045–2068. https://doi.org/10.1111/j.1559-1816.2004.tb02690.x

Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191–215. https://doi.org/10.1037/0033-295X.84.2.191
 
Bartholomew, K. J., Ntoumanis, N., Ryan, R. M., Bosch, J. A., &amp; Thøgersen-Ntoumani, C. (2011). Self-Determination Theory and Diminished Functioning: The Role of Interpersonal Control and Psychological Need Thwarting. Personality &amp; Social Psychology Bulletin, 37(11), 1459–1473. https://doi.org/10.1177/0146167211413125
 
Bureau, J. S., Howard, J. L., Chong, J. X. Y., &amp; Guay, F. (2022). Pathways to Student Motivation: A Meta-Analysis of Antecedents of Autonomous and Controlled Motivations. Review of Educational Research, 92(1), 46–72. https://doi.org/10.3102/00346543211042426
 
Cameron, J., &amp; Pierce, W. D. (1994). Reinforcement, Reward, and Intrinsic Motivation: A Meta-Analysis. Review of Educational Research, 64(3), 363–423. https://doi.org/10.3102/00346543064003363

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. Motivation and Emotion, 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1

Deci, E. L. (1971). Effects of externally mediated rewards on intrinsic motivation. Journal of Personality and Social Psychology, 18(1), 105–115. https://doi.org/10.1037/h0030644
 
Deci, E. L., Koestner, R., &amp; Ryan, R. M. (1999). A Meta-Analytic Review of Experiments Examining the Effects of Extrinsic Rewards on Intrinsic Motivation. Psychological Bulletin, 125(6), 627–668. https://doi.org/10.1037/0033-2909.125.6.627
 
Deci, E. L., &amp; Ryan, R. M. (1985). ''Intrinsic motivation and self-determination in human behavior''. Springer. https://doi.org/10.1016/j.cedpsych.2020.101860.

Fong, C. J., Patall, E. A., Vasquez, A. C., &amp; Stautberg, S. (2019). A Meta-Analysis of Negative Feedback on Intrinsic Motivation. Educational Psychology Review, 31(1), 121–162. https://doi.org/10.1007/s10648-018-9446-6
 
Locke, E. A., &amp; Latham, G. P. (2002). Building a practically useful theory of goal setting and task motivation: A 35-year odyssey. The American Psychologist, 57(9), 705–717. https://doi.org/10.1037/0003-066X.57.9.705

Maslow, A. H. (1943). A theory of human motivation. ''Psychological Review, 50''(4), 370–396. https://doi.org/10.1037/h0054346
 
Morsink, S., Van der Oord, S., Antrop, I., Danckaerts, M., &amp; Scheres, A. (2022). Studying motivation in ADHD: The role of internal motives and the relevance of self determination theory. ''Journal of Attention Disorders, 26''(8), 1139–1158. https://doi.org/10.1177/10870547211050948
 
Reeve, J. (2024). ''Understanding motivation and emotion'' (8th ed.). Wiley.
 
Ryan, R. M., &amp; Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. ''American Psychologist, 55''(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68
 
Ryan, R. M., &amp; Deci, E. L. (2017). ''Self-determination theory: Basic psychological needs in motivation, development, and wellness''. Guilford Press. https://doi.org/10.1521/978.14625/28806
 
Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology, 61'', Article 101860. https://doi.org/10.1016/j.cedpsych.2020.101860
 
Seligman, M. E. P., &amp; Maier, S. F. (1967). Failure to escape traumatic shock. ''Journal of Experimental Psychology, 74''(1), 1–9. https://doi.org/10.1037/h0024514
 
Slemp, G. R., Kern, M. L., Patrick, K. J., &amp; Ryan, R. M. (2018). Leader autonomy support in the workplace: A meta-analytic review. ''Motivation and Emotion, 42''(5), 706–724. https://doi.org/10.1007/s11031-018-9698-y
 
Tay, L., &amp; Diener, E. (2011). Needs and subjective well-being around the world. ''Journal of Personality and Social Psychology, 101''(2), 354–365. https://doi.org/10.1037/a0023779
 
Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A review of self-determination theory's basic psychological needs at work. ''Journal of Management, 42''(5), 1195–1229. https://doi.org/10.1177/0149206316632058
 
Vansteenkiste, M., &amp; Ryan, R. M. (2013). On psychological growth and vulnerability: Basic psychological need satisfaction and need frustration as a unifying principle. ''Journal of Psychotherapy Integration, 23''(3), 263–280. https://doi.org/10.1037/a0032359
 
Vansteenkiste, M., Ryan, R. M., &amp; Soenens, B. (2020). Basic psychological need theory: Advancements, critical themes, and future directions. ''Motivation and Emotion, 44''(1), 1–31. https://doi.org/10.1007/s11031-019-09818-1
 
White, R. W. (1959). Motivation reconsidered: The concept of competence. ''Psychological Review, 66''(5), 297–333. https://doi.org/10.1037/h0040934
}}


==External links==
* https://open.ncl.ac.uk/theories/20/self-determination-theory/
* https://www.apa.org/ed/schools/teaching-learning/top-twenty/motivation
* https://positivepsychology.com/self-determination-theory/
* https://lifestyle.sustainability-directory.com/term/motivation-continuum/

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      <text bytes="30336" sha1="dnx57om2b9m7cu6vuohaq12xctx2o1o" xml:space="preserve">{{title|Competence motivation in self-determination theory:&lt;br&gt;How does the need for competence function within self-determination theory to shape motivation and behaviour?}}
 __TOC__

==Overview==
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study:'''
[[File:Woman Suffering from Stress at Work (cropped).jpg|thumb|right|260px|'''Figure 1'''. Facing a large, unstructured task without guidance or feedback can leave a person doubting their own ability.]]
 
Maya, a 24-year-old administrative officer, has not opened her biggest project in three days. Instead, she has answered every email and tidied a shared drive she built herself: familiar tasks she knows she can do well.
 
Two months ago, Maya was excited when her manager asked her to review and reorganise more than 500 folders in the team's records system. But she received no guidance on where to start or what &quot;finished&quot; should look like. Each folder revealed new complexity, and nobody told her if her decisions were right. (see Figure 1). Some days she thinks, &quot;I just need clearer instructions.&quot; On other days her thoughts turn personal: &quot;I'm hopeless at this.&quot; The first thought sends her to ask for help; the second sends her back to her inbox.
 
''Why does the same task leave a person ready to improve on some days, and ready to give up on others?''
&lt;/div&gt;
 
 
According to [[w:Self-determination theory|self-determination theory]] (SDT), this difference often comes down to the need for [[Motivation and emotion/Book/2011/Self-determination theory|competence]]. Competence is the need to feel effective and capable (Ryan &amp; Deci, 2017). It is one of three basic psychological needs, alongside [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|autonomy]] and [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|relatedness]] (Ryan &amp; Deci, 2017). When competence is satisfied, people tend to show stronger [[Motivation and emotion/Book/2013/Intrinsic motivation|intrinsic motivation]], persistence, and wellbeing (Ryan &amp; Deci, 2020). When it is frustrated, as in Maya's case, people tend to avoid tasks and give up (Vansteenkiste et al., 2020).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Focus questions'''
* What is competence, according to self-determination theory?
* How does competence relate to intrinsic motivation?
* How does cognitive evaluation theory explain why feedback and rewards can strengthen or undermine motivation?
* What happens when the need for competence is frustrated?
* What does research show about how competence can be supported?
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Self-determination theory and competence==
 
===What is self-determination theory?===
SDT is a broad theory of human motivation. It proposes that people have three innate psychological needs: autonomy (feeling volitional), competence (feeling effective), as well as relatedness (feeling connected to others) (Deci &amp; Ryan, 1985; Ryan &amp; Deci, 2017). SDT is made up of six mini-theories, and two of these are central to this chapter. These are cognitive evaluation theory and basic psychological needs theory (Vansteenkiste et al., 2020). SDT is often compared with [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]]. Maslow (1943) proposed a hierarchy in which lower needs, such as physiological and safety needs, generally take priority over higher needs, such as esteem and self-actualisation. He placed mastery within esteem needs. SDT agrees that people strive to feel capable. However, SDT does not rank its needs and considers all three essential at all times (Ryan &amp; Deci, 2017).
 
[[File:MaslowsHierarchyOfNeeds.svg|thumb|right|300px|'''Figure 2'''. Maslow's hierarchy of needs places mastery within esteem needs, near the top of the hierarchy. SDT treats competence as essential at every level.]]
 
Tay and Diener (2011) tested these two views using Gallup World Poll data from 60,865 people in 123 countries. Although people did tend to meet basic and safety needs first, which partly supports Maslow, each need, including mastery, contributed to wellbeing regardless of whether the other needs were met (Tay &amp; Diener, 2011). The needs that mirror SDT, namely social relationships, autonomy, and mastery, were among the strongest predictors of everyday feelings across all eight world regions studied. One limitation is that the data were cross-sectional. Each need was also measured with only two or three yes or no questions, so the study shows association, not cause.
 
===What is competence within self-determination theory?===
The idea of competence as a motivational force dates back to White (1959), who challenged the drive theories of his time. He noticed that infants and young animals explore and play, as well as manipulate objects, even when they are fed and safe. He argued that this behaviour comes from a built-in need to have an effect on the environment, which he called effectance motivation. SDT builds on this idea and defines competence as the need to ''feel'' effective, not simply to possess a skill (Ryan &amp; Deci, 2017). This means that a highly skilled person can still feel incompetent if they receive no sign that their efforts are working.
 
According to SDT, competence is best satisfied in well-structured environments that offer ''[[wikipedia:Challenge_point_framework|optimal challenge]]'', positive feedback, and opportunities for growth (Ryan &amp; Deci, 2020). An optimally challenging task sits slightly beyond a person's current skill, but it comes with enough structure and support to close the gap. Tasks that are too easy offer no sense of growth, while tasks that are too hard, especially without guidance, signal failure (Reeve, 2024). Maya's difficulty illustrates how a lack of structure and feedback can make a manageable task feel too hard.
 
Basic psychological needs theory treats need satisfaction and need frustration as two separate experiences (Vansteenkiste &amp; Ryan, 2013). Need satisfaction is linked to a &quot;bright&quot; pathway of growth and engagement, as well as wellbeing (Vansteenkiste et al., 2020). Need frustration is linked to a &quot;dark&quot; pathway of defensiveness, avoidance, and ill-being (Vansteenkiste et al., 2020). Low satisfaction and active frustration are therefore not the same thing. Receiving no feedback may leave a person unfulfilled, but being repeatedly made to feel ineffective actively harms wellbeing (Vansteenkiste &amp; Ryan, 2013). The case study shows this shift. Maya moves from low satisfaction in the early weeks to active frustration after her manager's review, described later in the chapter.
 
===Competence and self-efficacy===
Competence overlaps closely with [[w:Self-efficacy|self-efficacy]], which is a person's belief that they can successfully perform a specific behaviour (Bandura, 1977). Bandura separated two expectations that shape whether people act. An ''efficacy expectation'' asks &quot;Can I do it?&quot;, and an ''outcome expectation'' asks &quot;Will it work?&quot; Efficacy beliefs are built from four sources: personal mastery experiences, watching similar others succeed, verbal persuasion, and how people interpret their own stress (Bandura, 1977). Of these, mastery experiences are the most powerful (Bandura, 1977).
 
In the case study, several of these sources are weakened. Without feedback, Maya cannot judge whether her decisions are effective, so her real progress is not experienced as mastery. As the case study later shows, her manager's comments act as negative persuasion. Her anxiety before opening the project is also likely to be read as evidence that she is not capable. The key difference between the two concepts is that self-efficacy is a belief about a specific future task (Bandura, 1977). In contrast, SDT treats competence as a universal need that shapes motivation and wellbeing over time (Ryan &amp; Deci, 2017). In practice, however, the two are difficult to separate, because both are usually measured with similar self-report questions. Some &quot;competence&quot; findings may therefore simply reflect confidence.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Competence and intrinsic motivation==
 
SDT's central claim is that the ''quality'' of motivation matters as much as its quantity (Ryan &amp; Deci, 2020). Feeling competent affects where people sit on the motivation continuum, as well as how they respond to feedback and rewards (Deci et al., 1999; Ryan &amp; Deci, 2020).
 
===The motivation continuum===
SDT describes motivation as a continuum (Ryan &amp; Deci, 2020; see Figure 3). The continuum ranges from [[Motivation and emotion/Book/2014/Amotivation|amotivation]], meaning no intention to act, through several forms of extrinsic motivation, to intrinsic motivation, meaning acting for enjoyment or interest (Ryan &amp; Deci, 2020). A lack of competence is one of the main causes of amotivation (Ryan &amp; Deci, 2000). It shows in thoughts such as &quot;I can't do this&quot; or &quot;my effort won't make a difference&quot;. In contrast, feeling capable helps people [[w:Internalization (sociology)|internalise]] the value of a task, so the task feels self-endorsed instead of obligatory (Ryan &amp; Deci, 2020). In the case study, Maya's growing avoidance of her project suggests she is sliding toward amotivation.
 
[[File:Taxonomy of motivation.png|thumb|center|600px|'''Figure 3'''. The SDT motivation continuum, ranging from amotivation, through controlled and autonomous forms of extrinsic motivation, to intrinsic motivation.]]
 
===Cognitive evaluation theory===
[[Motivation and emotion/Book/2021/Cognitive evaluation theory and motivation|Cognitive evaluation theory]] (CET) explains how external events such as feedback and rewards affect intrinsic motivation (Ryan &amp; Deci, 2000). According to CET, every such event has a ''controlling'' aspect, which affects autonomy, and an ''informational'' aspect, which affects competence (Ryan &amp; Deci, 2000). Informational feedback increases perceived competence and intrinsic motivation (Deci et al., 1999). In contrast, rewards that feel like pressure tend to undermine intrinsic motivation, even when they signal success (Deci et al., 1999). CET therefore predicts that ''how'' feedback is delivered matters as much as ''what'' it says. Later versions of CET added a third, ''amotivating'' aspect (Ryan &amp; Deci, 2017). Events that signal incompetence, or that effort will not change the outcome, can push people toward amotivation. Criticism that offers no way forward, such as the feedback Maya later receives, is likely to carry this amotivating message.
 
Research generally supports these predictions, although the earliest evidence was weak. RIn Deci's (1971) original experiment, students paid $1 for each puzzle they solved later spent less free time on the puzzles once payment stopped. However, the study had only 24 participants, and the result was only a trend (Deci, 1971). A later meta-analysis of 128 experiments, mostly with children and university students, found a clearer pattern (Deci et al., 1999). People who expected a tangible reward for an interesting task spent less free time on it afterwards. In studies with children, this effect was still present more than a week later. The most damaging rewards were those that signalled a person had fallen short (Deci et al., 1999). Feedback style also mattered. Informational praise increased intrinsic motivation, but the same praise with a controlling phrase such as &quot;just as you ''should''&quot; decreased it (Ryan et al., 1983, as cited in Deci et al., 1999). Negative feedback was less harmful when it included guidance on how to improve (Fong et al., 2019). Rewards did not undermine motivation for boring tasks or when they were unexpected (Deci et al., 1999).
 
CET assumes that these effects work ''through'' perceived competence (Ryan &amp; Deci, 2017). However, relatively few studies have measured perceived competence directly to test this (Deci et al., 1999). The results fit the theory, but the mechanism is more often assumed than demonstrated. Even so, the practical message is consistent. Feedback that identifies a problem, such as &quot;the scope needs to be better defined&quot;, without showing how to fix it is unlikely to support competence (Fong et al., 2019).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{According to cognitive evaluation theory, positive feedback is most likely to increase intrinsic motivation when it is:

|type=&quot;()&quot;}
- Given with a large financial reward
+ Informative and delivered in an autonomy-supportive way
- Delivered as a comparison with other people
- Given constantly, regardless of performance
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==When competence is frustrated==
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's first review'''
 
'''Week 6.''' Maya's manager reviews the project. She acknowledges some progress, then adds that the plan needs to be clearer and the scope better defined. She does not say what a clearer plan looks like or how to narrow the scope. Maya leaves the meeting feeling like a failure. She had enjoyed the first few folders, but now she dreads opening the system.
 
'''What is happening?''' The feedback identified a problem without giving Maya the information to solve it. Her effort no longer seems to lead anywhere, which is when a need starts to be actively frustrated, not just unmet.
&lt;/div&gt;
 
Research supports the distinction between low satisfaction and active frustration (Vansteenkiste &amp; Ryan, 2013). Bartholomew et al. (2011) found that athletes who saw their coach as controlling reported greater thwarting of all three needs. Need thwarting, in turn, predicted burnout, depressive symptoms, and negative emotion (Bartholomew et al., 2011). Feeling actively undermined was more harmful than simply not feeling supported. If the same pattern holds for competence, vague, critical feedback may harm Maya more than no feedback at all.
 
When people repeatedly experience that their effort makes no difference, they may develop [[w:Learned helplessness|learned helplessness]] (Seligman &amp; Maier, 1967). In classic experiments, dogs exposed to inescapable shocks later failed to escape shocks they could have avoided (Seligman &amp; Maier, 1967). Dogs that had been given control earlier learned to escape. In humans, helplessness reduces effort and is linked to apathy and depression (Abramson et al., 1978).How people explain failure also matters. The reformulated helplessness model proposes that explaining failure with internal, stable and global causes is more damaging than explaining it with external, unstable or specific causes (Abramson et al., 1978). Maya's two thoughts show this difference. &quot;I'm hopeless at this&quot; blames a lasting personal flaw and is more likely to lead to giving up, whereas &quot;I just need clearer instructions&quot; points to a specific, changeable cause that keeps her trying.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Maya thinks, &quot;I'm hopeless at this.&quot; According to research on explanatory style, why is this thought more harmful than &quot;I just need clearer instructions&quot;?

|type=&quot;()&quot;}
- It is less accurate
+ It explains failure with an internal, stable cause she cannot easily change
- It blames her manager instead of herself
- It focuses on the task rather than on herself
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==What supports or undermines competence?==
 
In two workplace studies, Baard et al. (2004) found that employees' satisfaction of autonomy, competence, and relatedness predicted their wellbeing as well as their performance evaluations. Because supervisors rated performance, this finding is less affected by self-report bias. However, the design still cannot show which came first. A meta-analysis by Van den Broeck et al. (2016) found that competence predicted wellbeing, work attitudes, and behaviour, even after the other two needs were taken into account. This suggests that competence is not simply a by-product of feeling autonomous or connected. Leadership also matters. Managers' autonomy-supportive behaviour is associated with greater need satisfaction as well as more autonomous motivation in employees (Slemp et al., 2018). This suggests that how Maya's manager behaves may affect her need satisfaction, including her sense of competence.
 
Similar patterns appear in classrooms. Bureau et al. (2022) pooled studies of what predicts student motivation and found that, of the three needs, support for competence was the strongest predictor of autonomous motivation (Bureau et al., 2022). This is a notable finding, because SDT has historically given autonomy the most attention (Ryan &amp; Deci, 2017). It suggests that, at least in classrooms, feeling capable may matter as much as feeling free to choose. However, the meta-analysis draws mainly on correlational studies, so it shows which students do well, but it does not prove that supporting competence causes better outcomes.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
The strength of the evidence depends on the methods used. The reward findings, for example, were contested. Cameron and Pierce (1994, as cited in Deci et al., 1999) found no overall undermining effect and argued that CET should be abandoned. Deci et al. (1999) argued that this result came from mixing boring and interesting tasks, as well as using inappropriate control groups. Laboratory studies also relied mostly on single sessions with children and students (Deci et al., 1999). Self-reported interest also showed much weaker effects than behaviour. Outside the laboratory, most studies are cross-sectional. This makes it unclear whether competence drives motivation or whether motivated people simply feel more competent (Van den Broeck et al., 2016).
 
Some critics have questioned whether basic needs are truly universal, because SDT was developed largely in Western contexts (Chen et al., 2015). However, a study of adults in Belgium, China, Peru, and the United States found that need satisfaction and need frustration predicted wellbeing and ill-being in all four cultures (Chen et al., 2015). Together with the overlap between competence and self-efficacy, these limitations point to the same gap noted in CET. SDT predicts outcomes well, but whether competence itself is the active ingredient remains less certain than the theory suggests (Deci et al., 1999).
 
Most competence research has also used neurotypical samples (Morsink et al., 2022). Morsink et al. (2022) noted that research on [[w:Attention deficit hyperactivity disorder|attention-deficit/hyperactivity disorder]] (ADHD) has mostly studied rewards and overlooked psychological needs. This is despite evidence that children with more ADHD symptoms report lower need satisfaction at school.(Morsink et al., 2022) Frequent correction may push teachers and parents toward controlling styles, which can further frustrate competence (Morsink et al., 2022). Whether supporting competence helps neurodivergent people in the same way remains largely untested.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Applying competence in practice==
The research reviewed so far points to a consistent set of conditions under which people feel capable. Table 1 contrasts environments that support competence with those that thwart it. These features reflect the four sources of competence support in SDT, which are clear expectations, optimal challenge, guidance, and constructive feedback (Reeve, 2024).
 
{| class=&quot;wikitable&quot; style=&quot;margin:1em auto; border-radius:8px;&quot;
|+ '''Table 1'''&lt;br&gt;''Features of Competence-Supportive and Competence-Thwarting Environments''
|-
! style=&quot;background:#eaf3fc;&quot; | Competence-supportive !! style=&quot;background:#fff6e8;&quot; | Competence-thwarting
|-
| Clear expectations about how to succeed || Vague or missing guidance
|-
| Guidance and modelling of &quot;how-to&quot; skills || Being left to work it out alone
|-
| Optimal challenge matched to current skills || Tasks far too hard or too easy
|-
| Specific, informative feedback || Absent, harsh, or controlling feedback
|-
| Long-term goals broken into short-term goals || No sense of progress
|-
| Mistakes framed as learning || Mistakes criticised or punished
|}

 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's turnaround'''
 
'''Week 8.''' Maya's manager notices the slowing progress and changes approach. They agree on what &quot;finished&quot; looks like and break the project into stages, starting with the 50 most-used folders.
 
'''Week 12.''' After each stage, Maya receives specific feedback on what is working. She now makes decisions confidently and has started suggesting improvements herself.
 
'''What changed?''' The structure around how the task would be completed: clear expectations, achievable steps, and feedback that informed instead of judged. Each gave Maya evidence that she was effective.
&lt;/div&gt;
 
Breaking Maya's project into stages draws on [[w:Goal setting|goal-setting theory]] (Locke &amp; Latham, 2002). Locke and Latham (2002) reviewed 35 years of laboratory and field studies. They found that specific, challenging goals combined with regular feedback consistently outperform vague &quot;do your best&quot; goals. Specific goals work partly because they show people exactly what success looks like. Each completed stage also acts as a mastery experience, which is the strongest source of self-efficacy (Bandura, 1977). This helps explain why Maya's confidence returned once the work was divided into stages.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Which change would best support Maya's need for competence?

|type=&quot;()&quot;}
- Offering her a bonus if she finishes faster
+ Breaking the project into stages with clear goals and specific feedback
- Telling her she is doing a great job regardless of progress
- Comparing her progress with a colleague's
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Conclusion==
Competence is the need to ''feel'' effective, and SDT treats it as important at all times, not only once basic needs are met (Ryan &amp; Deci, 2017; Tay &amp; Diener, 2011). Feeling competent moves people toward more autonomous motivation (Ryan &amp; Deci, 2020). CET explains why the same feedback can either energise or deflate a person, depending on whether it informs or controls (Deci et al., 1999).
 
When competence is actively frustrated, the consequences are more severe than when it is simply unmet. These consequences range from burnout to the helpless thinking shown in the case study (Abramson et al., 1978; Bartholomew et al., 2011). Research across workplaces, classrooms suggests that clear expectations and informational feedback, as well as challenges broken into achievable steps, can reverse this pattern (Baard et al., 2004; Locke &amp; Latham, 2002). However, much of this evidence is correlational and rarely tests competence directly as the mechanism (Van den Broeck et al., 2016).
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==See also==
* [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|Autonomy and intrinsic motivation in self-determination theory]] (Book chapter, 2025)
* [[Motivation and emotion/Book/2011/Self-determination theory|Self-determination theory]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Book chapter, 2026)
* [[w:Self-determination theory|Self-determination theory]] (Wikipedia)
* [[w:Self-efficacy|Self-efficacy]] (Wikipedia)
* [[w:Learned helplessness|Learned helplessness]] (Wikipedia)
 
 
==References==
{{Hanging indent|1=

Abramson, L. Y., Seligman, M. E., &amp; Teasdale, J. D. (1978). Learned helplessness in humans: Critique and reformulation. Journal of Abnormal Psychology (1965), 87(1), 49–74. https://doi.org/10.1037/0021-843X.87.1.49
 
Baard, P. P., Deci, E. L., &amp; Ryan, R. M. (2004). Intrinsic need satisfaction: a motivational basis of performance and well-being in two work settings. Journal of Applied Social Psychology, 34(10), 2045–2068. https://doi.org/10.1111/j.1559-1816.2004.tb02690.x

Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191–215. https://doi.org/10.1037/0033-295X.84.2.191
 
Bartholomew, K. J., Ntoumanis, N., Ryan, R. M., Bosch, J. A., &amp; Thøgersen-Ntoumani, C. (2011). Self-Determination Theory and Diminished Functioning: The Role of Interpersonal Control and Psychological Need Thwarting. Personality &amp; Social Psychology Bulletin, 37(11), 1459–1473. https://doi.org/10.1177/0146167211413125
 
Bureau, J. S., Howard, J. L., Chong, J. X. Y., &amp; Guay, F. (2022). Pathways to Student Motivation: A Meta-Analysis of Antecedents of Autonomous and Controlled Motivations. Review of Educational Research, 92(1), 46–72. https://doi.org/10.3102/00346543211042426
 
Cameron, J., &amp; Pierce, W. D. (1994). Reinforcement, Reward, and Intrinsic Motivation: A Meta-Analysis. Review of Educational Research, 64(3), 363–423. https://doi.org/10.3102/00346543064003363

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. Motivation and Emotion, 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1

Deci, E. L. (1971). Effects of externally mediated rewards on intrinsic motivation. Journal of Personality and Social Psychology, 18(1), 105–115. https://doi.org/10.1037/h0030644
 
Deci, E. L., Koestner, R., &amp; Ryan, R. M. (1999). A Meta-Analytic Review of Experiments Examining the Effects of Extrinsic Rewards on Intrinsic Motivation. Psychological Bulletin, 125(6), 627–668. https://doi.org/10.1037/0033-2909.125.6.627
 
Deci, E. L., &amp; Ryan, R. M. (1985). ''Intrinsic motivation and self-determination in human behavior''. Springer. https://doi.org/10.1016/j.cedpsych.2020.101860.

Fong, C. J., Patall, E. A., Vasquez, A. C., &amp; Stautberg, S. (2019). A Meta-Analysis of Negative Feedback on Intrinsic Motivation. Educational Psychology Review, 31(1), 121–162. https://doi.org/10.1007/s10648-018-9446-6
 
Locke, E. A., &amp; Latham, G. P. (2002). Building a practically useful theory of goal setting and task motivation: A 35-year odyssey. The American Psychologist, 57(9), 705–717. https://doi.org/10.1037/0003-066X.57.9.705

Maslow, A. H. (1943). A theory of human motivation. ''Psychological Review, 50''(4), 370–396. https://doi.org/10.1037/h0054346
 
Morsink, S., Van der Oord, S., Antrop, I., Danckaerts, M., &amp; Scheres, A. (2022). Studying motivation in ADHD: The role of internal motives and the relevance of self determination theory. ''Journal of Attention Disorders, 26''(8), 1139–1158. https://doi.org/10.1177/10870547211050948
 
Reeve, J. (2024). ''Understanding motivation and emotion'' (8th ed.). Wiley.
 
Ryan, R. M., &amp; Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. ''American Psychologist, 55''(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68
 
Ryan, R. M., &amp; Deci, E. L. (2017). ''Self-determination theory: Basic psychological needs in motivation, development, and wellness''. Guilford Press. https://doi.org/10.1521/978.14625/28806
 
Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology, 61'', Article 101860. https://doi.org/10.1016/j.cedpsych.2020.101860
 
Seligman, M. E. P., &amp; Maier, S. F. (1967). Failure to escape traumatic shock. ''Journal of Experimental Psychology, 74''(1), 1–9. https://doi.org/10.1037/h0024514
 
Slemp, G. R., Kern, M. L., Patrick, K. J., &amp; Ryan, R. M. (2018). Leader autonomy support in the workplace: A meta-analytic review. ''Motivation and Emotion, 42''(5), 706–724. https://doi.org/10.1007/s11031-018-9698-y
 
Tay, L., &amp; Diener, E. (2011). Needs and subjective well-being around the world. ''Journal of Personality and Social Psychology, 101''(2), 354–365. https://doi.org/10.1037/a0023779
 
Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A review of self-determination theory's basic psychological needs at work. ''Journal of Management, 42''(5), 1195–1229. https://doi.org/10.1177/0149206316632058
 
Vansteenkiste, M., &amp; Ryan, R. M. (2013). On psychological growth and vulnerability: Basic psychological need satisfaction and need frustration as a unifying principle. ''Journal of Psychotherapy Integration, 23''(3), 263–280. https://doi.org/10.1037/a0032359
 
Vansteenkiste, M., Ryan, R. M., &amp; Soenens, B. (2020). Basic psychological need theory: Advancements, critical themes, and future directions. ''Motivation and Emotion, 44''(1), 1–31. https://doi.org/10.1007/s11031-019-09818-1
 
White, R. W. (1959). Motivation reconsidered: The concept of competence. ''Psychological Review, 66''(5), 297–333. https://doi.org/10.1037/h0040934
}}


==External links==
* https://open.ncl.ac.uk/theories/20/self-determination-theory/
* https://www.apa.org/ed/schools/teaching-learning/top-twenty/motivation
* https://positivepsychology.com/self-determination-theory/
* https://lifestyle.sustainability-directory.com/term/motivation-continuum/

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      <text bytes="30259" sha1="pgjj11trxjomsxs8c2tbh0gmq0o9m73" xml:space="preserve">{{title|Competence motivation in self-determination theory:&lt;br&gt;How does the need for competence function within self-determination theory to shape motivation and behaviour?}}
 __TOC__

==Overview==
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study:'''
[[File:Woman Suffering from Stress at Work (cropped).jpg|thumb|right|260px|'''Figure 1'''. Facing a large, unstructured task without guidance or feedback can leave a person doubting their own ability.]]
 
Maya, a 24-year-old administrative officer, has not opened her biggest project in three days. Instead, she has answered every email and tidied a shared drive she built herself: familiar tasks she knows she can do well.
 
Two months ago, Maya was excited when her manager asked her to review and reorganise more than 500 folders in the team's records system. But she received no guidance on where to start or what &quot;finished&quot; should look like. Each folder revealed new complexity, and nobody told her if her decisions were right. (see Figure 1). Some days she thinks, &quot;I just need clearer instructions.&quot; On other days her thoughts turn personal: &quot;I'm hopeless at this.&quot; The first thought sends her to ask for help; the second sends her back to her inbox.
 
''Why does the same task leave a person ready to improve on some days, and ready to give up on others?''
&lt;/div&gt;
 
 
According to [[w:Self-determination theory|self-determination theory]] (SDT), this difference often comes down to the need for [[Motivation and emotion/Book/2011/Self-determination theory|competence]]. Competence is the need to feel effective and capable (Ryan &amp; Deci, 2017). It is one of three basic psychological needs, alongside [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|autonomy]] and [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|relatedness]] (Ryan &amp; Deci, 2017). When competence is satisfied, people tend to show stronger [[Motivation and emotion/Book/2013/Intrinsic motivation|intrinsic motivation]], persistence, and wellbeing (Ryan &amp; Deci, 2020). When it is frustrated, as in Maya's case, people tend to avoid tasks and give up (Vansteenkiste et al., 2020).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Focus questions'''
* What is competence, according to self-determination theory?
* How does competence relate to intrinsic motivation?
* How does cognitive evaluation theory explain why feedback and rewards can strengthen or undermine motivation?
* What happens when the need for competence is frustrated?
* What does research show about how competence can be supported?
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Self-determination theory and competence==
 
===What is self-determination theory?===
SDT is a broad theory of human motivation. It proposes that people have three innate psychological needs: autonomy (feeling volitional), competence (feeling effective), as well as relatedness (feeling connected to others) (Deci &amp; Ryan, 1985; Ryan &amp; Deci, 2017). SDT is made up of six mini-theories, and two of these are central to this chapter. These are cognitive evaluation theory and basic psychological needs theory (Vansteenkiste et al., 2020). SDT is often compared with [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]]. Maslow (1943) proposed a hierarchy in which lower needs, such as physiological and safety needs, generally take priority over higher needs, such as esteem and self-actualisation. He placed mastery within esteem needs. SDT agrees that people strive to feel capable. However, SDT does not rank its needs and considers all three essential at all times (Ryan &amp; Deci, 2017).
 
[[File:MaslowsHierarchyOfNeeds.svg|thumb|right|300px|'''Figure 2'''. Maslow's hierarchy of needs places mastery within esteem needs, near the top of the hierarchy. SDT treats competence as essential at every level.]]
 
Tay and Diener (2011) tested these two views using Gallup World Poll data from 60,865 people in 123 countries. Although people did tend to meet basic and safety needs first, which partly supports Maslow, each need, including mastery, contributed to wellbeing regardless of whether the other needs were met (Tay &amp; Diener, 2011). The needs that mirror SDT, namely social relationships, autonomy, and mastery, were among the strongest predictors of everyday feelings across all eight world regions studied. One limitation is that the data were cross-sectional. Each need was also measured with only two or three yes or no questions, so the study shows association, not cause.
 
===What is competence within self-determination theory?===
The idea of competence as a motivational force dates back to White (1959), who challenged the drive theories of his time. He noticed that infants and young animals explore and play, as well as manipulate objects, even when they are fed and safe. He argued that this behaviour comes from a built-in need to have an effect on the environment, which he called effectance motivation. SDT builds on this idea and defines competence as the need to ''feel'' effective, not simply to possess a skill (Ryan &amp; Deci, 2017). This means that a highly skilled person can still feel incompetent if they receive no sign that their efforts are working.
 
According to SDT, competence is best satisfied in well-structured environments that offer ''[[wikipedia:Challenge_point_framework|optimal challenge]]'', positive feedback, and opportunities for growth (Ryan &amp; Deci, 2020). An optimally challenging task sits slightly beyond a person's current skill, but it comes with enough structure and support to close the gap. Tasks that are too easy offer no sense of growth, while tasks that are too hard, especially without guidance, signal failure (Reeve, 2024). Maya's difficulty illustrates how a lack of structure and feedback can make a manageable task feel too hard.
 
Basic psychological needs theory treats need satisfaction and need frustration as two separate experiences (Vansteenkiste &amp; Ryan, 2013). Need satisfaction is linked to a &quot;bright&quot; pathway of growth and engagement, as well as wellbeing (Vansteenkiste et al., 2020). Need frustration is linked to a &quot;dark&quot; pathway of defensiveness, avoidance, and ill-being (Vansteenkiste et al., 2020). Low satisfaction and active frustration are therefore not the same thing. Receiving no feedback may leave a person unfulfilled, but being repeatedly made to feel ineffective actively harms wellbeing (Vansteenkiste &amp; Ryan, 2013). The case study shows this shift. Maya moves from low satisfaction in the early weeks to active frustration after her manager's review, described later in the chapter.
 
===Competence and self-efficacy===
Competence overlaps closely with [[w:Self-efficacy|self-efficacy]], which is a person's belief that they can successfully perform a specific behaviour (Bandura, 1977). Bandura separated two expectations that shape whether people act. An ''efficacy expectation'' asks &quot;Can I do it?&quot;, and an ''outcome expectation'' asks &quot;Will it work?&quot; Efficacy beliefs are built from four sources: personal mastery experiences, watching similar others succeed, verbal persuasion, and how people interpret their own stress (Bandura, 1977). Of these, mastery experiences are the most powerful (Bandura, 1977).
 
In the case study, several of these sources are weakened. Without feedback, Maya cannot judge whether her decisions are effective, so her real progress is not experienced as mastery. As the case study later shows, her manager's comments act as negative persuasion. Her anxiety before opening the project is also likely to be read as evidence that she is not capable. The key difference between the two concepts is that self-efficacy is a belief about a specific future task (Bandura, 1977). In contrast, SDT treats competence as a universal need that shapes motivation and wellbeing over time (Ryan &amp; Deci, 2017). In practice, however, the two are difficult to separate, because both are usually measured with similar self-report questions. Some &quot;competence&quot; findings may therefore simply reflect confidence.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Competence and intrinsic motivation==
 
SDT's central claim is that the ''quality'' of motivation matters as much as its quantity (Ryan &amp; Deci, 2020). Feeling competent affects where people sit on the motivation continuum, as well as how they respond to feedback and rewards (Deci et al., 1999; Ryan &amp; Deci, 2020).
 
===The motivation continuum===
SDT describes motivation as a continuum (Ryan &amp; Deci, 2020; see Figure 3). The continuum ranges from [[Motivation and emotion/Book/2014/Amotivation|amotivation]], meaning no intention to act, through several forms of extrinsic motivation, to intrinsic motivation, meaning acting for enjoyment or interest (Ryan &amp; Deci, 2020). A lack of competence is one of the main causes of amotivation (Ryan &amp; Deci, 2000). It shows in thoughts such as &quot;I can't do this&quot; or &quot;my effort won't make a difference&quot;. In contrast, feeling capable helps people [[w:Internalization (sociology)|internalise]] the value of a task, so the task feels self-endorsed instead of obligatory (Ryan &amp; Deci, 2020). In the case study, Maya's growing avoidance of her project suggests she is sliding toward amotivation.
 
[[File:Taxonomy of motivation.png|thumb|center|600px|'''Figure 3'''. The SDT motivation continuum, ranging from amotivation, through controlled and autonomous forms of extrinsic motivation, to intrinsic motivation.]]
 
===Cognitive evaluation theory===
[[Motivation and emotion/Book/2021/Cognitive evaluation theory and motivation|Cognitive evaluation theory]] (CET) explains how external events such as feedback and rewards affect intrinsic motivation (Ryan &amp; Deci, 2000). According to CET, every such event has a ''controlling'' aspect, which affects autonomy, and an ''informational'' aspect, which affects competence (Ryan &amp; Deci, 2000). Informational feedback increases perceived competence and intrinsic motivation (Deci et al., 1999). In contrast, rewards that feel like pressure tend to undermine intrinsic motivation, even when they signal success (Deci et al., 1999). CET therefore predicts that ''how'' feedback is delivered matters as much as ''what'' it says. Later versions of CET added a third, ''amotivating'' aspect (Ryan &amp; Deci, 2017). Events that signal incompetence, or that effort will not change the outcome, can push people toward amotivation. Criticism that offers no way forward, such as the feedback Maya later receives, is likely to carry this amotivating message.
 
Research generally supports these predictions, although the earliest evidence was weak. RIn Deci's (1971) original experiment, students paid $1 for each puzzle they solved later spent less free time on the puzzles once payment stopped. However, the study had only 24 participants, and the result was only a trend (Deci, 1971). A later meta-analysis of 128 experiments, mostly with children and university students, found a clearer pattern (Deci et al., 1999). People who expected a tangible reward for an interesting task spent less free time on it afterwards. In studies with children, this effect was still present more than a week later. The most damaging rewards were those that signalled a person had fallen short (Deci et al., 1999). Feedback style also mattered. Informational praise increased intrinsic motivation, but the same praise with a controlling phrase such as &quot;just as you ''should''&quot; decreased it (Ryan et al., 1983, as cited in Deci et al., 1999). Negative feedback was less harmful when it included guidance on how to improve (Fong et al., 2019). Rewards did not undermine motivation for boring tasks or when they were unexpected (Deci et al., 1999).
 
CET assumes that these effects work ''through'' perceived competence (Ryan &amp; Deci, 2017). However, relatively few studies have measured perceived competence directly to test this (Deci et al., 1999). The results fit the theory, but the mechanism is more often assumed than demonstrated. Even so, the practical message is consistent. Feedback that identifies a problem, such as &quot;the scope needs to be better defined&quot;, without showing how to fix it is unlikely to support competence (Fong et al., 2019).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{According to cognitive evaluation theory, positive feedback is most likely to increase intrinsic motivation when it is:

|type=&quot;()&quot;}
- Given with a large financial reward
+ Informative and delivered in an autonomy-supportive way
- Delivered as a comparison with other people
- Given constantly, regardless of performance
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==When competence is frustrated==
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's first review'''
 
'''Week 6.''' Maya's manager reviews the project. She acknowledges some progress, then adds that the plan needs to be clearer and the scope better defined. She does not say what a clearer plan looks like or how to narrow the scope. Maya leaves the meeting feeling like a failure. She had enjoyed the first few folders, but now she dreads opening the system.
 
'''What is happening?''' The feedback identified a problem without giving Maya the information to solve it. Her effort no longer seems to lead anywhere, which is when a need starts to be actively frustrated, not just unmet.
&lt;/div&gt;
 
Research supports the distinction between low satisfaction and active frustration (Vansteenkiste &amp; Ryan, 2013). Bartholomew et al. (2011) found that athletes who saw their coach as controlling reported greater thwarting of all three needs. Need thwarting, in turn, predicted burnout, depressive symptoms, and negative emotion (Bartholomew et al., 2011). Feeling actively undermined was more harmful than simply not feeling supported. If the same pattern holds for competence, vague, critical feedback may harm Maya more than no feedback at all.
 
When people repeatedly experience that their effort makes no difference, they may develop [[w:Learned helplessness|learned helplessness]] (Seligman &amp; Maier, 1967). In classic experiments, dogs exposed to inescapable shocks later failed to escape shocks they could have avoided (Seligman &amp; Maier, 1967). Dogs that had been given control earlier learned to escape. In humans, helplessness reduces effort and is linked to apathy and depression (Abramson et al., 1978).How people explain failure also matters. The reformulated helplessness model proposes that explaining failure with internal, stable and global causes is more damaging than explaining it with external, unstable or specific causes (Abramson et al., 1978). Maya's two thoughts show this difference. &quot;I'm hopeless at this&quot; blames a lasting personal flaw and is more likely to lead to giving up, whereas &quot;I just need clearer instructions&quot; points to a specific, changeable cause that keeps her trying.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Maya thinks, &quot;I'm hopeless at this.&quot; According to research on explanatory style, why is this thought more harmful than &quot;I just need clearer instructions&quot;?

|type=&quot;()&quot;}
- It is less accurate
+ It explains failure with an internal, stable cause she cannot easily change
- It blames her manager instead of herself
- It focuses on the task rather than on herself
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==What supports or undermines competence?==
 
In two workplace studies, Baard et al. (2004) found that employees' satisfaction of autonomy, competence, and relatedness predicted their wellbeing as well as their performance evaluations. Because supervisors rated performance, this finding is less affected by self-report bias. However, the design still cannot show which came first. A meta-analysis by Van den Broeck et al. (2016) found that competence predicted wellbeing, work attitudes, and behaviour, even after the other two needs were taken into account. This suggests that competence is not simply a by-product of feeling autonomous or connected. Leadership also matters. Managers' autonomy-supportive behaviour is associated with greater need satisfaction as well as more autonomous motivation in employees (Slemp et al., 2018). This suggests that how Maya's manager behaves may affect her need satisfaction, including her sense of competence.
 
Similar patterns appear in classrooms. Bureau et al. (2022) pooled studies of what predicts student motivation and found that, of the three needs, support for competence was the strongest predictor of autonomous motivation (Bureau et al., 2022). This is a notable finding, because SDT has historically given autonomy the most attention (Ryan &amp; Deci, 2017). It suggests that, at least in classrooms, feeling capable may matter as much as feeling free to choose. However, the meta-analysis draws mainly on correlational studies, so it shows which students do well, but it does not prove that supporting competence causes better outcomes.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==How strong is the evidence?==
The strength of the evidence depends on the methods used. The reward findings, for example, were contested. Cameron and Pierce (1994) found no overall undermining effect and argued that CET should be abandoned. Deci et al. (1999) argued that this result came from mixing boring and interesting tasks, as well as using inappropriate control groups. Laboratory studies also relied mostly on single sessions with children and students (Deci et al., 1999). Self-reported interest also showed much weaker effects than behaviour. Outside the laboratory, most studies are cross-sectional. This makes it unclear whether competence drives motivation or whether motivated people simply feel more competent (Van den Broeck et al., 2016).
 
Some critics have questioned whether basic needs are truly universal, because SDT was developed largely in Western contexts (Chen et al., 2015). However, a study of adults in Belgium, China, Peru, and the United States found that need satisfaction and need frustration predicted wellbeing and ill-being in all four cultures (Chen et al., 2015). Together with the overlap between competence and self-efficacy, these limitations point to the same gap noted in CET. SDT predicts outcomes well, but whether competence itself is the active ingredient remains less certain than the theory suggests (Deci et al., 1999).
 
Most competence research has also used neurotypical samples (Morsink et al., 2022). Morsink et al. (2022) noted that research on [[w:Attention deficit hyperactivity disorder|attention-deficit/hyperactivity disorder]] (ADHD) has mostly studied rewards and overlooked psychological needs. This is despite evidence that children with more ADHD symptoms report lower need satisfaction at school.(Morsink et al., 2022) Frequent correction may push teachers and parents toward controlling styles, which can further frustrate competence (Morsink et al., 2022). Whether supporting competence helps neurodivergent people in the same way remains largely untested.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Applying competence in practice==
The research reviewed so far points to a consistent set of conditions under which people feel capable. Table 1 contrasts environments that support competence with those that thwart it. These features reflect the four sources of competence support in SDT, which are clear expectations, optimal challenge, guidance, and constructive feedback (Reeve, 2024).
 
{| class=&quot;wikitable&quot; style=&quot;margin:1em auto; border-radius:8px;&quot;
|+ '''Table 1'''&lt;br&gt;''Features of Competence-Supportive and Competence-Thwarting Environments''
|-
! style=&quot;background:#eaf3fc;&quot; | Competence-supportive !! style=&quot;background:#fff6e8;&quot; | Competence-thwarting
|-
| Clear expectations about how to succeed || Vague or missing guidance
|-
| Guidance and modelling of &quot;how-to&quot; skills || Being left to work it out alone
|-
| Optimal challenge matched to current skills || Tasks far too hard or too easy
|-
| Specific, informative feedback || Absent, harsh, or controlling feedback
|-
| Long-term goals broken into short-term goals || No sense of progress
|-
| Mistakes framed as learning || Mistakes criticised or punished
|}

 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's turnaround'''
 
'''Week 8.''' Maya's manager notices the slowing progress and changes approach. They agree on what &quot;finished&quot; looks like and break the project into stages, starting with the 50 most-used folders.
 
'''Week 12.''' After each stage, Maya receives specific feedback on what is working. She now makes decisions confidently and has started suggesting improvements herself.
 
'''What changed?''' The structure around how the task would be completed: clear expectations, achievable steps, and feedback that informed instead of judged. Each gave Maya evidence that she was effective.
&lt;/div&gt;
 
Breaking Maya's project into stages draws on [[w:Goal setting|goal-setting theory]] (Locke &amp; Latham, 2002). Locke and Latham (2002) reviewed 35 years of laboratory and field studies. They found that specific, challenging goals combined with regular feedback consistently outperform vague &quot;do your best&quot; goals. Specific goals work partly because they show people exactly what success looks like. Each completed stage also acts as a mastery experience, which is the strongest source of self-efficacy (Bandura, 1977). This helps explain why Maya's confidence returned once the work was divided into stages.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Which change would best support Maya's need for competence?

|type=&quot;()&quot;}
- Offering her a bonus if she finishes faster
+ Breaking the project into stages with clear goals and specific feedback
- Telling her she is doing a great job regardless of progress
- Comparing her progress with a colleague's
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Conclusion==
Competence is the need to ''feel'' effective, and SDT treats it as important at all times, not only once basic needs are met (Ryan &amp; Deci, 2017; Tay &amp; Diener, 2011). Feeling competent moves people toward more autonomous motivation (Ryan &amp; Deci, 2020). CET explains why the same feedback can either energise or deflate a person, depending on whether it informs or controls (Deci et al., 1999).
 
When competence is actively frustrated, the consequences are more severe than when it is simply unmet. These consequences range from burnout to the helpless thinking shown in the case study (Abramson et al., 1978; Bartholomew et al., 2011). Research across workplaces and classrooms suggests, that clear expectations and informational feedback, as well as challenges broken into achievable steps, can reverse this pattern (Baard et al., 2004; Locke &amp; Latham, 2002). However, much of this evidence is correlational and rarely tests competence directly as the mechanism (Van den Broeck et al., 2016).
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==See also==
* [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|Autonomy and intrinsic motivation in self-determination theory]] (Book chapter, 2025)
* [[Motivation and emotion/Book/2011/Self-determination theory|Self-determination theory]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Book chapter, 2026)
* [[w:Self-determination theory|Self-determination theory]] (Wikipedia)
* [[w:Self-efficacy|Self-efficacy]] (Wikipedia)
* [[w:Learned helplessness|Learned helplessness]] (Wikipedia)
 
 
==References==
{{Hanging indent|1=

Abramson, L. Y., Seligman, M. E., &amp; Teasdale, J. D. (1978). Learned helplessness in humans: Critique and reformulation. Journal of Abnormal Psychology, 87(1), 49–74. https://doi.org/10.1037/0021-843X.87.1.49
 
Baard, P. P., Deci, E. L., &amp; Ryan, R. M. (2004). Intrinsic need satisfaction: a motivational basis of performance and well-being in two work settings. Journal of Applied Social Psychology, 34(10), 2045–2068. https://doi.org/10.1111/j.1559-1816.2004.tb02690.x

Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191–215. https://doi.org/10.1037/0033-295X.84.2.191
 
Bartholomew, K. J., Ntoumanis, N., Ryan, R. M., Bosch, J. A., &amp; Thøgersen-Ntoumani, C. (2011). Self-Determination Theory and Diminished Functioning: The Role of Interpersonal Control and Psychological Need Thwarting. Personality &amp; Social Psychology Bulletin, 37(11), 1459–1473. https://doi.org/10.1177/0146167211413125
 
Bureau, J. S., Howard, J. L., Chong, J. X. Y., &amp; Guay, F. (2022). Pathways to Student Motivation: A Meta-Analysis of Antecedents of Autonomous and Controlled Motivations. Review of Educational Research, 92(1), 46–72. https://doi.org/10.3102/00346543211042426
 
Cameron, J., &amp; Pierce, W. D. (1994). Reinforcement, Reward, and Intrinsic Motivation: A Meta-Analysis. Review of Educational Research, 64(3), 363–423. https://doi.org/10.3102/00346543064003363

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. Motivation and Emotion, 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1

Deci, E. L. (1971). Effects of externally mediated rewards on intrinsic motivation. Journal of Personality and Social Psychology, 18(1), 105–115. https://doi.org/10.1037/h0030644
 
Deci, E. L., Koestner, R., &amp; Ryan, R. M. (1999). A Meta-Analytic Review of Experiments Examining the Effects of Extrinsic Rewards on Intrinsic Motivation. Psychological Bulletin, 125(6), 627–668. https://doi.org/10.1037/0033-2909.125.6.627
 
Deci, E. L., &amp; Ryan, R. M. (1985). ''Intrinsic motivation and self-determination in human behavior''. Springer. https://doi.org/10.1016/j.cedpsych.2020.101860.

Fong, C. J., Patall, E. A., Vasquez, A. C., &amp; Stautberg, S. (2019). A Meta-Analysis of Negative Feedback on Intrinsic Motivation. Educational Psychology Review, 31(1), 121–162. https://doi.org/10.1007/s10648-018-9446-6
 
Locke, E. A., &amp; Latham, G. P. (2002). Building a practically useful theory of goal setting and task motivation: A 35-year odyssey. The American Psychologist, 57(9), 705–717. https://doi.org/10.1037/0003-066X.57.9.705

Maslow, A. H. (1943). A theory of human motivation. ''Psychological Review, 50''(4), 370–396. https://doi.org/10.1037/h0054346
 
Morsink, S., Van der Oord, S., Antrop, I., Danckaerts, M., &amp; Scheres, A. (2022). Studying motivation in ADHD: The role of internal motives and the relevance of self determination theory. ''Journal of Attention Disorders, 26''(8), 1139–1158. https://doi.org/10.1177/10870547211050948
 
Reeve, J. (2024). ''Understanding motivation and emotion'' (8th ed.). Wiley.
 
Ryan, R. M., &amp; Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. ''American Psychologist, 55''(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68
 
Ryan, R. M., &amp; Deci, E. L. (2017). ''Self-determination theory: Basic psychological needs in motivation, development, and wellness''. Guilford Press. https://doi.org/10.1521/978.14625/28806
 
Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology, 61'', Article 101860. https://doi.org/10.1016/j.cedpsych.2020.101860
 
Seligman, M. E. P., &amp; Maier, S. F. (1967). Failure to escape traumatic shock. ''Journal of Experimental Psychology, 74''(1), 1–9. https://doi.org/10.1037/h0024514
 
Slemp, G. R., Kern, M. L., Patrick, K. J., &amp; Ryan, R. M. (2018). Leader autonomy support in the workplace: A meta-analytic review. ''Motivation and Emotion, 42''(5), 706–724. https://doi.org/10.1007/s11031-018-9698-y
 
Tay, L., &amp; Diener, E. (2011). Needs and subjective well-being around the world. ''Journal of Personality and Social Psychology, 101''(2), 354–365. https://doi.org/10.1037/a0023779
 
Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A review of self-determination theory's basic psychological needs at work. ''Journal of Management, 42''(5), 1195–1229. https://doi.org/10.1177/0149206316632058
 
Vansteenkiste, M., &amp; Ryan, R. M. (2013). On psychological growth and vulnerability: Basic psychological need satisfaction and need frustration as a unifying principle. ''Journal of Psychotherapy Integration, 23''(3), 263–280. https://doi.org/10.1037/a0032359
 
Vansteenkiste, M., Ryan, R. M., &amp; Soenens, B. (2020). Basic psychological need theory: Advancements, critical themes, and future directions. ''Motivation and Emotion, 44''(1), 1–31. https://doi.org/10.1007/s11031-019-09818-1
 
White, R. W. (1959). Motivation reconsidered: The concept of competence. ''Psychological Review, 66''(5), 297–333. https://doi.org/10.1037/h0040934
}}


==External links==
* https://open.ncl.ac.uk/theories/20/self-determination-theory/
* https://www.apa.org/ed/schools/teaching-learning/top-twenty/motivation
* https://positivepsychology.com/self-determination-theory/


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      <text bytes="30241" sha1="na42pk8gfs8xs0agnzznlkbi45qnbcq" xml:space="preserve">{{title|Competence motivation in self-determination theory:&lt;br&gt;How does the need for competence function within self-determination theory to shape motivation and behaviour?}}
 __TOC__

==Overview==
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study:'''
[[File:Woman Suffering from Stress at Work (cropped).jpg|thumb|right|260px|'''Figure 1'''. Facing a large, unstructured task without guidance or feedback can leave a person doubting their own ability.]]
 
Maya, a 24-year-old administrative officer, has not opened her biggest project in three days. Instead, she has answered every email and tidied a shared drive she built herself: familiar tasks she knows she can do well.
 
Two months ago, Maya was excited when her manager asked her to review and reorganise more than 500 folders in the team's records system. But she received no guidance on where to start or what &quot;finished&quot; should look like. Each folder revealed new complexity, and nobody told her if her decisions were right. (see Figure 1). Some days she thinks, &quot;I just need clearer instructions.&quot; On other days her thoughts turn personal: &quot;I'm hopeless at this.&quot; The first thought sends her to ask for help; the second sends her back to her inbox.
 
''Why does the same task leave a person ready to improve on some days, and ready to give up on others?''
&lt;/div&gt;
 
 
According to [[Self-determination theory|self-determination theor]]&lt;nowiki/&gt;y (SDT), this difference often comes down to the need for [[Motivation and emotion/Book/2011/Self-determination theory|competence]]. Competence is the need to feel effective and capable (Ryan &amp; Deci, 2017). It is one of three basic psychological needs, alongside [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|autonomy]] and [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|relatedness]] (Ryan &amp; Deci, 2017). When competence is satisfied, people tend to show stronger [[Motivation and emotion/Book/2013/Intrinsic motivation|intrinsic motivation]], persistence, and wellbeing (Ryan &amp; Deci, 2020). When it is frustrated, as in Maya's case, people tend to avoid tasks and give up (Vansteenkiste et al., 2020).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Focus questions'''
* What is competence, according to self-determination theory?
* How does competence relate to intrinsic motivation?
* How does cognitive evaluation theory explain why feedback and rewards can strengthen or undermine motivation?
* What happens when the need for competence is frustrated?
* What does research show about how competence can be supported?
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Self-determination theory and competence==
 
===What is self-determination theory?===
SDT is a broad theory of human motivation. It proposes that people have three innate psychological needs: autonomy (feeling volitional), competence (feeling effective), as well as relatedness (feeling connected to others) (Deci &amp; Ryan, 1985; Ryan &amp; Deci, 2017). SDT is made up of six mini-theories, and two of these are central to this chapter. These are cognitive evaluation theory and basic psychological needs theory (Vansteenkiste et al., 2020). SDT is often compared with [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]]. Maslow (1943) proposed a hierarchy in which lower needs, such as physiological and safety needs, generally take priority over higher needs, such as esteem and self-actualisation. He placed mastery within esteem needs. SDT agrees that people strive to feel capable. However, SDT does not rank its needs and considers all three essential at all times (Ryan &amp; Deci, 2017).
 
[[File:MaslowsHierarchyOfNeeds.svg|thumb|right|300px|'''Figure 2'''. Maslow's hierarchy of needs places mastery within esteem needs, near the top of the hierarchy. SDT treats competence as essential at every level.]]
 
Tay and Diener (2011) tested these two views using Gallup World Poll data from 60,865 people in 123 countries. Although people did tend to meet basic and safety needs first, which partly supports Maslow, each need, including mastery, contributed to wellbeing regardless of whether the other needs were met (Tay &amp; Diener, 2011). The needs that mirror SDT, namely social relationships, autonomy, and mastery, were among the strongest predictors of everyday feelings across all eight world regions studied. One limitation is that the data were cross-sectional. Each need was also measured with only two or three yes or no questions, so the study shows association, not cause.
 
===What is competence within self-determination theory?===
The idea of competence as a motivational force dates back to White (1959), who challenged the drive theories of his time. He noticed that infants and young animals explore and play, as well as manipulate objects, even when they are fed and safe. He argued that this behaviour comes from a built-in need to have an effect on the environment, which he called effectance motivation. SDT builds on this idea and defines competence as the need to ''feel'' effective, not simply to possess a skill (Ryan &amp; Deci, 2017). As a result a highly skilled person can still feel incompetent if they receive no sign that their efforts are working.
 
According to SDT, competence is best satisfied in well-structured environments that offer ''[[wikipedia:Challenge_point_framework|optimal challenge]]'', positive feedback, and opportunities for growth (Ryan &amp; Deci, 2020). An optimally challenging task sits slightly beyond a person's current skill, but it comes with enough structure and support to close the gap. Tasks that are too easy offer no sense of growth, while tasks that are too hard, especially without guidance, signal failure (Reeve, 2024). Maya's difficulty illustrates how a lack of structure and feedback can make a manageable task feel too hard.
 
Basic psychological needs theory treats need satisfaction and need frustration as two separate experiences (Vansteenkiste &amp; Ryan, 2013). Need satisfaction is linked to a &quot;bright&quot; pathway of growth and engagement, as well as wellbeing (Vansteenkiste et al., 2020). Need frustration is linked to a &quot;dark&quot; pathway of defensiveness, avoidance, and ill-being (Vansteenkiste et al., 2020). Low satisfaction and active frustration are therefore not the same thing. Receiving no feedback may leave a person unfulfilled, but being repeatedly made to feel ineffective actively harms wellbeing (Vansteenkiste &amp; Ryan, 2013). The case study shows this shift. Maya moves from low satisfaction in the early weeks to active frustration after her manager's review, described later in the chapter.
 
===Competence and self-efficacy===
Competence overlaps closely with [[w:Self-efficacy|self-efficacy]], which is a person's belief that they can successfully perform a specific behaviour (Bandura, 1977). Bandura separated two expectations that shape whether people act. An ''efficacy expectation'' asks &quot;Can I do it?&quot;, and an ''outcome expectation'' asks &quot;Will it work?&quot; Efficacy beliefs are built from four sources: personal mastery experiences, watching similar others succeed, verbal persuasion, and how people interpret their own stress (Bandura, 1977). Of these, mastery experiences are the most powerful (Bandura, 1977).
 
In the case study, several of these sources are weakened. Without feedback, Maya cannot judge whether her decisions are effective, so her real progress is not experienced as mastery. As the case study later shows, her manager's comments act as negative persuasion. Her anxiety before opening the project is also likely to be read as evidence that she is not capable. The key difference between the two concepts is that self-efficacy is a belief about a specific future task (Bandura, 1977). In contrast, SDT treats competence as a universal need that shapes motivation and wellbeing over time (Ryan &amp; Deci, 2017). In practice, however, the two are difficult to separate, because both are usually measured with similar self-report questions. Some &quot;competence&quot; findings may therefore simply reflect confidence.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Competence and intrinsic motivation==
 
SDT's central claim is that the ''quality'' of motivation matters as much as its quantity (Ryan &amp; Deci, 2020). Feeling competent affects where people sit on the motivation continuum, as well as how they respond to feedback and rewards (Deci et al., 1999; Ryan &amp; Deci, 2020).
 
===The motivation continuum===
SDT describes motivation as a continuum (Ryan &amp; Deci, 2020; see Figure 3). The continuum ranges from [[Motivation and emotion/Book/2014/Amotivation|amotivation]], meaning no intention to act, through several forms of extrinsic motivation, to intrinsic motivation, meaning acting for enjoyment or interest (Ryan &amp; Deci, 2020). A lack of competence is one of the main causes of amotivation (Ryan &amp; Deci, 2000). It shows in thoughts such as &quot;I can't do this&quot; or &quot;my effort won't make a difference&quot;. In contrast, feeling capable helps people [[w:Internalization (sociology)|internalise]] the value of a task, so the task feels self-endorsed instead of obligatory (Ryan &amp; Deci, 2020). In the case study, Maya's growing avoidance of her project suggests she is sliding toward amotivation.
 
[[File:Taxonomy of motivation.png|thumb|center|600px|'''Figure 3'''. The SDT motivation continuum, ranging from amotivation, through controlled and autonomous forms of extrinsic motivation, to intrinsic motivation.]]
 
===Cognitive evaluation theory===
[[Motivation and emotion/Book/2021/Cognitive evaluation theory and motivation|Cognitive evaluation theory]] (CET) explains how external events such as feedback and rewards affect intrinsic motivation (Ryan &amp; Deci, 2000). According to CET, every such event has a ''controlling'' aspect, which affects autonomy, and an ''informational'' aspect, which affects competence (Ryan &amp; Deci, 2000). Informational feedback increases perceived competence and intrinsic motivation (Deci et al., 1999). In contrast, rewards that feel like pressure tend to undermine intrinsic motivation, even when they signal success (Deci et al., 1999). CET therefore predicts that ''how'' feedback is delivered matters as much as ''what'' it says. Later versions of CET added a third, ''amotivating'' aspect (Ryan &amp; Deci, 2017). Events that signal incompetence, or that effort will not change the outcome, can push people toward amotivation. Criticism that offers no way forward, such as the feedback Maya later receives, is likely to carry this amotivating message.
 
Research generally supports these predictions, although the earliest evidence was weak. RIn Deci's (1971) original experiment, students paid $1 for each puzzle they solved later spent less free time on the puzzles once payment stopped. However, the study had only 24 participants, and the result was only a trend (Deci, 1971). A later meta-analysis of 128 experiments, mostly with children and university students, found a clearer pattern (Deci et al., 1999). People who expected a tangible reward for an interesting task spent less free time on it afterwards. In studies with children, this effect was still present more than a week later. The most damaging rewards were those that signalled a person had fallen short (Deci et al., 1999). Feedback style also mattered. Informational praise increased intrinsic motivation, but the same praise with a controlling phrase such as &quot;just as you ''should''&quot; decreased it (Ryan et al., 1983, as cited in Deci et al., 1999). Negative feedback was less harmful when it included guidance on how to improve (Fong et al., 2019). Rewards did not undermine motivation for boring tasks or when they were unexpected (Deci et al., 1999).
 
CET assumes that these effects work ''through'' perceived competence (Ryan &amp; Deci, 2017). However, relatively few studies have measured perceived competence directly to test this (Deci et al., 1999). The results fit the theory, but the mechanism is more often assumed than demonstrated. Even so, the practical message is consistent. Feedback that identifies a problem, such as &quot;the scope needs to be better defined&quot;, without showing how to fix it is unlikely to support competence (Fong et al., 2019).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{According to cognitive evaluation theory, positive feedback is most likely to increase intrinsic motivation when it is:

|type=&quot;()&quot;}
- Given with a large financial reward
+ Informative and delivered in an autonomy-supportive way
- Delivered as a comparison with other people
- Given constantly, regardless of performance
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==When competence is frustrated==
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's first review'''
 
'''Week 6.''' Maya's manager reviews the project. She acknowledges some progress, then adds that the plan needs to be clearer and the scope better defined. She does not say what a clearer plan looks like or how to narrow the scope. Maya leaves the meeting feeling like a failure. She had enjoyed the first few folders, but now she dreads opening the system.
 
'''What is happening?''' The feedback identified a problem without giving Maya the information to solve it. Her effort no longer seems to lead anywhere, which is when a need starts to be actively frustrated, not just unmet.
&lt;/div&gt;
 
Research supports the distinction between low satisfaction and active frustration (Vansteenkiste &amp; Ryan, 2013). Bartholomew et al. (2011) found that athletes who saw their coach as controlling reported greater thwarting of all three needs. Need thwarting, in turn, predicted burnout, depressive symptoms, and negative emotion (Bartholomew et al., 2011). Feeling actively undermined was more harmful than simply not feeling supported. If the same pattern holds for competence, vague, critical feedback may harm Maya more than no feedback at all.
 
When people repeatedly experience that their effort makes no difference, they may develop [[w:Learned helplessness|learned helplessness]] (Seligman &amp; Maier, 1967). In classic experiments, dogs exposed to inescapable shocks later failed to escape shocks they could have avoided (Seligman &amp; Maier, 1967). Dogs that had been given control earlier learned to escape. In humans, helplessness reduces effort and is linked to apathy and depression (Abramson et al., 1978).How people explain failure also matters. The reformulated helplessness model proposes that explaining failure with internal, stable and global causes is more damaging than explaining it with external, unstable or specific causes (Abramson et al., 1978). Maya's two thoughts show this difference. &quot;I'm hopeless at this&quot; blames a lasting personal flaw and is more likely to lead to giving up, whereas &quot;I just need clearer instructions&quot; points to a specific, changeable cause that keeps her trying.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Maya thinks, &quot;I'm hopeless at this.&quot; According to research on explanatory style, why is this thought more harmful than &quot;I just need clearer instructions&quot;?

|type=&quot;()&quot;}
- It is less accurate
+ It explains failure with an internal, stable cause she cannot easily change
- It blames her manager instead of herself
- It focuses on the task rather than on herself
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==What supports or undermines competence?==
 
In two workplace studies, Baard et al. (2004) found that employees' satisfaction of autonomy, competence, and relatedness predicted their wellbeing as well as their performance evaluations. Because supervisors rated performance, this finding is less affected by self-report bias. However, the design still cannot show which came first. A meta-analysis by Van den Broeck et al. (2016) found that competence predicted wellbeing, work attitudes, and behaviour, even after the other two needs were taken into account. This suggests competence is not simply a by-product of feeling autonomous or connected. Leadership also matters. Managers' autonomy-supportive behaviour is associated with greater need satisfaction as well as more autonomous motivation in employees (Slemp et al., 2018). For Maya, her managers behavior may be affecting her need satisfaction, including her sense of competence.
 
Similar patterns appear in classrooms. Bureau et al. (2022) pooled studies of what predicts student motivation and found that, of the three needs, support for competence was the strongest predictor of autonomous motivation (Bureau et al., 2022). Notably, because SDT has historically given autonomy the most attention (Ryan &amp; Deci, 2017). Demonstrating that at least in classroom environments, feeling capable matters as much as feeling free to choose. However, the meta-analysis draws mainly on correlational studies, so it shows which students do well, but it does not prove that supporting competence causes better outcomes.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==How strong is the evidence?==
The strength of the evidence depends on the methods used. The reward findings, for example, were contested. Cameron and Pierce (1994) found no overall undermining effect and argued that CET should be abandoned. Deci et al. (1999) argued that this result came from mixing boring and interesting tasks, as well as using inappropriate control groups. Laboratory studies also relied mostly on single sessions with children and students (Deci et al., 1999). Self-reported interest also showed much weaker effects than behaviour. Outside the laboratory, most studies are cross-sectional. This makes it unclear whether competence drives motivation or whether motivated people simply feel more competent (Van den Broeck et al., 2016).
 
Some critics have questioned whether basic needs are truly universal, because SDT was developed largely in Western contexts (Chen et al., 2015). However, a study of adults in Belgium, China, Peru, and the United States found that need satisfaction and need frustration predicted wellbeing and ill-being in all four cultures (Chen et al., 2015). Together with the overlap between competence and self-efficacy, these limitations point to the same gap noted in CET. SDT predicts outcomes well, but whether competence itself is the active ingredient remains less certain than the theory suggests (Deci et al., 1999).
 
Most competence research has also used neurotypical samples (Morsink et al., 2022). Morsink et al. (2022) noted that research on [[w:Attention deficit hyperactivity disorder|attention-deficit/hyperactivity disorder]] (ADHD) has mostly studied rewards and overlooked psychological needs. This is despite evidence that children with more ADHD symptoms report lower need satisfaction at school.(Morsink et al., 2022) Frequent correction may push teachers and parents toward controlling styles, which can further frustrate competence (Morsink et al., 2022). Whether supporting competence helps neurodivergent people in the same way remains largely untested.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Applying competence in practice==
The research reviewed so far points to a consistent set of conditions under which people feel capable. Table 1 contrasts environments that support competence with those that thwart it. These features reflect the four sources of competence support in SDT, which are clear expectations, optimal challenge, guidance, and constructive feedback (Reeve, 2024).
 
{| class=&quot;wikitable&quot; style=&quot;margin:1em auto; border-radius:8px;&quot;
|+ '''Table 1'''&lt;br&gt;''Features of Competence-Supportive and Competence-Thwarting Environments''
|-
! style=&quot;background:#eaf3fc;&quot; | Competence-supportive !! style=&quot;background:#fff6e8;&quot; | Competence-thwarting
|-
| Clear expectations about how to succeed || Vague or missing guidance
|-
| Guidance and modelling of &quot;how-to&quot; skills || Being left to work it out alone
|-
| Optimal challenge matched to current skills || Tasks far too hard or too easy
|-
| Specific, informative feedback || Absent, harsh, or controlling feedback
|-
| Long-term goals broken into short-term goals || No sense of progress
|-
| Mistakes framed as learning || Mistakes criticised or punished
|}

 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's turnaround'''
 
'''Week 8.''' Maya's manager notices the slowing progress and changes approach. They agree on what &quot;finished&quot; looks like and break the project into stages, starting with the 50 most-used folders.
 
'''Week 12.''' After each stage, Maya receives specific feedback on what is working. She now makes decisions confidently and has started suggesting improvements herself.
 
'''What changed?''' The structure around how the task would be completed: clear expectations, achievable steps, and feedback that informed instead of judged. Each gave Maya evidence that she was effective.
&lt;/div&gt;
 
Breaking Maya's project into stages draws on [[w:Goal setting|goal-setting theory]] (Locke &amp; Latham, 2002). Locke and Latham (2002) reviewed 35 years of laboratory and field studies. They found that specific, challenging goals combined with regular feedback consistently outperform vague &quot;do your best&quot; goals. Specific goals work partly because they show people exactly what success looks like. Each completed stage also acts as a mastery experience, which is the strongest source of self-efficacy (Bandura, 1977). This helps explain why Maya's confidence returned once the work was divided into stages.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Which change would best support Maya's need for competence?

|type=&quot;()&quot;}
- Offering her a bonus if she finishes faster
+ Breaking the project into stages with clear goals and specific feedback
- Telling her she is doing a great job regardless of progress
- Comparing her progress with a colleague's
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Conclusion==
Competence is the need to ''feel'' effective, and SDT treats it as important at all times, not only once basic needs are met (Ryan &amp; Deci, 2017; Tay &amp; Diener, 2011). Feeling competent moves people toward more autonomous motivation (Ryan &amp; Deci, 2020). CET explains why the same feedback can either energise or deflate a person, depending on whether it informs or controls (Deci et al., 1999).
 
When competence is actively frustrated, the consequences are more severe than when it is simply unmet. These consequences range from burnout to the helpless thinking shown in the case study (Abramson et al., 1978; Bartholomew et al., 2011). Research across workplaces and classrooms suggests, that clear expectations and informational feedback, as well as challenges broken into achievable steps, can reverse this pattern (Baard et al., 2004; Locke &amp; Latham, 2002). However, much of this evidence is correlational and rarely tests competence directly as the mechanism (Van den Broeck et al., 2016).
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==See also==
* [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|Autonomy and intrinsic motivation in self-determination theory]] (Book chapter, 2025)
* [[Motivation and emotion/Book/2011/Self-determination theory|Self-determination theory]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Book chapter, 2026)
* [[w:Self-determination theory|Self-determination theory]] (Wikipedia)
* [[w:Self-efficacy|Self-efficacy]] (Wikipedia)
* [[w:Learned helplessness|Learned helplessness]] (Wikipedia)
 
 
==References==
{{Hanging indent|1=

Abramson, L. Y., Seligman, M. E., &amp; Teasdale, J. D. (1978). Learned helplessness in humans: Critique and reformulation. Journal of Abnormal Psychology, 87(1), 49–74. https://doi.org/10.1037/0021-843X.87.1.49
 
Baard, P. P., Deci, E. L., &amp; Ryan, R. M. (2004). Intrinsic need satisfaction: a motivational basis of performance and well-being in two work settings. Journal of Applied Social Psychology, 34(10), 2045–2068. https://doi.org/10.1111/j.1559-1816.2004.tb02690.x

Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191–215. https://doi.org/10.1037/0033-295X.84.2.191
 
Bartholomew, K. J., Ntoumanis, N., Ryan, R. M., Bosch, J. A., &amp; Thøgersen-Ntoumani, C. (2011). Self-Determination Theory and Diminished Functioning: The Role of Interpersonal Control and Psychological Need Thwarting. Personality &amp; Social Psychology Bulletin, 37(11), 1459–1473. https://doi.org/10.1177/0146167211413125
 
Bureau, J. S., Howard, J. L., Chong, J. X. Y., &amp; Guay, F. (2022). Pathways to Student Motivation: A Meta-Analysis of Antecedents of Autonomous and Controlled Motivations. Review of Educational Research, 92(1), 46–72. https://doi.org/10.3102/00346543211042426
 
Cameron, J., &amp; Pierce, W. D. (1994). Reinforcement, Reward, and Intrinsic Motivation: A Meta-Analysis. Review of Educational Research, 64(3), 363–423. https://doi.org/10.3102/00346543064003363

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. Motivation and Emotion, 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1

Deci, E. L. (1971). Effects of externally mediated rewards on intrinsic motivation. Journal of Personality and Social Psychology, 18(1), 105–115. https://doi.org/10.1037/h0030644
 
Deci, E. L., Koestner, R., &amp; Ryan, R. M. (1999). A Meta-Analytic Review of Experiments Examining the Effects of Extrinsic Rewards on Intrinsic Motivation. Psychological Bulletin, 125(6), 627–668. https://doi.org/10.1037/0033-2909.125.6.627
 
Deci, E. L., &amp; Ryan, R. M. (1985). ''Intrinsic motivation and self-determination in human behavior''. Springer. https://doi.org/10.1016/j.cedpsych.2020.101860.

Fong, C. J., Patall, E. A., Vasquez, A. C., &amp; Stautberg, S. (2019). A Meta-Analysis of Negative Feedback on Intrinsic Motivation. Educational Psychology Review, 31(1), 121–162. https://doi.org/10.1007/s10648-018-9446-6
 
Locke, E. A., &amp; Latham, G. P. (2002). Building a practically useful theory of goal setting and task motivation: A 35-year odyssey. The American Psychologist, 57(9), 705–717. https://doi.org/10.1037/0003-066X.57.9.705

Maslow, A. H. (1943). A theory of human motivation. ''Psychological Review, 50''(4), 370–396. https://doi.org/10.1037/h0054346
 
Morsink, S., Van der Oord, S., Antrop, I., Danckaerts, M., &amp; Scheres, A. (2022). Studying motivation in ADHD: The role of internal motives and the relevance of self determination theory. ''Journal of Attention Disorders, 26''(8), 1139–1158. https://doi.org/10.1177/10870547211050948
 
Reeve, J. (2024). ''Understanding motivation and emotion'' (8th ed.). Wiley.
 
Ryan, R. M., &amp; Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. ''American Psychologist, 55''(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68
 
Ryan, R. M., &amp; Deci, E. L. (2017). ''Self-determination theory: Basic psychological needs in motivation, development, and wellness''. Guilford Press. https://doi.org/10.1521/978.14625/28806
 
Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology, 61'', Article 101860. https://doi.org/10.1016/j.cedpsych.2020.101860
 
Seligman, M. E. P., &amp; Maier, S. F. (1967). Failure to escape traumatic shock. ''Journal of Experimental Psychology, 74''(1), 1–9. https://doi.org/10.1037/h0024514
 
Slemp, G. R., Kern, M. L., Patrick, K. J., &amp; Ryan, R. M. (2018). Leader autonomy support in the workplace: A meta-analytic review. ''Motivation and Emotion, 42''(5), 706–724. https://doi.org/10.1007/s11031-018-9698-y
 
Tay, L., &amp; Diener, E. (2011). Needs and subjective well-being around the world. ''Journal of Personality and Social Psychology, 101''(2), 354–365. https://doi.org/10.1037/a0023779
 
Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A review of self-determination theory's basic psychological needs at work. ''Journal of Management, 42''(5), 1195–1229. https://doi.org/10.1177/0149206316632058
 
Vansteenkiste, M., &amp; Ryan, R. M. (2013). On psychological growth and vulnerability: Basic psychological need satisfaction and need frustration as a unifying principle. ''Journal of Psychotherapy Integration, 23''(3), 263–280. https://doi.org/10.1037/a0032359
 
Vansteenkiste, M., Ryan, R. M., &amp; Soenens, B. (2020). Basic psychological need theory: Advancements, critical themes, and future directions. ''Motivation and Emotion, 44''(1), 1–31. https://doi.org/10.1007/s11031-019-09818-1
 
White, R. W. (1959). Motivation reconsidered: The concept of competence. ''Psychological Review, 66''(5), 297–333. https://doi.org/10.1037/h0040934
}}


==External links==
* https://open.ncl.ac.uk/theories/20/self-determination-theory/
* https://www.apa.org/ed/schools/teaching-learning/top-twenty/motivation
* https://positivepsychology.com/self-determination-theory/


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[[Category:Motivation and emotion/Book/Self-determination theory/Competence]]</text>
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      <comment>Linked learned helplessness and goal-setting sections back to SDT (amotivation; competence support). Final read-through: minor wording and formatting edits. Added Vallerand &amp; Reid (1984) to the CET section as an experimental test of perceived competence as the mediator, including its limitations (small all-male sample, single task).</comment>
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      <text bytes="31741" sha1="gmkz5fflogcwhp5s9xxfqcq3m5d66lw" xml:space="preserve">{{title|Competence motivation in self-determination theory:&lt;br&gt;How does the need for competence function within self-determination theory to shape motivation and behaviour?}}
 __TOC__

==Overview==
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study:'''
[[File:Woman Suffering from Stress at Work (cropped).jpg|thumb|right|260px|'''Figure 1'''. Facing a large, unstructured task without guidance or feedback can leave a person doubting their own ability.]]
 
Maya, a 24-year-old administrative officer, has not opened her biggest project in three days. Instead, she has answered every email and tidied a shared drive she built herself: familiar tasks she knows she can do well.
 
Two months ago, Maya was excited when her manager asked her to review and reorganise more than 500 folders in the team's records system. But she received no guidance on where to start or what &quot;finished&quot; should look like. Each folder revealed new complexity, and nobody told her if her decisions were right. (see Figure 1). Some days she thinks, &quot;I just need clearer instructions.&quot; On other days her thoughts turn personal: &quot;I'm hopeless at this.&quot; The first thought sends her to ask for help; the second sends her back to her inbox.
 
''Why does the same task leave a person ready to improve on some days, and ready to give up on others?''
&lt;/div&gt;
 
 
According to [[Self-determination theory|self-determination theory]]&lt;nowiki/&gt;y (SDT), this difference often comes down to the need for [[Motivation and emotion/Book/2011/Self-determination theory|competence]]. Competence is the need to feel effective and capable (Ryan &amp; Deci, 2017). It is one of three basic psychological needs, alongside [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|autonomy]] and [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|relatedness]] (Ryan &amp; Deci, 2017). When competence is satisfied, people tend to show stronger [[Motivation and emotion/Book/2013/Intrinsic motivation|intrinsic motivation]], persistence, and wellbeing (Ryan &amp; Deci, 2020). When it is frustrated, as in Maya's case, people tend to avoid tasks and give up (Vansteenkiste et al., 2020).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Focus questions'''
* What is competence, according to self-determination theory?
* How does competence relate to intrinsic motivation?
* How does cognitive evaluation theory explain why feedback and rewards can strengthen or undermine motivation?
* What happens when the need for competence is frustrated?
* What does research show about how competence can be supported?
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Self-determination theory and competence==
 
===What is self-determination theory?===
SDT is a broad theory of human motivation. It proposes that people have three innate psychological needs: autonomy (feeling volitional), competence (feeling effective), as well as relatedness (feeling connected to others) (Deci &amp; Ryan, 1985; Ryan &amp; Deci, 2017). SDT is made up of six mini-theories, and two of these are central to this chapter. These are cognitive evaluation theory and basic psychological needs theory (Vansteenkiste et al., 2020). SDT is often compared with [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]]. Maslow (1943) proposed a hierarchy in which lower needs, such as physiological and safety needs, generally take priority over higher needs, such as esteem and self-actualisation. He placed mastery within esteem needs. SDT agrees that people strive to feel capable. However, SDT does not rank its needs and considers all three essential at all times (Ryan &amp; Deci, 2017).
 
[[File:MaslowsHierarchyOfNeeds.svg|thumb|right|300px|'''Figure 2'''. Maslow's hierarchy of needs places mastery within esteem needs, near the top of the hierarchy. SDT treats competence as essential at every level.]]
 
Tay and Diener (2011) tested these two views using Gallup World Poll data from 60,865 people in 123 countries. Although people did tend to meet basic and safety needs first, which partly supports Maslow, each need, including mastery, contributed to wellbeing regardless of whether the other needs were met (Tay &amp; Diener, 2011). The needs that mirror SDT, namely social relationships, autonomy, and mastery, were among the strongest predictors of everyday feelings across all eight world regions studied. One limitation is that the data were cross-sectional. Each need was also measured with only two or three yes or no questions, so the study shows association, not cause.
 
===What is competence within self-determination theory?===
The idea of competence as a motivational force dates back to White (1959), who challenged the drive theories of his time. He noticed that infants and young animals explore and play, as well as manipulate objects, even when they are fed and safe. He argued that this behaviour comes from a built-in need to have an effect on the environment, which he called effectance motivation. SDT builds on this idea and defines competence as the need to ''feel'' effective, not simply to possess a skill (Ryan &amp; Deci, 2017). As a result a highly skilled person can still feel incompetent if they receive no sign that their efforts are working.
 
According to SDT, competence is best satisfied in well-structured environments that offer &quot;optimal challenge&quot;, positive feedback, and opportunities for growth (Ryan &amp; Deci, 2020). An optimally challenging task sits slightly beyond a person's current skill, but it comes with enough structure and support to close the gap. Tasks that are too easy offer no sense of growth, while tasks that are too hard, especially without guidance, signal failure (Reeve, 2024). Maya's difficulty illustrates how a lack of structure and feedback can make a manageable task feel too hard.
 
Basic psychological needs theory treats need satisfaction and need frustration as two separate experiences (Vansteenkiste &amp; Ryan, 2013). Need satisfaction is linked to a &quot;bright&quot; pathway of growth and engagement, as well as wellbeing (Vansteenkiste et al., 2020). Need frustration is linked to a &quot;dark&quot; pathway of defensiveness, avoidance, and ill-being (Vansteenkiste et al., 2020). Low satisfaction and active frustration are therefore not the same thing. Receiving no feedback may leave a person unfulfilled, but being repeatedly made to feel ineffective actively harms wellbeing (Vansteenkiste &amp; Ryan, 2013). The case study shows this shift. Maya moves from low satisfaction in the early weeks to active frustration after her manager's review, described later in the chapter.
 
===Competence and self-efficacy===
Competence overlaps closely with [[w:Self-efficacy|self-efficacy]], which is a person's belief that they can successfully perform a specific behaviour (Bandura, 1977). Bandura separated two expectations that shape whether people act. An ''efficacy expectation'' asks &quot;Can I do it?&quot;, and an ''outcome expectation'' asks &quot;Will it work?&quot; Efficacy beliefs are built from four sources: personal mastery experiences, watching similar others succeed, verbal persuasion, and how people interpret their own stress (Bandura, 1977). Of these, mastery experiences are the most powerful (Bandura, 1977).
 
In the case study, several of these sources are weakened. Without feedback, Maya cannot judge whether her decisions are effective, so her real progress is not experienced as mastery. As the case study later shows, her manager's comments act as negative persuasion. Her anxiety before opening the project is also likely to be read as evidence that she is not capable. The key difference between the two concepts is that self-efficacy is a belief about a specific future task (Bandura, 1977). In contrast, SDT treats competence as a universal need that shapes motivation and wellbeing over time (Ryan &amp; Deci, 2017). In practice, however, the two are difficult to separate, because both are usually measured with similar self-report questions. Some &quot;competence&quot; findings may therefore simply reflect confidence.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Competence and intrinsic motivation==
 
SDT's central claim is that the ''quality'' of motivation matters as much as its quantity (Ryan &amp; Deci, 2020). Feeling competent affects where people sit on the motivation continuum, as well as how they respond to feedback and rewards (Deci et al., 1999; Ryan &amp; Deci, 2020).
 
===The motivation continuum===
SDT describes motivation as a continuum (Ryan &amp; Deci, 2020; see Figure 3). The continuum ranges from [[Motivation and emotion/Book/2014/Amotivation|amotivation]], meaning no intention to act, through several forms of extrinsic motivation, to intrinsic motivation, meaning acting for enjoyment or interest (Ryan &amp; Deci, 2020). A lack of competence is one of the main causes of amotivation (Ryan &amp; Deci, 2000). It shows in thoughts such as &quot;I can't do this&quot; or &quot;my effort won't make a difference&quot;. In contrast, feeling capable helps people [[w:Internalization (sociology)|internalise]] the value of a task, so the task feels self-endorsed instead of obligatory (Ryan &amp; Deci, 2020). In the case study, Maya's growing avoidance of her project suggests she is sliding toward amotivation.
 
[[File:Taxonomy of motivation.png|thumb|center|600px|'''Figure 3'''. The SDT motivation continuum, ranging from amotivation, through controlled and autonomous forms of extrinsic motivation, to intrinsic motivation.]]
 
===Cognitive evaluation theory===
[[Motivation and emotion/Book/2021/Cognitive evaluation theory and motivation|Cognitive evaluation theory]] (CET) explains how external events such as feedback and rewards affect intrinsic motivation (Ryan &amp; Deci, 2000). According to CET, every such event has a ''controlling'' aspect, which affects autonomy, and an ''informational'' aspect, which affects competence (Ryan &amp; Deci, 2000). Informational feedback increases perceived competence and intrinsic motivation (Deci et al., 1999). In contrast, rewards that feel like pressure tend to undermine intrinsic motivation, even when they signal success (Deci et al., 1999). CET therefore predicts that ''how'' feedback is delivered matters as much as ''what'' it says. Later versions of CET added a third, ''amotivating'' aspect (Ryan &amp; Deci, 2017). Events that signal incompetence, or that effort will not change the outcome, can push people toward amotivation. Criticism that offers no way forward, such as the feedback Maya later receives, is likely to carry this amotivating message.
 
Research generally supports these predictions, although the earliest evidence was weak. In Deci's (1971) original experiment, students paid $1 for each puzzle they solved later spent less free time on the puzzles once payment stopped. However, the study had only 24 participants, and the result was only a trend (Deci, 1971). A later meta-analysis of 128 experiments, mostly with children and university students, found a clearer pattern (Deci et al., 1999). People who expected a tangible reward for an interesting task spent less free time on it afterwards. In studies with children, this effect was still present more than a week later. The most damaging rewards were those that signalled a person had fallen short (Deci et al., 1999). Feedback style also mattered. Informational praise increased intrinsic motivation, but the same praise with a controlling phrase such as &quot;just as you ''should''&quot; decreased it (Ryan et al., 1983, as cited in Deci et al., 1999). Negative feedback was less harmful when it included guidance on how to improve (Fong et al., 2019). Rewards did not undermine motivation for boring tasks or when they were unexpected (Deci et al., 1999).
 
CET assumes that these effects work ''through'' perceived competence (Ryan &amp; Deci, 2017). However, relatively few studies have measured perceived competence directly to test this (Deci et al., 1999). One exception is Vallerand and Reid (1984), who gave 84 male students positive, negative, or no verbal feedback on a balance task. Positive feedback raised both perceived competence and intrinsic motivation, while negative feedback lowered both. Perceived competence explained about 40% of the differences in intrinsic motivation, compared with under 8% for feedback alone. However it is important to note that competence was measured with a single question, and the all-male laboratory sample limits how far the findings generalise. Beyond this study, the mechanism is more often assumed than demonstrated. Even so, the practical message is consistent. Feedback that identifies a problem, such as &quot;the scope needs to be better defined&quot;, without showing how to fix it is unlikely to support competence (Fong et al., 2019).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{According to cognitive evaluation theory, positive feedback is most likely to increase intrinsic motivation when it is:

|type=&quot;()&quot;}
- Given with a large financial reward
+ Informative and delivered in an autonomy-supportive way
- Delivered as a comparison with other people
- Given constantly, regardless of performance
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==When competence is frustrated==
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's first review'''
 
'''Week 6.''' Maya's manager reviews the project. She acknowledges some progress, then adds that the plan needs to be clearer and the scope better defined. She does not say what a clearer plan looks like or how to narrow the scope. Maya leaves the meeting feeling like a failure. She had enjoyed the first few folders, but now she dreads opening the system.
 
'''What is happening?''' The feedback identified a problem without giving Maya the information to solve it. Her effort no longer seems to lead anywhere, which is when a need starts to be actively frustrated, not just unmet.
&lt;/div&gt;
 
Research supports the distinction between low satisfaction and active frustration (Vansteenkiste &amp; Ryan, 2013). Bartholomew et al. (2011) found that athletes who saw their coach as controlling reported greater thwarting of all three needs. Need thwarting, in turn, predicted burnout, depressive symptoms, and negative emotion (Bartholomew et al., 2011). Feeling actively undermined was more harmful than simply not feeling supported. If the same pattern holds for competence, vague, critical feedback may harm Maya more than no feedback at all.
 
When people repeatedly experience that their effort makes no difference, they may develop [[w:Learned helplessness|learned helplessness]] (Seligman &amp; Maier, 1967). In classic experiments, dogs exposed to inescapable shocks later failed to escape shocks they could have avoided (Seligman &amp; Maier, 1967). Dogs that had been given control earlier learned to escape. In SDT terms, helplessness resembles amotivation caused by repeated competence frustration Ryan and Deci (2017). In humans, helplessness reduces effort and is linked to apathy and depression (Abramson et al., 1978). How people explain failure also matters. The reformulated helplessness model proposes that explaining failure with internal, stable and global causes is more damaging than explaining it with external, unstable or specific causes (Abramson et al., 1978). Maya's two thoughts show this difference. &quot;I'm hopeless at this&quot; blames a lasting personal flaw and is more likely to lead to giving up, whereas &quot;I just need clearer instructions&quot; points to a specific, changeable cause that keeps her trying.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Maya thinks, &quot;I'm hopeless at this.&quot; According to research on explanatory style, why is this thought more harmful than &quot;I just need clearer instructions&quot;?

|type=&quot;()&quot;}
- It is less accurate
+ It explains failure with an internal, stable cause she cannot easily change
- It blames her manager instead of herself
- It focuses on the task rather than on herself
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==What supports or undermines competence?==
 
In two workplace studies, Baard et al. (2004) found that employees' satisfaction of autonomy, competence, and relatedness predicted their wellbeing as well as their performance evaluations. Because supervisors rated performance, this finding is less affected by self-report bias. However, the design still cannot show which came first. A meta-analysis by Van den Broeck et al. (2016) found that competence predicted wellbeing, work attitudes, and behaviour, even after the other two needs were taken into account. This suggests competence is not simply a by-product of feeling autonomous or connected. Leadership also matters. Managers' autonomy-supportive behaviour is associated with greater need satisfaction as well as more autonomous motivation in employees (Slemp et al., 2018). For Maya, her manager's behavior may be affecting her need satisfaction, including her sense of competence.
 
Similar patterns are found in classroom environments. Bureau et al. (2022) pooled studies of what predicts student motivation and found that, of the three needs, support for competence was the strongest predictor of autonomous motivation. Notably, because SDT has historically given autonomy the most attention (Ryan &amp; Deci, 2017). At least in classroom environments, feeling capable may matter as much as feeling free to choose. However, the meta-analysis draws mainly on correlational studies, so it shows which students do well, but it does not prove that supporting competence causes better outcomes.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==How strong is the evidence?==
The strength of the evidence depends on the methods used. The reward findings, for example, were contested. Cameron and Pierce (1994) found no overall undermining effect and argued that CET should be abandoned. Deci et al. (1999) argued that this result came from mixing boring and interesting tasks, as well as using inappropriate control groups. Laboratory studies also relied mostly on single sessions with children and students (Deci et al., 1999). Self-reported interest also showed much weaker effects than behaviour. Outside the laboratory, most studies are cross-sectional. This makes it unclear whether competence drives motivation or whether motivated people simply feel more competent (Van den Broeck et al., 2016).
 
Some critics have questioned whether basic needs are truly universal, because SDT was developed largely in Western contexts (Chen et al., 2015). However, a study of adults in Belgium, China, Peru, and the United States found that need satisfaction and need frustration predicted wellbeing and ill-being in all four cultures (Chen et al., 2015). Together with the overlap between competence and self-efficacy, these limitations point to the same gap noted in CET. SDT predicts outcomes well, but whether competence itself is the active ingredient remains less certain than the theory suggests (Deci et al., 1999).
 
Most competence research has also used neurotypical samples (Morsink et al., 2022). Morsink et al. (2022) noted that research on [[w:Attention deficit hyperactivity disorder|attention-deficit/hyperactivity disorder]] (ADHD) has mostly studied rewards and overlooked psychological needs. This is despite evidence that children with more ADHD symptoms report lower need satisfaction at school (Morsink et al., 2022). Frequent correction may push teachers and parents toward controlling styles, which can further frustrate competence (Morsink et al., 2022). Whether supporting competence helps neurodivergent people in the same way remains largely untested.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Applying competence in practice==
The research reviewed so far points to a consistent set of conditions under which people feel capable. Table 1 contrasts environments that support competence with those that thwart it. These features reflect the four sources of competence support in SDT, which are clear expectations, optimal challenge, guidance, and constructive feedback (Reeve, 2024).
 
{| class=&quot;wikitable&quot; style=&quot;margin:1em auto; border-radius:8px;&quot;
|+ '''Table 1'''&lt;br&gt;''Features of Competence-Supportive and Competence-Thwarting Environments''
|-
! style=&quot;background:#eaf3fc;&quot; | Competence-supportive !! style=&quot;background:#fff6e8;&quot; | Competence-thwarting
|-
| Clear expectations about how to succeed || Vague or missing guidance
|-
| Guidance and modelling of &quot;how-to&quot; skills || Being left to work it out alone
|-
| Optimal challenge matched to current skills || Tasks far too hard or too easy
|-
| Specific, informative feedback || Absent, harsh, or controlling feedback
|-
| Long-term goals broken into short-term goals || No sense of progress
|-
| Mistakes framed as learning || Mistakes criticised or punished
|}

 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's turnaround'''
 
'''Week 8.''' Maya's manager notices the slowing progress and changes approach. They agree on what &quot;finished&quot; looks like and break the project into stages, starting with the 50 most-used folders.
 
'''Week 12.''' After each stage, Maya receives specific feedback on what is working. She now makes decisions confidently and has started suggesting improvements herself.
 
'''What changed?''' The structure around how the task would be completed: clear expectations, achievable steps, and feedback that informed instead of judged. Each gave Maya evidence that she was effective.
&lt;/div&gt;
 
Breaking Maya's project into stages draws on [[w:Goal setting|goal-setting theory]] (Locke &amp; Latham, 2002). Locke and Latham (2002) reviewed 35 years of laboratory and field studies. They found that specific, challenging goals combined with regular feedback consistently outperform vague &quot;do your best&quot; goals. In SDT, this kind of structure is a form of competence support (Reeve, 2024). Specific goals work partly because they show people exactly what success looks like. Each completed stage also acts as a mastery experience, which is the strongest source of self-efficacy (Bandura, 1977). This helps explain why Maya's confidence returned once the work was divided into stages.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Which change would best support Maya's need for competence?

|type=&quot;()&quot;}
- Offering her a bonus if she finishes faster
+ Breaking the project into stages with clear goals and specific feedback
- Telling her she is doing a great job regardless of progress
- Comparing her progress with a colleague's
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Conclusion==
Competence is the need to ''feel'' effective, and SDT treats it as important at all times, not only once basic needs are met (Ryan &amp; Deci, 2017; Tay &amp; Diener, 2011). Feeling competent moves people toward more autonomous motivation (Ryan &amp; Deci, 2020). CET explains why the same feedback can either energise or deflate a person, depending on whether it informs or controls (Deci et al., 1999).
 
When competence is actively frustrated, the consequences are more severe than when it is simply unmet. These consequences range from burnout to the helpless thinking shown in the case study (Abramson et al., 1978; Bartholomew et al., 2011). Research across workplaces and classrooms suggests, that clear expectations and informational feedback, as well as challenges broken into achievable steps, can reverse this pattern (Baard et al., 2004; Locke &amp; Latham, 2002). However, much of this evidence is correlational and rarely tests competence directly as the mechanism (Van den Broeck et al., 2016).

'''Take-home messages'''
* '''Competence is about feeling effective:''' skilled people can still feel incompetent if they get no sign their effort is working.
* '''Feedback should inform, not control:''' say what is working and how to improve, without pressure.
* '''Make progress visible:''' break big tasks into stages and agree on what &quot;finished&quot; looks like.
* '''Notice the explanation:''' &quot;I'm hopeless&quot; leads towards giving up, while &quot;I need clearer instructions&quot; keeps people trying.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==See also==
* [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|Autonomy and intrinsic motivation in self-determination theory]] (Book chapter, 2025)
* [[Motivation and emotion/Book/2011/Self-determination theory|Self-determination theory]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Book chapter, 2026)
* [[w:Self-determination theory|Self-determination theory]] (Wikipedia)
* [[w:Self-efficacy|Self-efficacy]] (Wikipedia)
* [[w:Learned helplessness|Learned helplessness]] (Wikipedia)
 
 
==References==
{{Hanging indent|1=

Abramson, L. Y., Seligman, M. E., &amp; Teasdale, J. D. (1978). Learned helplessness in humans: Critique and reformulation. Journal of Abnormal Psychology, 87(1), 49–74. https://doi.org/10.1037/0021-843X.87.1.49
 
Baard, P. P., Deci, E. L., &amp; Ryan, R. M. (2004). Intrinsic need satisfaction: a motivational basis of performance and well-being in two work settings. Journal of Applied Social Psychology, 34(10), 2045–2068. https://doi.org/10.1111/j.1559-1816.2004.tb02690.x

Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191–215. https://doi.org/10.1037/0033-295X.84.2.191
 
Bartholomew, K. J., Ntoumanis, N., Ryan, R. M., Bosch, J. A., &amp; Thøgersen-Ntoumani, C. (2011). Self-Determination Theory and Diminished Functioning: The Role of Interpersonal Control and Psychological Need Thwarting. Personality &amp; Social Psychology Bulletin, 37(11), 1459–1473. https://doi.org/10.1177/0146167211413125
 
Bureau, J. S., Howard, J. L., Chong, J. X. Y., &amp; Guay, F. (2022). Pathways to Student Motivation: A Meta-Analysis of Antecedents of Autonomous and Controlled Motivations. Review of Educational Research, 92(1), 46–72. https://doi.org/10.3102/00346543211042426
 
Cameron, J., &amp; Pierce, W. D. (1994). Reinforcement, Reward, and Intrinsic Motivation: A Meta-Analysis. Review of Educational Research, 64(3), 363–423. https://doi.org/10.3102/00346543064003363

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. Motivation and Emotion, 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1

Deci, E. L. (1971). Effects of externally mediated rewards on intrinsic motivation. Journal of Personality and Social Psychology, 18(1), 105–115. https://doi.org/10.1037/h0030644
 
Deci, E. L., Koestner, R., &amp; Ryan, R. M. (1999). A Meta-Analytic Review of Experiments Examining the Effects of Extrinsic Rewards on Intrinsic Motivation. Psychological Bulletin, 125(6), 627–668. https://doi.org/10.1037/0033-2909.125.6.627
 
Deci, E. L., &amp; Ryan, R. M. (1985). ''Intrinsic motivation and self-determination in human behavior''. Springer. https://doi.org/10.1007/978-1-4899-2271-7

Fong, C. J., Patall, E. A., Vasquez, A. C., &amp; Stautberg, S. (2019). ''A Meta-Analysis of Negative Feedback on Intrinsic Motivation''. Educational Psychology Review, 31(1), 121–162. https://doi.org/10.1007/s10648-018-9446-6
 
Locke, E. A., &amp; Latham, G. P. (2002). '' Building a practically useful theory of goal setting and task motivation: A 35-year odyssey''. The American Psychologist, 57(9), 705–717. https://doi.org/10.1037/0003-066X.57.9.705

Maslow, A. H. (1943). A theory of human motivation. ''Psychological Review, 50''(4), 370–396. https://doi.org/10.1037/h0054346
 
Morsink, S., Van der Oord, S., Antrop, I., Danckaerts, M., &amp; Scheres, A. (2022). ''Studying motivation in ADHD: The role of internal motives and the relevance of self determination theory. ''Journal of Attention Disorders, 26''(8), 1139–1158. https://doi.org/10.1177/10870547211050948
 
Reeve, J. (2024). ''Understanding motivation and emotion'' (8th ed.). Wiley.
 
Ryan, R. M., &amp; Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. ''American Psychologist, 55''(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68
 
Ryan, R. M., &amp; Deci, E. L. (2017). ''Self-determination theory: Basic psychological needs in motivation, development, and wellness''. Guilford Press. https://doi.org/10.1521/978.14625/28806
 
Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology, 61'', Article 101860. https://doi.org/10.1016/j.cedpsych.2020.101860
 
Seligman, M. E. P., &amp; Maier, S. F. (1967). Failure to escape traumatic shock. ''Journal of Experimental Psychology, 74''(1), 1–9. https://doi.org/10.1037/h0024514
 
Slemp, G. R., Kern, M. L., Patrick, K. J., &amp; Ryan, R. M. (2018). Leader autonomy support in the workplace: A meta-analytic review. ''Motivation and Emotion, 42''(5), 706–724. https://doi.org/10.1007/s11031-018-9698-y
 
Tay, L., &amp; Diener, E. (2011). Needs and subjective well-being around the world. ''Journal of Personality and Social Psychology, 101''(2), 354–365. https://doi.org/10.1037/a0023779
 
Vallerand, R. J., &amp; Reid, G. (1984). On the causal effects of perceived competence on intrinsic motivation: A test of cognitive evaluation theory. ''Journal of Sport Psychology, 6''(1), 94–102. https://doi.org/10.1123/jsp.6.1.94

Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A review of self-determination theory's basic psychological needs at work. ''Journal of Management, 42''(5), 1195–1229. https://doi.org/10.1177/0149206316632058
 
Vansteenkiste, M., &amp; Ryan, R. M. (2013). On psychological growth and vulnerability: Basic psychological need satisfaction and need frustration as a unifying principle. ''Journal of Psychotherapy Integration, 23''(3), 263–280. https://doi.org/10.1037/a0032359
 
Vansteenkiste, M., Ryan, R. M., &amp; Soenens, B. (2020). Basic psychological need theory: Advancements, critical themes, and future directions. ''Motivation and Emotion, 44''(1), 1–31. https://doi.org/10.1007/s11031-019-09818-1
 
White, R. W. (1959). Motivation reconsidered: The concept of competence. ''Psychological Review, 66''(5), 297–333. https://doi.org/10.1037/h0040934
}}


==External links==
* [https://open.ncl.ac.uk/theories/20/self-determination-theory/]
* [https://www.apa.org/ed/schools/teaching-learning/top-twenty/motivation]
* [https://positivepsychology.com/self-determination-theory/]
* [https://open.ncl.ac.uk/theories/20/self-determination-theory/ Self-determination theory] (Newcastle University)


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      <text bytes="31765" sha1="tspz8otvo9n1zxdoaguoi5zd9fpaeqj" xml:space="preserve">{{title|Competence motivation in self-determination theory:&lt;br&gt;How does the need for competence function within self-determination theory to shape motivation and behaviour?}}
 __TOC__

==Overview==
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study:'''
[[File:Woman Suffering from Stress at Work (cropped).jpg|thumb|right|260px|'''Figure 1'''. Facing a large, unstructured task without guidance or feedback can leave a person doubting their own ability.]]
 
Maya, a 24-year-old administrative officer, has not opened her biggest project in three days. Instead, she has answered every email and tidied a shared drive she built herself: familiar tasks she knows she can do well.
 
Two months ago, Maya was excited when her manager asked her to review and reorganise more than 500 folders in the team's records system. But she received no guidance on where to start or what &quot;finished&quot; should look like. Each folder revealed new complexity, and nobody told her if her decisions were right. (see Figure 1). Some days she thinks, &quot;I just need clearer instructions.&quot; On other days her thoughts turn personal: &quot;I'm hopeless at this.&quot; The first thought sends her to ask for help; the second sends her back to her inbox.
 
''Why does the same task leave a person ready to improve on some days, and ready to give up on others?''
&lt;/div&gt;
 
 
According to [[Self-determination theory|self-determination theory]]&lt;nowiki/&gt;y (SDT), this difference often comes down to the need for [[Motivation and emotion/Book/2011/Self-determination theory|competence]]. Competence is the need to feel effective and capable (Ryan &amp; Deci, 2017). It is one of three basic psychological needs, alongside [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|autonomy]] and [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|relatedness]] (Ryan &amp; Deci, 2017). When competence is satisfied, people tend to show stronger [[Motivation and emotion/Book/2013/Intrinsic motivation|intrinsic motivation]], persistence, and wellbeing (Ryan &amp; Deci, 2020). When it is frustrated, as in Maya's case, people tend to avoid tasks and give up (Vansteenkiste et al., 2020).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Focus questions'''
* What is competence, according to self-determination theory?
* How does competence relate to intrinsic motivation?
* How does cognitive evaluation theory explain why feedback and rewards can strengthen or undermine motivation?
* What happens when the need for competence is frustrated?
* What does research show about how competence can be supported?
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Self-determination theory and competence==
 
===What is self-determination theory?===
SDT is a broad theory of human motivation. It proposes that people have three innate psychological needs: autonomy (feeling volitional), competence (feeling effective), as well as relatedness (feeling connected to others) (Deci &amp; Ryan, 1985; Ryan &amp; Deci, 2017). SDT is made up of six mini-theories, and two of these are central to this chapter. These are cognitive evaluation theory and basic psychological needs theory (Vansteenkiste et al., 2020). SDT is often compared with [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]]. Maslow (1943) proposed a hierarchy in which lower needs, such as physiological and safety needs, generally take priority over higher needs, such as esteem and self-actualisation. He placed mastery within esteem needs. SDT agrees that people strive to feel capable. However, SDT does not rank its needs and considers all three essential at all times (Ryan &amp; Deci, 2017).
 
[[File:MaslowsHierarchyOfNeeds.svg|thumb|right|300px|'''Figure 2'''. Maslow's hierarchy of needs places mastery within esteem needs, near the top of the hierarchy. SDT treats competence as essential at every level.]]
 
Tay and Diener (2011) tested these two views using Gallup World Poll data from 60,865 people in 123 countries. Although people did tend to meet basic and safety needs first, which partly supports Maslow, each need, including mastery, contributed to wellbeing regardless of whether the other needs were met (Tay &amp; Diener, 2011). The needs that mirror SDT, namely social relationships, autonomy, and mastery, were among the strongest predictors of everyday feelings across all eight world regions studied. One limitation is that the data were cross-sectional. Each need was also measured with only two or three yes or no questions, so the study shows association, not cause.
 
===What is competence within self-determination theory?===
The idea of competence as a motivational force dates back to White (1959), who challenged the drive theories of his time. He noticed that infants and young animals explore and play, as well as manipulate objects, even when they are fed and safe. He argued that this behaviour comes from a built-in need to have an effect on the environment, which he called effectance motivation. SDT builds on this idea and defines competence as the need to ''feel'' effective, not simply to possess a skill (Ryan &amp; Deci, 2017). As a result a highly skilled person can still feel incompetent if they receive no sign that their efforts are working.
 
According to SDT, competence is best satisfied in well-structured environments that offer &quot;optimal challenge&quot;, positive feedback, and opportunities for growth (Ryan &amp; Deci, 2020). An optimally challenging task sits slightly beyond a person's current skill, but it comes with enough structure and support to close the gap. Tasks that are too easy offer no sense of growth, while tasks that are too hard, especially without guidance, signal failure (Reeve, 2024). Maya's difficulty illustrates how a lack of structure and feedback can make a manageable task feel too hard.
 
Basic psychological needs theory treats need satisfaction and need frustration as two separate experiences (Vansteenkiste &amp; Ryan, 2013). Need satisfaction is linked to a &quot;bright&quot; pathway of growth and engagement, as well as wellbeing (Vansteenkiste et al., 2020). Need frustration is linked to a &quot;dark&quot; pathway of defensiveness, avoidance, and ill-being (Vansteenkiste et al., 2020). Low satisfaction and active frustration are therefore not the same thing. Receiving no feedback may leave a person unfulfilled, but being repeatedly made to feel ineffective actively harms wellbeing (Vansteenkiste &amp; Ryan, 2013). The case study shows this shift. Maya moves from low satisfaction in the early weeks to active frustration after her manager's review, described later in the chapter.
 
===Competence and self-efficacy===
Competence overlaps closely with [[w:Self-efficacy|self-efficacy]], which is a person's belief that they can successfully perform a specific behaviour (Bandura, 1977). Bandura separated two expectations that shape whether people act. An ''efficacy expectation'' asks &quot;Can I do it?&quot;, and an ''outcome expectation'' asks &quot;Will it work?&quot; Efficacy beliefs are built from four sources: personal mastery experiences, watching similar others succeed, verbal persuasion, and how people interpret their own stress (Bandura, 1977). Of these, mastery experiences are the most powerful (Bandura, 1977).
 
In the case study, several of these sources are weakened. Without feedback, Maya cannot judge whether her decisions are effective, so her real progress is not experienced as mastery. As the case study later shows, her manager's comments act as negative persuasion. Her anxiety before opening the project is also likely to be read as evidence that she is not capable. The key difference between the two concepts is that self-efficacy is a belief about a specific future task (Bandura, 1977). In contrast, SDT treats competence as a universal need that shapes motivation and wellbeing over time (Ryan &amp; Deci, 2017). In practice, however, the two are difficult to separate, because both are usually measured with similar self-report questions. Some &quot;competence&quot; findings may therefore simply reflect confidence.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Competence and intrinsic motivation==
 
SDT's central claim is that the ''quality'' of motivation matters as much as its quantity (Ryan &amp; Deci, 2020). Feeling competent affects where people sit on the motivation continuum, as well as how they respond to feedback and rewards (Deci et al., 1999; Ryan &amp; Deci, 2020).
 
===The motivation continuum===
SDT describes motivation as a continuum (Ryan &amp; Deci, 2020; see Figure 3). The continuum ranges from [[Motivation and emotion/Book/2014/Amotivation|amotivation]], meaning no intention to act, through several forms of extrinsic motivation, to intrinsic motivation, meaning acting for enjoyment or interest (Ryan &amp; Deci, 2020). A lack of competence is one of the main causes of amotivation (Ryan &amp; Deci, 2000). It shows in thoughts such as &quot;I can't do this&quot; or &quot;my effort won't make a difference&quot;. In contrast, feeling capable helps people [[w:Internalization (sociology)|internalise]] the value of a task, so the task feels self-endorsed instead of obligatory (Ryan &amp; Deci, 2020). In the case study, Maya's growing avoidance of her project suggests she is sliding toward amotivation.
 
[[File:Taxonomy of motivation.png|thumb|center|600px|'''Figure 3'''. The SDT motivation continuum, ranging from amotivation, through controlled and autonomous forms of extrinsic motivation, to intrinsic motivation.]]
 
===Cognitive evaluation theory===
[[Motivation and emotion/Book/2021/Cognitive evaluation theory and motivation|Cognitive evaluation theory]] (CET) explains how external events such as feedback and rewards affect intrinsic motivation (Ryan &amp; Deci, 2000). According to CET, every such event has a ''controlling'' aspect, which affects autonomy, and an ''informational'' aspect, which affects competence (Ryan &amp; Deci, 2000). Informational feedback increases perceived competence and intrinsic motivation (Deci et al., 1999). In contrast, rewards that feel like pressure tend to undermine intrinsic motivation, even when they signal success (Deci et al., 1999). CET therefore predicts that ''how'' feedback is delivered matters as much as ''what'' it says. Later versions of CET added a third, ''amotivating'' aspect (Ryan &amp; Deci, 2017). Events that signal incompetence, or that effort will not change the outcome, can push people toward amotivation. Criticism that offers no way forward, such as the feedback Maya later receives, is likely to carry this amotivating message.
 
Research generally supports these predictions, although the earliest evidence was weak. In Deci's (1971) original experiment, students paid $1 for each puzzle they solved later spent less free time on the puzzles once payment stopped. However, the study had only 24 participants, and the result was only a trend (Deci, 1971). A later meta-analysis of 128 experiments, mostly with children and university students, found a clearer pattern (Deci et al., 1999). People who expected a tangible reward for an interesting task spent less free time on it afterwards. In studies with children, this effect was still present more than a week later. The most damaging rewards were those that signalled a person had fallen short (Deci et al., 1999). Feedback style also mattered. Informational praise increased intrinsic motivation, but the same praise with a controlling phrase such as &quot;just as you ''should''&quot; decreased it (Ryan et al., 1983, as cited in Deci et al., 1999). Negative feedback was less harmful when it included guidance on how to improve (Fong et al., 2019). Rewards did not undermine motivation for boring tasks or when they were unexpected (Deci et al., 1999).
 
CET assumes that these effects work ''through'' perceived competence (Ryan &amp; Deci, 2017). However, relatively few studies have measured perceived competence directly to test this (Deci et al., 1999). One exception is Vallerand and Reid (1984), who gave 84 male students positive, negative, or no verbal feedback on a balance task. Positive feedback raised both perceived competence and intrinsic motivation, while negative feedback lowered both. Perceived competence explained about 40% of the differences in intrinsic motivation, compared with under 8% for feedback alone. However it is important to note that competence was measured with a single question, and the all-male laboratory sample limits how far the findings generalise. Beyond this study, the mechanism is more often assumed than demonstrated. Even so, the practical message is consistent. Feedback that identifies a problem, such as &quot;the scope needs to be better defined&quot;, without showing how to fix it is unlikely to support competence (Fong et al., 2019).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{According to cognitive evaluation theory, positive feedback is most likely to increase intrinsic motivation when it is:

|type=&quot;()&quot;}
- Given with a large financial reward
+ Informative and delivered in an autonomy-supportive way
- Delivered as a comparison with other people
- Given constantly, regardless of performance
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==When competence is frustrated==
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's first review'''
 
'''Week 6.''' Maya's manager reviews the project. She acknowledges some progress, then adds that the plan needs to be clearer and the scope better defined. She does not say what a clearer plan looks like or how to narrow the scope. Maya leaves the meeting feeling like a failure. She had enjoyed the first few folders, but now she dreads opening the system.
 
'''What is happening?''' The feedback identified a problem without giving Maya the information to solve it. Her effort no longer seems to lead anywhere, which is when a need starts to be actively frustrated, not just unmet.
&lt;/div&gt;
 
Research supports the distinction between low satisfaction and active frustration (Vansteenkiste &amp; Ryan, 2013). Bartholomew et al. (2011) found that athletes who saw their coach as controlling reported greater thwarting of all three needs. Need thwarting, in turn, predicted burnout, depressive symptoms, and negative emotion (Bartholomew et al., 2011). Feeling actively undermined was more harmful than simply not feeling supported. If the same pattern holds for competence, vague, critical feedback may harm Maya more than no feedback at all.
 
When people repeatedly experience that their effort makes no difference, they may develop [[w:Learned helplessness|learned helplessness]] (Seligman &amp; Maier, 1967). In classic experiments, dogs exposed to inescapable shocks later failed to escape shocks they could have avoided (Seligman &amp; Maier, 1967). Dogs that had been given control earlier learned to escape. In SDT terms, helplessness resembles amotivation caused by repeated competence frustration Ryan and Deci (2017). In humans, helplessness reduces effort and is linked to apathy and depression (Abramson et al., 1978). How people explain failure also matters. The reformulated helplessness model proposes that explaining failure with internal, stable and global causes is more damaging than explaining it with external, unstable or specific causes (Abramson et al., 1978). Maya's two thoughts show this difference. &quot;I'm hopeless at this&quot; blames a lasting personal flaw and is more likely to lead to giving up, whereas &quot;I just need clearer instructions&quot; points to a specific, changeable cause that keeps her trying.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Maya thinks, &quot;I'm hopeless at this.&quot; According to research on explanatory style, why is this thought more harmful than &quot;I just need clearer instructions&quot;?

|type=&quot;()&quot;}
- It is less accurate
+ It explains failure with an internal, stable cause she cannot easily change
- It blames her manager instead of herself
- It focuses on the task rather than on herself
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==What supports or undermines competence?==
 
In two workplace studies, Baard et al. (2004) found that employees' satisfaction of autonomy, competence, and relatedness predicted their wellbeing as well as their performance evaluations. Because supervisors rated performance, this finding is less affected by self-report bias. However, the design still cannot show which came first. A meta-analysis by Van den Broeck et al. (2016) found that competence predicted wellbeing, work attitudes, and behaviour, even after the other two needs were taken into account. This suggests competence is not simply a by-product of feeling autonomous or connected. Leadership also matters. Managers' autonomy-supportive behaviour is associated with greater need satisfaction as well as more autonomous motivation in employees (Slemp et al., 2018). For Maya, her manager's behavior may be affecting her need satisfaction, including her sense of competence.
 
Similar patterns are found in classroom environments. Bureau et al. (2022) pooled studies of what predicts student motivation and found that, of the three needs, support for competence was the strongest predictor of autonomous motivation. Notably, because SDT has historically given autonomy the most attention (Ryan &amp; Deci, 2017). At least in classroom environments, feeling capable may matter as much as feeling free to choose. However, the meta-analysis draws mainly on correlational studies, so it shows which students do well, but it does not prove that supporting competence causes better outcomes.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==How strong is the evidence?==
The strength of the evidence depends on the methods used. The reward findings, for example, were contested. Cameron and Pierce (1994) found no overall undermining effect and argued that CET should be abandoned. Deci et al. (1999) argued that this result came from mixing boring and interesting tasks, as well as using inappropriate control groups. Laboratory studies also relied mostly on single sessions with children and students (Deci et al., 1999). Self-reported interest also showed much weaker effects than behaviour. Outside the laboratory, most studies are cross-sectional. This makes it unclear whether competence drives motivation or whether motivated people simply feel more competent (Van den Broeck et al., 2016).
 
Some critics have questioned whether basic needs are truly universal, because SDT was developed largely in Western contexts (Chen et al., 2015). However, a study of adults in Belgium, China, Peru, and the United States found that need satisfaction and need frustration predicted wellbeing and ill-being in all four cultures (Chen et al., 2015). Together with the overlap between competence and self-efficacy, these limitations point to the same gap noted in CET. SDT predicts outcomes well, but whether competence itself is the active ingredient remains less certain than the theory suggests (Deci et al., 1999).
 
Most competence research has also used neurotypical samples (Morsink et al., 2022). Morsink et al. (2022) noted that research on [[w:Attention deficit hyperactivity disorder|attention-deficit/hyperactivity disorder]] (ADHD) has mostly studied rewards and overlooked psychological needs. This is despite evidence that children with more ADHD symptoms report lower need satisfaction at school (Morsink et al., 2022). Frequent correction may push teachers and parents toward controlling styles, which can further frustrate competence (Morsink et al., 2022). Whether supporting competence helps neurodivergent people in the same way remains largely untested.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Applying competence in practice==
The research reviewed so far points to a consistent set of conditions under which people feel capable. Table 1 contrasts environments that support competence with those that thwart it. These features reflect the four sources of competence support in SDT, which are clear expectations, optimal challenge, guidance, and constructive feedback (Reeve, 2024).
 
{| class=&quot;wikitable&quot; style=&quot;margin:1em auto; border-radius:8px;&quot;
|+ '''Table 1'''&lt;br&gt;''Features of Competence-Supportive and Competence-Thwarting Environments''
|-
! style=&quot;background:#eaf3fc;&quot; | Competence-supportive !! style=&quot;background:#fff6e8;&quot; | Competence-thwarting
|-
| Clear expectations about how to succeed || Vague or missing guidance
|-
| Guidance and modelling of &quot;how-to&quot; skills || Being left to work it out alone
|-
| Optimal challenge matched to current skills || Tasks far too hard or too easy
|-
| Specific, informative feedback || Absent, harsh, or controlling feedback
|-
| Long-term goals broken into short-term goals || No sense of progress
|-
| Mistakes framed as learning || Mistakes criticised or punished
|}

 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's turnaround'''
 
'''Week 8.''' Maya's manager notices the slowing progress and changes approach. They agree on what &quot;finished&quot; looks like and break the project into stages, starting with the 50 most-used folders.
 
'''Week 12.''' After each stage, Maya receives specific feedback on what is working. She now makes decisions confidently and has started suggesting improvements herself.
 
'''What changed?''' The structure around how the task would be completed: clear expectations, achievable steps, and feedback that informed instead of judged. Each gave Maya evidence that she was effective.
&lt;/div&gt;
 
Breaking Maya's project into stages draws on [[w:Goal setting|goal-setting theory]] (Locke &amp; Latham, 2002). Locke and Latham (2002) reviewed 35 years of laboratory and field studies. They found that specific, challenging goals combined with regular feedback consistently outperform vague &quot;do your best&quot; goals. In SDT, this kind of structure is a form of competence support (Reeve, 2024). Specific goals work partly because they show people exactly what success looks like. Each completed stage also acts as a mastery experience, which is the strongest source of self-efficacy (Bandura, 1977). This helps explain why Maya's confidence returned once the work was divided into stages.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Which change would best support Maya's need for competence?

|type=&quot;()&quot;}
- Offering her a bonus if she finishes faster
+ Breaking the project into stages with clear goals and specific feedback
- Telling her she is doing a great job regardless of progress
- Comparing her progress with a colleague's
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Conclusion==
Competence is the need to ''feel'' effective, and SDT treats it as important at all times, not only once basic needs are met (Ryan &amp; Deci, 2017; Tay &amp; Diener, 2011). Feeling competent moves people toward more autonomous motivation (Ryan &amp; Deci, 2020). CET explains why the same feedback can either energise or deflate a person, depending on whether it informs or controls (Deci et al., 1999).
 
When competence is actively frustrated, the consequences are more severe than when it is simply unmet. These consequences range from burnout to the helpless thinking shown in the case study (Abramson et al., 1978; Bartholomew et al., 2011). Research across workplaces and classrooms suggests, that clear expectations and informational feedback, as well as challenges broken into achievable steps, can reverse this pattern (Baard et al., 2004; Locke &amp; Latham, 2002). However, much of this evidence is correlational and rarely tests competence directly as the mechanism (Van den Broeck et al., 2016).

'''Take-home messages'''
* '''Competence is about feeling effective:''' skilled people can still feel incompetent if they get no sign their effort is working.
* '''Feedback should inform, not control:''' say what is working and how to improve, without pressure.
* '''Make progress visible:''' break big tasks into stages and agree on what &quot;finished&quot; looks like.
* '''Notice the explanation:''' &quot;I'm hopeless&quot; leads towards giving up, while &quot;I need clearer instructions&quot; keeps people trying.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==See also==
* [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|Autonomy and intrinsic motivation in self-determination theory]] (Book chapter, 2025)
* [[Motivation and emotion/Book/2011/Self-determination theory|Self-determination theory]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Book chapter, 2026)
* [[w:Self-determination theory|Self-determination theory]] (Wikipedia)
* [[w:Self-efficacy|Self-efficacy]] (Wikipedia)
* [[w:Learned helplessness|Learned helplessness]] (Wikipedia)
 
 
==References==
{{Hanging indent|1=

Abramson, L. Y., Seligman, M. E., &amp; Teasdale, J. D. (1978). Learned helplessness in humans: Critique and reformulation. Journal of Abnormal Psychology, 87(1), 49–74. https://doi.org/10.1037/0021-843X.87.1.49
 
Baard, P. P., Deci, E. L., &amp; Ryan, R. M. (2004). Intrinsic need satisfaction: a motivational basis of performance and well-being in two work settings. Journal of Applied Social Psychology, 34(10), 2045–2068. https://doi.org/10.1111/j.1559-1816.2004.tb02690.x

Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191–215. https://doi.org/10.1037/0033-295X.84.2.191
 
Bartholomew, K. J., Ntoumanis, N., Ryan, R. M., Bosch, J. A., &amp; Thøgersen-Ntoumani, C. (2011). Self-Determination Theory and Diminished Functioning: The Role of Interpersonal Control and Psychological Need Thwarting. Personality &amp; Social Psychology Bulletin, 37(11), 1459–1473. https://doi.org/10.1177/0146167211413125
 
Bureau, J. S., Howard, J. L., Chong, J. X. Y., &amp; Guay, F. (2022). Pathways to Student Motivation: A Meta-Analysis of Antecedents of Autonomous and Controlled Motivations. Review of Educational Research, 92(1), 46–72. https://doi.org/10.3102/00346543211042426
 
Cameron, J., &amp; Pierce, W. D. (1994). Reinforcement, Reward, and Intrinsic Motivation: A Meta-Analysis. Review of Educational Research, 64(3), 363–423. https://doi.org/10.3102/00346543064003363

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. Motivation and Emotion, 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1

Deci, E. L. (1971). Effects of externally mediated rewards on intrinsic motivation. Journal of Personality and Social Psychology, 18(1), 105–115. https://doi.org/10.1037/h0030644
 
Deci, E. L., Koestner, R., &amp; Ryan, R. M. (1999). A Meta-Analytic Review of Experiments Examining the Effects of Extrinsic Rewards on Intrinsic Motivation. Psychological Bulletin, 125(6), 627–668. https://doi.org/10.1037/0033-2909.125.6.627
 
Deci, E. L., &amp; Ryan, R. M. (1985). ''Intrinsic motivation and self-determination in human behavior''. Springer. https://doi.org/10.1007/978-1-4899-2271-7

Fong, C. J., Patall, E. A., Vasquez, A. C., &amp; Stautberg, S. (2019). ''A Meta-Analysis of Negative Feedback on Intrinsic Motivation''. Educational Psychology Review, 31(1), 121–162. https://doi.org/10.1007/s10648-018-9446-6
 
Locke, E. A., &amp; Latham, G. P. (2002). '' Building a practically useful theory of goal setting and task motivation: A 35-year odyssey''. The American Psychologist, 57(9), 705–717. https://doi.org/10.1037/0003-066X.57.9.705

Maslow, A. H. (1943). A theory of human motivation. ''Psychological Review, 50''(4), 370–396. https://doi.org/10.1037/h0054346
 
Morsink, S., Van der Oord, S., Antrop, I., Danckaerts, M., &amp; Scheres, A. (2022). ''Studying motivation in ADHD: The role of internal motives and the relevance of self determination theory. ''Journal of Attention Disorders, 26''(8), 1139–1158. https://doi.org/10.1177/10870547211050948
 
Reeve, J. (2024). ''Understanding motivation and emotion'' (8th ed.). Wiley.
 
Ryan, R. M., &amp; Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. ''American Psychologist, 55''(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68
 
Ryan, R. M., &amp; Deci, E. L. (2017). ''Self-determination theory: Basic psychological needs in motivation, development, and wellness''. Guilford Press. https://doi.org/10.1521/978.14625/28806
 
Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology, 61'', Article 101860. https://doi.org/10.1016/j.cedpsych.2020.101860
 
Seligman, M. E. P., &amp; Maier, S. F. (1967). Failure to escape traumatic shock. ''Journal of Experimental Psychology, 74''(1), 1–9. https://doi.org/10.1037/h0024514
 
Slemp, G. R., Kern, M. L., Patrick, K. J., &amp; Ryan, R. M. (2018). Leader autonomy support in the workplace: A meta-analytic review. ''Motivation and Emotion, 42''(5), 706–724. https://doi.org/10.1007/s11031-018-9698-y
 
Tay, L., &amp; Diener, E. (2011). Needs and subjective well-being around the world. ''Journal of Personality and Social Psychology, 101''(2), 354–365. https://doi.org/10.1037/a0023779
 
Vallerand, R. J., &amp; Reid, G. (1984). On the causal effects of perceived competence on intrinsic motivation: A test of cognitive evaluation theory. ''Journal of Sport Psychology, 6''(1), 94–102. https://doi.org/10.1123/jsp.6.1.94

Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A review of self-determination theory's basic psychological needs at work. ''Journal of Management, 42''(5), 1195–1229. https://doi.org/10.1177/0149206316632058
 
Vansteenkiste, M., &amp; Ryan, R. M. (2013). On psychological growth and vulnerability: Basic psychological need satisfaction and need frustration as a unifying principle. ''Journal of Psychotherapy Integration, 23''(3), 263–280. https://doi.org/10.1037/a0032359
 
Vansteenkiste, M., Ryan, R. M., &amp; Soenens, B. (2020). Basic psychological need theory: Advancements, critical themes, and future directions. ''Motivation and Emotion, 44''(1), 1–31. https://doi.org/10.1007/s11031-019-09818-1
 
White, R. W. (1959). Motivation reconsidered: The concept of competence. ''Psychological Review, 66''(5), 297–333. https://doi.org/10.1037/h0040934
}}


==External links==
* [https://selfdeterminationtheory.org/the-theory/ The theory] (Center for Self-Determination Theory)
* [https://www.apa.org/education-career/k12/motivation Motivating students] (American Psychological Association)
* [https://positivepsychology.com/self-determination-theory/ Self-determination theory of motivation] (PositivePsychology.com)


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      <text bytes="31868" sha1="0bjrhjjqyj64wufsz26cngymx5cov98" xml:space="preserve">{{title|Competence motivation in self-determination theory:&lt;br&gt;How does the need for competence function within self-determination theory to shape motivation and behaviour?}}
 __TOC__

==Overview==
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study:'''
[[File:Woman Suffering from Stress at Work (cropped).jpg|thumb|right|260px|'''Figure 1'''. Facing a large, unstructured task without guidance or feedback can leave a person doubting their own ability.]]
 
Maya, a 24-year-old administrative officer, has not opened her biggest project in three days. Instead, she has answered every email and tidied a shared drive she built herself: familiar tasks she knows she can do well.
 
Two months ago, Maya was excited when her manager asked her to review and reorganise more than 500 folders in the team's records system. But she received no guidance on where to start or what &quot;finished&quot; should look like. Each folder revealed new complexity, and nobody told her if her decisions were right. (see Figure 1). Some days she thinks, &quot;I just need clearer instructions.&quot; On other days her thoughts turn personal: &quot;I'm hopeless at this.&quot; The first thought sends her to ask for help; the second sends her back to her inbox.
 
''Why does the same task leave a person ready to improve on some days, and ready to give up on others?''
&lt;/div&gt;
 
 
According to [[Self-determination theory|self-determination theory]]&lt;nowiki/&gt;y (SDT), this difference often comes down to the need for [[Motivation and emotion/Book/2011/Self-determination theory|competence]]. Competence is the need to feel effective and capable (Ryan &amp; Deci, 2017). It is one of three basic psychological needs, alongside [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|autonomy]] and [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|relatedness]] (Ryan &amp; Deci, 2017). When competence is satisfied, people tend to show stronger [[Motivation and emotion/Book/2013/Intrinsic motivation|intrinsic motivation]], persistence, and wellbeing (Ryan &amp; Deci, 2020). When it is frustrated, as in Maya's case, people tend to avoid tasks and give up (Vansteenkiste et al., 2020).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Focus questions'''
* What is competence, according to self-determination theory?
* How does competence relate to intrinsic motivation?
* How does cognitive evaluation theory explain why feedback and rewards can strengthen or undermine motivation?
* What happens when the need for competence is frustrated?
* What does research show about how competence can be supported?
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Self-determination theory and competence==
 
===What is self-determination theory?===
SDT is a broad theory of human motivation. It proposes that people have three innate psychological needs: autonomy (feeling volitional), competence (feeling effective), as well as relatedness (feeling connected to others) (Deci &amp; Ryan, 1985; Ryan &amp; Deci, 2017). SDT is made up of six mini-theories, and two of these are central to this chapter. These are cognitive evaluation theory and basic psychological needs theory (Vansteenkiste et al., 2020). SDT is often compared with [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]]. Maslow (1943) proposed a hierarchy in which lower needs, such as physiological and safety needs, generally take priority over higher needs, such as esteem and self-actualisation. He placed mastery within esteem needs. SDT agrees that people strive to feel capable. However, SDT does not rank its needs and considers all three essential at all times (Ryan &amp; Deci, 2017).
 
[[File:MaslowsHierarchyOfNeeds.svg|thumb|right|300px|'''Figure 2'''. Maslow's hierarchy of needs places mastery within esteem needs, near the top of the hierarchy. SDT treats competence as essential at every level.]]
 
Tay and Diener (2011) tested these two views using Gallup World Poll data from 60,865 people in 123 countries. Although people did tend to meet basic and safety needs first, which partly supports Maslow, each need, including mastery, contributed to wellbeing regardless of whether the other needs were met (Tay &amp; Diener, 2011). The needs that mirror SDT, namely social relationships, autonomy, and mastery, were among the strongest predictors of everyday feelings across all eight world regions studied. One limitation is that the data were cross-sectional. Each need was also measured with only two or three yes or no questions, so the study shows association, not cause.
 
===What is competence within self-determination theory?===
The idea of competence as a motivational force dates back to White (1959), who challenged the drive theories of his time. He noticed that infants and young animals explore and play, as well as manipulate objects, even when they are fed and safe. He argued that this behaviour comes from a built-in need to have an effect on the environment, which he called effectance motivation. SDT builds on this idea and defines competence as the need to ''feel'' effective, not simply to possess a skill (Ryan &amp; Deci, 2017). As a result a highly skilled person can still feel incompetent if they receive no sign that their efforts are working.
 
According to SDT, competence is best satisfied in well-structured environments that offer &quot;optimal challenge&quot;, positive feedback, and opportunities for growth (Ryan &amp; Deci, 2020). An optimally challenging task sits slightly beyond a person's current skill, but it comes with enough structure and support to close the gap. Tasks that are too easy offer no sense of growth, while tasks that are too hard, especially without guidance, signal failure (Reeve, 2024). Maya's difficulty illustrates how a lack of structure and feedback can make a manageable task feel too hard.
 
Basic psychological needs theory treats need satisfaction and need frustration as two separate experiences (Vansteenkiste &amp; Ryan, 2013). Need satisfaction is linked to a &quot;bright&quot; pathway of growth and engagement, as well as wellbeing (Vansteenkiste et al., 2020). Need frustration is linked to a &quot;dark&quot; pathway of defensiveness, avoidance, and ill-being (Vansteenkiste et al., 2020). Low satisfaction and active frustration are therefore not the same thing. Receiving no feedback may leave a person unfulfilled, but being repeatedly made to feel ineffective actively harms wellbeing (Vansteenkiste &amp; Ryan, 2013). The case study shows this shift. Maya moves from low satisfaction in the early weeks to active frustration after her manager's review, described later in the chapter.
 
===Competence and self-efficacy===
Competence overlaps closely with [[w:Self-efficacy|self-efficacy]], which is a person's belief that they can successfully perform a specific behaviour (Bandura, 1977). Bandura separated two expectations that shape whether people act. An ''efficacy expectation'' asks &quot;Can I do it?&quot;, and an ''outcome expectation'' asks &quot;Will it work?&quot; Efficacy beliefs are built from four sources: personal mastery experiences, watching similar others succeed, verbal persuasion, and how people interpret their own stress (Bandura, 1977). Of these, mastery experiences are the most powerful (Bandura, 1977).
 
In the case study, several of these sources are weakened. Without feedback, Maya cannot judge whether her decisions are effective, so her real progress is not experienced as mastery. As the case study later shows, her manager's comments act as negative persuasion. Her anxiety before opening the project is also likely to be read as evidence that she is not capable. The key difference between the two concepts is that self-efficacy is a belief about a specific future task (Bandura, 1977). In contrast, SDT treats competence as a universal need that shapes motivation and wellbeing over time (Ryan &amp; Deci, 2017). In practice, however, the two are difficult to separate, because both are usually measured with similar self-report questions. Some &quot;competence&quot; findings may therefore simply reflect confidence.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Competence and intrinsic motivation==
 
SDT's central claim is that the ''quality'' of motivation matters as much as its quantity (Ryan &amp; Deci, 2020). Feeling competent affects where people sit on the motivation continuum, as well as how they respond to feedback and rewards (Deci et al., 1999; Ryan &amp; Deci, 2020).
 
===The motivation continuum===
SDT describes motivation as a continuum (Ryan &amp; Deci, 2020; see Figure 3). The continuum ranges from [[Motivation and emotion/Book/2014/Amotivation|amotivation]], meaning no intention to act, through several forms of extrinsic motivation, to intrinsic motivation, meaning acting for enjoyment or interest (Ryan &amp; Deci, 2020). A lack of competence is one of the main causes of amotivation (Ryan &amp; Deci, 2000). It shows in thoughts such as &quot;I can't do this&quot; or &quot;my effort won't make a difference&quot;. In contrast, feeling capable helps people [[w:Internalization (sociology)|internalise]] the value of a task, so the task feels self-endorsed instead of obligatory (Ryan &amp; Deci, 2020). In the case study, Maya's growing avoidance of her project suggests she is sliding toward amotivation.
 
[[File:Taxonomy of motivation.png|thumb|center|600px|'''Figure 3'''. The SDT motivation continuum, ranging from amotivation, through controlled and autonomous forms of extrinsic motivation, to intrinsic motivation.]]
 
===Cognitive evaluation theory===
[[Motivation and emotion/Book/2021/Cognitive evaluation theory and motivation|Cognitive evaluation theory]] (CET) explains how external events such as feedback and rewards affect intrinsic motivation (Ryan &amp; Deci, 2000). According to CET, every such event has a ''controlling'' aspect, which affects autonomy, and an ''informational'' aspect, which affects competence (Ryan &amp; Deci, 2000). Informational feedback increases perceived competence and intrinsic motivation (Deci et al., 1999). In contrast, rewards that feel like pressure tend to undermine intrinsic motivation, even when they signal success (Deci et al., 1999). CET therefore predicts that ''how'' feedback is delivered matters as much as ''what'' it says. Later versions of CET added a third, ''amotivating'' aspect (Ryan &amp; Deci, 2017). Events that signal incompetence, or that effort will not change the outcome, can push people toward amotivation. Criticism that offers no way forward, such as the feedback Maya later receives, is likely to carry this amotivating message.
 
Research generally supports these predictions, although the earliest evidence was weak. In Deci's (1971) original experiment, students paid $1 for each puzzle they solved later spent less free time on the puzzles once payment stopped. However, the study had only 24 participants, and the result was only a trend (Deci, 1971). A later meta-analysis of 128 experiments, mostly with children and university students, found a clearer pattern (Deci et al., 1999). People who expected a tangible reward for an interesting task spent less free time on it afterwards. In studies with children, this effect was still present more than a week later. The most damaging rewards were those that signalled a person had fallen short (Deci et al., 1999). Feedback style also mattered. Informational praise increased intrinsic motivation, but the same praise with a controlling phrase such as &quot;just as you ''should''&quot; decreased it (Ryan et al., 1983, as cited in Deci et al., 1999). Negative feedback was less harmful when it included guidance on how to improve (Fong et al., 2019). Rewards did not undermine motivation for boring tasks or when they were unexpected (Deci et al., 1999).
 
CET assumes that these effects work ''through'' perceived competence (Ryan &amp; Deci, 2017). However, relatively few studies have measured perceived competence directly to test this (Deci et al., 1999). One exception is Vallerand and Reid (1984), who gave 84 male students positive, negative, or no verbal feedback on a balance task. Positive feedback raised both perceived competence and intrinsic motivation, while negative feedback lowered both. Perceived competence explained about 40% of the differences in intrinsic motivation, compared with under 8% for feedback alone. However it is important to note that competence was measured with a single question, and the all-male laboratory sample limits how far the findings generalise. Beyond this study, the mechanism is more often assumed than demonstrated. Even so, the practical message is consistent. Feedback that identifies a problem, such as &quot;the scope needs to be better defined&quot;, without showing how to fix it is unlikely to support competence (Fong et al., 2019).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{According to cognitive evaluation theory, positive feedback is most likely to increase intrinsic motivation when it is:

|type=&quot;()&quot;}
- Given with a large financial reward
+ Informative and delivered in an autonomy-supportive way
- Delivered as a comparison with other people
- Given constantly, regardless of performance
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==When competence is frustrated==
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's first review'''
 
'''Week 6.''' Maya's manager reviews the project. She acknowledges some progress, then adds that the plan needs to be clearer and the scope better defined. She does not say what a clearer plan looks like or how to narrow the scope. Maya leaves the meeting feeling like a failure. She had enjoyed the first few folders, but now she dreads opening the system.
 
'''What is happening?''' The feedback identified a problem without giving Maya the information to solve it. Her effort no longer seems to lead anywhere, which is when a need starts to be actively frustrated, not just unmet.
&lt;/div&gt;
 
Research supports the distinction between low satisfaction and active frustration (Vansteenkiste &amp; Ryan, 2013). Bartholomew et al. (2011) found that athletes who saw their coach as controlling reported greater thwarting of all three needs. Need thwarting, in turn, predicted burnout, depressive symptoms, and negative emotion (Bartholomew et al., 2011). Feeling actively undermined was more harmful than simply not feeling supported. If the same pattern holds for competence, vague, critical feedback may harm Maya more than no feedback at all.
 
When people repeatedly experience that their effort makes no difference, they may develop [[w:Learned helplessness|learned helplessness]] (Seligman &amp; Maier, 1967). In classic experiments, dogs exposed to inescapable shocks later failed to escape shocks they could have avoided (Seligman &amp; Maier, 1967). Dogs that had been given control earlier learned to escape. In SDT terms, helplessness resembles amotivation caused by repeated competence frustration Ryan and Deci (2017). In humans, helplessness reduces effort and is linked to apathy and depression (Abramson et al., 1978). How people explain failure also matters. The reformulated helplessness model proposes that explaining failure with internal, stable and global causes is more damaging than explaining it with external, unstable or specific causes (Abramson et al., 1978). Maya's two thoughts show this difference. &quot;I'm hopeless at this&quot; blames a lasting personal flaw and is more likely to lead to giving up, whereas &quot;I just need clearer instructions&quot; points to a specific, changeable cause that keeps her trying.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Maya thinks, &quot;I'm hopeless at this.&quot; According to research on explanatory style, why is this thought more harmful than &quot;I just need clearer instructions&quot;?

|type=&quot;()&quot;}
- It is less accurate
+ It explains failure with an internal, stable cause she cannot easily change
- It blames her manager instead of herself
- It focuses on the task rather than on herself
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==What supports or undermines competence?==
 
In two workplace studies, Baard et al. (2004) found that employees' satisfaction of autonomy, competence, and relatedness predicted their wellbeing as well as their performance evaluations. Because supervisors rated performance, this finding is less affected by self-report bias. However, the design still cannot show which came first. A meta-analysis by Van den Broeck et al. (2016) found that competence predicted wellbeing, work attitudes, and behaviour, even after the other two needs were taken into account. This suggests competence is not simply a by-product of feeling autonomous or connected. Leadership also matters. Managers' autonomy-supportive behaviour is associated with greater need satisfaction as well as more autonomous motivation in employees (Slemp et al., 2018). For Maya, her manager's behavior may be affecting her need satisfaction, including her sense of competence.
 
Similar patterns are found in classroom environments. Bureau et al. (2022) pooled studies of what predicts student motivation and found that, of the three needs, support for competence was the strongest predictor of autonomous motivation. Notably, because SDT has historically given autonomy the most attention (Ryan &amp; Deci, 2017). At least in classroom environments, feeling capable may matter as much as feeling free to choose. However, the meta-analysis draws mainly on correlational studies, so it shows which students do well, but it does not prove that supporting competence causes better outcomes.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==How strong is the evidence?==
The strength of the evidence depends on the methods used. The reward findings, for example, were contested. Cameron and Pierce (1994) found no overall undermining effect and argued that CET should be abandoned. Deci et al. (1999) argued that this result came from mixing boring and interesting tasks, as well as using inappropriate control groups. Laboratory studies also relied mostly on single sessions with children and students (Deci et al., 1999). Self-reported interest also showed much weaker effects than behaviour. Outside the laboratory, most studies are cross-sectional. This makes it unclear whether competence drives motivation or whether motivated people simply feel more competent (Van den Broeck et al., 2016).
 
Some critics have questioned whether basic needs are truly universal, because SDT was developed largely in Western contexts (Chen et al., 2015). However, a study of adults in Belgium, China, Peru, and the United States found that need satisfaction and need frustration predicted wellbeing and ill-being in all four cultures (Chen et al., 2015). Together with the overlap between competence and self-efficacy, these limitations point to the same gap noted in CET. SDT predicts outcomes well, but whether competence itself is the active ingredient remains less certain than the theory suggests (Deci et al., 1999).
 
Most competence research has also used neurotypical samples (Morsink et al., 2022). Morsink et al. (2022) noted that research on [[w:Attention deficit hyperactivity disorder|attention-deficit/hyperactivity disorder]] (ADHD) has mostly studied rewards and overlooked psychological needs. This is despite evidence that children with more ADHD symptoms report lower need satisfaction at school (Morsink et al., 2022). Frequent correction may push teachers and parents toward controlling styles, which can further frustrate competence (Morsink et al., 2022). Whether supporting competence helps neurodivergent people in the same way remains largely untested.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Applying competence in practice==
The research reviewed so far points to a consistent set of conditions under which people feel capable. Table 1 contrasts environments that support competence with those that thwart it. These features reflect the four sources of competence support in SDT, which are clear expectations, optimal challenge, guidance, and constructive feedback (Reeve, 2024).
 
{| class=&quot;wikitable&quot; style=&quot;margin:1em auto; border-radius:8px;&quot;
|+ '''Table 1'''&lt;br&gt;''Features of Competence-Supportive and Competence-Thwarting Environments''
|-
! style=&quot;background:#eaf3fc;&quot; | Competence-supportive !! style=&quot;background:#fff6e8;&quot; | Competence-thwarting
|-
| Clear expectations about how to succeed || Vague or missing guidance
|-
| Guidance and modelling of &quot;how-to&quot; skills || Being left to work it out alone
|-
| Optimal challenge matched to current skills || Tasks far too hard or too easy
|-
| Specific, informative feedback || Absent, harsh, or controlling feedback
|-
| Long-term goals broken into short-term goals || No sense of progress
|-
| Mistakes framed as learning || Mistakes criticised or punished
|}

 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's turnaround'''
 
'''Week 8.''' Maya's manager notices the slowing progress and changes approach. They agree on what &quot;finished&quot; looks like and break the project into stages, starting with the 50 most-used folders.
 
'''Week 12.''' After each stage, Maya receives specific feedback on what is working. She now makes decisions confidently and has started suggesting improvements herself.
 
'''What changed?''' The structure around how the task would be completed: clear expectations, achievable steps, and feedback that informed instead of judged. Each gave Maya evidence that she was effective.
&lt;/div&gt;
 
Breaking Maya's project into stages draws on [[w:Goal setting|goal-setting theory]] (Locke &amp; Latham, 2002). Locke and Latham (2002) reviewed 35 years of laboratory and field studies. They found that specific, challenging goals combined with regular feedback consistently outperform vague &quot;do your best&quot; goals. In SDT, this kind of structure is a form of competence support (Reeve, 2024). Specific goals work partly because they show people exactly what success looks like. Each completed stage also acts as a mastery experience, which is the strongest source of self-efficacy (Bandura, 1977). This helps explain why Maya's confidence returned once the work was divided into stages.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Which change would best support Maya's need for competence?

|type=&quot;()&quot;}
- Offering her a bonus if she finishes faster
+ Breaking the project into stages with clear goals and specific feedback
- Telling her she is doing a great job regardless of progress
- Comparing her progress with a colleague's
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Conclusion==
Competence is the need to ''feel'' effective, and SDT treats it as important at all times, not only once basic needs are met (Ryan &amp; Deci, 2017; Tay &amp; Diener, 2011). Feeling competent moves people toward more autonomous motivation (Ryan &amp; Deci, 2020). CET explains why the same feedback can either energise or deflate a person, depending on whether it informs or controls (Deci et al., 1999).
 
When competence is actively frustrated, the consequences are more severe than when it is simply unmet. These consequences range from burnout to the helpless thinking shown in the case study (Abramson et al., 1978; Bartholomew et al., 2011). Research across workplaces and classrooms suggests, that clear expectations and informational feedback, as well as challenges broken into achievable steps, can reverse this pattern (Baard et al., 2004; Locke &amp; Latham, 2002). However, much of this evidence is correlational and rarely tests competence directly as the mechanism (Van den Broeck et al., 2016).

'''Take-home messages'''
* '''Competence is about feeling effective:''' skilled people can still feel incompetent if they get no sign their effort is working.
* '''Feedback should inform, not control:''' say what is working and how to improve, without pressure.
* '''Make progress visible:''' break big tasks into stages and agree on what &quot;finished&quot; looks like.
* '''Notice the explanation:''' &quot;I'm hopeless&quot; leads towards giving up, while &quot;I need clearer instructions&quot; keeps people trying.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==See also==
* [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|Autonomy and intrinsic motivation in self-determination theory]] (Book chapter, 2025)
* [[Motivation and emotion/Book/2011/Self-determination theory|Self-determination theory]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Book chapter, 2026)
* [[w:Self-determination theory|Self-determination theory]] (Wikipedia)
* [[w:Self-efficacy|Self-efficacy]] (Wikipedia)
* [[w:Learned helplessness|Learned helplessness]] (Wikipedia)
 
 
==References==
{{Hanging indent|1=

Abramson, L. Y., Seligman, M. E., &amp; Teasdale, J. D. (1978). Learned helplessness in humans: Critique and reformulation. Journal of Abnormal Psychology, 87(1), 49–74. https://doi.org/10.1037/0021-843X.87.1.49
 
Baard, P. P., Deci, E. L., &amp; Ryan, R. M. (2004). Intrinsic need satisfaction: a motivational basis of performance and well-being in two work settings. Journal of Applied Social Psychology, 34(10), 2045–2068. https://doi.org/10.1111/j.1559-1816.2004.tb02690.x

Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191–215. https://doi.org/10.1037/0033-295X.84.2.191
 
Bartholomew, K. J., Ntoumanis, N., Ryan, R. M., Bosch, J. A., &amp; Thøgersen-Ntoumani, C. (2011). Self-Determination Theory and Diminished Functioning: The Role of Interpersonal Control and Psychological Need Thwarting. Personality &amp; Social Psychology Bulletin, 37(11), 1459–1473. https://doi.org/10.1177/0146167211413125
 
Bureau, J. S., Howard, J. L., Chong, J. X. Y., &amp; Guay, F. (2022). Pathways to Student Motivation: A Meta-Analysis of Antecedents of Autonomous and Controlled Motivations. Review of Educational Research, 92(1), 46–72. https://doi.org/10.3102/00346543211042426
 
Cameron, J., &amp; Pierce, W. D. (1994). Reinforcement, Reward, and Intrinsic Motivation: A Meta-Analysis. Review of Educational Research, 64(3), 363–423. https://doi.org/10.3102/00346543064003363

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. Motivation and Emotion, 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1

Deci, E. L. (1971). Effects of externally mediated rewards on intrinsic motivation. Journal of Personality and Social Psychology, 18(1), 105–115. https://doi.org/10.1037/h0030644
 
Deci, E. L., Koestner, R., &amp; Ryan, R. M. (1999). A Meta-Analytic Review of Experiments Examining the Effects of Extrinsic Rewards on Intrinsic Motivation. Psychological Bulletin, 125(6), 627–668. https://doi.org/10.1037/0033-2909.125.6.627
 
Deci, E. L., &amp; Ryan, R. M. (1985). ''Intrinsic motivation and self-determination in human behavior''. Springer. https://doi.org/10.1007/978-1-4899-2271-7

Fong, C. J., Patall, E. A., Vasquez, A. C., &amp; Stautberg, S. (2019). ''A Meta-Analysis of Negative Feedback on Intrinsic Motivation''. Educational Psychology Review, 31(1), 121–162. https://doi.org/10.1007/s10648-018-9446-6
 
Locke, E. A., &amp; Latham, G. P. (2002). '' Building a practically useful theory of goal setting and task motivation: A 35-year odyssey''. The American Psychologist, 57(9), 705–717. https://doi.org/10.1037/0003-066X.57.9.705

Maslow, A. H. (1943). A theory of human motivation. ''Psychological Review, 50''(4), 370–396. https://doi.org/10.1037/h0054346
 
Morsink, S., Van der Oord, S., Antrop, I., Danckaerts, M., &amp; Scheres, A. (2022). ''Studying motivation in ADHD: The role of internal motives and the relevance of self determination theory. ''Journal of Attention Disorders, 26''(8), 1139–1158. https://doi.org/10.1177/10870547211050948
 
Reeve, J. (2024). ''Understanding motivation and emotion'' (8th ed.). Wiley.
 
Ryan, R. M., &amp; Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. ''American Psychologist, 55''(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68
 
Ryan, R. M., &amp; Deci, E. L. (2017). ''Self-determination theory: Basic psychological needs in motivation, development, and wellness''. Guilford Press. https://doi.org/10.1521/978.14625/28806
 
Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology, 61'', Article 101860. https://doi.org/10.1016/j.cedpsych.2020.101860
 
Seligman, M. E. P., &amp; Maier, S. F. (1967). Failure to escape traumatic shock. ''Journal of Experimental Psychology, 74''(1), 1–9. https://doi.org/10.1037/h0024514
 
Slemp, G. R., Kern, M. L., Patrick, K. J., &amp; Ryan, R. M. (2018). Leader autonomy support in the workplace: A meta-analytic review. ''Motivation and Emotion, 42''(5), 706–724. https://doi.org/10.1007/s11031-018-9698-y
 
Tay, L., &amp; Diener, E. (2011). Needs and subjective well-being around the world. ''Journal of Personality and Social Psychology, 101''(2), 354–365. https://doi.org/10.1037/a0023779
 
Vallerand, R. J., &amp; Reid, G. (1984). On the causal effects of perceived competence on intrinsic motivation: A test of cognitive evaluation theory. ''Journal of Sport Psychology, 6''(1), 94–102. https://doi.org/10.1123/jsp.6.1.94

Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A review of self-determination theory's basic psychological needs at work. ''Journal of Management, 42''(5), 1195–1229. https://doi.org/10.1177/0149206316632058
 
Vansteenkiste, M., &amp; Ryan, R. M. (2013). On psychological growth and vulnerability: Basic psychological need satisfaction and need frustration as a unifying principle. ''Journal of Psychotherapy Integration, 23''(3), 263–280. https://doi.org/10.1037/a0032359
 
Vansteenkiste, M., Ryan, R. M., &amp; Soenens, B. (2020). Basic psychological need theory: Advancements, critical themes, and future directions. ''Motivation and Emotion, 44''(1), 1–31. https://doi.org/10.1007/s11031-019-09818-1
 
White, R. W. (1959). Motivation reconsidered: The concept of competence. ''Psychological Review, 66''(5), 297–333. https://doi.org/10.1037/h0040934
}}


==External links==
* [https://selfdeterminationtheory.org/the-theory/ The theory] (Center for Self-Determination Theory)
* [https://www.apa.org/education-career/k12/motivation Motivating students] (American Psychological Association)
* [https://positivepsychology.com/self-determination-theory/ Self-determination theory of motivation] (PositivePsychology.com)
* [https://www.youtube.com/watch?v=_juPDoa3GBY Self-determination theory explained] (Sprouts, YouTube)


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      <text bytes="31866" sha1="n20uqcfm0lywf9293qwfzgeoccoxs7d" xml:space="preserve">{{title|Competence motivation in self-determination theory:&lt;br&gt;How does the need for competence function within self-determination theory to shape motivation and behaviour?}}
 __TOC__

==Overview==
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study:'''
[[File:Woman Suffering from Stress at Work (cropped).jpg|thumb|right|260px|'''Figure 1'''. Facing a large, unstructured task without guidance or feedback can leave a person doubting their own ability.]]
 
Maya, a 24-year-old administrative officer, has not opened her biggest project in three days. Instead, she has answered every email and tidied a shared drive she built herself: familiar tasks she knows she can do well.
 
Two months ago, Maya was excited when her manager asked her to review and reorganise more than 500 folders in the team's records system. But she received no guidance on where to start or what &quot;finished&quot; should look like. Each folder revealed new complexity, and nobody told her if her decisions were right. (see Figure 1). Some days she thinks, &quot;I just need clearer instructions.&quot; On other days her thoughts turn personal: &quot;I'm hopeless at this.&quot; The first thought sends her to ask for help; the second sends her back to her inbox.
 
''Why does the same task leave a person ready to improve on some days, and ready to give up on others?''
&lt;/div&gt;
 
 
According to [[Self-determination theory|self-determination theory]]&lt;nowiki/&gt;y (SDT), this difference often comes down to the need for [[Motivation and emotion/Book/2011/Self-determination theory|competence]]. Competence is the need to feel effective and capable (Ryan &amp; Deci, 2017). It is one of three basic psychological needs, alongside [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|autonomy]] and [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|relatedness]] (Ryan &amp; Deci, 2017). When competence is satisfied, people tend to show stronger [[Motivation and emotion/Book/2013/Intrinsic motivation|intrinsic motivation]], persistence, and wellbeing (Ryan &amp; Deci, 2020). When it is frustrated, as in Maya's case, people tend to avoid tasks and give up (Vansteenkiste et al., 2020).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Focus questions'''
* What is competence, according to self-determination theory?
* How does competence relate to intrinsic motivation?
* How does cognitive evaluation theory explain why feedback and rewards can strengthen or undermine motivation?
* What happens when the need for competence is frustrated?
* What does research show about how competence can be supported?
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Self-determination theory and competence==
 
===What is self-determination theory?===
SDT is a broad theory of human motivation. It proposes that people have three innate psychological needs: autonomy (feeling volitional), competence (feeling effective), as well as relatedness (feeling connected to others) (Deci &amp; Ryan, 1985; Ryan &amp; Deci, 2017). SDT is made up of six mini-theories, and two of these are central to this chapter. These are cognitive evaluation theory and basic psychological needs theory (Vansteenkiste et al., 2020). SDT is often compared with [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]]. Maslow (1943) proposed a hierarchy in which lower needs, such as physiological and safety needs, generally take priority over higher needs, such as esteem and self-actualisation. He placed mastery within esteem needs. SDT agrees that people strive to feel capable. However, SDT does not rank its needs and considers all three essential at all times (Ryan &amp; Deci, 2017).
 
[[File:MaslowsHierarchyOfNeeds.svg|thumb|right|300px|'''Figure 2'''. Maslow's hierarchy of needs places mastery within esteem needs, near the top of the hierarchy. SDT treats competence as essential at every level.]]
 
Tay and Diener (2011) tested these two views using Gallup World Poll data from 60,865 people in 123 countries. Although people did tend to meet basic and safety needs first, which partly supports Maslow, each need, including mastery, contributed to wellbeing regardless of whether the other needs were met (Tay &amp; Diener, 2011). The needs that mirror SDT, namely social relationships, autonomy, and mastery, were among the strongest predictors of everyday feelings across all eight world regions studied. One limitation is that the data were cross-sectional. Each need was also measured with only two or three yes or no questions, so the study shows association, not cause.
 
===What is competence within self-determination theory?===
The idea of competence as a motivational force dates back to White (1959), who challenged the drive theories of his time. He noticed that infants and young animals explore and play, as well as manipulate objects, even when they are fed and safe. He argued that this behaviour comes from a built-in need to have an effect on the environment, which he called effectance motivation. SDT builds on this idea and defines competence as the need to ''feel'' effective, not simply to possess a skill (Ryan &amp; Deci, 2017). As a result a highly skilled person can still feel incompetent if they receive no sign that their efforts are working.
 
According to SDT, competence is best satisfied in well-structured environments that offer &quot;optimal challenge&quot;, positive feedback, and opportunities for growth (Ryan &amp; Deci, 2020). An optimally challenging task sits slightly beyond a person's current skill, but it comes with enough structure and support to close the gap. Tasks that are too easy offer no sense of growth, while tasks that are too hard, especially without guidance, signal failure (Reeve, 2024). Maya's difficulty illustrates how a lack of structure and feedback can make a manageable task feel too hard.
 
Basic psychological needs theory treats need satisfaction and need frustration as two separate experiences (Vansteenkiste &amp; Ryan, 2013). Need satisfaction is linked to a &quot;bright&quot; pathway of growth and engagement, as well as wellbeing (Vansteenkiste et al., 2020). Need frustration is linked to a &quot;dark&quot; pathway of defensiveness, avoidance, and ill-being (Vansteenkiste et al., 2020). Low satisfaction and active frustration are therefore not the same thing. Receiving no feedback may leave a person unfulfilled, but being repeatedly made to feel ineffective actively harms wellbeing (Vansteenkiste &amp; Ryan, 2013). The case study shows this shift. Maya moves from low satisfaction in the early weeks to active frustration after her manager's review, described later in the chapter.
 
===Competence and self-efficacy===
Competence overlaps closely with [[w:Self-efficacy|self-efficacy]], which is a person's belief that they can successfully perform a specific behaviour (Bandura, 1977). Bandura separated two expectations that shape whether people act. An ''efficacy expectation'' asks &quot;Can I do it?&quot;, and an ''outcome expectation'' asks &quot;Will it work?&quot; Efficacy beliefs are built from four sources: personal mastery experiences, watching similar others succeed, verbal persuasion, and how people interpret their own stress (Bandura, 1977). Of these, mastery experiences are the most powerful (Bandura, 1977).
 
In the case study, several of these sources are weakened. Without feedback, Maya cannot judge whether her decisions are effective, so her real progress is not experienced as mastery. As the case study later shows, her manager's comments act as negative persuasion. Her anxiety before opening the project is also likely to be read as evidence that she is not capable. The key difference between the two concepts is that self-efficacy is a belief about a specific future task (Bandura, 1977). In contrast, SDT treats competence as a universal need that shapes motivation and wellbeing over time (Ryan &amp; Deci, 2017). In practice, however, the two are difficult to separate, because both are usually measured with similar self-report questions. Some &quot;competence&quot; findings may therefore simply reflect confidence.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Competence and intrinsic motivation==
 
SDT's central claim is that the ''quality'' of motivation matters as much as its quantity (Ryan &amp; Deci, 2020). Feeling competent affects where people sit on the motivation continuum, as well as how they respond to feedback and rewards (Deci et al., 1999; Ryan &amp; Deci, 2020).
 
===The motivation continuum===
SDT describes motivation as a continuum (Ryan &amp; Deci, 2020; see Figure 3). The continuum ranges from [[Motivation and emotion/Book/2014/Amotivation|amotivation]], meaning no intention to act, through several forms of extrinsic motivation, to intrinsic motivation, meaning acting for enjoyment or interest (Ryan &amp; Deci, 2020). A lack of competence is one of the main causes of amotivation (Ryan &amp; Deci, 2000). It shows in thoughts such as &quot;I can't do this&quot; or &quot;my effort won't make a difference&quot;. In contrast, feeling capable helps people [[w:Internalization (sociology)|internalise]] the value of a task, so the task feels self-endorsed instead of obligatory (Ryan &amp; Deci, 2020). In the case study, Maya's growing avoidance of her project suggests she is sliding toward amotivation.
 
[[File:Taxonomy of motivation.png|thumb|center|600px|'''Figure 3'''. The SDT motivation continuum, ranging from amotivation, through controlled and autonomous forms of extrinsic motivation, to intrinsic motivation.]]
 
===Cognitive evaluation theory===
[[Motivation and emotion/Book/2021/Cognitive evaluation theory and motivation|Cognitive evaluation theory]] (CET) explains how external events such as feedback and rewards affect intrinsic motivation (Ryan &amp; Deci, 2000). According to CET, every such event has a ''controlling'' aspect, which affects autonomy, and an ''informational'' aspect, which affects competence (Ryan &amp; Deci, 2000). Informational feedback increases perceived competence and intrinsic motivation (Deci et al., 1999). In contrast, rewards that feel like pressure tend to undermine intrinsic motivation, even when they signal success (Deci et al., 1999). CET therefore predicts that ''how'' feedback is delivered matters as much as ''what'' it says. Later versions of CET added a third, ''amotivating'' aspect (Ryan &amp; Deci, 2017). Events that signal incompetence, or that effort will not change the outcome, can push people toward amotivation. Criticism that offers no way forward, such as the feedback Maya later receives, is likely to carry this amotivating message.
 
Research generally supports these predictions, although the earliest evidence was weak. In Deci's (1971) original experiment, students paid $1 for each puzzle they solved later spent less free time on the puzzles once payment stopped. However, the study had only 24 participants, and the result was only a trend (Deci, 1971). A later meta-analysis of 128 experiments, mostly with children and university students, found a clearer pattern (Deci et al., 1999). People who expected a tangible reward for an interesting task spent less free time on it afterwards. In studies with children, this effect was still present more than a week later. The most damaging rewards were those that signalled a person had fallen short (Deci et al., 1999). Feedback style also mattered. Informational praise increased intrinsic motivation, but the same praise with a controlling phrase such as &quot;just as you ''should''&quot; decreased it (Ryan et al., 1983, as cited in Deci et al., 1999). Negative feedback was less harmful when it included guidance on how to improve (Fong et al., 2019). Rewards did not undermine motivation for boring tasks or when they were unexpected (Deci et al., 1999).
 
CET assumes that these effects work ''through'' perceived competence (Ryan &amp; Deci, 2017). However, relatively few studies have measured perceived competence directly to test this (Deci et al., 1999). One exception is Vallerand and Reid (1984), who gave 84 male students positive, negative, or no verbal feedback on a balance task. Positive feedback raised both perceived competence and intrinsic motivation, while negative feedback lowered both. Perceived competence explained about 40% of the differences in intrinsic motivation, compared with under 8% for feedback alone. However it is important to note that competence was measured with a single question, and the all-male laboratory sample limits how far the findings generalise. Beyond this study, the mechanism is more often assumed than demonstrated. Even so, the practical message is consistent. Feedback that identifies a problem, such as &quot;the scope needs to be better defined&quot;, without showing how to fix it is unlikely to support competence (Fong et al., 2019).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{According to cognitive evaluation theory, positive feedback is most likely to increase intrinsic motivation when it is:

|type=&quot;()&quot;}
- Given with a large financial reward
+ Informative and delivered in an autonomy-supportive way
- Delivered as a comparison with other people
- Given constantly, regardless of performance
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==When competence is frustrated==
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's first review'''
 
'''Week 6.''' Maya's manager reviews the project. She acknowledges some progress, then adds that the plan needs to be clearer and the scope better defined. She does not say what a clearer plan looks like or how to narrow the scope. Maya leaves the meeting feeling like a failure. She had enjoyed the first few folders, but now she dreads opening the system.
 
'''What is happening?''' The feedback identified a problem without giving Maya the information to solve it. Her effort no longer seems to lead anywhere, which is when a need starts to be actively frustrated, not just unmet.
&lt;/div&gt;
 
Research supports the distinction between low satisfaction and active frustration (Vansteenkiste &amp; Ryan, 2013). Bartholomew et al. (2011) found that athletes who saw their coach as controlling reported greater thwarting of all three needs. Need thwarting, in turn, predicted burnout, depressive symptoms, and negative emotion (Bartholomew et al., 2011). Feeling actively undermined was more harmful than simply not feeling supported. If the same pattern holds for competence, vague, critical feedback may harm Maya more than no feedback at all.
 
When people repeatedly experience that their effort makes no difference, they may develop [[w:Learned helplessness|learned helplessness]] (Seligman &amp; Maier, 1967). In classic experiments, dogs exposed to inescapable shocks later failed to escape shocks they could have avoided (Seligman &amp; Maier, 1967). Dogs that had been given control earlier learned to escape. In SDT terms, helplessness resembles amotivation caused by repeated competence frustration Ryan and Deci (2017). In humans, helplessness reduces effort and is linked to apathy and depression (Abramson et al., 1978). How people explain failure also matters. The reformulated helplessness model proposes that explaining failure with internal, stable and global causes is more damaging than explaining it with external, unstable or specific causes (Abramson et al., 1978). Maya's two thoughts show this difference. &quot;I'm hopeless at this&quot; blames a lasting personal flaw and is more likely to lead to giving up, whereas &quot;I just need clearer instructions&quot; points to a specific, changeable cause that keeps her trying.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Maya thinks, &quot;I'm hopeless at this.&quot; According to research on explanatory style, why is this thought more harmful than &quot;I just need clearer instructions&quot;?

|type=&quot;()&quot;}
- It is less accurate
+ It explains failure with an internal, stable cause she cannot easily change
- It blames her manager instead of herself
- It focuses on the task rather than on herself
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==What supports or undermines competence?==
 
In two workplace studies, Baard et al. (2004) found that employees' satisfaction of autonomy, competence, and relatedness predicted their wellbeing as well as their performance evaluations. Because supervisors rated performance, this finding is less affected by self-report bias. However, the design still cannot show which came first. A meta-analysis by Van den Broeck et al. (2016) found that competence predicted wellbeing, work attitudes, and behaviour, even after the other two needs were taken into account. This suggests competence is not simply a by-product of feeling autonomous or connected. Leadership also matters. Managers' autonomy-supportive behaviour is associated with greater need satisfaction as well as more autonomous motivation in employees (Slemp et al., 2018). For Maya, her manager's behavior may be affecting her need satisfaction, including her sense of competence.
 
Similar patterns are found in classroom environments. Bureau et al. (2022) pooled studies of what predicts student motivation and found that, of the three needs, support for competence was the strongest predictor of autonomous motivation. Notably, because SDT has historically given autonomy the most attention (Ryan &amp; Deci, 2017). At least in classroom environments, feeling capable may matter as much as feeling free to choose. However, the meta-analysis draws mainly on correlational studies, so it shows which students do well, but it does not prove that supporting competence causes better outcomes.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==How strong is the evidence?==
The strength of the evidence depends on the methods used. The reward findings, for example, were contested. Cameron and Pierce (1994) found no overall undermining effect and argued that CET should be abandoned. Deci et al. (1999) argued that this result came from mixing boring and interesting tasks, as well as using inappropriate control groups. Laboratory studies also relied mostly on single sessions with children and students (Deci et al., 1999). Self-reported interest also showed much weaker effects than behaviour. Outside the laboratory, most studies are cross-sectional. This makes it unclear whether competence drives motivation or whether motivated people simply feel more competent (Van den Broeck et al., 2016).
 
Some critics have questioned whether basic needs are truly universal, because SDT was developed largely in Western contexts (Chen et al., 2015). However, a study of adults in Belgium, China, Peru, and the United States found that need satisfaction and need frustration predicted wellbeing and ill-being in all four cultures (Chen et al., 2015). Together with the overlap between competence and self-efficacy, these limitations point to the same gap noted in CET. SDT predicts outcomes well, but whether competence itself is the active ingredient remains less certain than the theory suggests (Deci et al., 1999).
 
Most competence research has also used neurotypical samples (Morsink et al., 2022). Morsink et al. (2022) noted that research on [[w:Attention deficit hyperactivity disorder|attention-deficit/hyperactivity disorder]] (ADHD) has mostly studied rewards and overlooked psychological needs. This is despite evidence that children with more ADHD symptoms report lower need satisfaction at school (Morsink et al., 2022). Frequent correction may push teachers and parents toward controlling styles, which can further frustrate competence (Morsink et al., 2022). Whether supporting competence helps neurodivergent people in the same way remains largely untested.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Applying competence in practice==
The research reviewed so far points to a consistent set of conditions under which people feel capable. Table 1 contrasts environments that support competence with those that thwart it. These features reflect the four sources of competence support in SDT, which are clear expectations, optimal challenge, guidance, and constructive feedback (Reeve, 2024).
 
{| class=&quot;wikitable&quot; style=&quot;margin:1em auto; border-radius:8px;&quot;
|+ '''Table 1'''&lt;br&gt;''Features of Competence-Supportive and Competence-Thwarting Environments''
|-
! style=&quot;background:#eaf3fc;&quot; | Competence-supportive !! style=&quot;background:#fff6e8;&quot; | Competence-thwarting
|-
| Clear expectations about how to succeed || Vague or missing guidance
|-
| Guidance and modelling of &quot;how-to&quot; skills || Being left to work it out alone
|-
| Optimal challenge matched to current skills || Tasks far too hard or too easy
|-
| Specific, informative feedback || Absent, harsh, or controlling feedback
|-
| Long-term goals broken into short-term goals || No sense of progress
|-
| Mistakes framed as learning || Mistakes criticised or punished
|}

 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's turnaround'''
 
'''Week 8.''' Maya's manager notices the slowing progress and changes approach. They agree on what &quot;finished&quot; looks like and break the project into stages, starting with the 50 most-used folders.
 
'''Week 12.''' After each stage, Maya receives specific feedback on what is working. She now makes decisions confidently and has started suggesting improvements herself.
 
'''What changed?''' The structure around how the task would be completed: clear expectations, achievable steps, and feedback that informed instead of judged. Each gave Maya evidence that she was effective.
&lt;/div&gt;
 
Breaking Maya's project into stages draws on [[w:Goal setting|goal-setting theory]] (Locke &amp; Latham, 2002). Locke and Latham (2002) reviewed 35 years of laboratory and field studies. They found that specific, challenging goals combined with regular feedback consistently outperform vague &quot;do your best&quot; goals. In SDT, this kind of structure is a form of competence support (Reeve, 2024). Specific goals work partly because they show people exactly what success looks like. Each completed stage also acts as a mastery experience, which is the strongest source of self-efficacy (Bandura, 1977). This helps explain why Maya's confidence returned once the work was divided into stages.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Which change would best support Maya's need for competence?

|type=&quot;()&quot;}
- Offering her a bonus if she finishes faster
+ Breaking the project into stages with clear goals and specific feedback
- Telling her she is doing a great job regardless of progress
- Comparing her progress with a colleague's
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Conclusion==
Competence is the need to ''feel'' effective, and SDT treats it as important at all times, not only once basic needs are met (Ryan &amp; Deci, 2017; Tay &amp; Diener, 2011). Feeling competent moves people toward more autonomous motivation (Ryan &amp; Deci, 2020). CET explains why the same feedback can either energise or deflate a person, depending on whether it informs or controls (Deci et al., 1999).
 
When competence is actively frustrated, the consequences are more severe than when it is simply unmet. These consequences range from burnout to the helpless thinking shown in the case study (Abramson et al., 1978; Bartholomew et al., 2011). Research across workplaces and classrooms suggests, that clear expectations and informational feedback, as well as challenges broken into achievable steps, can reverse this pattern (Baard et al., 2004; Locke &amp; Latham, 2002). However, much of this evidence is correlational and rarely tests competence directly as the mechanism (Van den Broeck et al., 2016).

'''Take-home messages'''
* '''Competence is about feeling effective:''' skilled people can still feel incompetent if they get no sign their effort is working.
* '''Feedback should inform, not control:''' say what is working and how to improve, without pressure.
* '''Make progress visible:''' break big tasks into stages and agree on what &quot;finished&quot; looks like.
* '''Notice the explanation:''' &quot;I'm hopeless&quot; leads towards giving up, while &quot;I need clearer instructions&quot; keeps people trying.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==See also==
* [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|Autonomy and intrinsic motivation in self-determination theory]] (Book chapter, 2025)
* [[Motivation and emotion/Book/2011/Self-determination theory|Self-determination theory]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Book chapter, 2026)
* [[w:Self-determination theory|Self-determination theory]] (Wikipedia)
* [[w:Self-efficacy|Self-efficacy]] (Wikipedia)
* [[w:Learned helplessness|Learned helplessness]] (Wikipedia)
 
==References==
{{Hanging indent|1=

Abramson, L. Y., Seligman, M. E., &amp; Teasdale, J. D. (1978). Learned helplessness in humans: Critique and reformulation. Journal of Abnormal Psychology, 87(1), 49–74. https://doi.org/10.1037/0021-843X.87.1.49
 
Baard, P. P., Deci, E. L., &amp; Ryan, R. M. (2004). Intrinsic need satisfaction: a motivational basis of performance and well-being in two work settings. Journal of Applied Social Psychology, 34(10), 2045–2068. https://doi.org/10.1111/j.1559-1816.2004.tb02690.x

Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191–215. https://doi.org/10.1037/0033-295X.84.2.191
 
Bartholomew, K. J., Ntoumanis, N., Ryan, R. M., Bosch, J. A., &amp; Thøgersen-Ntoumani, C. (2011). Self-Determination Theory and Diminished Functioning: The Role of Interpersonal Control and Psychological Need Thwarting. Personality &amp; Social Psychology Bulletin, 37(11), 1459–1473. https://doi.org/10.1177/0146167211413125
 
Bureau, J. S., Howard, J. L., Chong, J. X. Y., &amp; Guay, F. (2022). Pathways to Student Motivation: A Meta-Analysis of Antecedents of Autonomous and Controlled Motivations. Review of Educational Research, 92(1), 46–72. https://doi.org/10.3102/00346543211042426
 
Cameron, J., &amp; Pierce, W. D. (1994). Reinforcement, Reward, and Intrinsic Motivation: A Meta-Analysis. Review of Educational Research, 64(3), 363–423. https://doi.org/10.3102/00346543064003363

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. Motivation and Emotion, 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1

Deci, E. L. (1971). Effects of externally mediated rewards on intrinsic motivation. Journal of Personality and Social Psychology, 18(1), 105–115. https://doi.org/10.1037/h0030644
 
Deci, E. L., Koestner, R., &amp; Ryan, R. M. (1999). A Meta-Analytic Review of Experiments Examining the Effects of Extrinsic Rewards on Intrinsic Motivation. Psychological Bulletin, 125(6), 627–668. https://doi.org/10.1037/0033-2909.125.6.627
 
Deci, E. L., &amp; Ryan, R. M. (1985). ''Intrinsic motivation and self-determination in human behavior''. Springer. https://doi.org/10.1007/978-1-4899-2271-7

Fong, C. J., Patall, E. A., Vasquez, A. C., &amp; Stautberg, S. (2019). ''A Meta-Analysis of Negative Feedback on Intrinsic Motivation''. Educational Psychology Review, 31(1), 121–162. https://doi.org/10.1007/s10648-018-9446-6
 
Locke, E. A., &amp; Latham, G. P. (2002). '' Building a practically useful theory of goal setting and task motivation: A 35-year odyssey''. The American Psychologist, 57(9), 705–717. https://doi.org/10.1037/0003-066X.57.9.705

Maslow, A. H. (1943). A theory of human motivation. ''Psychological Review, 50''(4), 370–396. https://doi.org/10.1037/h0054346
 
Morsink, S., Van der Oord, S., Antrop, I., Danckaerts, M., &amp; Scheres, A. (2022). ''Studying motivation in ADHD: The role of internal motives and the relevance of self determination theory. ''Journal of Attention Disorders, 26''(8), 1139–1158. https://doi.org/10.1177/10870547211050948
 
Reeve, J. (2024). ''Understanding motivation and emotion'' (8th ed.). Wiley.
 
Ryan, R. M., &amp; Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. ''American Psychologist, 55''(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68
 
Ryan, R. M., &amp; Deci, E. L. (2017). ''Self-determination theory: Basic psychological needs in motivation, development, and wellness''. Guilford Press. https://doi.org/10.1521/978.14625/28806
 
Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology, 61'', Article 101860. https://doi.org/10.1016/j.cedpsych.2020.101860
 
Seligman, M. E. P., &amp; Maier, S. F. (1967). Failure to escape traumatic shock. ''Journal of Experimental Psychology, 74''(1), 1–9. https://doi.org/10.1037/h0024514
 
Slemp, G. R., Kern, M. L., Patrick, K. J., &amp; Ryan, R. M. (2018). Leader autonomy support in the workplace: A meta-analytic review. ''Motivation and Emotion, 42''(5), 706–724. https://doi.org/10.1007/s11031-018-9698-y
 
Tay, L., &amp; Diener, E. (2011). Needs and subjective well-being around the world. ''Journal of Personality and Social Psychology, 101''(2), 354–365. https://doi.org/10.1037/a0023779
 
Vallerand, R. J., &amp; Reid, G. (1984). On the causal effects of perceived competence on intrinsic motivation: A test of cognitive evaluation theory. ''Journal of Sport Psychology, 6''(1), 94–102. https://doi.org/10.1123/jsp.6.1.94

Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A review of self-determination theory's basic psychological needs at work. ''Journal of Management, 42''(5), 1195–1229. https://doi.org/10.1177/0149206316632058
 
Vansteenkiste, M., &amp; Ryan, R. M. (2013). On psychological growth and vulnerability: Basic psychological need satisfaction and need frustration as a unifying principle. ''Journal of Psychotherapy Integration, 23''(3), 263–280. https://doi.org/10.1037/a0032359
 
Vansteenkiste, M., Ryan, R. M., &amp; Soenens, B. (2020). Basic psychological need theory: Advancements, critical themes, and future directions. ''Motivation and Emotion, 44''(1), 1–31. https://doi.org/10.1007/s11031-019-09818-1
 
White, R. W. (1959). Motivation reconsidered: The concept of competence. ''Psychological Review, 66''(5), 297–333. https://doi.org/10.1037/h0040934
}}


==External links==
* [https://selfdeterminationtheory.org/the-theory/ The theory] (Center for Self-Determination Theory)
* [https://www.apa.org/education-career/k12/motivation Motivating students] (American Psychological Association)
* [https://positivepsychology.com/self-determination-theory/ Self-determination theory of motivation] (PositivePsychology.com)
* [https://www.youtube.com/watch?v=_juPDoa3GBY Self-determination theory explained] (Sprouts, YouTube)


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      <text bytes="31865" sha1="s8p7thq1iam9lt30mofry38tng1ax2l" xml:space="preserve">{{title|Competence motivation in self-determination theory:&lt;br&gt;How does the need for competence function within self-determination theory to shape motivation and behaviour?}}
 __TOC__

==Overview==
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study:'''
[[File:Woman Suffering from Stress at Work (cropped).jpg|thumb|right|260px|'''Figure 1'''. Facing a large, unstructured task without guidance or feedback can leave a person doubting their own ability.]]
 
Maya, a 24-year-old administrative officer, has not opened her biggest project in three days. Instead, she has answered every email and tidied a shared drive she built herself: familiar tasks she knows she can do well.
 
Two months ago, Maya was excited when her manager asked her to review and reorganise more than 500 folders in the team's records system. But she received no guidance on where to start or what &quot;finished&quot; should look like. Each folder revealed new complexity, and nobody told her if her decisions were right. (see Figure 1). Some days she thinks, &quot;I just need clearer instructions.&quot; On other days her thoughts turn personal: &quot;I'm hopeless at this.&quot; The first thought sends her to ask for help; the second sends her back to her inbox.
 
''Why does the same task leave a person ready to improve on some days, and ready to give up on others?''
&lt;/div&gt;
 
 
According to [[Self-determination theory|self-determination theory]]&lt;nowiki/&gt;y (SDT), this difference often comes down to the need for [[Motivation and emotion/Book/2011/Self-determination theory|competence]]. Competence is the need to feel effective and capable (Ryan &amp; Deci, 2017). It is one of three basic psychological needs, alongside [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|autonomy]] and [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|relatedness]] (Ryan &amp; Deci, 2017). When competence is satisfied, people tend to show stronger [[Motivation and emotion/Book/2013/Intrinsic motivation|intrinsic motivation]], persistence, and wellbeing (Ryan &amp; Deci, 2020). When it is frustrated, as in Maya's case, people tend to avoid tasks and give up (Vansteenkiste et al., 2020).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Focus questions'''
* What is competence, according to self-determination theory?
* How does competence relate to intrinsic motivation?
* How does cognitive evaluation theory explain why feedback and rewards can strengthen or undermine motivation?
* What happens when the need for competence is frustrated?
* What does research show about how competence can be supported?
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Self-determination theory and competence==
 
===What is self-determination theory?===
SDT is a broad theory of human motivation. It proposes that people have three innate psychological needs: autonomy (feeling volitional), competence (feeling effective), as well as relatedness (feeling connected to others) (Deci &amp; Ryan, 1985; Ryan &amp; Deci, 2017). SDT is made up of six mini-theories, and two of these are central to this chapter. These are cognitive evaluation theory and basic psychological needs theory (Vansteenkiste et al., 2020). SDT is often compared with [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]]. Maslow (1943) proposed a hierarchy in which lower needs, such as physiological and safety needs, generally take priority over higher needs, such as esteem and self-actualisation. He placed mastery within esteem needs. SDT agrees that people strive to feel capable. However, SDT does not rank its needs and considers all three essential at all times (Ryan &amp; Deci, 2017).
 
[[File:MaslowsHierarchyOfNeeds.svg|thumb|right|300px|'''Figure 2'''. Maslow's hierarchy of needs places mastery within esteem needs, near the top of the hierarchy. SDT treats competence as essential at every level.]]
 
Tay and Diener (2011) tested these two views using Gallup World Poll data from 60,865 people in 123 countries. Although people did tend to meet basic and safety needs first, which partly supports Maslow, each need, including mastery, contributed to wellbeing regardless of whether the other needs were met (Tay &amp; Diener, 2011). The needs that mirror SDT, namely social relationships, autonomy, and mastery, were among the strongest predictors of everyday feelings across all eight world regions studied. One limitation is that the data were cross-sectional. Each need was also measured with only two or three yes or no questions, so the study shows association, not cause.
 
===What is competence within self-determination theory?===
The idea of competence as a motivational force dates back to White (1959), who challenged the drive theories of his time. He noticed that infants and young animals explore and play, as well as manipulate objects, even when they are fed and safe. He argued that this behaviour comes from a built-in need to have an effect on the environment, which he called effectance motivation. SDT builds on this idea and defines competence as the need to ''feel'' effective, not simply to possess a skill (Ryan &amp; Deci, 2017). As a result a highly skilled person can still feel incompetent if they receive no sign that their efforts are working.
 
According to SDT, competence is best satisfied in well-structured environments that offer &quot;optimal challenge&quot;, positive feedback, and opportunities for growth (Ryan &amp; Deci, 2020). An optimally challenging task sits slightly beyond a person's current skill, but it comes with enough structure and support to close the gap. Tasks that are too easy offer no sense of growth, while tasks that are too hard, especially without guidance, signal failure (Reeve, 2024). Maya's difficulty illustrates how a lack of structure and feedback can make a manageable task feel too hard.
 
Basic psychological needs theory treats need satisfaction and need frustration as two separate experiences (Vansteenkiste &amp; Ryan, 2013). Need satisfaction is linked to a &quot;bright&quot; pathway of growth and engagement, as well as wellbeing (Vansteenkiste et al., 2020). Need frustration is linked to a &quot;dark&quot; pathway of defensiveness, avoidance, and ill-being (Vansteenkiste et al., 2020). Low satisfaction and active frustration are therefore not the same thing. Receiving no feedback may leave a person unfulfilled, but being repeatedly made to feel ineffective actively harms wellbeing (Vansteenkiste &amp; Ryan, 2013). The case study shows this shift. Maya moves from low satisfaction in the early weeks to active frustration after her manager's review, described later in the chapter.
 
===Competence and self-efficacy===
Competence overlaps closely with [[w:Self-efficacy|self-efficacy]], which is a person's belief that they can successfully perform a specific behaviour (Bandura, 1977). Bandura separated two expectations that shape whether people act. An ''efficacy expectation'' asks &quot;Can I do it?&quot;, and an ''outcome expectation'' asks &quot;Will it work?&quot; Efficacy beliefs are built from four sources: personal mastery experiences, watching similar others succeed, verbal persuasion, and how people interpret their own stress (Bandura, 1977). Of these, mastery experiences are the most powerful (Bandura, 1977).
 
In the case study, several of these sources are weakened. Without feedback, Maya cannot judge whether her decisions are effective, so her real progress is not experienced as mastery. As the case study later shows, her manager's comments act as negative persuasion. Her anxiety before opening the project is also likely to be read as evidence that she is not capable. The key difference between the two concepts is that self-efficacy is a belief about a specific future task (Bandura, 1977). In contrast, SDT treats competence as a universal need that shapes motivation and wellbeing over time (Ryan &amp; Deci, 2017). In practice, however, the two are difficult to separate, because both are usually measured with similar self-report questions. Some &quot;competence&quot; findings may therefore simply reflect confidence.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Competence and intrinsic motivation==
 
SDT's central claim is that the ''quality'' of motivation matters as much as its quantity (Ryan &amp; Deci, 2020). Feeling competent affects where people sit on the motivation continuum, as well as how they respond to feedback and rewards (Deci et al., 1999; Ryan &amp; Deci, 2020).
 
===The motivation continuum===
SDT describes motivation as a continuum (Ryan &amp; Deci, 2020; see Figure 3). The continuum ranges from [[Motivation and emotion/Book/2014/Amotivation|amotivation]], meaning no intention to act, through several forms of extrinsic motivation, to intrinsic motivation, meaning acting for enjoyment or interest (Ryan &amp; Deci, 2020). A lack of competence is one of the main causes of amotivation (Ryan &amp; Deci, 2000). It shows in thoughts such as &quot;I can't do this&quot; or &quot;my effort won't make a difference&quot;. In contrast, feeling capable helps people [[w:Internalization (sociology)|internalise]] the value of a task, so the task feels self-endorsed instead of obligatory (Ryan &amp; Deci, 2020). In the case study, Maya's growing avoidance of her project suggests she is sliding toward amotivation.
 
[[File:Taxonomy of motivation.png|thumb|center|600px|'''Figure 3'''. The SDT motivation continuum, ranging from amotivation, through controlled and autonomous forms of extrinsic motivation, to intrinsic motivation.]]
 
===Cognitive evaluation theory===
[[Motivation and emotion/Book/2021/Cognitive evaluation theory and motivation|Cognitive evaluation theory]] (CET) explains how external events such as feedback and rewards affect intrinsic motivation (Ryan &amp; Deci, 2000). According to CET, every such event has a ''controlling'' aspect, which affects autonomy, and an ''informational'' aspect, which affects competence (Ryan &amp; Deci, 2000). Informational feedback increases perceived competence and intrinsic motivation (Deci et al., 1999). In contrast, rewards that feel like pressure tend to undermine intrinsic motivation, even when they signal success (Deci et al., 1999). CET therefore predicts that ''how'' feedback is delivered matters as much as ''what'' it says. Later versions of CET added a third, ''amotivating'' aspect (Ryan &amp; Deci, 2017). Events that signal incompetence, or that effort will not change the outcome, can push people toward amotivation. Criticism that offers no way forward, such as the feedback Maya later receives, is likely to carry this amotivating message.
 
Research generally supports these predictions, although the earliest evidence was weak. In Deci's (1971) original experiment, students paid $1 for each puzzle they solved later spent less free time on the puzzles once payment stopped. However, the study had only 24 participants, and the result was only a trend (Deci, 1971). A later meta-analysis of 128 experiments, mostly with children and university students, found a clearer pattern (Deci et al., 1999). People who expected a tangible reward for an interesting task spent less free time on it afterwards. In studies with children, this effect was still present more than a week later. The most damaging rewards were those that signalled a person had fallen short (Deci et al., 1999). Feedback style also mattered. Informational praise increased intrinsic motivation, but the same praise with a controlling phrase such as &quot;just as you ''should''&quot; decreased it (Ryan et al., 1983, as cited in Deci et al., 1999). Negative feedback was less harmful when it included guidance on how to improve (Fong et al., 2019). Rewards did not undermine motivation for boring tasks or when they were unexpected (Deci et al., 1999).
 
CET assumes that these effects work ''through'' perceived competence (Ryan &amp; Deci, 2017). However, relatively few studies have measured perceived competence directly to test this (Deci et al., 1999). One exception is Vallerand and Reid (1984), who gave 84 male students positive, negative, or no verbal feedback on a balance task. Positive feedback raised both perceived competence and intrinsic motivation, while negative feedback lowered both. Perceived competence explained about 40% of the differences in intrinsic motivation, compared with under 8% for feedback alone. However it is important to note that competence was measured with a single question, and the all-male laboratory sample limits how far the findings generalise. Beyond this study, the mechanism is more often assumed than demonstrated. Even so, the practical message is consistent. Feedback that identifies a problem, such as &quot;the scope needs to be better defined&quot;, without showing how to fix it is unlikely to support competence (Fong et al., 2019).
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{According to cognitive evaluation theory, positive feedback is most likely to increase intrinsic motivation when it is:

|type=&quot;()&quot;}
- Given with a large financial reward
+ Informative and delivered in an autonomy-supportive way
- Delivered as a comparison with other people
- Given constantly, regardless of performance
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==When competence is frustrated==
 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's first review'''
 
'''Week 6.''' Maya's manager reviews the project. She acknowledges some progress, then adds that the plan needs to be clearer and the scope better defined. She does not say what a clearer plan looks like or how to narrow the scope. Maya leaves the meeting feeling like a failure. She had enjoyed the first few folders, but now she dreads opening the system.
 
'''What is happening?''' The feedback identified a problem without giving Maya the information to solve it. Her effort no longer seems to lead anywhere, which is when a need starts to be actively frustrated, not just unmet.
&lt;/div&gt;
 
Research supports the distinction between low satisfaction and active frustration (Vansteenkiste &amp; Ryan, 2013). Bartholomew et al. (2011) found that athletes who saw their coach as controlling reported greater thwarting of all three needs. Need thwarting, in turn, predicted burnout, depressive symptoms, and negative emotion (Bartholomew et al., 2011). Feeling actively undermined was more harmful than simply not feeling supported. If the same pattern holds for competence, vague, critical feedback may harm Maya more than no feedback at all.
 
When people repeatedly experience that their effort makes no difference, they may develop [[w:Learned helplessness|learned helplessness]] (Seligman &amp; Maier, 1967). In classic experiments, dogs exposed to inescapable shocks later failed to escape shocks they could have avoided (Seligman &amp; Maier, 1967). Dogs that had been given control earlier learned to escape. In SDT terms, helplessness resembles amotivation caused by repeated competence frustration Ryan and Deci (2017). In humans, helplessness reduces effort and is linked to apathy and depression (Abramson et al., 1978). How people explain failure also matters. The reformulated helplessness model proposes that explaining failure with internal, stable and global causes is more damaging than explaining it with external, unstable or specific causes (Abramson et al., 1978). Maya's two thoughts show this difference. &quot;I'm hopeless at this&quot; blames a lasting personal flaw and is more likely to lead to giving up, whereas &quot;I just need clearer instructions&quot; points to a specific, changeable cause that keeps her trying.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Maya thinks, &quot;I'm hopeless at this.&quot; According to research on explanatory style, why is this thought more harmful than &quot;I just need clearer instructions&quot;?

|type=&quot;()&quot;}
- It is less accurate
+ It explains failure with an internal, stable cause she cannot easily change
- It blames her manager instead of herself
- It focuses on the task rather than on herself
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==What supports or undermines competence?==
 
In two workplace studies, Baard et al. (2004) found that employees' satisfaction of autonomy, competence, and relatedness predicted their wellbeing as well as their performance evaluations. Because supervisors rated performance, this finding is less affected by self-report bias. However, the design still cannot show which came first. A meta-analysis by Van den Broeck et al. (2016) found that competence predicted wellbeing, work attitudes, and behaviour, even after the other two needs were taken into account. This suggests competence is not simply a by-product of feeling autonomous or connected. Leadership also matters. Managers' autonomy-supportive behaviour is associated with greater need satisfaction as well as more autonomous motivation in employees (Slemp et al., 2018). For Maya, her manager's behavior may be affecting her need satisfaction, including her sense of competence.
 
Similar patterns are found in classroom environments. Bureau et al. (2022) pooled studies of what predicts student motivation and found that, of the three needs, support for competence was the strongest predictor of autonomous motivation. Notably, because SDT has historically given autonomy the most attention (Ryan &amp; Deci, 2017). At least in classroom environments, feeling capable may matter as much as feeling free to choose. However, the meta-analysis draws mainly on correlational studies, so it shows which students do well, but it does not prove that supporting competence causes better outcomes.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==How strong is the evidence?==
The strength of the evidence depends on the methods used. The reward findings, for example, were contested. Cameron and Pierce (1994) found no overall undermining effect and argued that CET should be abandoned. Deci et al. (1999) argued that this result came from mixing boring and interesting tasks, as well as using inappropriate control groups. Laboratory studies also relied mostly on single sessions with children and students (Deci et al., 1999). Self-reported interest also showed much weaker effects than behaviour. Outside the laboratory, most studies are cross-sectional. This makes it unclear whether competence drives motivation or whether motivated people simply feel more competent (Van den Broeck et al., 2016).
 
Some critics have questioned whether basic needs are truly universal, because SDT was developed largely in Western contexts (Chen et al., 2015). However, a study of adults in Belgium, China, Peru, and the United States found that need satisfaction and need frustration predicted wellbeing and ill-being in all four cultures (Chen et al., 2015). Together with the overlap between competence and self-efficacy, these limitations point to the same gap noted in CET. SDT predicts outcomes well, but whether competence itself is the active ingredient remains less certain than the theory suggests (Deci et al., 1999).
 
Most competence research has also used neurotypical samples (Morsink et al., 2022). Morsink et al. (2022) noted that research on [[w:Attention deficit hyperactivity disorder|attention-deficit/hyperactivity disorder]] (ADHD) has mostly studied rewards and overlooked psychological needs. This is despite evidence that children with more ADHD symptoms report lower need satisfaction at school (Morsink et al., 2022). Frequent correction may push teachers and parents toward controlling styles, which can further frustrate competence (Morsink et al., 2022). Whether supporting competence helps neurodivergent people in the same way remains largely untested.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Applying competence in practice==
The research reviewed so far points to a consistent set of conditions under which people feel capable. Table 1 contrasts environments that support competence with those that thwart it. These features reflect the four sources of competence support in SDT, which are clear expectations, optimal challenge, guidance, and constructive feedback (Reeve, 2024).
 
{| class=&quot;wikitable&quot; style=&quot;margin:1em auto; border-radius:8px;&quot;
|+ '''Table 1'''&lt;br&gt;''Features of Competence-Supportive and Competence-Thwarting Environments''
|-
! style=&quot;background:#eaf3fc;&quot; | Competence-supportive !! style=&quot;background:#fff6e8;&quot; | Competence-thwarting
|-
| Clear expectations about how to succeed || Vague or missing guidance
|-
| Guidance and modelling of &quot;how-to&quot; skills || Being left to work it out alone
|-
| Optimal challenge matched to current skills || Tasks far too hard or too easy
|-
| Specific, informative feedback || Absent, harsh, or controlling feedback
|-
| Long-term goals broken into short-term goals || No sense of progress
|-
| Mistakes framed as learning || Mistakes criticised or punished
|}

 
&lt;div style=&quot;background:#fff6e8; border:2px solid #f2b866; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Case study continued: Maya's turnaround'''
 
'''Week 8.''' Maya's manager notices the slowing progress and changes approach. They agree on what &quot;finished&quot; looks like and break the project into stages, starting with the 50 most-used folders.
 
'''Week 12.''' After each stage, Maya receives specific feedback on what is working. She now makes decisions confidently and has started suggesting improvements herself.
 
'''What changed?''' The structure around how the task would be completed: clear expectations, achievable steps, and feedback that informed instead of judged. Each gave Maya evidence that she was effective.
&lt;/div&gt;
 
Breaking Maya's project into stages draws on [[w:Goal setting|goal-setting theory]] (Locke &amp; Latham, 2002). Locke and Latham (2002) reviewed 35 years of laboratory and field studies. They found that specific, challenging goals combined with regular feedback consistently outperform vague &quot;do your best&quot; goals. In SDT, this kind of structure is a form of competence support (Reeve, 2024). Specific goals work partly because they show people exactly what success looks like. Each completed stage also acts as a mastery experience, which is the strongest source of self-efficacy (Bandura, 1977). This helps explain why Maya's confidence returned once the work was divided into stages.
 
&lt;div style=&quot;background:#eaf3fc; border:2px solid #8fbce6; border-radius:12px; padding:1em 1.2em; margin:1em 0; overflow:hidden; clear:both;&quot;&gt;
'''Check your understanding'''
&lt;quiz display=simple&gt;
{Which change would best support Maya's need for competence?

|type=&quot;()&quot;}
- Offering her a bonus if she finishes faster
+ Breaking the project into stages with clear goals and specific feedback
- Telling her she is doing a great job regardless of progress
- Comparing her progress with a colleague's
&lt;/quiz&gt;
&lt;/div&gt;
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==Conclusion==
Competence is the need to ''feel'' effective, and SDT treats it as important at all times, not only once basic needs are met (Ryan &amp; Deci, 2017; Tay &amp; Diener, 2011). Feeling competent moves people toward more autonomous motivation (Ryan &amp; Deci, 2020). CET explains why the same feedback can either energise or deflate a person, depending on whether it informs or controls (Deci et al., 1999).
 
When competence is actively frustrated, the consequences are more severe than when it is simply unmet. These consequences range from burnout to the helpless thinking shown in the case study (Abramson et al., 1978; Bartholomew et al., 2011). Research across workplaces and classrooms suggests, that clear expectations and informational feedback, as well as challenges broken into achievable steps, can reverse this pattern (Baard et al., 2004; Locke &amp; Latham, 2002). However, much of this evidence is correlational and rarely tests competence directly as the mechanism (Van den Broeck et al., 2016).

'''Take-home messages'''
* '''Competence is about feeling effective:''' skilled people can still feel incompetent if they get no sign their effort is working.
* '''Feedback should inform, not control:''' say what is working and how to improve, without pressure.
* '''Make progress visible:''' break big tasks into stages and agree on what &quot;finished&quot; looks like.
* '''Notice the explanation:''' &quot;I'm hopeless&quot; leads towards giving up, while &quot;I need clearer instructions&quot; keeps people trying.
 
&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;
==See also==
* [[Motivation and emotion/Book/2025/Autonomy and intrinsic motivation in self-determination theory|Autonomy and intrinsic motivation in self-determination theory]] (Book chapter, 2025)
* [[Motivation and emotion/Book/2011/Self-determination theory|Self-determination theory]] (Book chapter, 2011)
* [[Motivation and emotion/Book/2026/Relatedness motivation in self-determination theory|Relatedness motivation in self-determination theory]] (Book chapter, 2026)
* [[w:Self-determination theory|Self-determination theory]] (Wikipedia)
* [[w:Self-efficacy|Self-efficacy]] (Wikipedia)
* [[w:Learned helplessness|Learned helplessness]] (Wikipedia)
 
==References==
{{Hanging indent|1=

Abramson, L. Y., Seligman, M. E., &amp; Teasdale, J. D. (1978). Learned helplessness in humans: Critique and reformulation. Journal of Abnormal Psychology, 87(1), 49–74. https://doi.org/10.1037/0021-843X.87.1.49
 
Baard, P. P., Deci, E. L., &amp; Ryan, R. M. (2004). Intrinsic need satisfaction: a motivational basis of performance and well-being in two work settings. Journal of Applied Social Psychology, 34(10), 2045–2068. https://doi.org/10.1111/j.1559-1816.2004.tb02690.x

Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191–215. https://doi.org/10.1037/0033-295X.84.2.191
 
Bartholomew, K. J., Ntoumanis, N., Ryan, R. M., Bosch, J. A., &amp; Thøgersen-Ntoumani, C. (2011). Self-Determination Theory and Diminished Functioning: The Role of Interpersonal Control and Psychological Need Thwarting. Personality &amp; Social Psychology Bulletin, 37(11), 1459–1473. https://doi.org/10.1177/0146167211413125
 
Bureau, J. S., Howard, J. L., Chong, J. X. Y., &amp; Guay, F. (2022). Pathways to Student Motivation: A Meta-Analysis of Antecedents of Autonomous and Controlled Motivations. Review of Educational Research, 92(1), 46–72. https://doi.org/10.3102/00346543211042426
 
Cameron, J., &amp; Pierce, W. D. (1994). Reinforcement, Reward, and Intrinsic Motivation: A Meta-Analysis. Review of Educational Research, 64(3), 363–423. https://doi.org/10.3102/00346543064003363

Chen, B., Vansteenkiste, M., Beyers, W., Boone, L., Deci, E. L., Van der Kaap-Deeder, J., Duriez, B., Lens, W., Matos, L., Mouratidis, A., Ryan, R. M., Sheldon, K. M., Soenens, B., Van Petegem, S., &amp; Verstuyf, J. (2015). Basic psychological need satisfaction, need frustration, and need strength across four cultures. Motivation and Emotion, 39(2), 216–236. https://doi.org/10.1007/s11031-014-9450-1

Deci, E. L. (1971). Effects of externally mediated rewards on intrinsic motivation. Journal of Personality and Social Psychology, 18(1), 105–115. https://doi.org/10.1037/h0030644
 
Deci, E. L., Koestner, R., &amp; Ryan, R. M. (1999). A Meta-Analytic Review of Experiments Examining the Effects of Extrinsic Rewards on Intrinsic Motivation. Psychological Bulletin, 125(6), 627–668. https://doi.org/10.1037/0033-2909.125.6.627
 
Deci, E. L., &amp; Ryan, R. M. (1985). ''Intrinsic motivation and self-determination in human behavior''. Springer. https://doi.org/10.1007/978-1-4899-2271-7

Fong, C. J., Patall, E. A., Vasquez, A. C., &amp; Stautberg, S. (2019). ''A Meta-Analysis of Negative Feedback on Intrinsic Motivation''. Educational Psychology Review, 31(1), 121–162. https://doi.org/10.1007/s10648-018-9446-6
 
Locke, E. A., &amp; Latham, G. P. (2002). '' Building a practically useful theory of goal setting and task motivation: A 35-year odyssey''. The American Psychologist, 57(9), 705–717. https://doi.org/10.1037/0003-066X.57.9.705

Maslow, A. H. (1943). A theory of human motivation. ''Psychological Review, 50''(4), 370–396. https://doi.org/10.1037/h0054346
 
Morsink, S., Van der Oord, S., Antrop, I., Danckaerts, M., &amp; Scheres, A. (2022). ''Studying motivation in ADHD: The role of internal motives and the relevance of self determination theory. ''Journal of Attention Disorders, 26''(8), 1139–1158. https://doi.org/10.1177/10870547211050948
 
Reeve, J. (2024). ''Understanding motivation and emotion'' (8th ed.). Wiley.
 
Ryan, R. M., &amp; Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. ''American Psychologist, 55''(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68
 
Ryan, R. M., &amp; Deci, E. L. (2017). ''Self-determination theory: Basic psychological needs in motivation, development, and wellness''. Guilford Press. https://doi.org/10.1521/978.14625/28806
 
Ryan, R. M., &amp; Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. ''Contemporary Educational Psychology, 61'', Article 101860. https://doi.org/10.1016/j.cedpsych.2020.101860
 
Seligman, M. E. P., &amp; Maier, S. F. (1967). Failure to escape traumatic shock. ''Journal of Experimental Psychology, 74''(1), 1–9. https://doi.org/10.1037/h0024514
 
Slemp, G. R., Kern, M. L., Patrick, K. J., &amp; Ryan, R. M. (2018). Leader autonomy support in the workplace: A meta-analytic review. ''Motivation and Emotion, 42''(5), 706–724. https://doi.org/10.1007/s11031-018-9698-y
 
Tay, L., &amp; Diener, E. (2011). Needs and subjective well-being around the world. ''Journal of Personality and Social Psychology, 101''(2), 354–365. https://doi.org/10.1037/a0023779
 
Vallerand, R. J., &amp; Reid, G. (1984). On the causal effects of perceived competence on intrinsic motivation: A test of cognitive evaluation theory. ''Journal of Sport Psychology, 6''(1), 94–102. https://doi.org/10.1123/jsp.6.1.94

Van den Broeck, A., Ferris, D. L., Chang, C.-H., &amp; Rosen, C. C. (2016). A review of self-determination theory's basic psychological needs at work. ''Journal of Management, 42''(5), 1195–1229. https://doi.org/10.1177/0149206316632058
 
Vansteenkiste, M., &amp; Ryan, R. M. (2013). On psychological growth and vulnerability: Basic psychological need satisfaction and need frustration as a unifying principle. ''Journal of Psychotherapy Integration, 23''(3), 263–280. https://doi.org/10.1037/a0032359
 
Vansteenkiste, M., Ryan, R. M., &amp; Soenens, B. (2020). Basic psychological need theory: Advancements, critical themes, and future directions. ''Motivation and Emotion, 44''(1), 1–31. https://doi.org/10.1007/s11031-019-09818-1
 
White, R. W. (1959). Motivation reconsidered: The concept of competence. ''Psychological Review, 66''(5), 297–333. https://doi.org/10.1037/h0040934
}}

==External links==
* [https://selfdeterminationtheory.org/the-theory/ The theory] (Center for Self-Determination Theory)
* [https://www.apa.org/education-career/k12/motivation Motivating students] (American Psychological Association)
* [https://positivepsychology.com/self-determination-theory/ Self-determination theory of motivation] (PositivePsychology.com)
* [https://www.youtube.com/watch?v=_juPDoa3GBY Self-determination theory explained] (Sprouts, YouTube)


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    <title>Talk:Motivation and emotion/Book/2026/Parental motivations for homeschooling</title>
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      <comment>Book chapter feedback</comment>
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      <text bytes="17280" sha1="1fd6sitea3duppmxalzf9ckksw9ikif" xml:space="preserve">==Comment==
Hey, I am excited to see how this chapter turns out. With the use of social media, homeschooling (and something called unschooling) are becoming more popularised. Here are three sources about homeschooling and unschooling:

[https://www.researchgate.net/profile/Gina-Riley-2/publication/305720522%20The%20Challenges%20and%20Benefits%20of%20Unschooling%20According%20to%20232%20Families%20Who%20Have%20Chosen%20that%20Route/links/579b8a8d08ae5d5e1e138042/The-Challenges-and-Benefits-of-Unschooling-According-to-] 

DOI:10.1080/2331186X.2016.1163651

 https://doi.org/10.1080/02732173.2014.895640 

-Kayla H
--[[User:U3279062|U3279062]] ([[User talk:U3279062|discuss]] • [[Special:Contributions/U3279062|contribs]]) 08:32, 23 August 2026 (UTC)

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# Develop closer alignment between the sub-title, focus questions, and top-level headings
# The focus questions are quite specific, which is usually a good thing, but in this case, may be overly specific
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&lt;!-- Key points--&gt;
&lt;!-- Overall --&gt;
# Promising development: Many parental motivations are suggested, with citations, and organised into categories/themes
# It is unclear, however, what the main motivations are, or what the main theories are; strive to critically synthesise the theoretical and empriical literature
# Provide more detailed edit summaries
&lt;!-- Scope --&gt;
# The scope is about right, but it may be that all planned aspects cannot be reasonably covered within the book chapter word count; in that case, be selective and concentrate on key aspects that address the question in the sub-title
&lt;!-- GenAI ---&gt;
# Do these key points include [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, this needs to be acknowledged in the edit summaries, otherwise it violates academic integrity.
&lt;!-- Conclusion --&gt;
# Conclusion is well underway
# What are the practical, take-home messages? (address the focus questions)
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# Excellent - Relevant figure(s) presented, captioned, and cited
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# Figure(s) are cited at least once in the main text
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&lt;!-- Learning feature --&gt;
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# Add in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]] (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
&lt;!-- Scenarios/examples/case studies --&gt;
# Consider incorporating additional scenarios, examples, or case studies to illustrate key concepts. These could build on the Overview scenario or introduce new real-world situations in the main body of the chapter to demonstrate how the concepts apply in practice.
&lt;!-- Quiz --&gt;
# Consider including quiz question(s) about the take-home messages
&lt;!-- Tables --&gt;
# Also consider using [[Motivation and emotion/Wikiversity/Tables|table(s)]] to summarise key information
|7=
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# Excellent
# Very good
# Good
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# Insufficient
# To be developed
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# Move non-academic / non-peer reviewed sources to the &quot;External links&quot; section
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# Only include references which have been accessed and read
&lt;!-- APA style --&gt;
# Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]:
## remove bullet points
## capitalisation
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## include hyperlinked dois
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## do not use &quot;Retrieved from&quot;
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&lt;!-- Resources --&gt;
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## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Link to the most relevant Wikiversity book chapters and Wikipedia resources about this topic
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## Excellent
## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Link to the most relevant external resources about this topic
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&lt;!-- User page --&gt;
# Basic
# Not created – see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]
&lt;!-- Description about self --&gt;
# Brief description about self – consider expanding
&lt;!-- Links to profile(s) --&gt;
# Consider linking to your [https://portfolio.canberra.edu.au/ eportfolio] page and/or any other professional online profile or resume such as [https://www.linkedin.com/ LinkedIn]. This is not required, but it can be useful to interlink your professional networks.
&lt;!-- Link to book chapter --&gt;
# Add link to book chapter
|10=
&lt;!-- Social contribution --&gt;
# None summarised on user page with direct link(s) to evidence (see [[Motivation and emotion/Tutorials/Wiki editing#Social contributions|Tutorial 2]]). Looking ahead to the book chapter, see [[Motivation and emotion/Assessment/Chapter#Socialcontribution|social contributions]].
}}

==  Resource recommendations ==
Hey there, 

I enjoyed reading through your chapter so far! I noticed that you hadn't yet included any internal or external links to related resources, so I gathered a few that I think are interesting and could be a valuable addition to your chapter.

''See also''

* [[Motivation and emotion/Book/2015/Family influences on academic motivation|Family influences on academic motivation]] (Book chapter, 2015)
* [[wikipedia:Homeschooling|Homeschooling]] (Wikipedia)

''External links''

* [http://learnmate.com.au/homeschool-vs-school/ Homeschooling vs school: what’s better?] (Learnmate)
* [https://theconversation.com/the-lasting-appeal-of-homeschooling-what-motivated-families-to-continue-after-schools-reopened-post-pandemic-280118 The lasting appeal of homeschooling: what motivated families to continue after schools reopened post‑pandemic] (The Conversation) 
* [https://theconversation.com/why-parents-of-twice-exceptional-children-choose-homeschooling-over-public-school-244385 Why parents of ‘twice‑exceptional’ children choose homeschooling over public school] (The Conversation)

Best regards.  [[User:U3285438|U3285438]] ([[User talk:U3285438|discuss]] • [[Special:Contributions/U3285438|contribs]]) 04:51, 1 October 2026 (UTC)

&lt;!-- Official book chapter feedback --&gt;
{{MEBF/2026
|1=
&lt;!-- Overall comments... --&gt;
# This is an insufficient chapter
# The main area(s) for potential improvement:
#* provide a more indepth explanation of the best psychological theory about the topic
#* integrate more detailed review of the best psychological research about the topic
#* integrate more strongly with other chapters by using embedded links to related topics
#* overuse of unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] (watch out for [[w:AI slop|AI slop]])—express more in your own words
#* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter
&lt;!-- Overall - Edit summaries --&gt;
#* Use [[w:Help:Edit summary|edit summaries]] to briefly describe the changes made in each edit
&lt;!-- Overall - GenAI --&gt;
#* [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] has not been appropriately acknowledged in edit summaries with links to the conversation sources despite previous feedback about this issue. Unacknowledged use of GenAI-generated content raises concerns about compliance with academic integrity principles and assessment requirements and [[Wikiversity:Artificial intelligence|Wikiversity's artificial intelligence policy]].
&lt;!-- Overall – Citations --&gt;
# Insufficient use of academic, peer-reviewed citations to support claims
&lt;!-- Overall – Word count --&gt;
# Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand
&lt;!-- Overall – Copyedits --&gt;
# For additional feedback, see the following comments and [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FParental_motivations_for_homeschooling&amp;diff=2841498&amp;oldid=2841195 these copyedits]
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&lt;!-- Overview – Comments... --&gt;
# Excellent
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# The focus questions are very good (clear and relevant)
# The focus questions are probably overambitious (may have been written by genAI)
|3=
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# A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic
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# Builds in a basic way on [[w:|Wikipedia]] articles but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
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# Insufficient depth is provided about key theory(ies)
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# Reasonably good use of tables, figures, and/or lists to clearly convey key theoretical information
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# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
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# Insufficient use of examples to illustrate theoretical concepts
|4=
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# Insufficient review of relevant research
# Greater emphasis on systematic reviews and/or meta-analyses would be ideal
# More detail about key studies would be ideal
# Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags)
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## considering the strength of relationships
## acknowledging limitations
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# Insufficient integration betwe en the most relevant theory(ies) and the best research
# Insufficient integration with related [[Motivation and emotion/Book|chapters]]
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# Reasonably good, if somewhat vague, summary and conclusion
# Highlight the importance of the problem or phenomenon of interest
&lt;!-- Conclusion – Key points --&gt;
# Key points are summarised in a basic way
&lt;!-- Conclusion – Focus questions --&gt;
# Address the focus questions
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# Add practical, take-home message(s)
&lt;!-- Written expression – Style comments... --&gt;
&lt;!-- Written expression – Written expression --&gt;
# Written expression
## The quality of written expression is OK but there are several aspects which are below professional standard:
### genAI is over-used; write more in your own words, based on your own knowledge based on reading the primary sources
### there are insufficient citations to support claims
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## The chapter is well structured, with major sections using sub-sections
## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags)
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## Use past tense when describing research studies, although implications of findings could be in the present tense
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## Use [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies sentence casing for disorders, therapies, theories, etc.]
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## Figures
### Brief captions; provide more detail to help connect the figure to the text
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## Tables
### Very well captioned
&lt;!-- Written expression – Tables - Citations --&gt;
### Refer to each Table at least once within the main text (e.g., see Table 1)
&lt;!-- Written expression – References --&gt;
## The reference list is insufficiently short; it does not represent the best psychological theory and research about this topic
## References use very good APA style:
### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization]
&lt;!-- Feedback responsiveness ---&gt;
## No evidence of responsiveness to feedback on talk page
|8=
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# Good use of learning features
&lt;!-- Learning features – Wikipedia embedded links --&gt;
# Add more embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
&lt;!-- Learning features – Wikiversity embedded links --&gt;
# Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
&lt;!-- Learning features – Figures, tables, feature boxes, scenarios --&gt;
# Reasonably good use of figure(s)
# Reasonably good use of table(s)
# Basic use of feature box(es)
# No use of scenarios, case studies, or examples, other than opening scenario
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# Basic use of quiz(zes) and/or reflection question(s)
# The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end
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# Insufficient use of the [[{{PAGENAME}}#See also|See also]] section
## Also include links to related book chapters
## Add more links
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# Reasonably good use of the [[{{PAGENAME}}#External links|External links]] section
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## Use alphabetical order
## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link
|9=
&lt;!-- Social contribution comments... --&gt;
# ~2 logged contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]]
# ~1 logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence.
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:31, 19 October 2026 (UTC)</text>
      <sha1>1fd6sitea3duppmxalzf9ckksw9ikif</sha1>
    </revision>
  </page>
  <page>
    <title>Talk:Motivation and emotion/Book/2026/Value congruence and motivation</title>
    <ns>1</ns>
    <id>331468</id>
    <revision>
      <id>2841457</id>
      <parentid>2833133</parentid>
      <timestamp>2026-10-19T04:46:21Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <comment>Book chapter feedback</comment>
      <origin>2841457</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="15161" sha1="khwvft8hsxzhwguifsra9b608ydzbbv" xml:space="preserve">== Perceived control and value misalignment ==

Hi

I really like your opening scenario with Jane; it makes the topic relatable right away and ties in well with your focus questions.

A couple of thoughts on your outline:

You've got five theories listed SDT, Self-Concordance, Motivational Congruence, P-O Fit, and Amity Goal Orientation. That's a lot to fit into one chapter might be worth picking one as your main theory and using the others more briefly to support it, so it doesn't end up feeling like five separate mini-sections.
I haven't heard of Amity Goal Orientation Theory before, check that there's enough solid research behind it; otherwise, it might work better as a short mention rather than its own section.
For the BPD example under individual differences, it might help to note that this is a different, clinical situation, so readers don't assume it works the same way for everyone.
The perceived vs actual congruence point looks really promising. I think that's actually the key to your original discussion question maybe it's not misalignment itself that hurts motivation, but feeling misaligned.

Great structure overall, keen to see it filled in! [[User:U3239236|U3239236]] ([[User talk:U3239236|discuss]] • [[Special:Contributions/U3239236|contribs]]) 00:47, 25 August 2026 (UTC)

== Heading casing ==
{| style=&quot;float: center; background:transparent;color:inherit;&quot;
|-
| [[File:Crystal Clear app ktip.svg|48px|left]]
| {{#if:U3275775|Hi [[User:U3275775|U3275775]].|}} FYI, the recommended [[Wikiversity]] heading style uses [[w:Letter case#Sentence_case|sentence casing]]. For example:&lt;br&gt;
&lt;big&gt;&lt;big&gt;Self-determination theory&lt;/big&gt;&lt;/big&gt;
rather than
&lt;big&gt;&lt;big&gt;Self-Determination Theory&lt;/big&gt;&lt;/big&gt;

Here's an example chapter with correct heading casing: [[Motivation and emotion/Book/2019/Growth mindset development|Growth mindset development]]

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:49, 31 August 2026 (UTC)
|}

&lt;!-- Official topic development feedback --&gt;
{{METF/2026
|1=
&lt;!-- Title --&gt;
# Title and subtitle are correctly worded and use [[w:Letter case#Sentence casing|sentence casing]]
# User name removed from the page; for authorship see [[Special:History/{{PAGENAME}}|the page's edit history]]
|2=
&lt;!-- Headings --&gt;
# See earlier comment about [[#heading casing|heading casing]]
&lt;!-- Heading structure --&gt;
&lt;!-- 2-level --&gt;
# Excellent – Well developed [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]]. Meaningful headings clearly relate directly to the core topic.
# Use default heading formatting (i.e., avoid additional formatting such as bold, italics, underline, changing the size etc.)
&lt;!-- Alignment with focus questions --&gt;
# Excellent alignment between sub-title, focus questions, and heading structure

&lt;!-- GenAI ---&gt;
# Are the headings based on [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, this needs to be acknowledged in the edit summaries, otherwise it violates academic integrity.
|3=
&lt;!-- Overview--&gt;
# Excellent – Scenario, image, evocative description of the problem/topic, and focus questions
&lt;!-- Scenario --&gt;
# A scenario or case study is presented in a feature box with an image at the start of this section
# It is unclear how the scenario relates to value congruence
&lt;!-- Description --&gt;
# A clear description of the problem/topic is planned or presented
&lt;!-- Style --&gt;
# Use 3rd person point of view for main body text (except 1st/2nd person point of view can work within feature boxes for scenarios)
&lt;!-- Focus questions --&gt;
# Focus questions are aligned with sub-title and top-level headings
|4=
&lt;!-- Key points--&gt;
&lt;!-- Overall --&gt;
# Kkey points are well developed for each section
# My key suggestion is strive to integrate key ideas across several sources, rather than summarising each source in a separate paragraph
# Provide more detailed edit summaries
&lt;!-- Scope --&gt;
# The scope is about very good, but it may be that all planned aspects cannot be reasonably covered within the book chapter word count; in that case, be selective and concentrate on key aspects that address the question in the sub-title
&lt;!-- Theory and research --&gt;
# Good balance of theory and research
&lt;!-- Citations --&gt;
# Very good use of citations
# Remove underline (not APA style)

&lt;!-- Conclusion --&gt;
# Conclusion is underway
# What are the practical, take-home messages? (address the focus questions)
|5=
&lt;!-- Figure --&gt;
# Relevant figure(s) presented, captioned, and cited
&lt;!-- Cite --&gt;
# Cite each figure at least once in the main text using APA style (e.g., see Figure 1)
|6=
&lt;!-- Learning feature --&gt;
&lt;!-- Interwiki links ---&gt;
# Add in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]] (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
&lt;!-- Scenarios/examples/case studies --&gt;
# Excellent use of scenarios/examples/case studies
&lt;!-- Quiz --&gt;
# Promising use of quiz question(s)
&lt;!-- Tables --&gt;
# Promising use of table(s)
|7=
&lt;!-- References --&gt;
&lt;!-- Overall --&gt;
# Excellent
# Very good
# Good
# Basic
# Insufficient
# To be developed
&lt;!-- Systematic reviews --&gt;
# Well done on identifying relevant systematic reviews and/or meta-analyses
&lt;!-- APA style --&gt;
# Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]:
## [[Help:Wikitext quick reference|italicisation]]
|8=
&lt;!-- Resources --&gt;
&lt;!-- See also --&gt;
# See also
## Excellent
&lt;!-- External links --&gt;
# External links
## Excellent
|9=
&lt;!-- User page --&gt;
# Used effectively
&lt;!-- Description about self --&gt;
# Description about self provided
&lt;!-- Links to profile(s) --&gt;
# Consider linking to your [https://portfolio.canberra.edu.au/ eportfolio] page and/or any other professional online profile or resume such as [https://www.linkedin.com/ LinkedIn]. This is not required, but it can be useful to interlink your professional networks.
&lt;!-- Link to book chapter --&gt;
# A link to the book chapter is provided
|10=
&lt;!-- Social contribution --&gt;
# Excellent – at least three different types of contributions with direct link(s) to evidence
# Well done on uploading images. Thank-you.
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:49, 31 August 2026 (UTC)

== Feedback  ==
Hi, I love your overview scenario! I was captivated the entire time and I particularly enjoyed the perspective I was placed in and how you ended it with the question of &quot;So why is your routine so different to Jane's&quot;. It made me start thinking about your topic, creating assumptions and made me genuinely enthusiastic to read your chapter. The only suggestion I have would be to perhaps edit the first sentence so the times both end with &quot;am&quot; to maintain consistency. Otherwise I'm excited to see what you find as it is a truly fascinating topic, well done!  [[User:Reillyu3280706|Reillyu3280706]] ([[User talk:Reillyu3280706|discuss]] • [[Special:Contributions/Reillyu3280706|contribs]]) 09:00, 14 September 2026 (UTC)

:I believe your noted theories to explore: Self-Determinism Theory (SDT), Self Concordance Theory, Motivational Congruence Theory, Person Organisation (P-O) Fit, and Amity Goal Orientation Theory are highly applicable  [[User:Reillyu3280706|Reillyu3280706]] ([[User talk:Reillyu3280706|discuss]] • [[Special:Contributions/Reillyu3280706|contribs]]) 09:04, 14 September 2026 (UTC)

&lt;!-- Official book chapter feedback --&gt;
{{MEBF/2026
|1=
&lt;!-- Overall comments... --&gt;
# This is an excellent chapter that successfully uses psychological theory and research to address a practical, real-world phenomenon or problem
# The main area(s) for potential improvement:
#* critical review of research
#* use third-person perspective
&lt;!-- Overall - Edit summaries --&gt;
#* Use [[w:Help:Edit summary|edit summaries]] to briefly describe the changes made in each edit
&lt;!-- Overall – Citations --&gt;
# Excellent use of academic, peer-reviewed citations to support claims
&lt;!-- Overall – Copyedits --&gt;
# For additional feedback, see the following comments and [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FValue_congruence_and_motivation&amp;diff=2841455&amp;oldid=2837334 these copyedits]
|2=
&lt;!-- Overview – Comments... --&gt;
# Very good
&lt;!-- Overview – Scenario --&gt;
&lt;!-- Overview – Scenario - Description --&gt;
# Engaging scenario or case study
# The scenario illustrates individual differences in motivation but not value-congruence
&lt;!-- Overview – Scenario - Figure --&gt;
# Figure 1 is relevant to the scenario
&lt;!-- Overview – Scenario - Feature box --&gt;
# The scenario uses an appropriate feature box
&lt;!-- Overview – Explains problem --&gt;
# Reasonably good problem overview
# Description of problem is too long/complicated—explain the psychological problem or phenomenon in a simpler way. Move detail into subsequent sections.
&lt;!-- Overview – Focus questions --&gt;
# The focus questions are good
# The fourth focus question isn't needed
|3=
&lt;!-- Theory comments... --&gt;
&lt;!-- Theory – Breadth --&gt;
# Excellent—key theories are very well explained and applied
&lt;!-- Theory – Builds on --&gt;
# Builds effectively on [[w:|Wikipedia]] articles but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
&lt;!-- Theory – Depth --&gt;
# Insightful depth is provided about key theory(ies)
&lt;!-- Theory – Tables/Figures/Lists --&gt;
# Excellent use of tables, figures, and/or lists to clearly convey key theoretical information
&lt;!-- Theory – Citations --&gt;
# Key citations are well used
&lt;!-- Theory – Examples --&gt;
# Very good use of examples to illustrate theoretical concepts
|4=
&lt;!-- Research comments... --&gt;
&lt;!-- Research – Key findings --&gt;
# Very good review of relevant research
# Greater emphasis on systematic reviews and/or meta-analyses would be ideal
# More detail about key studies would be ideal
&lt;!-- Research – Critical thinking --&gt;
# [[w:Critical thinking|Critical thinking]] about research could be further evidenced by:
## describing the methodology (e.g., sample, measures) in important studies
## considering the strength of relationships
## acknowledging limitations
## pointing out critiques/counterarguments
## suggesting ''specific'' directions for future research
|5=
&lt;!-- Integration comments... --&gt;
# Very good integration between the most relevant theory(ies) and the best research
# The chapter places more emphasis on theory than on research; strive for an integrated balance
# The chapter could be strengthened through deeper integration with related [[Motivation and emotion/Book|chapters]] by including more embedded links
|6=
&lt;!-- Conclusion comments... --&gt;
# Excellent summary and conclusion
# Highlight the importance of the problem or phenomenon of interest
&lt;!-- Conclusion – Key points --&gt;
# Key points are well summarised
&lt;!-- Conclusion – Focus questions --&gt;
# The focus questions are addressed
&lt;!-- Conclusion – Take-home messages --&gt;
# Clear take-home message(s)
|7=
&lt;!-- Written expression – Style comments... --&gt;
&lt;!-- Written expression – Written expression --&gt;
# Written expression
## The quality of written expression is very good
&lt;!-- Written expression – Language --&gt;
## Use [https://www.grammarly.com/blog/first-second-and-third-person/ 3rd person perspective] (e.g., &quot;it&quot;) instead of 1st (e.g., &quot;we&quot;) or 2nd person (e.g., &quot;you&quot;) in the main text. 1st or 2nd person can work well for case studies or feature boxes.
&lt;!-- Written expression – Layout --&gt;
# Layout
## The chapter is well structured, with major sections using sub-sections
&lt;!-- Written expression – Grammar --&gt;
# Grammar and spelling are excellent
## Use past tense when describing research studies, although implications of findings could be in the present tense
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# Proofreading
## Remove unnecessary capitalisation – [https://polishedpaper.com/blog/capitalization-apa-style more info]
&lt;!-- Written expression – APA style - Quotes --&gt;
## Use double (not single) quotation marks &quot;to introduce a word or phrase used ... as slang, or as an invented or coined expression&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
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## Figures
### I fixed the display of captions
&lt;!-- Written expression – Figures - Citations --&gt;
### Refer to each Figure at least once within the main text (e.g., &quot;(see Figure 1)&quot;)
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## Tables
### Well captioned
&lt;!-- Written expression – Tables - Citations --&gt;
### Each Table is referred to at least once within the main text using APA style
&lt;!-- Written expression – Citations --&gt;
# Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
&lt;!-- Written expression – References --&gt;
## References use excellent APA style:
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## No evidence of responsiveness to feedback on talk page
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&lt;!-- Learning features comments... --&gt;
# Excellent use of learning features
&lt;!-- Learning features – Wikipedia embedded links --&gt;
# Very good use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
&lt;!-- Learning features – Wikiversity embedded links --&gt;
# Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
&lt;!-- Learning features – Figures, tables, feature boxes, scenarios --&gt;
# Excellent use of figure(s)
# Excellent use of table(s)
# Excellent use of feature box(es)
# Very good use of scenarios, case studies, or examples
&lt;!-- Learning features – Quizzes --&gt;
# Excellent use of quiz(zes) and/or reflection question(s)
# The quiz questions could be improved by being more focused on the key points and/or take-home messages
# The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end
&lt;!-- Learning features – See also --&gt;
# Excellent use of the [[{{PAGENAME}}#See also|See also]] section
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# Excellent/Very good/Good/Reasonably good/Basic/Insufficient/No use of the [[{{PAGENAME}}#External links|External links]] section
|9=
&lt;!-- Social contribution comments... --&gt;
# ~7 logged, useful, mostly moderate to major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]]
# Thanks for the Wiki Commons uploads
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:46, 19 October 2026 (UTC)</text>
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  <page>
    <title>Talk:Motivation and emotion/Book/2026/Self-concept and motivation</title>
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      <id>2841436</id>
      <parentid>2834602</parentid>
      <timestamp>2026-10-19T02:59:56Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <comment>Book chapter feedback</comment>
      <origin>2841436</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="11640" sha1="0zrxff94qcgz3sy97vcjrn8ufv716bp" xml:space="preserve">== Feedback on chapter clarity  ==

Hi, I really liked how you have used Ash’s swimming scenario throughout the chapter to connect self-concept and motivation to a clear example. The use of psychological theories and research also provides support for the key ideas. One suggestion would be to simplify some of the more detailed sections where several theories and studies are discussed together. This could make the main points clearer and easier to follow and understand.
Well done you have done an amazing job altogether!! [[User:U3253354|U3253354]] ([[User talk:U3253354|discuss]] • [[Special:Contributions/U3253354|contribs]]) 02:36, 25 August 2026 (UTC)

&lt;!-- Official topic development feedback --&gt;
{{METF/2026
|1=
&lt;!-- Title --&gt;
# Title and subtitle are correctly worded and use [[w:Letter case#Sentence casing|sentence casing]]
|2=
# See earlier comment about [[#heading casing|heading casing]]
&lt;!-- Heading structure --&gt;
&lt;!-- 2-level --&gt;
# Well developed [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]]. Meaningful headings clearly relate directly to the core topic.
# There may be too many sub-headings given that the plan already exceeds the maximum word count for a full chapter e.g., consider simplifying the &quot;understanding self-concept&quot; section (i.e., summarise and link to other resources).
# Good to see the intervention section; but this content could be probably be condensed e.g., into some case studies/feature boxes to highlight activities to try
&lt;!-- Alignment with focus questions --&gt;
# Good alignment between between sub-title, focus questions, and top-level headings. Consider closer alignment (e.g., by using the focus questions as headings)
|3=
&lt;!-- Overview--&gt;
# Excellent – Scenario, image, evocative description of the problem/topic, and focus questions
&lt;!-- Scenario --&gt;
# A scenario or case study is presented in a feature box with an image at the start of this section
&lt;!-- Description --&gt;
# A clear description of the problem/topic is planned or presented
# Use 3rd person point of view for main body text (except 1st/2nd person point of view can work within feature boxes for scenarios)
&lt;!-- Focus questions --&gt;
# Promising focus questions
# Develop closer alignment between the sub-title, focus questions, and top-level headings
|4=
&lt;!-- Key points--&gt;
&lt;!-- Overall --&gt;
# Excellent – key points are well developed for each section
# The scope is excellent (i.e., not too little/narrow or too big/broad)
# However, it is unlikely that all planned aspects can be reasonably covered within the book chapter word count, so be selective and concentrate on the most important aspects which address the question in the sub-title
&lt;!-- Theory and research --&gt;
# Promising balance of theory and research
&lt;!-- Citations --&gt;
# Excellent use of citations
&lt;!-- Conclusion --&gt;
# Conclusion is underway
# What are the practical, take-home messages? (address the focus questions)
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&lt;!-- Figure --&gt;
# Excellent - Relevant figure(s) presented, captioned, and cited
&lt;!-- Creation --&gt;
# Well done on creating and uploading your own image! {{smile}}
|6=
&lt;!-- Learning feature --&gt;
&lt;!-- Interwiki links ---&gt;
# Excellent in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]]
&lt;!-- Scenarios/examples/case studies --&gt;
# Promising use of scenarios/examples/case studies
&lt;!-- Tables --&gt;
# Promising use of table(s); I suggest using a table to summarise the relation between SC and M (i.e., directly address the topic) (rather than on general SC info)
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&lt;!-- References --&gt;
&lt;!-- Overall --&gt;
# Excellent
&lt;!-- Systematic reviews --&gt;
# Well done on identifying relevant systematic reviews and/or meta-analyses
&lt;!-- APA style --&gt;
# Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]:
## capitalisation
|8=
&lt;!-- Resources --&gt;
&lt;!-- See also --&gt;
# See also
## Excellent
## Use alphabetical order
&lt;!-- External links --&gt;
# External links
## Very good
## Use [[w:Letter case#Sentence casing|sentence casing]]
&lt;!-- User page --&gt;
# Excellent
&lt;!-- Description about self --&gt;
# Excellent description about self provided
&lt;!-- Links to profile(s) --&gt;
# Link(s) provided to professional profile(s)
&lt;!-- Link to book chapter --&gt;
# A link to the book chapter is provided
&lt;!-- Social contribution --&gt;
# Excellent – at least three different types of contributions with direct link(s) to evidence
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:38, 28 August 2026 (UTC)

== Quiz Template ==

I liked your chapter draft, and while reading it, I noticed you don't include a quiz template as a learning option. I added a draft one for you based on your introductory scenario and what I read. Good luck [[User:StretchBeyond|StretchBeyond]] ([[User talk:StretchBeyond|discuss]] • [[Special:Contributions/StretchBeyond|contribs]]) 00:41, 8 September 2026 (UTC)

== Feedback ==
This is looking really good Pepper! I was only really able to make one minuscule edit. I really enjoyed the section on self-handicapping, which would be interesting to compare with self-fulfilling prophecies (though I appreciate this is beyond the scope of your book chapter). Well done! [[User:U3254168|U3254168]] ([[User talk:U3254168|discuss]] • [[Special:Contributions/U3254168|contribs]]) 02:30, 27 September 2026 (UTC)

&lt;!-- Official book chapter feedback --&gt;
{{MEBF/2026
|1=
&lt;!-- Overall comments... --&gt;
# This is an outstanding chapter that successfully integrates psychological theory and research in a highly readable way to address a practical, real-world phenomenon or problem
#* I suspect that the [[Motivation and emotion/Assessment#Assessment items|recommended 75 hours]] were not invested in preparing this chapter
&lt;!-- Overall - Edit summaries --&gt;
#* [[w:Help:Edit summary|Edit summaries]] are used to clearly communicated the changes made in most or all edits
&lt;!-- Overall - GenAI --&gt;
# [[Motivation and emotion/Assessment/Using generative AI|GenAI use]] is very well acknowledged. The chapter has been added as an example to [[Motivation and emotion/Assessment/Using generative AI#Examples]]
&lt;!-- Overall – Citations --&gt;
# Excellent use of academic, peer-reviewed citations to support claims
&lt;!-- Overall – Copyedits --&gt;
# For additional feedback, see the following comments and [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FSelf-concept_and_motivation&amp;diff=2841435&amp;oldid=2839534 these copyedits]
|2=
&lt;!-- Overview – Comments... --&gt;
# Excellent
&lt;!-- Overview – Scenario --&gt;
&lt;!-- Overview – Scenario - Description --&gt;
# Engaging scenario or case study
&lt;!-- Overview – Scenario - Figure --&gt;
# Figure 1 is relevant to the scenario
&lt;!-- Overview – Scenario - Feature box --&gt;
# The scenario uses an appropriate feature box
&lt;!-- Overview – Explains problem --&gt;
# Clearly explains the psychological problem or phenomenon
&lt;!-- Overview – Focus questions --&gt;
# The focus questions are clear and relevant
|3=
&lt;!-- Theory comments... --&gt;
&lt;!-- Theory – Breadth --&gt;
# Excellent—key theories are very well explained, critically contrasted, and applied to examples
&lt;!-- Theory – Builds on --&gt;
# Builds exceptionally well on [[w:|Wikipedia]] articles and related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
&lt;!-- Theory – Depth --&gt;
# Insightfu depth is provided about key theory(ies)
&lt;!-- Theory – Tables/Figures/Lists --&gt;
# Excellent use of tables, figures, and/or lists to clearly convey key theoretical information
&lt;!-- Theory – Citations --&gt;
# Key citations are well used
&lt;!-- Theory – Examples --&gt;
# Excellent use of examples to illustrate theoretical concepts
|4=
&lt;!-- Research comments... --&gt;
&lt;!-- Research – Key findings --&gt;
# Excellent review of relevant research
# Some emphasis on systematic reviews and/or meta-analyses
# Claims are well referenced
&lt;!-- Research – Critical thinking --&gt;
# Excellent [[w:Critical thinking|critical thinking]] about relevant research is evident
# [[w:Critical thinking|Critical thinking]] about research could be further evidenced by:
## describing the methodology (e.g., sample, measures) in important studies
## considering the strength of relationships
|5=
&lt;!-- Integration comments... --&gt;
# Excellent integration between the most relevant theory(ies) and the best research
|6=
&lt;!-- Conclusion comments... --&gt;
# Excellent summary and conclusion
# Highlight the importance of the problem or phenomenon of interest
&lt;!-- Conclusion – Key points --&gt;
# Key points are well summarised
&lt;!-- Conclusion – Focus questions --&gt;
# The focus questions are addressed
&lt;!-- Conclusion – Take-home messages --&gt;
# Clear take-home message(s)
|7=
&lt;!-- Written expression – Style comments... --&gt;
&lt;!-- Written expression – Written expression --&gt;
# Written expression
## The quality of written expression is excellent
&lt;!-- Written expression – Layout --&gt;
# Layout
## The chapter is well structured, with major sections using sub-sections
&lt;!-- Written expression – Grammar --&gt;
# Grammar and spelling are excellent
## Use past tense when describing research studies, although implications of findings could be in the present tense
&lt;!-- Written expression – Abbreviations --&gt;
## Abbreviations
### Spell out abbreviations on their first use, to explain them to the reader
&lt;!-- Written expression – Figures --&gt;
## Figures
### Very well captioned
&lt;!-- Written expression – Figures - Citations --&gt;
### Each Figure is referred to at least once within the main text using APA style

&lt;!-- Written expression – Tables --&gt;
## Tables
### Very well captioned
&lt;!-- Written expression – Tables - Citations --&gt;
### Each Table is referred to at least once within the main text using APA style
&lt;!-- Written expression – Citations --&gt;
# Citations use excellent [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
&lt;!-- Written expression – References --&gt;
## References use excellent APA style:
&lt;!-- Feedback responsiveness ---&gt;
## No evidence of responsiveness to feedback on talk page
|8=
&lt;!-- Learning features comments... --&gt;
# Excellent use of learning features
&lt;!-- Learning features – Wikipedia embedded links --&gt;
# Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles
&lt;!-- Learning features – Wikiversity embedded links --&gt;
# Excellent use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]
&lt;!-- Learning features – Figures, tables, feature boxes, scenarios --&gt;
# Very good use of figure(s)
# Excellent use of table(s)
# Excellent use of feature box(es)
# Excellent use of scenarios, case studies, or examples
&lt;!-- Learning features – Quizzes --&gt;
# Excellent use of quiz(zes) and/or reflection question(s)
&lt;!-- Learning features – See also --&gt;
# Excellent use of the [[{{PAGENAME}}#See also|See also]] section
&lt;!-- Learning features – External links --&gt;
# Excellent use of the [[{{PAGENAME}}#External links|External links]] section
|9=
&lt;!-- Social contribution comments... --&gt;
# ~20 logged, useful, mostly moderate to major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]]
# Thanks for the Wiki Commons uploads
# Thanks very much for your extensive contributions
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:59, 19 October 2026 (UTC)</text>
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    <title>Motivation and emotion/Book/2026/Trust rebuilding after trauma</title>
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      <id>2841376</id>
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      <timestamp>2026-10-18T21:04:20Z</timestamp>
      <contributor>
        <username>Jack4234</username>
        <id>3106762</id>
      </contributor>
      <comment>internal link embedded</comment>
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      <text bytes="25622" sha1="g8wftjq8dkoyy140eh7w30f8otmgpa1" xml:space="preserve">{{title|Trust rebuilding after trauma:&lt;br&gt;How can trauma survivors develop trust in similar situations again?}}
__TOC__

==Overview==
{{RoundBoxTop|theme=3}}
[[File:Sad Teen Girl Portrait.jpg|thumb|200x200px|'''Figure 1'''.  Even years after trauma, the fear of being hurt can remain]]

;Scenario

Imagine a girl named Zara, who experienced a traumatic event several years ago with an ex-boyfriend. This event is very much over, however, Zara continues to feel unsafe and insecure in relationships. When she meets a new boy she likes, she worries they are angry or that she's done something wrong, if they take a little while to respond to her messages. She often struggles to be vulnerable with these people and avoids communicating her feelings for fear of judgement and abandonment. Zara has recently made a new friend at college, someone who is incredibly kind, communicates openly, and doesn't make her second-guess. Despite these consistent, kind behaviours, Zara finds it difficult to believe that person will never hurt her.
{{RoundBoxBottom}}

[[w:Trust (social science|Trust]] is crucial to the success, fulfilment, and longevity of romantic relationships. Trust isn't a single emotion or choice, but a vital concept built on intimacy, love, respect, and care. However, trust can be broken. In this chapter, we discuss how trauma survivors can develop their trust again in similar situations, while learning to accept the emotional responses that may be brought up from previous traumatic experiences. The following points explain the importance and psychological theories that can assist in understanding these processes.  

* A lack of trust negatively impacts a relationship, causing interpersonal problems through lying and anxiety
* Within monogamous relationships, emotional and physical infidelity is the most common experience that destroys trust with partners.
* Betrayal trauma leads to trauma responses, in many instances, causing great emotion and psychological damage.* Rebuilding trust is crucial to relationship recovery and health.
* Psychological science provides several perspectives that can explain the process of rebuilding trust in trauma survivors.
* This research and theory includes: Attachment theory and betrayal trauma theory

{{RoundBoxTop|theme=3}}
;Focus questions

{{ic|}}
1. How can experiences of betrayal trauma disrupt trust and influence future relationships?

2. Why do trauma survivors experience distrust in new situations that correspond with the original traumatic experience?

3. How can trauma survivors rebuild trust through new relationship experiences?
{{RoundBoxBottom}}

== How Does Betrayal Trauma Affect Future Relationships? ==
Trauma can arise from an extremely distressing or disturbing experience and has lasting effects on an individual's psychological health (Das &amp; Jain, 2024). These traumatic experiences contribute to many psychological impacts, with symptoms of anxiety and depression, difficulties with trust, and disruptions to personal connections (Freyd et al., 2005). Betrayal trauma is the experience when a person or institution that an individual trusts violates that trust, leading to severe psychological harm (Freyd, 1994). When betrayal occurs within a romantic relationship, it can influence how they approach intimacy, trust, and reliability in future romantic relationships. 

=== Understanding Betrayal Trauma ===
Jennifer Freyd's betrayal trauma theory suggests that the psychological impact of betrayal depends on the relationship between the person who experiences the harm and the person responsible for it (Freyd, 1994). The theory suggests that when someone relies on a person who betrays them, it may be difficult to recognise the betrayal (Das &amp; Jain, 2024). Betrayal trauma assists in explaining the emotional hurt an individual is affected by after their trust and wellbeing are violated by significant people in their life (Freyd, 1994). Partner infidelity or “cheating” is a form of interpersonal trauma, which causes PTSD, depression and anxiety in 30% to 60% of betrayed people. The act of intimate betrayal causes a traumatic memory. Clinically, this combination of symptoms points toward a stress-related disorder (Lonergan et al., 2020). An act of betrayal between romantic partners is one that harms a shared set of core beliefs established in the relationship and destroys the ability to have a partner as a source of safety and comfort (Lonergan et al., 2020). In romantic relationships, infidelity may challenge a victim's ability to trust their partner but also the expectations they established of honesty and reliability. Understanding the psychological impacts of partner betrayal provides insights into how trust can be affected in future relationships.

=== Betrayal Trauma and Interpersonal Trust ===
According to the betrayal trauma theory, individuals are susceptible to developing betrayal blindness when they are unable to fully recognise betrayal by someone they trust. In a relationship, betrayal blindness can be severely impactful. Difficulty recognising betrayal can affect an individual's ability to judge someone's trustworthiness and leave them more vulnerable to being hurt in future relationships (Gobin &amp; Freyd, 2014). Zurbriggen and Freyd (2004) suggest that traumatic betrayals damage the cognitive functions that enable individuals to judge a person's trustworthiness, which could lead them to trust unworthy people and increase the chances of future betrayal. Supporting this theory, Gobin and Freyd (2009) discovered that victims of high betrayal trauma (HBT) had an increased likelihood of staying in a romantic relationship after experiencing infidelity and a betrayal of trust. 

Gobin and Freyd (2014) conducted an experiment investigating the relationship between betrayal trauma and interpersonal trust by examining their participants' trust in others, their romantic partners, and their behaviours in an experimental trust game. They discovered that participants who reported HBT also reported having lower trust in romantic partners. Following infidelity, victims may be hesitant and show caution when trusting future partners, because they don't wish to experience betrayal again. However, developing trust may involve not only learning to trust romantic partners in future relationships but also regaining confidence in their own judgement of others.

[[File:Figure 2. Jennifer J. Freyd's Two-Dimensional Model for Traumatic Events.png|309x309px]]

Jennifer J. Freyd's Two-Dimensional Model for Traumatic Events

=== Attachment and Intimacy after Betrayal ===
Interpersonal trauma has been shown to influence attachment styles, with a dependency on the attachment between the victim and the perpetrator (Brennan et al., 1998, as cited in Das &amp; Jain, 2024). Although attachment theory was originally developed to explain relationships between children and their caregivers, researchers have since applied it to romantic relationships (Das &amp; Jain, 2024). Attachment theory emphasises human beings' natural tendency to form and maintain loving, caring, and affectionate bonds with others. (Bowlby, 1988 as cited in Mosley, 2022). In a romantic relationship, secure attachment is associated with emotional security, physical closeness, and a reciprocal sense of safety between partners. However, betrayal by a romantic partner threatens relationship safety and security, resulting in an attachment injury, a violation of trust that affects a victim's beliefs about the relationship (Johnson et al., 2001, as cited in Mosley, 2022). Research suggests that the more intimate the relationship in which the betrayal occurs, the more likely it is to create traumatic memories that affect a person's attachment (Butler et al., 2021, as cited in Mosley, 2022). This has devastating consequences, not only psychologically and physically, because a victim might also struggle to feel confident in another person's trustworthiness as a result. Further impacting how they approach trust and future romantic relationships.

== How Does Betrayal Trauma Affect Well-being? ==

Betrayal trauma has the ability to impact the psychological and physiological health of betrayal trauma victims by increasing fear and stress in future relationships. Research links betrayal trauma with difficulties in emotional regulation and mental illness symptoms associated with PTSD, depression and dissociation (Mosley, 2022; Ward, 2026).

=== Physical and Emotional Responses ===
In recent history, trauma responses performed by a victim have been associated with feelings of fear during and after the traumatic experience. When we experience trauma, our body and brain's primary reaction is fear, triggering a range of physiological and emotional responses (DePrince et al., 2011). In the context of betrayal, the emotional reaction can be described as similar to the emotions people feel when confronted with death or horrific events (Mosley, 2022). Research suggests that emotional regulation capacities are impacted among survivors of Betrayal trauma, with great impacts towards psychological and physiological functioning (Mosley, 2022). Continuous exposure to relationship problems has been shown to disrupt stress regulation systems, with the prefrontal cortex and limbic reactivity most affected. Evidence from trauma and stress research supports the likelihood of neurobiological dysregulation in individuals experiencing relationship betrayal (Ward, 2026). Clinical studies have further observed a change in emotional regulation and impaired executive functioning after continuous betrayal is experienced (Ward, 2026). There are also great physical consequences as a result of experiencing betrayal trauma. Our bodies' autonomic nervous system works within nanoseconds, activating to prepare for threats. Our bodies are built to detect danger by increasing adrenaline and cortisol, which prepare us to fight, flee, or shut down (Sutherland, 2019, as cited in Ward, 2026). However, the body works by continuously returning to equilibrium, responding rapidly to stress, and then relaxing. Victims of betrayal, as a result of heightened stress, experience an unhealthy state of emotional threat and danger. López Martínez et al. (2018, as cited in Ward, 2026) found that the body's continual response to betrayal, and a heightened sense of dread about future betrayals, creates emotional dysregulation by keeping the response system persistently engaged. Researchers have also discovered that victims of high betrayal trauma are more susceptible to experiencing pain in the form of soft tissue, chronic fatigue, diabetes, bladder issues, pelvic pain and asthma (Silber, 2020).

=== Post-traumatic stress disorder (PTSD) and Mental Illness ===
PTSD, or post-traumatic stress disorder, is a mental illness most noticeably caused by previous traumatic experiences, characterised by symptoms of depression, alcohol and drug abuse, dissociative tendencies, personality disorders and health concerns (Bremner, 2006). Betrayal trauma has been associated with multiple psychological diagnoses. These include PTSD, depression and dissociation (Mosley, 2022). Through a variety of studies, betrayal trauma was further associated with symptoms of PTSD, being impacted by intrusive thoughts and an impairment in self-concept (Ward, 2026). Atlas and Ingram (1998, as cited in Freyd et al., 2005) reported a stronger association between betrayal trauma and PTSD than between non-betrayal trauma and PTSD. Further research conducted by Kelley (2009, as cited in DePrince et al., 2011) discovered that insights of betrayal had a stronger association with PTSD than perceptions of life threat. Furthermore, Kaehler and Freyd (2009, DePrince et al., 2011) found an association between middle and high levels of betrayal trauma exposure and borderline personality characteristics among a college student population.

== How Can Trauma Survivors Rebuild Trust and Feel Safe in Future Relationships? ==
Rebuilding trust after infidelity is a gradual process which takes time and emphasises the importance for consistent honest, behaviour and support. Counselling, forgiveness and managing painful memories can work towards rebuilding trust (Abrahamson et al., 2012). However recovery is dependant on the victims decision about whether they will continue with the relationship. 

=== Rebuilding Trust and Emotional Safety ===
Although infidelity is a severely damaging event, not all couples choose to end their relationship after discovering an affair (Abrahamson et al., 2012). Trust in a relationship involves accepting a degree of vulnerability in relation to expectations of monogamy shaped by a partner's intentions and behaviour (Rousseau et al., 1998, as cited in Pramudito &amp; Minza, 2021). Infidelity damages these expectations, causing the betrayed partner to lose confidence in their partner's honesty and reliability (Pramudito &amp; Minza, 2021). Rebuilding trust is a gradual process that requires more than forgiveness. Olson, Russell, Higgins-Kessler, and Miller (2002, as cited in Abrahamson et al., 2012) describe a three-phase step to rebuilding trust. The first phase is known as the roller coaster phase, describing the continual change or “roller coaster” of emotions. This can be seen in the initial shock, strong feelings of disclosure, and the many uncontrollable emotions that come up. The second phase, known as the moratorium phase, begins when the couple agrees to set  hurt aside and move forward with their lives. Lastly, the third phase suggests the couple look to the future and focus on rebuilding trust in the relationship. Abrahamson et al. (2012) identified that forgiveness, counselling, managing painful memories of the infidelity, and changes in that relationship are all steps towards rebuilding that trust. In addition, Anderson (2025) suggested that viewing infidelity through a trauma-based perspective may assist marriage counsellors to better recognise and assist clients' experiences and provide further evidence-based support. Furthermore, Pramudito and Minza (2021) emphasised the importance of restoring trust over time through consistent demonstrations of faithfulness and honest behaviour. However, more importantly, the perspectives of the betrayed partner are necessary, as it is their decision to remain within the relationship in order to learn to rebuild trust again (Mitchell et al., 2025). However, Mitchell et al. (2025) explains that the betrayed partner may feel pressure to forgive in order for the relationship to continue, and this responsibility, along with overwhelming, ever-changing emotions, can affect their ability to make accurate, necessary decisions about the relationship. To rebuild the victim's trust in the perpetrator, signs of faithfulness and integrity are crucial. Goldie (2013, as cited in Pramudito and Minza, 2021). Furthermore, there is an emphasis on resolving conflicts positively in order to rebuild the victim's trust and to rebuild trustworthiness to work towards building a fully recovered marital relationship (Baucom et al., 2009, as cited in Pramudito &amp; Minza, 2021; Dickie, 2015, as cited in Pramudito &amp; Minza, 2021).

== Learning Features ==

=== Learning Feature - 1 ===
'''According to the betrayal trauma theory (discussed in the first heading) why can betrayal from a trusted partner make it more difficult in the future to trust another partner?'''
{| class=&quot;wikitable&quot;
|+
! colspan=&quot;3&quot; valign=&quot;top&quot; |Quiz 1 - Multiple Choice 
|-
! valign=&quot;top&quot; |A
| valign=&quot;top&quot; |It makes them dislike their parents and all their friends
| rowspan=&quot;4&quot; |Answer (B)
|-
! valign=&quot;top&quot; |B
| valign=&quot;top&quot; |It ruins their trust, safety, and judgement of whether others are trustworthy
|-
! valign=&quot;top&quot; |C
| valign=&quot;top&quot; |It makes them unable to communicate with people
|-
! valign=&quot;top&quot; |D
| valign=&quot;top&quot; |It makes them sad
|}

=== Learning Feature - 2 ===
'''Zara was cheated on by her ex-boyfriend. It's a few years later now and she has a new boyfriend. They are both incredibly happy. However, as the days go by, and not to his fault, she becomes more noticeable of the small changes in her partners behaviours as they develop their relationship. One day he forgets to message her while he's at work. Even though it was a mistake she still feels like something is wrong. What is she experiencing?''' 
{| class=&quot;wikitable&quot;
|+
! colspan=&quot;3&quot; valign=&quot;top&quot; |'''Quiz 2 - Multiple Choice''' 
|-
! valign=&quot;top&quot; |A
| valign=&quot;top&quot; |Confidence, in herself and her boyfriend
| rowspan=&quot;4&quot; |Answer (C)
|-
! valign=&quot;top&quot; |B
| valign=&quot;top&quot; |Fatigue, she has had a very long day
|-
! valign=&quot;top&quot; |C
| valign=&quot;top&quot; |Hypervigilance, she is highly alert to supposed danger
|-
! valign=&quot;top&quot; |D
| valign=&quot;top&quot; |Brain fog, she forgets what has happened
|}

== Conclusion ==
Experiences of betrayal, especially those within romantic relationships, are incredibly traumatic experiences and have lasting impacts on a victim's sense of trust and emotional safety in the people around them. As discussed throughout this chapter, betrayal trauma theory assists in explaining how harm caused by a trusted person can impact beliefs about relationships, while attachment theory assists us in understanding how these experiences may affect intimacy and emotional security. However, the difficulties victims face do not mean they are incapable of developing trust in relationships again. Rebuilding trust is a gradual process in which we learn to recognise signs of trustworthiness and develop confidence in our ability to judge others' trustworthiness. Relationships are built on communication, reliability, safety, and honesty, and experiencing this in a new relationship may build a greater sense of safety. Attempting to recover after infidelity will take time, trust will take time to fully restore, and forgiveness will continue to develop. However, rebuilding trust is not about guaranteeing that betrayal will ever happen again, but is about learning to recognise trustworthiness and to adopt a sense of security that will help victims form meaningful connections despite past hurt.

==See also==

=== Wikipedia Link - PTSD &lt;ref&gt;{{Cite journal|date=2026-09-05|title=Post-traumatic stress disorder in children and adolescents|url=https://en.wikipedia.org/w/index.php?title=Post-traumatic_stress_disorder_in_children_and_adolescents&amp;oldid=1373411231|journal=Wikipedia|language=en}}&lt;/ref&gt; ===
Discusses PTSD in children and adolescents and the diagnosis, risk factors, trauma and symptoms. [https://en.wikipedia.org/wiki/Post-traumatic_stress_disorder_in_children_and_adolescents]

=== Wikiversity Link – Trauma and Attachment Development &lt;ref&gt;{{Cite web|url=https://en.wikiversity.org/wiki/Motivation_and_emotion/Book/2025/Trauma_and_attachment_development|title=Motivation and emotion/Book/2025/Trauma and attachment development - Wikiversity|website=en.wikiversity.org|language=en|access-date=2026-10-11}}&lt;/ref&gt; ===
Discusses various attachment styles and trauma and the way they both interconnect.[https://en.wikipedia.org/wiki/Post-traumatic_stress_disorder_in_children_and_adolescents]

==References==
Abrahamson, I., Hussain, R., Khan, A., &amp; Schofield, M. J. (2012, October 21). ''What helps couples rebuild their relationship after infidelity?'' SAGE Publications. ResearchGate. https://www.researchgate.net/publication/233341758_What_Helps_Couples_Rebuild_Their_Relationship_After_Infidelity

Affair Recovery. (2021, July 1). ''How to rebuild trust after infidelity: Become reliable'' [Video]. YouTube. https://www.youtube.com/watch?v=k8foEEWnsFw

Anderson, M. (2025). The impact and connection between infidelity and PTSD. ''Journal of Counseling Sexology and Sexual Wellness'', ''6''(2). [https://digitalcommons.unf.edu/jcssw/vol6/iss2/ https://doi.org/10.34296/06022017]

Beresford, L. (2018, August 24). Infidelity: To stay or go…? | Lucy Beresford | TEDxFolkestone [YouTube Video]. In ''YouTube''. https://www.youtube.com/watch?v=5TUxH2izTGI

Bremner, J. D. (2006). Traumatic stress: Effects on the brain. ''Dialogues in Clinical Neuroscience'', ''8''(4), 445–461. [https://www.tandfonline.com/doi/full/10.31887/DCNS.2006.8.4/jbremner https://doi.org/10.31887/dcns.2006.8.4/jbremner]

Das, M., &amp; Jain, N. (2024). Partner Betrayal Trauma and trust: Understanding the impact on attachment style and self-esteem. ''European Journal of Trauma &amp; Dissociation'', ''8''(2), 100409–100409. [https://www.sciencedirect.com/science/article/abs/pii/S2468749924000334?via%3Dihub https://doi.org/10.1016/j.ejtd.2024.100409]

DePrince, A. P., Brown, L. S., Cheit, R. E., Freyd, J. J., Gold, S. N., Pezdek, K., &amp; Quina, K. (2011). Motivated forgetting and misremembering: Perspectives from betrayal trauma theory. ''Nebraska Symposium on Motivation'', 193–242. [https://link.springer.com/chapter/10.1007/978-1-4614-1195-6_7 https://doi.org/10.1007/978-1-4614-1195-6_7]

Ford, J. D, &amp; Courtois, C. A. (2016). ''Treating complex traumatic stress disorders in children and adolescents : Scientific foundations and therapeutic models''. New York ; London The Guilford Press. https://books.google.com.au/books?hl=en&amp;lr=&amp;id=Uv0E4W3bMYcC&amp;oi=fnd&amp;pg=PA62&amp;dq=betrayal+trauma+theory+1996&amp;ots=cKuxJAUZUq&amp;sig=-k98_BIIGp4gzPyPBcidj1WZ-qI#v=onepage&amp;q=betrayal%20trauma%20theory%201996&amp;f=false

Freyd, J. J. (1994). Betrayal trauma: Traumatic amnesia as an adaptive response to childhood abuse. ''Ethics &amp; Behavior'', ''4''(4), 307–329. [https://www.tandfonline.com/doi/abs/10.1207/s15327019eb0404_1 https://doi.org/10.1207/s15327019eb0404_1]

Freyd, J. J. (2013). ''Definition of Betrayal Trauma Theory''. Uoregon.Edu. https://dynamic.uoregon.edu/jjf/defineBT.html

Freyd, J. J., Klest, B., &amp; Allard, C. B. (2005). Betrayal trauma: Relationship to physical health, psychological distress, and a written disclosure intervention. ''Journal of Trauma &amp; Dissociation'', ''6''(3), 83–104. [https://www.tandfonline.com/doi/abs/10.1300/J229v06n03_04 https://doi.org/10.1300/j229v06n03_04]

Gobin, R. L., &amp; Freyd, J. J. (2009). Betrayal and revictimization: Preliminary findings. ''Psychological Trauma: Theory, Research, Practice, and Policy'', ''1''(3), 242–257. [https://psycnet.apa.org/doiLanding?doi=10.1037%2Fa0017469 https://doi.org/10.1037/a0017469]

Gobin, R. L., &amp; Freyd, J. J. (2014). The impact of betrayal trauma on the tendency to trust. ''Psychological Trauma: Theory, Research, Practice, and Policy'', ''6''(5), 505–511. [https://psycnet.apa.org/doiLanding?doi=10.1037%2Fa0032452 https://doi.org/10.1037/a0032452]

Lonergan, M., Brunet, A., Rivest‐Beauregard, M., &amp; Groleau, D. (2020). Is romantic partner betrayal a form of traumatic experience? A qualitative study. ''Stress and Health'', ''37''(1), 19–31. [https://onlinelibrary.wiley.com/doi/10.1002/smi.2968 https://doi.org/10.1002/smi.2968]

Martin, C. G., Cromer, L. D., DePrince, A. P., &amp; Freyd, J. J. (2013). The role of cumulative trauma, betrayal, and appraisals in understanding trauma symptomatology. ''Psychological Trauma: Theory, Research, Practice, and Policy'', ''5''(2), 110–118. https://doi.org/10.1037/a0025686

Mitchell, E. A., Brown, K. S., Spencer, J., &amp; Harris, K. (2025). Staying together after infidelity: An exploration of the decision-making process of recovery from the perspective of the injured partner. ''Journal of Marital and Family Therapy'', ''52''(1), e70110. PubMed Central. [https://onlinelibrary.wiley.com/doi/10.1111/jmft.70110 https://doi.org/10.1111/jmft.70110]

Mosley, T. L. (2022). ''Forever imprinted: Understanding the relationship between betrayal trauma within intimate relationships and attachment - ProQuest''. Proquest.Com. https://www.proquest.com/openview/c437e8a57b6e9a35babbdda9171ccee0/1?pq-origsite=gscholar&amp;cbl=18750&amp;diss=y

Pramudito, A. A., &amp; Minza, W. M. (2021). The dynamics of rebuilding trust and trustworthiness in marital relationship post infidelity disclosure. ''Jurnal Psikologi'', ''48''(2), 16. [https://eprints.ukmc.ac.id/6452/5/Published%20-%20The%20Dynamics%20of%20Rebuilding%20Trust%20and%20Trustworthiness%20in%20Marital%20Relationship%20Post%20Infidelity%20Disclosure.pdf https://doi.org/10.22146/jpsi.60974]

Silber, D. (2020). ''Trust again'' (pp. 1–229). Rowman &amp; Littlefield Publishers. https://books.google.com.au/books?hl=en&amp;lr=&amp;id=Yq_uDwAAQBAJ&amp;oi=fnd&amp;pg=PR7&amp;dq=How+can+betrayal+trauma+survivors+develop+trust+in+similar+situations+again%3F&amp;ots=qPVXjqErDK&amp;sig=MZhvi-7EBgNXJXGcfQrj4abtJ60&amp;redir_esc=y#v=onepage&amp;q&amp;f=false

Ward, R. (2026). Serial infidelity and psychological abuse: Diagnostic blind spots in recognising betrayal trauma. ''The International Journal of Psychiatry in Medicine''. [https://journals.sagepub.com/doi/10.1177/00912174261428855 https://doi.org/10.1177/00912174261428855]

Zurbriggen, E. L., &amp; Freyd, J. J. (2004). The link between childhood sexual abuse and risky sexual behavior: The role of dissociative tendencies, information-processing effects, and consensual sex decision mechanisms. In E. L. Zurbriggen &amp; J. J. Freyd, ''From child sexual abuse to adult sexual risk: Trauma, revictimization, and intervention'' (pp. pp. 135–157). https://pages.uoregon.edu/dynamic/jjf/articles/zf2004.pdf

==External links==
[https://www.youtube.com/watch?v=5TUxH2izTGI Infidelity: to stay or go?] (Lucy Beresford, TEDX)

[https://www.youtube.com/watch?v=k8foEEWnsFw How to Rebuild Trust After Infidelity] (Samuel from Affair Recovery)
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      <text bytes="37151" sha1="hhi0year4bg0jh416eg90qh7fkaom86" xml:space="preserve">{{title|Psychedelic treatment of eating disorders:&lt;br&gt;How might psychedelic-assisted therapy influence psychological mechanisms involved in eating disorders?}}
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== Overview ==
{{RoundBoxTop|theme=7}}[[File:Neural network - Midjourney and Grok.png|thumb|'''Figure 1.''' Psychedelics are thought to temporarily disrupt rigid neural communication pathways, promoting more flexible patterns of connectivity across networks involved in mood regulation, fear processing, reward learning, and cognitive adaptability. These changes may support therapeutic shifts in behaviour and emotional processing (Hatzipantelis &amp; Olson, 2025).]]Emma, a 27‑year‑old from Canberra, has lived with an eating disorder for nearly two decades. She describes her problem eating behaviours to have started at school, after being bullied about her appearance. Ever since, they have remained in her life as “a way for me to feel in control”. Although she is aware of the harm caused by restrictive eating and compulsive exercise, she feels trapped in her thought patterns characterised by a preoccupation about food and weight concerns which have become entrenched in her daily life. 

After reading an article describing emerging research suggesting that psychedelics may alter patterns of neural connectivity that shape behaviour (see Figure 1), she expressed interest in pursuing psychedelic‑assisted therapy through a provider accessible to her.

After participating in her first supervised psilocybin‑assisted therapy session, Emma reported experiencing an emotional journey that allowed her to feel “connected to my body for the first time in years”. After 3 months, she has noticed a shift in how she relates to her body, and is finding it easier to actively call into question how she responds to distress with the support of her psychotherapist. 


Her experience raises a central question: What psychological mechanisms could explain these changes?{{RoundBoxBottom|theme=3}}  

This chapter explores how psychedelic‑assisted therapy (PAT) may influence the emotional, cognitive, and neurobiological processes that underpin eating disorders (EDs).   

{{RoundBoxTop|theme=11}}'''Focus questions'''
{{ic|}}Two central questions will be addressed:
* What psychological processes underpin eating disorders, and how do they guide ED behaviour?
* How might psychedelic‑assisted therapy influence these processes to support recovery?
{{ic|}}{{ic|}}{{RoundBoxBottom}}

== Introduction ==
'''Eating Disorders'''  

[[wikipedia:Eating_disorder|Eating disorders]] (EDs) are psychiatric conditions characterised by abnormal eating behaviours that negatively affect physical and mental health. They are associated with chronic illness, disability, reduced quality of life, increased suicide risk, and are highly comorbid with [[wikipedia:Mood_disorder|mood disorders]], [[wikipedia:Post-traumatic_stress_disorder|post-traumatic stress disorder]] (PTSD), [[wikipedia:Obsessive–compulsive_disorder|obsessive-compulsive disorder]] (OCD), and [[wikipedia:Substance_use_disorder|substance use disorders]] (Calder et al., 2023). [[wikipedia:Anorexia|Anorexia nervosa]] (AN) has the highest mortality rate of any psychiatric disorder, while [[wikipedia:Bulimia|bulimia nervosa]] (BN) and [[wikipedia:Binge_eating_disorder|binge‑eating disorder]] (BED) are also highly prevalent types of eating disorders.  

In Australia, the prevalence of EDs is rising, particularly among young people. Approximately 10.46% of the population has experienced an eating disorder at some point, with an estimated economic burden of $84 billion (Hay et al., 2023). Despite decades of research, the pathogenesis of EDs remains incompletely understood (Calder et al., 2023). Current evidence suggests a complex interplay between genetic predisposition, temperament, hormonal dysregulation, cognitive abnormalities, sociocultural pressures, and traumatic experiences.

Although cognitive‑behavioural therapy (CBT‑E) combined with pharmacological treatment has demonstrated beneficial outcomes, efficacy remains limited and varies across ED types (Calder et al., 2023). Recovery is often long and difficult, with only two‑thirds of individuals with AN and BN eventually recovering, while others can remain ill for many years. This highlights the need for treatment approaches that can accelerate recovery and provide benefit for individuals who do not respond to conventional therapies.


'''Psychedelic-Assisted Therapy'''

In 2023, Australia legalised the prescription of MDMA and psilocybin under professional supervision, marking a significant shift in mental‑health treatment options. Psychedelic compounds, including [[wikipedia:LSD|LSD]], [[wikipedia:Psilocybin|psilocybin]], [[wikipedia:Dimethyltryptamine|DMT]], [[wikipedia:Ketamine|ketamine]], and [[wikipedia:MDMA|MDMA]], have demonstrated promising therapeutic effects across a wide range of psychiatric conditions. Researchers propose that psychedelics act through psychological and neural mechanisms that increase [[wikipedia:Neuroplasticity|neuroplasticity]], facilitate insight, and foster emotional acceptance (Peled‑Avron et al., 2024). At a neurobiological level, psychedelics influence processes that inform perception, emotion, and behaviour, offering a potential avenue for addressing entrenched ED mechanisms.

PAT differs from pharmacological treatment alone because the drug is administered within a structured therapeutic context designed to maximise safety and clinical benefit (Calder et al., 2023). Treatment typically involves three types of sessions. Preparatory sessions feature participants undergoing psychoeducation, where the clinician establishes rapport and clear safety protocols. Followed by supervised medication where the participant has an inward experience with the reassurance of clinicians present in the same space. Lastly, integrative sessions where individuals process and explore insights from the previous session with their psychotherapist to foster behavioural change (Wolfgang &amp; Hoge, 2023). This combination of pharmacological and psychological intervention is theorised to effectively target underlying psychological mechanisms common across various mental health disorders, illustrating PAT’s potential as a valuable transdiagnostic treatment option. 

PAT has become a subject of increasing popularity in ED research because many of the psychological mechanisms it is proposed to influence are the same ones implicated in ED maintenance and comorbidities (Calder et al., 2023; Peled-Avron et al., 2024). Early research, including case study reports, small clinical studies, meta-analyses and reviews indicate that PAT produces improvements in affect, reductions in ED symptom severity, enhanced body image, weight restoration, and reductions in comorbid symptoms. Although preliminary, these findings indicate that PAT may disrupt and promote shifts away from maladaptive coping patterns that become entrenched in treatment resistant ED populations.

== Psychological Mechanisms in Eating Disorders ==


'''Emotion Dysregulation'''

Emotion dysregulation is considered to be a significant risk factor for the onset and maintenance of EDs. It refers to difficulties recognising, assessing, and modifying emotional responses to meet situational demands (Zhou et al., 2025). 

Research consistently shows that individuals with EDs experience significant challenges in regulating emotions, increasing their vulnerability to comorbid symptoms, which contribute to the emergence of disordered eating patterns (Leppanen et al., 2022). This idea is supported by affect regulation theory which posits that eating disorders develop and are maintained as maladaptive strategies to manage, tolerate and escape from negative emotions and psychological distress (Schaefer et al., 2020). This is further exemplified in Fitzsimmons &amp; Bardone-Cone’s article examining differences in coping within eating disorder patients (2010). The authors explain that avoidance and emotion-oriented coping styles often function as maladaptive attempts to manage (di)stress. They explain that behaviours such as binge eating, purging, starvation, and/or compulsive exercise provide temporary relief by shifting attention away from uncomfortable emotions. 

Furthermore, alexithymia, characterised by difficulty identifying and describing one’s own emotions, is strongly associated with ED pathology (Shank et al., 2019). Individuals with high alexithymia often struggle to differentiate emotional states from bodily sensations, contributing to behaviours such as emotional eating, eating in the absence of hunger, or rigid restriction. In BED, alexithymia is linked to binge episodes triggered by poorly understood emotional cues, while in AN and BN, alexithymia may contribute to emotional avoidance and reliance on ED behaviours for affect regulation. 

The effects of trauma are contributing factors to emotion dysregulation, and considered a risk factor for ED development. Individuals who experience sexual, physical, or emotional abuse, neglect, and bullying are likely to experience heightened emotional reactivity, threat perception, and avoidance behaviours (Calder et al., 2023). Researchers explain that trauma often results in lowered distress tolerance and increased reliance on maladaptive coping behaviours, including disordered eating. Furthermore, PTSD comorbidity is common, hence trauma‑related symptoms are hypothesised to frequently interact with ED behaviours in complex ways.  


'''Reward Processing Dysfunction'''
[[File:Striatum.gif|thumb|'''Figure 2.''' Striatum]]
[[File:Anterior cingulate gyrus animation.gif|thumb|'''Figure 3'''. Anterior Cingulate Cortex ]]
Abnormal reward valuation is understood to be a central psychological mechanism that maintains ED behaviours. Research consistently shows that individuals with eating disorders display altered neural activity response to various stimuli, as well as disruptions in reinforcement learning (Calder et al., 2023). Brain regions involved in reward processing, habit formation, and learning, such as the striatum and anterior cingulate cortex (see figures 2 &amp; 3), exhibit atypical activation patterns and differences in dopamine receptor binding across ED types. The insula (see figure 4), which integrates bodily sensations with conscious thought, emotion, and behaviour, also shows altered responses. Together, these regions have been shown to react differently to food images, taste, and social feedback compared to healthy controls, indicating that reward dysfunction extends beyond eating‑related stimuli for ED populations.
[[File:Insular cortex.gif|thumb|'''Figure 4.''' Insula. ]]
In the context of BN and BED, research shows that food is valued more highly than other types of rewards, thus shaping behaviour through its heightened influence on reward outcomes (Calder et al., 2023). Compulsive behaviours specific to each condition (e.g. bingeing, purging) are therefore more likely to occur when food is overvalued and alternative rewards are discounted or ignored. In addition to the neural changes already described, BN and BED are associated with reduced structural and functional connectivity between frontal control regions and the striatum. This combination of highly salient food rewards, and weakened fronto‑striatal pathways, reduces an individual’s ability to inhibit or modulate reward‑seeking impulses. Weak connectivity in these circuits is thought to predict compulsive reward‑seeking behaviour. As a result, even when individuals experience negative consequences from binge episodes, they may struggle to learn from these outcomes or adjust their behaviour accordingly.


Anhedonia, a global reduction in reward responsiveness, is frequently reported by people who experience AN, resulting in food and eating becoming undervalued or aversive to them (Calder et al., 2023). Researchers propose that reward contamination further contributes to this pattern, where the brain learns to associate normally punishing stimuli (e.g., starvation, excessive exercise) with reward, while normally rewarding stimuli (e.g., high‑calorie foods) become experienced as punishment. Structural reductions in the striatum and somatosensory cortex have also been observed, which accounts for distorted bodily sensations and contributes to anhedonia. These changes support maladaptive conditioning in which starvation and weight loss embody a sense of safety, achievement, and emotional relief. Restrictive and preoccupied behaviours centred on food, body shape, and exercise are therefore reinforced over time.

Consistent with affect‑regulation models, eating‑disorder behaviours also become negatively reinforced because they reduce emotional discomfort. This relief increases the likelihood that the behaviours will be repeated, further embedding them within the individual’s coping pattern.


'''Cognitive Rigidity'''

Cognitive rigidity refers to inflexible thinking and behavioural patterns, including difficulty adapting to new information and modifying behaviour. Researchers believe that individuals with EDs often exhibit rigid beliefs about food and weight which interact with a need to exert control over negative emotions. This interaction is the proposed process in which compulsive behaviours and obsessive thoughts develop (Calder et al., 2023). In AN, rigidity manifests as strict dietary rules and fear of losing control, while in BN and BED, binge episodes may feel compulsive and uncontrollable.


'''Interoceptive Awareness'''

Interoceptive awareness (IA) refers to the ability to recognise and process internal bodily states such as hunger, satiety, pain, and arousal. IA is impaired across EDs, and contributes to body mistrust, distorted hunger cues, and inappropriate responses to internal sensations (Brown et al., 2020). Individuals may ignore physical discomfort, misinterpret bodily signals, or avoid sensations altogether, reinforcing maladaptive coping.  

 &lt;blockquote&gt;'''''QUIZ: Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{What coping style do people who experience EDs tend to show?
|type=&quot;()&quot;}
+ Avoidance-oriented
- Problem-oriented

{Compulsive behaviours are more likely to occur when food is ... and alternative rewards are ...
|type=&quot;()&quot;}
- undervalued; overvalued
+ overvalued; undervalued
&lt;/quiz&gt;&lt;/blockquote&gt;

== Psychological Mechanisms of Psychedelic-Assisted Therapy ==

PAT is proposed to influence several psychological mechanisms implicated in EDs, particularly those discussed in the previous section. The next part of this chapter aims to examine the theorised therapeutic mechanisms PAT possesses and practical implications for ED treatment.  

'''Emotion Regulation''' 

Emotion dysregulation is a core mechanism implicated in EDs. Affect regulation theory proposes that ED behaviours emerge as maladaptive strategies to escape, reduce, or blunt overwhelming emotional experiences (Schaefer et al., 2020). Restriction, bingeing, purging, and compulsive exercise may temporarily alleviate distress while reinforcing avoidance-oriented coping and limiting opportunities to learn more adaptive ways of responding to difficult emotions. 

Psychedelics often evoke intense emotional experiences that may disrupt habitual avoidance patterns. Researchers propose that, during psychedelic sessions, attempts to suppress or avoid difficult emotions can intensify these experiences, creating conditions in which emotional acceptance becomes a preferred response (Calder et al., 2023). Although this shift does not occur in every individual, experiencing difficult emotions without resorting to ED behaviours may weaken the association between emotional distress and maladaptive coping, particularly when emotional acceptance becomes associated with a more positive or tolerable experience.

The therapeutic value of this process lies in its potential to reshape affective responses. When individuals experience strong emotions without engaging in maladaptive behaviours, they may begin to develop a new approach towards emotional tolerance. Integration sessions can consolidate this learning by helping individuals articulate, differentiate, and reflect on the emotions experienced during dosing. This process may support the development of more adaptive coping strategies, including task-oriented, problem-focused, and socially supported approaches, which are associated with improved ED outcomes (Fitzsimmons &amp; Bardone-Cone, 2010). In this way, PAT may strengthen emotion regulation and reduce reliance on ED behaviours as strategies for managing affect. 

'''Reward Processing''' 

Reward dysfunction may contribute to the maintenance of EDs by reinforcing maladaptive behaviours while diminishing the perceived value of adaptive rewards. Predictive coding provides a useful framework for understanding how PAT might influence these processes. Individuals with EDs may hold rigid beliefs, conceptualised as high-level priors, about themselves in relation to food, body weight, and rewarding behaviours (Calder et al., 2023; Mograbi et al., 2024). These beliefs can influence how experiences are perceived and valued, potentially reinforcing existing behavioural patterns. Psychedelics are proposed to weaken high-level priors, allowing bottom-up sensory information to exert greater influence on perception and the valuation of experiences. 

During psychedelic experiences, individuals frequently report a heightened appreciation of sensory, social, and bodily experiences. This shift may counteract anhedonia and support the revaluation of previously feared or avoided stimuli. The therapeutic opportunity lies in translating these temporary changes in perception and reward into meaningful behavioural change. Integration sessions can explore positive and negative moments experienced during dosing and connect them to concrete goals. An example of this, inspired from Calder et al.’s (2023) review, could be to clarify specific plans to nourish the body due to the participant unpacks having experienced themselves as a decaying skeleton followed by the realisation of the body being a gift. If the period following dosing provides an opportunity for increased neuroplasticity, it may also be particularly conducive to reinforcing adaptive reward learning through behavioural activation with the help of a therapist. 

'''Cognitive Flexibility''' 

Cognitive rigidity is a hallmark of EDs and is characterised by inflexible beliefs about food, weight, body shape, and control. Predictive coding provides a framework for understanding this rigidity, as EDs may involve entrenched priors that resist updating even when confronted with contradictory sensory evidence. Psychedelics are proposed to disrupt these entrenched priors by increasing neural entropy and reducing the dominance of top-down processing (Calder et al., 2023). This temporary loosening of cognitive constraints may allow individuals to consider alternative perspectives and question long-held beliefs. 

Experiences of ego dissolution may further contribute to cognitive flexibility by reducing attachment to rigid self-concepts (Peled-Avron, 2024; Mograbi et al., 2024). When the boundaries of the self become less defined, individuals may find it easier to question identity-related beliefs that sustain ED pathology. Integration sessions can harness this potential flexibility by supporting cognitive reframing, encouraging behavioural experiments, and strengthening metacognitive awareness. Through these processes, individuals may be better able to translate insights gained during psychedelic experiences into sustained changes in thinking and behaviour.


'''Reconnecting with Bodily Signals'''

Interoceptive deficits are central to ED pathology, contributing to body mistrust, distorted perceptions of hunger cues, and difficulties responding appropriately to internal sensations (Brown et al., 2020). Psychedelics may enhance interoceptive awareness by altering sensory processing and increasing sensitivity to bodily signals. This proposed mechanism is closely related to autonomic regulation, for which polyvagal theory provides a framework for understanding the relationship between bodily signals, emotional regulation, and perceived safety.

Polyvagal theory emphasises the role of the vagus nerve in interoception, emotional regulation, and the perception of safety (Porges, 2022). Vagal afferents transmit information from the body to the insula, where interoceptive signals are integrated with emotional and cognitive processes. Individuals with EDs may exhibit chronic sympathetic arousal and reduced vagal tone, potentially impairing interoceptive accuracy and contributing to emotional rigidity. Psychedelics may initially increase sympathetic activity, as reflected in physiological responses such as increased heart rate, followed by a parasympathetic shift associated with greater relaxation and an increased capacity for rest (Hongyuan et al., 2025). Within a polyvagal framework, these changes may have implications for vagal regulation, interoceptive awareness, and emotional regulation.

The therapeutic value of this proposed mechanism lies in its potential to restore trust in bodily signals. Integration sessions may support this process by helping individuals explore bodily sensations experienced during dosing, connect interoceptive cues with emotional states, and practise interoceptive exposure to hunger, fullness, and anxiety-related sensations. Incorporating mindfulness techniques may further support autonomic regulation and help individuals develop a more adaptive relationship with their bodily experiences.

 A Brief Note Concerning The Gut-Brain Interaction 
Although gut microbiome disruption is not a primary psychological mechanism in EDs, it is a relevant biological factor to consider when examining the potential effects of PAT. Restrictive or chaotic eating patterns can contribute to gut dysbiosis, which may weaken gut-barrier integrity and contribute to inflammation affecting the brain. These changes have been shown to influence mood, stress responsivity, cognitive rigidity, and interoceptive awareness through HPA-axis activation, altered neurotransmitter synthesis, and disrupted hunger–satiety signalling (Anton-Paduraru et al., 2024). 

Emerging research suggests that psychedelics may also interact with the gut–brain system. Certain microbes can metabolise psychedelic compounds, and microbial activity has been associated with modulatory effects on behavioural outcomes. Additionally, psychedelic use may alter microbial composition towards anti-inflammatory profiles, with potential implications for neuroplasticity, neurotransmitter synthesis and signalling improvements (Caspani et al., 2024). These microbiome-related effects may therefore contribute to changes in mood, cognitive flexibility, and appetite regulation.

Although the therapeutic potential of psychedelics in EDs is considered primarily in relation to psychological mechanisms, including changes in perception, emotional processing, and reduced avoidance, microbiome-related effects may represent an additional pathway through which biological processes influence psychological outcomes. However, the extent to which these interactions contribute to therapeutic outcomes in EDs remains to be established.


&lt;blockquote&gt;'''QUIZ: ''Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{ In predictive coding terms, what are “high‑level priors” in eating disorders? 
|type=&quot;()&quot;}
+ Rigid, entrenched beliefs about food, weight, and the self that shape perception and behaviour
- Flexible beliefs that easily update with new sensory information
- Momentary emotional reactions triggered by external cues

{What is the proposed mechanism by which psychedelics support emotion regulation in PAT for EDs? 
|type=&quot;()&quot;}
- By suppressing emotional intensity to prevent distress
+ By evoking strong emotions that disrupt avoidance patterns and promote emotional acceptance
- By eliminating negative emotions through serotonin release

{What is interoceptive awareness?
|type=&quot;()&quot;}
- The ability to evaluate reward value and anticipate pleasurable outcomes
+ The capacity to sense, interpret, and respond to internal bodily signals such as hunger, fullness, and emotional arousal
- The process of weakening cognitive rigidity through ego dissolution
&lt;/quiz&gt;&lt;/blockquote&gt;

== Limitations ==
Despite the potential of PAT to influence psychological mechanisms implicated in EDs, several limitations constrain current understanding of these processes and their therapeutic relevance. Research examining emotion dysregulation in EDs illustrates broader challenges in establishing the mechanisms underlying these conditions. Although non-acceptance of emotions has been identified as a transdiagnostic risk factor across psychiatric conditions (Paulus et al., 2021), Zhou et al.’s meta-analysis (2025) highlights that the causal pathways linking emotional dysregulation and EDs remain unclear, largely because of a lack of experimental and longitudinal studies. Further limitations include restricted availability of measurement scales, insufficient cultural specificity, heterogeneity across samples, gender imbalance, and limited developmental analysis. Together, these factors constrain understanding of how specific emotional processes relate to different ED presentations across the lifespan and stages of recovery.

These limitations are also relevant when considering the proposed mechanisms of PAT. Although existing theoretical frameworks offer ways to conceptualise how psychedelic experiences may influence psychological processes responsible for EDs, the emerging nature of psychedelic therapy limits the extent to which proposed mechanisms have been tested. However, with the number of clinical trials increasing as of recently, it will be interesting to see how the theorised therapeutic mechanisms across different ED presentations and stages of recovery emerges during further warranted investigation.

Nevertheless, current limitations in the evidence highlight the need for research that clarifies the relationships between psychological processes that underscore ED behaviours, and treatment outcomes. There are several important psychological components of ED maintenance that represent meaningful targets for treatment, but they should not be considered in isolation from eachother or the neurobiological processes that influence them. A more comprehensive understanding of how these mechanisms interact may help clarify the therapeutic potential of PAT and inform the development of more targeted treatment approaches.

== Conclusion ==
PAT offers a potential framework for addressing several interconnected psychological mechanisms implicated in EDs. Through its proposed effects on emotional processing, reward valuation, cognitive flexibility, and interoceptive awareness, PAT may create opportunities to disrupt established patterns of avoidance, rigid thinking, and maladaptive behavioural reinforcement. The gut–brain interaction may represent an additional biological pathway relevant to these processes.

These mechanisms should not be understood as independent processes. Changes in emotion regulation may influence the ability to tolerate bodily sensations, while shifts in reward valuation and cognitive flexibility may create opportunities to respond differently to distress and challenge entrenched beliefs. However, the extent to which PAT produces these changes, and whether they translate into sustained improvements in ED outcomes, requires further investigation, although preliminary evidence is promising. 

The therapeutic potential of PAT lies not only in the acute psychedelic experience but also in the structured integration process that follows. Integration sessions provide an opportunity to translate emotional breakthroughs, changes in cognitive flexibility, interoceptive shifts, and reward processing into sustained behavioural change. Effective integration involves helping individuals articulate insights, connect them to ED-related patterns, and develop concrete strategies for change. These may include strengthening adaptive coping, challenging rigid beliefs, practising interoceptive awareness, reinforcing positive reward experiences, and supporting nutritional rehabilitation.

By grounding the understanding of PAT in affect regulation theory and the predictive coding framework, therapists may be better positioned to help individuals explore how psychedelic experiences could disrupt maladaptive emotional and cognitive patterns and create opportunities for new learning. Polyvagal-informed approaches may further support the development of mind–body awareness and emotional regulation through mindfulness strategies. Together, these approaches offer a multifaceted framework for translating psychedelic experiences into therapeutic change and addressing the interconnected mechanisms that maintain EDs and associated suffering. 

==See Also==
* [https://w.wiki/TsdG Ayahuasca and the brain] (Wikiversity)
* [https://w.wiki/TscF Emotional effects of psychedelics] (Wikiversity)
* [https://w.wiki/Tsdb Psilocybin and emotion] (Wikiversity)
* [https://w.wiki/TsdS Psilocibyn assisted psychotherapy] (Wikiversity)
* [https://w.wiki/Tsce Psychedelics, altered consciousness, and personal growth] (Wikiversity)
* [[Eating Disorders|Eating disorders]] (Wikiversity)

==References==
{{Hanging indent|1=

(I can't figure out how to italisice this section yet!) {{ic|Try &quot;Edit source&quot; and then wrapping any text to be italicised in two apostrophes e.g., ''this is italics''}}

Abdoli, M., Schiechtl, E., Rosato, M. S., Mangweth-Matzek, B., Cotrufo, P., &amp; Hüfner, K. (2025). Body image, self-esteem, emotion regulation, and eating disorders in adults: a systematic review. Körperbild, Selbstwert, Emotionsregulation und Essstörungen bei Erwachsenen: eine systematische Übersicht. Neuropsychiatrie : Klinik, Diagnostik, Therapie und Rehabilitation : Organ der Gesellschaft Osterreichischer Nervenarzte und Psychiater, 39(3), 118–132. https://doi.org/10.1007/s40211-025-00544-4

Brown, T. A., Vanzhula, I. A., Reilly, E. E., Levinson, C. A., Berner, L. A., Krueger, A., Lavender, J. M., Kaye, W. H., &amp; Wierenga, C. E. (2020). Body mistrust bridges interoceptive awareness and eating disorder symptoms. Journal of abnormal psychology, 129(5), 445–456. https://doi.org/10.1037/abn0000516

Burr, E. K., Dvorak, R. D., De Leon, A. N., Leary, A. V., Peterson, R., Schaefer, L. M., &amp; Wonderlich, S. A. (2023). The role of eating expectancies and eating motives in the association between mood and loss-of-control eating: A national sample daily diary study. Appetite, 180, 106322. https://doi.org/10.1016/j.appet.2022.106322

Frank, G. K. W., DeGuzman, M. C., &amp; Shott, M. E. (2019). Motivation to eat and not to eat - The psycho-biological conflict in anorexia nervosa. Physiology &amp; behavior, 206, 185–190. https://doi.org/10.1016/j.physbeh.2019.04.007

Henderson, Z. B., Fox, J. R. E., Trayner, P., &amp; Wittkowski, A. (2019). Emotional development in eating disorders: A qualitative metasynthesis. Clinical psychology &amp; psychotherapy, 26(4), 440–457. https://doi.org/10.1002/cpp.2365

Lavender, J. M., Wonderlich, S. A., Engel, S. G., Gordon, K. H., Kaye, W. H., &amp; Mitchell, J. E. (2015). Dimensions of emotion dysregulation in anorexia nervosa and bulimia nervosa: A conceptual review of the empirical literature. Clinical psychology review, 40, 111–122. https://doi.org/10.1016/j.cpr.2015.05.010

Leppanen, J., Brown, D., McLinden, H., Williams, S., &amp; Tchanturia, K. (2022). The Role of Emotion Regulation in Eating Disorders: A Network Meta-Analysis Approach. Frontiers in psychiatry, 13, 793094. https://doi.org/10.3389/fpsyt.2022.793094

Marano G, Lanzetta M, Scialpi C, Sottile A, Giacomi OD, Brisi C, Traversi G, Mazza O, Capristo E, Sani G, et al. Disordered Minds, Disordered Meals: When Emotions Masquerade as Hunger in Eating Disorders—A Systematic Review. Nutrients. 2026; 18(9):1350. https://doi.org/10.3390/nu18091350

Monteleone, A. M., Pellegrino, F., Croatto, G., Carfagno, M., Hilbert, A., Treasure, J., Wade, T., Bulik, C. M., Zipfel, S., Hay, P., Schmidt, U., Castellini, G., Favaro, A., Fernandez-Aranda, F., Il Shin, J., Voderholzer, U., Ricca, V., Moretti, D., Busatta, D., Abbate-Daga, G., … Solmi, M. (2022). Treatment of eating disorders: A systematic meta-review of meta-analyses and network meta-analyses. Neuroscience and biobehavioral reviews, 142, 104857. https://doi.org/10.1016/j.neubiorev.2022.104857

Murphy, R., Straebler, S., Cooper, Z., &amp; Fairburn, C. G. (2010). Cognitive behavioral therapy for eating disorders. The Psychiatric clinics of North America, 33(3), 611–627. https://doi.org/10.1016/j.psc.2010.04.004

Nasini, S., Casile, A., Bonaldo, B., Mancini, C., Guzzo, S. M., Botticelli, L., &amp; Comai, S. (2025). The role of motivation in eating disorders: understanding sex differences in the circuits. Frontiers in behavioral neuroscience, 19, 1644383. https://doi.org/10.3389/fnbeh.2025.1644383

Norman, G. J., Berntson, G. G., &amp; Cacioppo, J. T. (2014). Emotion, somatovisceral afference, and autonomic regulation. Emotion Review, 6(2), 113–123. https://doi.org/10.1177/1754073913512006

Prefit, A. B., Cândea, D. M., &amp; Szentagotai-Tătar, A. (2019). Emotion regulation across eating pathology: A meta-analysis. Appetite, 143, 104438. https://doi.org/10.1016/j.appet.2019.104438

Reichenberger, J., Schnepper, R., Arend, A. K., &amp; Blechert, J. (2020). Emotional eating in healthy individuals and patients with an eating disorder: evidence from psychometric, experimental and naturalistic studies. The Proceedings of the Nutrition Society, 79(3), 290–299. https://doi.org/10.1017/S0029665120007004

Salias, C., Gross, J. J., Petrova, K., Forbush, K. T., &amp; Preece, D. A. (2025). Eating disorder symptoms and profiles of emotion regulation strategy use. Journal of affective disorders, 380, 94–103. https://doi.org/10.1016/j.jad.2025.03.050

Schaefer, L. M., Forester, G., Burr, E. K., Laam, L., Crosby, R. D., Peterson, C. B., Crow, S. J., Engel, S. G., Dvorak, R. D., &amp; Wonderlich, S. A. (2023). Examining the role of craving in affect regulation models of binge eating: Evidence from an ecological momentary assessment study. Journal of psychopathology and clinical science, 132(6), 725–732. https://doi.org/10.1037/abn0000839

Selby, E. A., Cornelius, T., Fehling, K. B., Kranzler, A., Panza, E. A., Lavender, J. M., Wonderlich, S. A., Crosby, R. D., Engel, S. G., Mitchell, J. E., Crow, S. J., Peterson, C. B., &amp; Le Grange, D. (2015). A perfect storm: examining the synergistic effects of negative and positive emotional instability on promoting weight loss activities in anorexia nervosa. Frontiers in psychology, 6, 1260. https://doi.org/10.3389/fpsyg.2015.01260

Tabuenca, K., Crowe, D. E., Gillis, A. J., Kabiling, C., Saccacio, B., Velkova, A. V., &amp; Murray, S. B. (2025). Updates in the treatment of eating disorders in 2024: a year in review in Eating Disorders: The Journal of Treatment &amp; Prevention. Eating Disorders, 33(4), 434–450. https://doi.org/10.1080/10640266.2025.2497750

Wong, V. Z., Koithan, E. M., Santos, B. M., Johnson, A., &amp; Haynos, A. F. (2025). Does Evidence Support an Emotion Regulation Model of Anorexia Nervosa? A Systematic Review of Over a Decade of Research. Clinical psychology : a publication of the Division of Clinical Psychology of the American Psychological Association, 32(1), 1–17. https://doi.org/10.1037/cps0000244

}}

==External links==
* [https://www.abct.org/fact-sheets/psychedelic-assisted-therapy/ Psychedelic-Assisted Therapy | Fact Sheet] (ABCT - Association for Behavioral and Cognitive Therapies)
* [https://podcasts.apple.com/au/podcast/can-magic-mushrooms-help-treat-anorexia/id189330872?i=1000784809236 Can magic mushrooms help treat anorexia?] (Apple Podcasts)
* [https://www.apa.org/news/podcasts/speaking-of-psychology/eating-disorder The ‘silent epidemic’ of eating disorders] (American Psychological Association)
* [https://www.apa.org/monitor/2023/04/sensations-eating-disorders-suicidal-behavior What is interoception, and how does it affect mental health]? 5 questions for April Smith (American Psychological Association)
* [https://www.cbte.co/what-is-cbte/transdiagnostic-view-eating-disorders/ Transdiagnostic view of eating disorders] (cbte.co)
* [https://psychedelic.support/resources/polyvagal-theory-mind-body-dr-erica-zelfand/ Polyvagal Theory with Dr. Erica Zelfand: Mind-Body Connection] ·(Psychedelic Support)
* [https://www.wholeselfnutrition.org/post/nervous-system-regulation-a-missing-piece-in-eating-disorder-recovery Nervous System Regulation: A Missing Piece in Eating Disorder Recovery]  (wholeselfnutrition.org)

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      <text bytes="37158" sha1="qv6h50vw0lywmhk7u71xtbi1srdyill" xml:space="preserve">{{title|Psychedelic treatment of eating disorders:&lt;br&gt;How might psychedelic-assisted therapy influence psychological mechanisms involved in eating disorders?}}
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== Overview ==
{{RoundBoxTop|theme=7}}[[File:Neural network - Midjourney and Grok.png|thumb|'''Figure 1.''' Psychedelics are thought to temporarily disrupt rigid neural communication pathways, promoting more flexible patterns of connectivity across networks involved in mood regulation, fear processing, reward learning, and cognitive adaptability. These changes may support therapeutic shifts in behaviour and emotional processing (Hatzipantelis &amp; Olson, 2025).]]Emma, a 27‑year‑old from Canberra, has lived with an eating disorder for nearly two decades. She describes her problem eating behaviours to have started at school, after being bullied about her appearance. Ever since, they have remained in her life as “a way for me to feel in control”. Although she is aware of the harm caused by restrictive eating and compulsive exercise, she feels trapped in her thought patterns characterised by a preoccupation about food and weight concerns which have become entrenched in her daily life. 

After reading an article describing emerging research suggesting that psychedelics may alter patterns of neural connectivity that shape behaviour (see Figure 1), she expressed interest in pursuing psychedelic‑assisted therapy through a provider accessible to her.

After participating in her first supervised psilocybin‑assisted therapy session, Emma reported experiencing an emotional journey that allowed her to feel “connected to my body for the first time in years”. After 3 months, she has noticed a shift in how she relates to her body, and is finding it easier to actively call into question how she responds to distress with the support of her psychotherapist. 


Her experience raises a central question: What psychological mechanisms could explain these changes?{{RoundBoxBottom|theme=3}}  

This chapter explores how psychedelic‑assisted therapy (PAT) may influence the emotional, cognitive, and neurobiological processes that underpin eating disorders (EDs).   

{{RoundBoxTop|theme=11}}'''Focus questions'''
{{ic|}}Two central questions will be addressed:
* What psychological processes underpin eating disorders, and how do they guide ED behaviour?
* How might psychedelic‑assisted therapy influence these processes to support recovery?
{{ic|}}{{ic|}}{{RoundBoxBottom}}

== Introduction ==
'''Eating Disorders'''  

[[wikipedia:Eating_disorder|Eating disorders]] (EDs) are psychiatric conditions characterised by abnormal eating behaviours that negatively affect physical and mental health. They are associated with chronic illness, disability, reduced quality of life, increased suicide risk, and are highly comorbid with [[wikipedia:Mood_disorder|mood disorders]], [[wikipedia:Post-traumatic_stress_disorder|post-traumatic stress disorder]] (PTSD), [[wikipedia:Obsessive–compulsive_disorder|obsessive-compulsive disorder]] (OCD), and [[wikipedia:Substance_use_disorder|substance use disorders]] (Calder et al., 2023). [[wikipedia:Anorexia|Anorexia nervosa]] (AN) has the highest mortality rate of any psychiatric disorder, while [[wikipedia:Bulimia|bulimia nervosa]] (BN) and [[wikipedia:Binge_eating_disorder|binge‑eating disorder]] (BED) are also highly prevalent types of eating disorders.  

In Australia, the prevalence of EDs is rising, particularly among young people. Approximately 10.46% of the population has experienced an eating disorder at some point, with an estimated economic burden of $84 billion (Hay et al., 2023). Despite decades of research, the pathogenesis of EDs remains incompletely understood (Calder et al., 2023). Current evidence suggests a complex interplay between genetic predisposition, temperament, hormonal dysregulation, cognitive abnormalities, sociocultural pressures, and traumatic experiences.

Although cognitive‑behavioural therapy (CBT‑E) combined with pharmacological treatment has demonstrated beneficial outcomes, efficacy remains limited and varies across ED types (Calder et al., 2023). Recovery is often long and difficult, with only two‑thirds of individuals with AN and BN eventually recovering, while others can remain ill for many years. This highlights the need for treatment approaches that can accelerate recovery and provide benefit for individuals who do not respond to conventional therapies.


'''Psychedelic-Assisted Therapy'''

In 2023, Australia legalised the prescription of MDMA and psilocybin under professional supervision, marking a significant shift in mental‑health treatment options. Psychedelic compounds, including [[wikipedia:LSD|LSD]], [[wikipedia:Psilocybin|psilocybin]], [[wikipedia:Dimethyltryptamine|DMT]], [[wikipedia:Ketamine|ketamine]], and [[wikipedia:MDMA|MDMA]], have demonstrated promising therapeutic effects across a wide range of psychiatric conditions. Researchers propose that psychedelics act through psychological and neural mechanisms that increase [[wikipedia:Neuroplasticity|neuroplasticity]], facilitate insight, and foster emotional acceptance (Peled‑Avron et al., 2024). At a neurobiological level, psychedelics influence processes that inform perception, emotion, and behaviour, offering a potential avenue for addressing entrenched ED mechanisms.

PAT differs from pharmacological treatment alone because the drug is administered within a structured therapeutic context designed to maximise safety and clinical benefit (Calder et al., 2023). Treatment typically involves three types of sessions. Preparatory sessions feature participants undergoing psychoeducation, where the clinician establishes rapport and clear safety protocols. Followed by supervised medication where the participant has an inward experience with the reassurance of clinicians present in the same space. Lastly, integrative sessions where individuals process and explore insights from the previous session with their psychotherapist to foster behavioural change (Wolfgang &amp; Hoge, 2023). This combination of pharmacological and psychological intervention is theorised to effectively target underlying psychological mechanisms common across various mental health disorders, illustrating PAT’s potential as a valuable transdiagnostic treatment option. 

PAT has become a subject of increasing popularity in ED research because many of the psychological mechanisms it is proposed to influence are the same ones implicated in ED maintenance and comorbidities (Calder et al., 2023; Peled-Avron et al., 2024). Early research, including case study reports, small clinical studies, meta-analyses and reviews indicate that PAT produces improvements in affect, reductions in ED symptom severity, enhanced body image, weight restoration, and reductions in comorbid symptoms. Although preliminary, these findings indicate that PAT may disrupt and promote shifts away from maladaptive coping patterns that become entrenched in treatment resistant ED populations.

== Psychological Mechanisms in Eating Disorders ==


'''Emotion Dysregulation'''

Emotion dysregulation is considered to be a significant risk factor for the onset and maintenance of EDs. It refers to difficulties recognising, assessing, and modifying emotional responses to meet situational demands (Zhou et al., 2025). 

Research consistently shows that individuals with EDs experience significant challenges in regulating emotions, increasing their vulnerability to comorbid symptoms, which contribute to the emergence of disordered eating patterns (Leppanen et al., 2022). This idea is supported by affect regulation theory which posits that eating disorders develop and are maintained as maladaptive strategies to manage, tolerate and escape from negative emotions and psychological distress (Schaefer et al., 2020). This is further exemplified in Fitzsimmons &amp; Bardone-Cone’s article examining differences in coping within eating disorder patients (2010). The authors explain that avoidance and emotion-oriented coping styles often function as maladaptive attempts to manage (di)stress. They explain that behaviours such as binge eating, purging, starvation, and/or compulsive exercise provide temporary relief by shifting attention away from uncomfortable emotions. 

Furthermore, alexithymia, characterised by difficulty identifying and describing one’s own emotions, is strongly associated with ED pathology (Shank et al., 2019). Individuals with high alexithymia often struggle to differentiate emotional states from bodily sensations, contributing to behaviours such as emotional eating, eating in the absence of hunger, or rigid restriction. In BED, alexithymia is linked to binge episodes triggered by poorly understood emotional cues, while in AN and BN, alexithymia may contribute to emotional avoidance and reliance on ED behaviours for affect regulation. 

The effects of trauma are contributing factors to emotion dysregulation, and considered a risk factor for ED development. Individuals who experience sexual, physical, or emotional abuse, neglect, and bullying are likely to experience heightened emotional reactivity, threat perception, and avoidance behaviours (Calder et al., 2023). Researchers explain that trauma often results in lowered distress tolerance and increased reliance on maladaptive coping behaviours, including disordered eating. Furthermore, PTSD comorbidity is common, hence trauma‑related symptoms are hypothesised to frequently interact with ED behaviours in complex ways.  


'''Reward Processing Dysfunction'''
[[File:Striatum.gif|thumb|'''Figure 2.''' Striatum]]
[[File:Anterior cingulate gyrus animation.gif|thumb|'''Figure 3'''. Anterior Cingulate Cortex ]]
Abnormal reward valuation is understood to be a central psychological mechanism that maintains ED behaviours. Research consistently shows that individuals with eating disorders display altered neural activity response to various stimuli, as well as disruptions in reinforcement learning (Calder et al., 2023). Brain regions involved in reward processing, habit formation, and learning, such as the striatum and anterior cingulate cortex (see figures 2 &amp; 3), exhibit atypical activation patterns and differences in dopamine receptor binding across ED types. The insula (see figure 4), which integrates bodily sensations with conscious thought, emotion, and behaviour, also shows altered responses. Together, these regions have been shown to react differently to food images, taste, and social feedback compared to healthy controls, indicating that reward dysfunction extends beyond eating‑related stimuli for ED populations.
[[File:Insular cortex.gif|thumb|'''Figure 4.''' Insula. ]]
In the context of BN and BED, research shows that food is valued more highly than other types of rewards, thus shaping behaviour through its heightened influence on reward outcomes (Calder et al., 2023). Compulsive behaviours specific to each condition (e.g. bingeing, purging) are therefore more likely to occur when food is overvalued and alternative rewards are discounted or ignored. In addition to the neural changes already described, BN and BED are associated with reduced structural and functional connectivity between frontal control regions and the striatum. This combination of highly salient food rewards, and weakened fronto‑striatal pathways, reduces an individual’s ability to inhibit or modulate reward‑seeking impulses. Weak connectivity in these circuits is thought to predict compulsive reward‑seeking behaviour. As a result, even when individuals experience negative consequences from binge episodes, they may struggle to learn from these outcomes or adjust their behaviour accordingly.


Anhedonia, a global reduction in reward responsiveness, is frequently reported by people who experience AN, resulting in food and eating becoming undervalued or aversive to them (Calder et al., 2023). Researchers propose that reward contamination further contributes to this pattern, where the brain learns to associate normally punishing stimuli (e.g., starvation, excessive exercise) with reward, while normally rewarding stimuli (e.g., high‑calorie foods) become experienced as punishment. Structural reductions in the striatum and somatosensory cortex have also been observed, which accounts for distorted bodily sensations and contributes to anhedonia. These changes support maladaptive conditioning in which starvation and weight loss embody a sense of safety, achievement, and emotional relief. Restrictive and preoccupied behaviours centred on food, body shape, and exercise are therefore reinforced over time.

Consistent with affect‑regulation models, eating‑disorder behaviours also become negatively reinforced because they reduce emotional discomfort. This relief increases the likelihood that the behaviours will be repeated, further embedding them within the individual’s coping pattern.


'''Cognitive Rigidity'''

Cognitive rigidity refers to inflexible thinking and behavioural patterns, including difficulty adapting to new information and modifying behaviour. Researchers believe that individuals with EDs often exhibit rigid beliefs about food and weight which interact with a need to exert control over negative emotions. This interaction is the proposed process in which compulsive behaviours and obsessive thoughts develop (Calder et al., 2023). In AN, rigidity manifests as strict dietary rules and fear of losing control, while in BN and BED, binge episodes may feel compulsive and uncontrollable.


'''Interoceptive Awareness'''

Interoceptive awareness (IA) refers to the ability to recognise and process internal bodily states such as hunger, satiety, pain, and arousal. IA is impaired across EDs, and contributes to body mistrust, distorted hunger cues, and inappropriate responses to internal sensations (Brown et al., 2020). Individuals may ignore physical discomfort, misinterpret bodily signals, or avoid sensations altogether, reinforcing maladaptive coping.      

 &lt;blockquote&gt;'''''QUIZ: Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{What coping style do people who experience EDs tend to show?
|type=&quot;()&quot;}
+ Avoidance-oriented
- Problem-oriented

{Compulsive behaviours are more likely to occur when food is ... and alternative rewards are ...
|type=&quot;()&quot;}
- undervalued; overvalued
+ overvalued; undervalued
&lt;/quiz&gt;&lt;/blockquote&gt;

== Psychological Mechanisms of Psychedelic-Assisted Therapy ==

PAT is proposed to influence several psychological mechanisms implicated in EDs, particularly those discussed in the previous section. The next part of this chapter aims to examine the theorised therapeutic mechanisms PAT possesses and practical implications for ED treatment.  


'''Emotion Regulation''' 

Emotion dysregulation is a core mechanism implicated in EDs. Affect regulation theory proposes that ED behaviours emerge as maladaptive strategies to escape, reduce, or blunt overwhelming emotional experiences (Schaefer et al., 2020). Restriction, bingeing, purging, and compulsive exercise may temporarily alleviate distress while reinforcing avoidance-oriented coping and limiting opportunities to learn more adaptive ways of responding to difficult emotions. 

Psychedelics often evoke intense emotional experiences that may disrupt habitual avoidance patterns. Researchers propose that, during psychedelic sessions, attempts to suppress or avoid difficult emotions can intensify these experiences, creating conditions in which emotional acceptance becomes a preferred response (Calder et al., 2023). Although this shift does not occur in every individual, experiencing difficult emotions without resorting to ED behaviours may weaken the association between emotional distress and maladaptive coping, particularly when emotional acceptance becomes associated with a more positive or tolerable experience.

The therapeutic value of this process lies in its potential to reshape affective responses. When individuals experience strong emotions without engaging in maladaptive behaviours, they may begin to develop a new approach towards emotional tolerance. Integration sessions can consolidate this learning by helping individuals articulate, differentiate, and reflect on the emotions experienced during dosing. This process may support the development of more adaptive coping strategies, including task-oriented, problem-focused, and socially supported approaches, which are associated with improved ED outcomes (Fitzsimmons &amp; Bardone-Cone, 2010). In this way, PAT may strengthen emotion regulation and reduce reliance on ED behaviours as strategies for managing affect. 


'''Reward Processing''' 

Reward dysfunction may contribute to the maintenance of EDs by reinforcing maladaptive behaviours while diminishing the perceived value of adaptive rewards. Predictive coding provides a useful framework for understanding how PAT might influence these processes. Individuals with EDs may hold rigid beliefs, conceptualised as high-level priors, about themselves in relation to food, body weight, and rewarding behaviours (Calder et al., 2023; Mograbi et al., 2024). These beliefs can influence how experiences are perceived and valued, potentially reinforcing existing behavioural patterns. Psychedelics are proposed to weaken high-level priors, allowing bottom-up sensory information to exert greater influence on perception and the valuation of experiences. 

During psychedelic experiences, individuals frequently report a heightened appreciation of sensory, social, and bodily experiences. This shift may counteract anhedonia and support the revaluation of previously feared or avoided stimuli. The therapeutic opportunity lies in translating these temporary changes in perception and reward into meaningful behavioural change. Integration sessions can explore positive and negative moments experienced during dosing and connect them to concrete goals. An example of this, inspired from Calder et al.’s (2023) review, could be to clarify specific plans to nourish the body due to the participant unpacks having experienced themselves as a decaying skeleton followed by the realisation of the body being a gift. If the period following dosing provides an opportunity for increased neuroplasticity, it may also be particularly conducive to reinforcing adaptive reward learning through behavioural activation with the help of a therapist. 


'''Cognitive Flexibility''' 

Cognitive rigidity is a hallmark of EDs and is characterised by inflexible beliefs about food, weight, body shape, and control. Predictive coding provides a framework for understanding this rigidity, as EDs may involve entrenched priors that resist updating even when confronted with contradictory sensory evidence. Psychedelics are proposed to disrupt these entrenched priors by increasing neural entropy and reducing the dominance of top-down processing (Calder et al., 2023). This temporary loosening of cognitive constraints may allow individuals to consider alternative perspectives and question long-held beliefs. 

Experiences of ego dissolution may further contribute to cognitive flexibility by reducing attachment to rigid self-concepts (Peled-Avron, 2024; Mograbi et al., 2024). When the boundaries of the self become less defined, individuals may find it easier to question identity-related beliefs that sustain ED pathology. Integration sessions can harness this potential flexibility by supporting cognitive reframing, encouraging behavioural experiments, and strengthening metacognitive awareness. Through these processes, individuals may be better able to translate insights gained during psychedelic experiences into sustained changes in thinking and behaviour.


'''Reconnecting with Bodily Signals'''

Interoceptive deficits are central to ED pathology, contributing to body mistrust, distorted perceptions of hunger cues, and difficulties responding appropriately to internal sensations (Brown et al., 2020). Psychedelics may enhance interoceptive awareness by altering sensory processing and increasing sensitivity to bodily signals. This proposed mechanism is closely related to autonomic regulation, for which polyvagal theory provides a framework for understanding the relationship between bodily signals, emotional regulation, and perceived safety.

Polyvagal theory emphasises the role of the vagus nerve in interoception, emotional regulation, and the perception of safety (Porges, 2022). Vagal afferents transmit information from the body to the insula, where interoceptive signals are integrated with emotional and cognitive processes. Individuals with EDs may exhibit chronic sympathetic arousal and reduced vagal tone, potentially impairing interoceptive accuracy and contributing to emotional rigidity. Psychedelics may initially increase sympathetic activity, as reflected in physiological responses such as increased heart rate, followed by a parasympathetic shift associated with greater relaxation and an increased capacity for rest (Hongyuan et al., 2025). Within a polyvagal framework, these changes may have implications for vagal regulation, interoceptive awareness, and emotional regulation.

The therapeutic value of this proposed mechanism lies in its potential to restore trust in bodily signals. Integration sessions may support this process by helping individuals explore bodily sensations experienced during dosing, connect interoceptive cues with emotional states, and practise interoceptive exposure to hunger, fullness, and anxiety-related sensations. Incorporating mindfulness techniques may further support autonomic regulation and help individuals develop a more adaptive relationship with their bodily experiences.

 A Brief Note Concerning The Gut-Brain Interaction 
Although gut microbiome disruption is not a primary psychological mechanism in EDs, it is a relevant biological factor to consider when examining the potential effects of PAT. Restrictive or chaotic eating patterns can contribute to gut dysbiosis, which may weaken gut-barrier integrity and contribute to inflammation affecting the brain. These changes have been shown to influence mood, stress responsivity, cognitive rigidity, and interoceptive awareness through HPA-axis activation, altered neurotransmitter synthesis, and disrupted hunger–satiety signalling (Anton-Paduraru et al., 2024). 

Emerging research suggests that psychedelics may also interact with the gut–brain system. Certain microbes can metabolise psychedelic compounds, and microbial activity has been associated with modulatory effects on behavioural outcomes. Additionally, psychedelic use may alter microbial composition towards anti-inflammatory profiles, with potential implications for neuroplasticity, neurotransmitter synthesis and signalling improvements (Caspani et al., 2024). These microbiome-related effects may therefore contribute to changes in mood, cognitive flexibility, and appetite regulation.

Although the therapeutic potential of psychedelics in EDs is considered primarily in relation to psychological mechanisms, including changes in perception, emotional processing, and reduced avoidance, microbiome-related effects may represent an additional pathway through which biological processes influence psychological outcomes. However, the extent to which these interactions contribute to therapeutic outcomes in EDs remains to be established.


&lt;blockquote&gt;'''QUIZ: ''Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{ In predictive coding terms, what are “high‑level priors” in eating disorders? 
|type=&quot;()&quot;}
+ Rigid, entrenched beliefs about food, weight, and the self that shape perception and behaviour
- Flexible beliefs that easily update with new sensory information
- Momentary emotional reactions triggered by external cues

{What is the proposed mechanism by which psychedelics support emotion regulation in PAT for EDs? 
|type=&quot;()&quot;}
- By suppressing emotional intensity to prevent distress
+ By evoking strong emotions that disrupt avoidance patterns and promote emotional acceptance
- By eliminating negative emotions through serotonin release

{What is interoceptive awareness?
|type=&quot;()&quot;}
- The ability to evaluate reward value and anticipate pleasurable outcomes
+ The capacity to sense, interpret, and respond to internal bodily signals such as hunger, fullness, and emotional arousal
- The process of weakening cognitive rigidity through ego dissolution
&lt;/quiz&gt;&lt;/blockquote&gt;

== Limitations ==
Despite the potential of PAT to influence psychological mechanisms implicated in EDs, several limitations constrain current understanding of these processes and their therapeutic relevance. Research examining emotion dysregulation in EDs illustrates broader challenges in establishing the mechanisms underlying these conditions. Although non-acceptance of emotions has been identified as a transdiagnostic risk factor across psychiatric conditions (Paulus et al., 2021), Zhou et al.’s meta-analysis (2025) highlights that the causal pathways linking emotional dysregulation and EDs remain unclear, largely because of a lack of experimental and longitudinal studies. Further limitations include restricted availability of measurement scales, insufficient cultural specificity, heterogeneity across samples, gender imbalance, and limited developmental analysis. Together, these factors constrain understanding of how specific emotional processes relate to different ED presentations across the lifespan and stages of recovery.

These limitations are also relevant when considering the proposed mechanisms of PAT. Although existing theoretical frameworks offer ways to conceptualise how psychedelic experiences may influence psychological processes responsible for EDs, the emerging nature of psychedelic therapy limits the extent to which proposed mechanisms have been tested. However, with the number of clinical trials increasing as of recently, it will be interesting to see how the theorised therapeutic mechanisms across different ED presentations and stages of recovery emerges during further warranted investigation.

Nevertheless, current limitations in the evidence highlight the need for research that clarifies the relationships between psychological processes that underscore ED behaviours, and treatment outcomes. There are several important psychological components of ED maintenance that represent meaningful targets for treatment, but they should not be considered in isolation from eachother or the neurobiological processes that influence them. A more comprehensive understanding of how these mechanisms interact may help clarify the therapeutic potential of PAT and inform the development of more targeted treatment approaches.

== Conclusion ==
PAT offers a potential framework for addressing several interconnected psychological mechanisms implicated in EDs. Through its proposed effects on emotional processing, reward valuation, cognitive flexibility, and interoceptive awareness, PAT may create opportunities to disrupt established patterns of avoidance, rigid thinking, and maladaptive behavioural reinforcement. The gut–brain interaction may represent an additional biological pathway relevant to these processes.

These mechanisms should not be understood as independent processes. Changes in emotion regulation may influence the ability to tolerate bodily sensations, while shifts in reward valuation and cognitive flexibility may create opportunities to respond differently to distress and challenge entrenched beliefs. However, the extent to which PAT produces these changes, and whether they translate into sustained improvements in ED outcomes, requires further investigation, although preliminary evidence is promising. 

The therapeutic potential of PAT lies not only in the acute psychedelic experience but also in the structured integration process that follows. Integration sessions provide an opportunity to translate emotional breakthroughs, changes in cognitive flexibility, interoceptive shifts, and reward processing into sustained behavioural change. Effective integration involves helping individuals articulate insights, connect them to ED-related patterns, and develop concrete strategies for change. These may include strengthening adaptive coping, challenging rigid beliefs, practising interoceptive awareness, reinforcing positive reward experiences, and supporting nutritional rehabilitation.

By grounding the understanding of PAT in affect regulation theory and the predictive coding framework, therapists may be better positioned to help individuals explore how psychedelic experiences could disrupt maladaptive emotional and cognitive patterns and create opportunities for new learning. Polyvagal-informed approaches may further support the development of mind–body awareness and emotional regulation through mindfulness strategies. Together, these approaches offer a multifaceted framework for translating psychedelic experiences into therapeutic change and addressing the interconnected mechanisms that maintain EDs and associated suffering. 

==See Also==
* [https://w.wiki/TsdG Ayahuasca and the brain] (Wikiversity)
* [https://w.wiki/TscF Emotional effects of psychedelics] (Wikiversity)
* [https://w.wiki/Tsdb Psilocybin and emotion] (Wikiversity)
* [https://w.wiki/TsdS Psilocibyn assisted psychotherapy] (Wikiversity)
* [https://w.wiki/Tsce Psychedelics, altered consciousness, and personal growth] (Wikiversity)
* [[Eating Disorders|Eating disorders]] (Wikiversity)

==References==
{{Hanging indent|1=

(I can't figure out how to italisice this section yet!) {{ic|Try &quot;Edit source&quot; and then wrapping any text to be italicised in two apostrophes e.g., ''this is italics''}}

Abdoli, M., Schiechtl, E., Rosato, M. S., Mangweth-Matzek, B., Cotrufo, P., &amp; Hüfner, K. (2025). Body image, self-esteem, emotion regulation, and eating disorders in adults: a systematic review. Körperbild, Selbstwert, Emotionsregulation und Essstörungen bei Erwachsenen: eine systematische Übersicht. Neuropsychiatrie : Klinik, Diagnostik, Therapie und Rehabilitation : Organ der Gesellschaft Osterreichischer Nervenarzte und Psychiater, 39(3), 118–132. https://doi.org/10.1007/s40211-025-00544-4

Brown, T. A., Vanzhula, I. A., Reilly, E. E., Levinson, C. A., Berner, L. A., Krueger, A., Lavender, J. M., Kaye, W. H., &amp; Wierenga, C. E. (2020). Body mistrust bridges interoceptive awareness and eating disorder symptoms. Journal of abnormal psychology, 129(5), 445–456. https://doi.org/10.1037/abn0000516

Burr, E. K., Dvorak, R. D., De Leon, A. N., Leary, A. V., Peterson, R., Schaefer, L. M., &amp; Wonderlich, S. A. (2023). The role of eating expectancies and eating motives in the association between mood and loss-of-control eating: A national sample daily diary study. Appetite, 180, 106322. https://doi.org/10.1016/j.appet.2022.106322

Frank, G. K. W., DeGuzman, M. C., &amp; Shott, M. E. (2019). Motivation to eat and not to eat - The psycho-biological conflict in anorexia nervosa. Physiology &amp; behavior, 206, 185–190. https://doi.org/10.1016/j.physbeh.2019.04.007

Henderson, Z. B., Fox, J. R. E., Trayner, P., &amp; Wittkowski, A. (2019). Emotional development in eating disorders: A qualitative metasynthesis. Clinical psychology &amp; psychotherapy, 26(4), 440–457. https://doi.org/10.1002/cpp.2365

Lavender, J. M., Wonderlich, S. A., Engel, S. G., Gordon, K. H., Kaye, W. H., &amp; Mitchell, J. E. (2015). Dimensions of emotion dysregulation in anorexia nervosa and bulimia nervosa: A conceptual review of the empirical literature. Clinical psychology review, 40, 111–122. https://doi.org/10.1016/j.cpr.2015.05.010

Leppanen, J., Brown, D., McLinden, H., Williams, S., &amp; Tchanturia, K. (2022). The Role of Emotion Regulation in Eating Disorders: A Network Meta-Analysis Approach. Frontiers in psychiatry, 13, 793094. https://doi.org/10.3389/fpsyt.2022.793094

Marano G, Lanzetta M, Scialpi C, Sottile A, Giacomi OD, Brisi C, Traversi G, Mazza O, Capristo E, Sani G, et al. Disordered Minds, Disordered Meals: When Emotions Masquerade as Hunger in Eating Disorders—A Systematic Review. Nutrients. 2026; 18(9):1350. https://doi.org/10.3390/nu18091350

Monteleone, A. M., Pellegrino, F., Croatto, G., Carfagno, M., Hilbert, A., Treasure, J., Wade, T., Bulik, C. M., Zipfel, S., Hay, P., Schmidt, U., Castellini, G., Favaro, A., Fernandez-Aranda, F., Il Shin, J., Voderholzer, U., Ricca, V., Moretti, D., Busatta, D., Abbate-Daga, G., … Solmi, M. (2022). Treatment of eating disorders: A systematic meta-review of meta-analyses and network meta-analyses. Neuroscience and biobehavioral reviews, 142, 104857. https://doi.org/10.1016/j.neubiorev.2022.104857

Murphy, R., Straebler, S., Cooper, Z., &amp; Fairburn, C. G. (2010). Cognitive behavioral therapy for eating disorders. The Psychiatric clinics of North America, 33(3), 611–627. https://doi.org/10.1016/j.psc.2010.04.004

Nasini, S., Casile, A., Bonaldo, B., Mancini, C., Guzzo, S. M., Botticelli, L., &amp; Comai, S. (2025). The role of motivation in eating disorders: understanding sex differences in the circuits. Frontiers in behavioral neuroscience, 19, 1644383. https://doi.org/10.3389/fnbeh.2025.1644383

Norman, G. J., Berntson, G. G., &amp; Cacioppo, J. T. (2014). Emotion, somatovisceral afference, and autonomic regulation. Emotion Review, 6(2), 113–123. https://doi.org/10.1177/1754073913512006

Prefit, A. B., Cândea, D. M., &amp; Szentagotai-Tătar, A. (2019). Emotion regulation across eating pathology: A meta-analysis. Appetite, 143, 104438. https://doi.org/10.1016/j.appet.2019.104438

Reichenberger, J., Schnepper, R., Arend, A. K., &amp; Blechert, J. (2020). Emotional eating in healthy individuals and patients with an eating disorder: evidence from psychometric, experimental and naturalistic studies. The Proceedings of the Nutrition Society, 79(3), 290–299. https://doi.org/10.1017/S0029665120007004

Salias, C., Gross, J. J., Petrova, K., Forbush, K. T., &amp; Preece, D. A. (2025). Eating disorder symptoms and profiles of emotion regulation strategy use. Journal of affective disorders, 380, 94–103. https://doi.org/10.1016/j.jad.2025.03.050

Schaefer, L. M., Forester, G., Burr, E. K., Laam, L., Crosby, R. D., Peterson, C. B., Crow, S. J., Engel, S. G., Dvorak, R. D., &amp; Wonderlich, S. A. (2023). Examining the role of craving in affect regulation models of binge eating: Evidence from an ecological momentary assessment study. Journal of psychopathology and clinical science, 132(6), 725–732. https://doi.org/10.1037/abn0000839

Selby, E. A., Cornelius, T., Fehling, K. B., Kranzler, A., Panza, E. A., Lavender, J. M., Wonderlich, S. A., Crosby, R. D., Engel, S. G., Mitchell, J. E., Crow, S. J., Peterson, C. B., &amp; Le Grange, D. (2015). A perfect storm: examining the synergistic effects of negative and positive emotional instability on promoting weight loss activities in anorexia nervosa. Frontiers in psychology, 6, 1260. https://doi.org/10.3389/fpsyg.2015.01260

Tabuenca, K., Crowe, D. E., Gillis, A. J., Kabiling, C., Saccacio, B., Velkova, A. V., &amp; Murray, S. B. (2025). Updates in the treatment of eating disorders in 2024: a year in review in Eating Disorders: The Journal of Treatment &amp; Prevention. Eating Disorders, 33(4), 434–450. https://doi.org/10.1080/10640266.2025.2497750

Wong, V. Z., Koithan, E. M., Santos, B. M., Johnson, A., &amp; Haynos, A. F. (2025). Does Evidence Support an Emotion Regulation Model of Anorexia Nervosa? A Systematic Review of Over a Decade of Research. Clinical psychology : a publication of the Division of Clinical Psychology of the American Psychological Association, 32(1), 1–17. https://doi.org/10.1037/cps0000244

}}

==External links==
* [https://www.abct.org/fact-sheets/psychedelic-assisted-therapy/ Psychedelic-Assisted Therapy | Fact Sheet] (ABCT - Association for Behavioral and Cognitive Therapies)
* [https://podcasts.apple.com/au/podcast/can-magic-mushrooms-help-treat-anorexia/id189330872?i=1000784809236 Can magic mushrooms help treat anorexia?] (Apple Podcasts)
* [https://www.apa.org/news/podcasts/speaking-of-psychology/eating-disorder The ‘silent epidemic’ of eating disorders] (American Psychological Association)
* [https://www.apa.org/monitor/2023/04/sensations-eating-disorders-suicidal-behavior What is interoception, and how does it affect mental health]? 5 questions for April Smith (American Psychological Association)
* [https://www.cbte.co/what-is-cbte/transdiagnostic-view-eating-disorders/ Transdiagnostic view of eating disorders] (cbte.co)
* [https://psychedelic.support/resources/polyvagal-theory-mind-body-dr-erica-zelfand/ Polyvagal Theory with Dr. Erica Zelfand: Mind-Body Connection] ·(Psychedelic Support)
* [https://www.wholeselfnutrition.org/post/nervous-system-regulation-a-missing-piece-in-eating-disorder-recovery Nervous System Regulation: A Missing Piece in Eating Disorder Recovery]  (wholeselfnutrition.org)

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      <text bytes="36255" sha1="8mqaypi93430za8p093iale85xgam3c" xml:space="preserve">{{title|Psychedelic treatment of eating disorders:&lt;br&gt;How might psychedelic-assisted therapy influence psychological mechanisms involved in eating disorders?}}
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== Overview ==
{{RoundBoxTop|theme=7}}[[File:Neural network - Midjourney and Grok.png|thumb|'''Figure 1.''' Psychedelics are thought to temporarily disrupt rigid neural communication pathways, promoting more flexible patterns of connectivity across networks involved in mood regulation, fear processing, reward learning, and cognitive adaptability. These changes may support therapeutic shifts in behaviour and emotional processing (Hatzipantelis &amp; Olson, 2025).]]Emma, a 27‑year‑old from Canberra, has lived with an eating disorder for nearly two decades. She describes her problem eating behaviours to have started at school, after being bullied about her appearance. Ever since, they have remained in her life as “a way for me to feel in control”. Although she is aware of the harm caused by restrictive eating and compulsive exercise, she feels trapped in her thought patterns characterised by a preoccupation about food and weight concerns which have become entrenched in her daily life. 

After reading an article describing emerging research suggesting that psychedelics may alter patterns of neural connectivity that shape behaviour (see Figure 1), she expressed interest in pursuing psychedelic‑assisted therapy through a provider accessible to her.

After participating in her first supervised psilocybin‑assisted therapy session, Emma reported experiencing an emotional journey that allowed her to feel “connected to my body for the first time in years”. After 3 months, she has noticed a shift in how she relates to her body, and is finding it easier to actively call into question how she responds to distress with the support of her psychotherapist. 


Her experience raises a central question: What psychological mechanisms could explain these changes?{{RoundBoxBottom|theme=3}}  

This chapter explores how psychedelic‑assisted therapy (PAT) may influence the emotional, cognitive, and neurobiological processes that underpin eating disorders (EDs).   

{{RoundBoxTop|theme=11}}'''Focus questions'''
{{ic|}}Two central questions will be addressed:
* What psychological processes underpin eating disorders, and how do they guide ED behaviour?
* How might psychedelic‑assisted therapy influence these processes to support recovery?
{{ic|}}{{ic|}}{{RoundBoxBottom}}

== Introduction ==
'''Eating Disorders'''  

[[wikipedia:Eating_disorder|Eating disorders]] (EDs) are psychiatric conditions characterised by abnormal eating behaviours that negatively affect physical and mental health. They are associated with chronic illness, disability, reduced quality of life, increased suicide risk, and are highly comorbid with [[wikipedia:Mood_disorder|mood disorders]], [[wikipedia:Post-traumatic_stress_disorder|post-traumatic stress disorder]] (PTSD), [[wikipedia:Obsessive–compulsive_disorder|obsessive-compulsive disorder]] (OCD), and [[wikipedia:Substance_use_disorder|substance use disorders]] (Calder et al., 2023). [[wikipedia:Anorexia|Anorexia nervosa]] (AN) has the highest mortality rate of any psychiatric disorder, while [[wikipedia:Bulimia|bulimia nervosa]] (BN) and [[wikipedia:Binge_eating_disorder|binge‑eating disorder]] (BED) are also highly prevalent types of eating disorders.  

In Australia, the prevalence of EDs is rising, particularly among young people. Approximately 10.46% of the population has experienced an eating disorder at some point, with an estimated economic burden of $84 billion (Hay et al., 2023). Despite decades of research, the pathogenesis of EDs remains incompletely understood (Calder et al., 2023). Current evidence suggests a complex interplay between genetic predisposition, temperament, hormonal dysregulation, cognitive abnormalities, sociocultural pressures, and traumatic experiences.

Although cognitive‑behavioural therapy (CBT‑E) combined with pharmacological treatment has demonstrated beneficial outcomes, efficacy remains limited and varies across ED types (Calder et al., 2023). Recovery is often long and difficult, with only two‑thirds of individuals with AN and BN eventually recovering, while others can remain ill for many years. This highlights the need for treatment approaches that can accelerate recovery and provide benefit for individuals who do not respond to conventional therapies.


'''Psychedelic-Assisted Therapy'''

In 2023, Australia legalised the prescription of MDMA and psilocybin under professional supervision, marking a significant shift in mental‑health treatment options. Psychedelic compounds, including [[wikipedia:LSD|LSD]], [[wikipedia:Psilocybin|psilocybin]], [[wikipedia:Dimethyltryptamine|DMT]], [[wikipedia:Ketamine|ketamine]], and [[wikipedia:MDMA|MDMA]], have demonstrated promising therapeutic effects across a wide range of psychiatric conditions. Researchers propose that psychedelics act through psychological and neural mechanisms that increase [[wikipedia:Neuroplasticity|neuroplasticity]], facilitate insight, and foster emotional acceptance (Peled‑Avron et al., 2024). At a neurobiological level, psychedelics influence processes that inform perception, emotion, and behaviour, offering a potential avenue for addressing entrenched ED mechanisms.

PAT differs from pharmacological treatment alone because the drug is administered within a structured therapeutic context designed to maximise safety and clinical benefit (Calder et al., 2023). Treatment typically involves three types of sessions. Preparatory sessions feature participants undergoing psychoeducation, where the clinician establishes rapport and clear safety protocols. Followed by supervised medication where the participant has an inward experience with the reassurance of clinicians present in the same space. Lastly, integrative sessions where individuals process and explore insights from the previous session with their psychotherapist to foster behavioural change (Wolfgang &amp; Hoge, 2023). This combination of pharmacological and psychological intervention is theorised to effectively target underlying psychological mechanisms common across various mental health disorders, illustrating PAT’s potential as a valuable transdiagnostic treatment option. 

PAT has become a subject of increasing popularity in ED research because many of the psychological mechanisms it is proposed to influence are the same ones implicated in ED maintenance and comorbidities (Calder et al., 2023; Peled-Avron et al., 2024). Early research, including case study reports, small clinical studies, meta-analyses and reviews indicate that PAT produces improvements in affect, reductions in ED symptom severity, enhanced body image, weight restoration, and reductions in comorbid symptoms. Although preliminary, these findings indicate that PAT may disrupt and promote shifts away from maladaptive coping patterns that become entrenched in treatment resistant ED populations.

== Psychological Mechanisms in Eating Disorders ==


'''Emotion Dysregulation'''

Emotion dysregulation is considered to be a significant risk factor for the onset and maintenance of EDs. It refers to difficulties recognising, assessing, and modifying emotional responses to meet situational demands (Zhou et al., 2025). 

Research consistently shows that individuals with EDs experience significant challenges in regulating emotions, increasing their vulnerability to comorbid symptoms, which contribute to the emergence of disordered eating patterns (Leppanen et al., 2022). This idea is supported by affect regulation theory which posits that eating disorders develop and are maintained as maladaptive strategies to manage, tolerate and escape from negative emotions and psychological distress (Schaefer et al., 2020; Zanella &amp; Lee, 2022). This is further exemplified in Fitzsimmons &amp; Bardone-Cone’s article examining differences in coping within eating disorder patients (2010). The authors explain that avoidance and emotion-oriented coping styles often function as maladaptive attempts to manage (di)stress. They explain that behaviours such as binge eating, purging, starvation, and/or compulsive exercise provide temporary relief by shifting attention away from uncomfortable emotions. 

Furthermore, alexithymia, characterised by difficulty identifying and describing one’s own emotions, is strongly associated with ED pathology (Shank et al., 2019). Individuals with high alexithymia often struggle to differentiate emotional states from bodily sensations, contributing to behaviours such as emotional eating, eating in the absence of hunger, or rigid restriction. In BED, alexithymia is linked to binge episodes triggered by poorly understood emotional cues, while in AN and BN, alexithymia may contribute to emotional avoidance and reliance on ED behaviours for affect regulation. 

The effects of trauma are contributing factors to emotion dysregulation, and considered a risk factor for ED development. Individuals who experience sexual, physical, or emotional abuse, neglect, and bullying are likely to experience heightened emotional reactivity, threat perception, and avoidance behaviours (Calder et al., 2023). Researchers explain that trauma often results in lowered distress tolerance and increased reliance on maladaptive coping behaviours, including disordered eating. Furthermore, PTSD comorbidity is common, hence trauma‑related symptoms are hypothesised to frequently interact with ED behaviours in complex ways.  


'''Reward Processing Dysfunction'''
[[File:Striatum.gif|thumb|'''Figure 2.''' Striatum]]
[[File:Anterior cingulate gyrus animation.gif|thumb|'''Figure 3'''. Anterior Cingulate Cortex ]]
Abnormal reward valuation is understood to be a central psychological mechanism that maintains ED behaviours. Research consistently shows that individuals with eating disorders display altered neural activity response to various stimuli, as well as disruptions in reinforcement learning (Calder et al., 2023). Brain regions involved in reward processing, habit formation, and learning, such as the striatum and anterior cingulate cortex (see figures 2 &amp; 3), exhibit atypical activation patterns and differences in dopamine receptor binding across ED types. The insula (see figure 4), which integrates bodily sensations with conscious thought, emotion, and behaviour, also shows altered responses. Together, these regions have been shown to react differently to food images, taste, and social feedback compared to healthy controls, indicating that reward dysfunction extends beyond eating‑related stimuli for ED populations.
[[File:Insular cortex.gif|thumb|'''Figure 4.''' Insula. ]]
In the context of BN and BED, research shows that food is valued more highly than other types of rewards, thus shaping behaviour through its heightened influence on reward outcomes (Calder et al., 2023). Compulsive behaviours specific to each condition (e.g. bingeing, purging) are therefore more likely to occur when food is overvalued and alternative rewards are discounted or ignored. In addition to the neural changes already described, BN and BED are associated with reduced structural and functional connectivity between frontal control regions and the striatum. This combination of highly salient food rewards, and weakened fronto‑striatal pathways, reduces an individual’s ability to inhibit or modulate reward‑seeking impulses. Weak connectivity in these circuits is thought to predict compulsive reward‑seeking behaviour. As a result, even when individuals experience negative consequences from binge episodes, they may struggle to learn from these outcomes or adjust their behaviour accordingly.


Anhedonia, a global reduction in reward responsiveness, is frequently reported by people who experience AN, resulting in food and eating becoming undervalued or aversive to them (Calder et al., 2023). Researchers propose that reward contamination further contributes to this pattern, where the brain learns to associate normally punishing stimuli (e.g., starvation, excessive exercise) with reward, while normally rewarding stimuli (e.g., high‑calorie foods) become experienced as punishment. Structural reductions in the striatum and somatosensory cortex have also been observed, which accounts for distorted bodily sensations and contributes to anhedonia. These changes support maladaptive conditioning in which starvation and weight loss embody a sense of safety, achievement, and emotional relief. Restrictive and preoccupied behaviours centred on food, body shape, and exercise are therefore reinforced over time.

Consistent with affect‑regulation models, eating‑disorder behaviours also become negatively reinforced because they reduce emotional discomfort. This relief increases the likelihood that the behaviours will be repeated, further embedding them within the individual’s coping pattern.


'''Cognitive Rigidity'''

Cognitive rigidity refers to inflexible thinking and behavioural patterns, including difficulty adapting to new information and modifying behaviour. Researchers believe that individuals with EDs often exhibit rigid beliefs about food and weight which interact with a need to exert control over negative emotions. This interaction is the proposed process in which compulsive behaviours and obsessive thoughts develop (Calder et al., 2023). In AN, rigidity manifests as strict dietary rules and fear of losing control, while in BN and BED, binge episodes may feel compulsive and uncontrollable.


'''Interoceptive Awareness'''

Interoceptive awareness (IA) refers to the ability to recognise and process internal bodily states such as hunger, satiety, pain, and arousal. IA is impaired across EDs, and contributes to body mistrust, distorted hunger cues, and inappropriate responses to internal sensations (Brown et al., 2020). Individuals may ignore physical discomfort, misinterpret bodily signals, or avoid sensations altogether, reinforcing maladaptive coping.      

 &lt;blockquote&gt;'''''QUIZ: Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{What coping style do people who experience EDs tend to show?
|type=&quot;()&quot;}
+ Avoidance-oriented
- Problem-oriented

{Compulsive behaviours are more likely to occur when food is ... and alternative rewards are ...
|type=&quot;()&quot;}
- undervalued; overvalued
+ overvalued; undervalued
&lt;/quiz&gt;&lt;/blockquote&gt;

== Psychological Mechanisms of Psychedelic-Assisted Therapy ==

PAT is proposed to influence several psychological mechanisms implicated in EDs, particularly those discussed in the previous section. The next part of this chapter aims to examine the theorised therapeutic mechanisms PAT possesses and practical implications for ED treatment.  


'''Emotion Regulation''' 

Emotion dysregulation is a core mechanism implicated in EDs. Affect regulation theory proposes that ED behaviours emerge as maladaptive strategies to escape, reduce, or blunt overwhelming emotional experiences (Schaefer et al., 2020). Restriction, bingeing, purging, and compulsive exercise may temporarily alleviate distress while reinforcing avoidance-oriented coping and limiting opportunities to learn more adaptive ways of responding to difficult emotions. 

Psychedelics often evoke intense emotional experiences that may disrupt habitual avoidance patterns. Researchers propose that, during psychedelic sessions, attempts to suppress or avoid difficult emotions can intensify these experiences, creating conditions in which emotional acceptance becomes a preferred response (Calder et al., 2023). Although this shift does not occur in every individual, experiencing difficult emotions without resorting to ED behaviours may weaken the association between emotional distress and maladaptive coping, particularly when emotional acceptance becomes associated with a more positive or tolerable experience.

The therapeutic value of this process lies in its potential to reshape affective responses. When individuals experience strong emotions without engaging in maladaptive behaviours, they may begin to develop a new approach towards emotional tolerance. Integration sessions can consolidate this learning by helping individuals articulate, differentiate, and reflect on the emotions experienced during dosing. This process may support the development of more adaptive coping strategies, including task-oriented, problem-focused, and socially supported approaches, which are associated with improved ED outcomes (Fitzsimmons &amp; Bardone-Cone, 2010). In this way, PAT may strengthen emotion regulation and reduce reliance on ED behaviours as strategies for managing affect. 


'''Reward Processing''' 

Reward dysfunction may contribute to the maintenance of EDs by reinforcing maladaptive behaviours while diminishing the perceived value of adaptive rewards. Predictive coding provides a useful framework for understanding how PAT might influence these processes. Individuals with EDs may hold rigid beliefs, conceptualised as high-level priors, about themselves in relation to food, body weight, and rewarding behaviours (Calder et al., 2023; Mograbi et al., 2024). These beliefs can influence how experiences are perceived and valued, potentially reinforcing existing behavioural patterns. Psychedelics are proposed to weaken high-level priors, allowing bottom-up sensory information to exert greater influence on perception and the valuation of experiences. 

During psychedelic experiences, individuals frequently report a heightened appreciation of sensory, social, and bodily experiences. This shift may counteract anhedonia and support the revaluation of previously feared or avoided stimuli. The therapeutic opportunity lies in translating these temporary changes in perception and reward into meaningful behavioural change. Integration sessions can explore positive and negative moments experienced during dosing and connect them to concrete goals. An example of this, inspired from Calder et al.’s (2023) review, could be to clarify specific plans to nourish the body due to the participant unpacks having experienced themselves as a decaying skeleton followed by the realisation of the body being a gift. If the period following dosing provides an opportunity for increased neuroplasticity, it may also be particularly conducive to reinforcing adaptive reward learning through behavioural activation with the help of a therapist. 


'''Cognitive Flexibility''' 

Cognitive rigidity is a hallmark of EDs and is characterised by inflexible beliefs about food, weight, body shape, and control. Predictive coding provides a framework for understanding this rigidity, as EDs may involve entrenched priors that resist updating even when confronted with contradictory sensory evidence (Zanella &amp; Lee, 2022). Psychedelics are proposed to disrupt these entrenched priors by increasing neural entropy and reducing the dominance of top-down processing (Calder et al., 2023). This temporary loosening of cognitive constraints may allow individuals to consider alternative perspectives and question long-held beliefs. 

Experiences of ego dissolution may further contribute to cognitive flexibility by reducing attachment to rigid self-concepts (Peled-Avron, 2024; Mograbi et al., 2024). When the boundaries of the self become less defined, individuals may find it easier to question identity-related beliefs that sustain ED pathology. Integration sessions can harness this potential flexibility by supporting cognitive reframing, encouraging behavioural experiments, and strengthening metacognitive awareness. Through these processes, individuals may be better able to translate insights gained during psychedelic experiences into sustained changes in thinking and behaviour.


'''Reconnecting with Bodily Signals'''

Interoceptive deficits are central to ED pathology, contributing to body mistrust, distorted perceptions of hunger cues, and difficulties responding appropriately to internal sensations (Brown et al., 2020). Psychedelics may enhance interoceptive awareness by altering sensory processing and increasing sensitivity to bodily signals. This proposed mechanism is closely related to autonomic regulation, for which polyvagal theory provides a framework for understanding the relationship between bodily signals, emotional regulation, and perceived safety.

Polyvagal theory emphasises the role of the vagus nerve in interoception, emotional regulation, and the perception of safety (Porges, 2022). Vagal afferents transmit information from the body to the insula, where interoceptive signals are integrated with emotional and cognitive processes. Individuals with EDs may exhibit chronic sympathetic arousal and reduced vagal tone, potentially impairing interoceptive accuracy and contributing to emotional rigidity. Psychedelics may initially increase sympathetic activity, as reflected in physiological responses such as increased heart rate, followed by a parasympathetic shift associated with greater relaxation and an increased capacity for rest (Li et al., 2025). Within a polyvagal framework, these changes may have implications for vagal regulation, interoceptive awareness, and emotional regulation.

The therapeutic value of this proposed mechanism lies in its potential to restore trust in bodily signals. Integration sessions may support this process by helping individuals explore bodily sensations experienced during dosing, connect interoceptive cues with emotional states, and practise interoceptive exposure to hunger, fullness, and anxiety-related sensations. Incorporating mindfulness techniques may further support autonomic regulation and help individuals develop a more adaptive relationship with their bodily experiences.

 A Brief Note Concerning The Gut-Brain Interaction 
Although gut microbiome disruption is not a direct psychological mechanism in EDs, it is a relevant biological factor to consider when examining the potential effects of PAT. Restrictive or chaotic eating patterns can contribute to gut dysbiosis, which may weaken gut-barrier integrity and contribute to inflammation affecting the brain (Anton-Paduraru et al., 2024). These changes have been shown to influence mood, stress responsivity, cognitive rigidity, and interoceptive awareness through HPA-axis activation, altered neurotransmitter synthesis, and disrupted hunger–satiety signalling. 

Emerging research suggests that psychedelics may also interact with the gut–brain axis. Certain microbes can metabolise psychedelic compounds, and microbial activity has been associated with modulatory effects on behavioural outcomes. Additionally, psychedelic use may alter microbial composition towards anti-inflammatory profiles, with potential implications for neuroplasticity, neurotransmitter synthesis and signalling improvements (Caspani et al., 2024). These microbiome-related effects may therefore contribute to changes in mood, cognitive flexibility, and appetite regulation.

Although the therapeutic potential of psychedelics in EDs is considered primarily in relation to psychological mechanisms, including changes in perception, emotional processing, and reduced avoidance, microbiome-related effects may represent an additional pathway through which biological processes influence psychological outcomes. However, the extent to which these interactions contribute to therapeutic outcomes in EDs remains to be established.


&lt;blockquote&gt;'''QUIZ: ''Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{ In predictive coding terms, what are “high‑level priors” in eating disorders? 
|type=&quot;()&quot;}
+ Rigid, entrenched beliefs about food, weight, and the self that shape perception and behaviour
- Flexible beliefs that easily update with new sensory information
- Momentary emotional reactions triggered by external cues

{What is the proposed mechanism by which psychedelics support emotion regulation in PAT for EDs? 
|type=&quot;()&quot;}
- By suppressing emotional intensity to prevent distress
+ By evoking strong emotions that disrupt avoidance patterns and promote emotional acceptance
- By eliminating negative emotions through serotonin release

{What is interoceptive awareness?
|type=&quot;()&quot;}
- The ability to evaluate reward value and anticipate pleasurable outcomes
+ The capacity to sense, interpret, and respond to internal bodily signals such as hunger, fullness, and emotional arousal
- The process of weakening cognitive rigidity through ego dissolution
&lt;/quiz&gt;&lt;/blockquote&gt;

== Limitations ==
Despite the potential of PAT to influence psychological mechanisms implicated in EDs, several limitations constrain current understanding of these processes and their therapeutic relevance. Research examining emotion dysregulation in EDs illustrates broader challenges in establishing the mechanisms underlying these conditions. Although non-acceptance of emotions has been identified as a transdiagnostic risk factor across psychiatric conditions (Paulus et al., 2021), Zhou et al.’s meta-analysis (2025) highlights that the causal pathways linking emotional dysregulation and EDs remain unclear, largely because of a lack of experimental and longitudinal studies. Further limitations include restricted availability of measurement scales, insufficient cultural specificity, heterogeneity across samples, gender imbalance, and limited developmental analysis. Together, these factors constrain understanding of how specific emotional processes relate to different ED presentations across the lifespan and stages of recovery.

These limitations are also relevant when considering the proposed mechanisms of PAT. Although existing theoretical frameworks offer ways to conceptualise how psychedelic experiences may influence psychological processes responsible for EDs, the emerging nature of psychedelic therapy limits the extent to which proposed mechanisms have been tested. However, with the number of clinical trials increasing as of recently, it will be interesting to see how the theorised therapeutic mechanisms across different ED presentations and stages of recovery emerges during further warranted investigation.

Nevertheless, current limitations in the evidence highlight the need for research that clarifies the relationships between psychological processes that underscore ED behaviours, and treatment outcomes. There are several important psychological components of ED maintenance that represent meaningful targets for treatment, but they should not be considered in isolation from eachother or the neurobiological processes that influence them. A more comprehensive understanding of how these mechanisms interact may help clarify the therapeutic potential of PAT and inform the development of more targeted treatment approaches.

== Conclusion ==
PAT offers a potential framework for addressing several interconnected psychological mechanisms implicated in EDs. Through its proposed effects on emotional processing, reward valuation, cognitive flexibility, and interoceptive awareness, PAT may create opportunities to disrupt established patterns of avoidance, rigid thinking, and maladaptive behavioural reinforcement. The gut–brain interaction may represent an additional biological pathway relevant to these processes.

These mechanisms should not be understood as independent processes. Changes in emotion regulation may influence the ability to tolerate bodily sensations, while shifts in reward valuation and cognitive flexibility may create opportunities to respond differently to distress and challenge entrenched beliefs. However, the extent to which PAT produces these changes, and whether they translate into sustained improvements in ED outcomes, requires further investigation, although preliminary evidence is promising. 

The therapeutic potential of PAT lies not only in the acute psychedelic experience but also in the structured integration process that follows. Integration sessions provide an opportunity to translate emotional breakthroughs, changes in cognitive flexibility, interoceptive shifts, and reward processing into sustained behavioural change. Effective integration involves helping individuals articulate insights, connect them to ED-related patterns, and develop concrete strategies for change. These may include strengthening adaptive coping, challenging rigid beliefs, practising interoceptive awareness, reinforcing positive reward experiences, and supporting nutritional rehabilitation.

By grounding the understanding of PAT in affect regulation theory and the predictive coding framework, therapists may be better positioned to help individuals explore how psychedelic experiences could disrupt maladaptive emotional and cognitive patterns and create opportunities for new learning. Polyvagal-informed approaches may further support the development of mind–body awareness and emotional regulation through mindfulness strategies. Together, these approaches offer a multifaceted framework for translating psychedelic experiences into therapeutic change and addressing the interconnected mechanisms that maintain EDs and associated suffering. 

==See Also==
* [https://w.wiki/TsdG Ayahuasca and the brain] (Wikiversity)
* [https://w.wiki/TscF Emotional effects of psychedelics] (Wikiversity)
* [https://w.wiki/Tsdb Psilocybin and emotion] (Wikiversity)
* [https://w.wiki/TsdS Psilocibyn assisted psychotherapy] (Wikiversity)
* [https://w.wiki/Tsce Psychedelics, altered consciousness, and personal growth] (Wikiversity)
* [[Eating Disorders|Eating disorders]] (Wikiversity)

==References==
{{Hanging indent|1=

{{ic|Try &quot;Edit source&quot; and then wrapping any text to be italicised in two apostrophes e.g., ''this is italics''}}

Anton-Păduraru, D. T., Trofin, F., Nastase, E. V., Miftode, R. S., Miftode, I. L., Trandafirescu, M. F., Cojocaru, E., Țarcă, E., Mindru, D. E., &amp; Dorneanu, O. S. (2023). The Role of the Gut Microbiota in Anorexia Nervosa in Children and Adults-Systematic Review. &quot;International journal of molecular sciences, 25&quot;(1), 41. https://doi.org/10.3390/ijms25010041

Brown, T. A., Vanzhula, I. A., Reilly, E. E., Levinson, C. A., Berner, L. A., Krueger, A., Lavender, J. M., Kaye, W. H., &amp; Wierenga, C. E. (2020). Body mistrust bridges interoceptive awareness and eating disorder symptoms. &quot;Journal of abnormal psychology, 129&quot;(5), 445–456. https://doi.org/10.1037/abn0000516 

Calder, A., Mock, S., Friedli, N., Pasi, P., &amp; Hasler, G. (2023). Psychedelics in the treatment of eating disorders: Rationale and potential mechanisms. &quot;European Neuropsychopharmacology, 75&quot;, 1–14. https://doi.org/10.1016/j.euroneuro.2023.05.008 

Caspani, G., Ruffell, S. G. D., Tsang, W., Netzband, N., Rohani-Shukla, C., Swann, J. R., &amp; Jefferies, W. A. (2024). Mind over matter: the microbial mindscapes of psychedelics and the gut-brain axis. &quot;Pharmacological research, 207&quot;, 107338. https://doi.org/10.1016/j.phrs.2024.107338  

Fitzsimmons, E. E., &amp; Bardone-Cone, A. M. (2010). Differences in coping across stages of recovery from an eating disorder. &quot;The International journal of eating disorders, 43&quot;(8), 689–693. https://doi.org/10.1002/eat.20781 

Hatzipantelis, C. J., &amp; Olson, D. E. (2024). The Effects of Psychedelics on Neuronal Physiology. &quot;Annual review of physiology, 86&quot;, 27–47. https://doi.org/10.1146/annurev-physiol-042022-020923

Hay, P., Aouad, P., Le, A., Marks, P., Maloney, D., National Eating Disorder Research Consortium, Touyz, S., &amp; Maguire, S. (2023). Epidemiology of eating disorders: population, prevalence, disease burden and quality of life informing public policy in Australia-a rapid review. &quot;Journal of eating disorders, 11&quot;(1), 23. https://doi.org/10.1186/s40337-023-00738-7

Li, H., Wang, H., &amp; Wang, X. (2025). Psychedelics and the Autonomic Nervous System: A Perspective on Their Interplay and Therapeutic Potential. &quot;ACS pharmacology &amp; translational science, 8&quot;(3), 899–902. https://doi.org/10.1021/acsptsci.5c00005 

Leppanen, J., Brown, D., McLinden, H., Williams, S., &amp; Tchanturia, K. (2022). The Role of Emotion Regulation in Eating Disorders: A Network Meta-Analysis Approach. &quot;Frontiers in psychiatry, 13&quot;, 793094. https://doi.org/10.3389/fpsyt.2022.793094 

Mograbi, D. C., Rodrigues, R., Bienemann, B., &amp; Huntley, J. (2024). Brain Networks, Neurotransmitters and Psychedelics: Towards a Neurochemistry of Self-Awareness. &quot;Current neurology and neuroscience reports, 24&quot;(8), 323–340. https://doi.org/10.1007/s11910-024-01353-y

Paulus F. W., Ohmann S., Möhler E., Plener P. &amp; Popow C. (2021). Emotional Dysregulation in Children and Adolescents With Psychiatric Disorders. A Narrative Review. &quot;Frontiers in Psychiatry 12&quot;:628252. doi: 10.3389/fpsyt.2021.628252

Peled-Avron L., Aday J. Ss, Kalafateli A. L., Hamilton H. K., Woolley J. D. (2024). Editorial: Down the rabbit hole – the psychological and neural mechanisms of psychedelic compounds and their use in treating mental health and medical conditions. &quot;Frontiers in Psychiatry 15&quot;:1431389. doi: 10.3389/fpsyt.2024.1431389

Porges S. W. (2025). Polyvagal Theory: Current Status, Clinical Applications, and Future Directions. &quot;Clinical neuropsychiatry, 22&quot;(3), 169–184. https://doi.org/10.36131/cnfioritieditore20250301

Schaefer, L. M., Smith, K. E., Anderson, L. M., Cao, L., Crosby, R. D., Engel, S. G., Crow, S. J., Peterson, C. B., &amp; Wonderlich, S. A. (2020). The role of affect in the maintenance of binge-eating disorder: Evidence from an ecological momentary assessment study. &quot;Journal of abnormal psychology, 129&quot;(4), 387–396. https://doi.org/10.1037/abn0000517 

Shank, L. M., Tanofsky-Kraff, M., Kelly, N. R., Jaramillo, M., Rubin, S. G., Altman, D. R., Byrne, M. E., LeMay-Russell, S., Schvey, N. A., Broadney, M. M., Brady, S. M., Yang, S. B., Courville, A. B., Ramirez, S., Crist, A. C., Yanovski, S. Z., &amp; Yanovski, J. A. (2019). The association between alexithymia and eating behavior in children and adolescents. &quot;Appetite, 142&quot;, 104381. https://doi.org/10.1016/j.appet.2019.104381

Wolfgang, A. S., &amp; Hoge, C. W. (2023). Psychedelic-Assisted Therapy in Military and Veterans Healthcare Systems: Clinical, Legal, and Implementation Considerations. &quot;Current psychiatry reports, 25&quot;(10), 513–532. https://doi.org/10.1007/s11920-023-01446-4 

Zanella, E., &amp; Lee, E. (2022). Integrative review on psychological and social risk and prevention factors of eating disorders including anorexia nervosa and bulimia nervosa: seven major theories. &quot;Heliyon, 8&quot;(11), e11422. https://doi.org/10.1016/j.heliyon.2022.e11422 

Zhou, R., Zhang, L., Liu, Z., &amp; Cao, B. (2025). Emotion regulation difficulties and disordered eating in adolescents and young adults: a meta-analysis. &quot;Journal of eating disorders, 13&quot;(1), 25. https://doi.org/10.1186/s40337-025-01197-y

}}

==External links==
* [https://www.abct.org/fact-sheets/psychedelic-assisted-therapy/ Psychedelic-Assisted Therapy | Fact Sheet] (ABCT - Association for Behavioral and Cognitive Therapies)
* [https://podcasts.apple.com/au/podcast/can-magic-mushrooms-help-treat-anorexia/id189330872?i=1000784809236 Can magic mushrooms help treat anorexia?] (Apple Podcasts)
* [https://www.apa.org/news/podcasts/speaking-of-psychology/eating-disorder The ‘silent epidemic’ of eating disorders] (American Psychological Association)
* [https://www.apa.org/monitor/2023/04/sensations-eating-disorders-suicidal-behavior What is interoception, and how does it affect mental health]? 5 questions for April Smith (American Psychological Association)
* [https://www.cbte.co/what-is-cbte/transdiagnostic-view-eating-disorders/ Transdiagnostic view of eating disorders] (cbte.co)
* [https://psychedelic.support/resources/polyvagal-theory-mind-body-dr-erica-zelfand/ Polyvagal Theory with Dr. Erica Zelfand: Mind-Body Connection] ·(Psychedelic Support)
* [https://www.wholeselfnutrition.org/post/nervous-system-regulation-a-missing-piece-in-eating-disorder-recovery Nervous System Regulation: A Missing Piece in Eating Disorder Recovery]  (wholeselfnutrition.org)

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      <text bytes="36248" sha1="evy8sftkpdivbexhsnjuxy3qt80jzle" xml:space="preserve">{{title|Psychedelic treatment of eating disorders:&lt;br&gt;How might psychedelic-assisted therapy influence psychological mechanisms involved in eating disorders?}}
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== Overview ==
{{RoundBoxTop|theme=7}}[[File:Neural network - Midjourney and Grok.png|thumb|'''Figure 1.''' Psychedelics are thought to temporarily disrupt rigid neural communication pathways, promoting more flexible patterns of connectivity across networks involved in mood regulation, fear processing, reward learning, and cognitive adaptability. These changes may support therapeutic shifts in behaviour and emotional processing (Hatzipantelis &amp; Olson, 2025).]]Emma, a 27‑year‑old from Canberra, has lived with an eating disorder for nearly two decades. She describes her problem eating behaviours to have started at school, after being bullied about her appearance. Ever since, they have remained in her life as “a way for me to feel in control”. Although she is aware of the harm caused by restrictive eating and compulsive exercise, she feels trapped in her thought patterns characterised by a preoccupation about food and weight concerns which have become entrenched in her daily life. 

After reading an article describing emerging research suggesting that psychedelics may alter patterns of neural connectivity that shape behaviour (see Figure 1), she expressed interest in pursuing psychedelic‑assisted therapy through a provider accessible to her.

After participating in her first supervised psilocybin‑assisted therapy session, Emma reported experiencing an emotional journey that allowed her to feel “connected to my body for the first time in years”. After 3 months, she has noticed a shift in how she relates to her body, and is finding it easier to actively call into question how she responds to distress with the support of her psychotherapist. 


Her experience raises a central question: What psychological mechanisms could explain these changes?{{RoundBoxBottom|theme=3}}  

This chapter explores how psychedelic‑assisted therapy (PAT) may influence the emotional, cognitive, and neurobiological processes that underpin eating disorders (EDs).   

{{RoundBoxTop|theme=11}}'''Focus questions'''
{{ic|}}Two central questions will be addressed:
* What psychological processes underpin eating disorders, and how do they guide ED behaviour?
* How might psychedelic‑assisted therapy influence these processes to support recovery?
{{ic|}}{{ic|}}{{RoundBoxBottom}}

== Introduction ==
'''Eating Disorders'''  

[[wikipedia:Eating_disorder|Eating disorders]] (EDs) are psychiatric conditions characterised by abnormal eating behaviours that negatively affect physical and mental health. They are associated with chronic illness, disability, reduced quality of life, increased suicide risk, and are highly comorbid with [[wikipedia:Mood_disorder|mood disorders]], [[wikipedia:Post-traumatic_stress_disorder|post-traumatic stress disorder]] (PTSD), [[wikipedia:Obsessive–compulsive_disorder|obsessive-compulsive disorder]] (OCD), and [[wikipedia:Substance_use_disorder|substance use disorders]] (Calder et al., 2023). [[wikipedia:Anorexia|Anorexia nervosa]] (AN) has the highest mortality rate of any psychiatric disorder, while [[wikipedia:Bulimia|bulimia nervosa]] (BN) and [[wikipedia:Binge_eating_disorder|binge‑eating disorder]] (BED) are also highly prevalent types of eating disorders.  

In Australia, the prevalence of EDs is rising, particularly among young people. Approximately 10.46% of the population has experienced an eating disorder at some point, with an estimated economic burden of $84 billion (Hay et al., 2023). Despite decades of research, the pathogenesis of EDs remains incompletely understood (Calder et al., 2023). Current evidence suggests a complex interplay between genetic predisposition, temperament, hormonal dysregulation, cognitive abnormalities, sociocultural pressures, and traumatic experiences.

Although cognitive‑behavioural therapy (CBT‑E) combined with pharmacological treatment has demonstrated beneficial outcomes, efficacy remains limited and varies across ED types (Calder et al., 2023). Recovery is often long and difficult, with only two‑thirds of individuals with AN and BN eventually recovering, while others can remain ill for many years. This highlights the need for treatment approaches that can accelerate recovery and provide benefit for individuals who do not respond to conventional therapies.


'''Psychedelic-Assisted Therapy'''

In 2023, Australia legalised the prescription of MDMA and psilocybin under professional supervision, marking a significant shift in mental‑health treatment options. Psychedelic compounds, including [[wikipedia:LSD|LSD]], [[wikipedia:Psilocybin|psilocybin]], [[wikipedia:Dimethyltryptamine|DMT]], [[wikipedia:Ketamine|ketamine]], and [[wikipedia:MDMA|MDMA]], have demonstrated promising therapeutic effects across a wide range of psychiatric conditions. Researchers propose that psychedelics act through psychological and neural mechanisms that increase [[wikipedia:Neuroplasticity|neuroplasticity]], facilitate insight, and foster emotional acceptance (Peled‑Avron et al., 2024). At a neurobiological level, psychedelics influence processes that inform perception, emotion, and behaviour, offering a potential avenue for addressing entrenched ED mechanisms.

PAT differs from pharmacological treatment alone because the drug is administered within a structured therapeutic context designed to maximise safety and clinical benefit (Calder et al., 2023). Treatment typically involves three types of sessions. Preparatory sessions feature participants undergoing psychoeducation, where the clinician establishes rapport and clear safety protocols. Followed by supervised medication where the participant has an inward experience with the reassurance of clinicians present in the same space. Lastly, integrative sessions where individuals process and explore insights from the previous session with their psychotherapist to foster behavioural change (Wolfgang &amp; Hoge, 2023). This combination of pharmacological and psychological intervention is theorised to effectively target underlying psychological mechanisms common across various mental health disorders, illustrating PAT’s potential as a valuable transdiagnostic treatment option. 

PAT has become a subject of increasing popularity in ED research because many of the psychological mechanisms it is proposed to influence are the same ones implicated in ED maintenance and comorbidities (Calder et al., 2023; Peled-Avron et al., 2024). Early research, including case study reports, small clinical studies, meta-analyses and reviews indicate that PAT produces improvements in affect, reductions in ED symptom severity, enhanced body image, weight restoration, and reductions in comorbid symptoms. Although preliminary, these findings indicate that PAT may disrupt and promote shifts away from maladaptive coping patterns that become entrenched in treatment resistant ED populations.

== Psychological Mechanisms in Eating Disorders ==


'''Emotion Dysregulation'''

Emotion dysregulation is considered to be a significant risk factor for the onset and maintenance of EDs. It refers to difficulties recognising, assessing, and modifying emotional responses to meet situational demands (Zhou et al., 2025). 

Research consistently shows that individuals with EDs experience significant challenges in regulating emotions, increasing their vulnerability to comorbid symptoms, which contribute to the emergence of disordered eating patterns (Leppanen et al., 2022). This idea is supported by affect regulation theory which posits that eating disorders develop and are maintained as maladaptive strategies to manage, tolerate and escape from negative emotions and psychological distress (Schaefer et al., 2020; Zanella &amp; Lee, 2022). This is further exemplified in Fitzsimmons &amp; Bardone-Cone’s article examining differences in coping within eating disorder patients (2010). The authors explain that avoidance and emotion-oriented coping styles often function as maladaptive attempts to manage (di)stress. They explain that behaviours such as binge eating, purging, starvation, and/or compulsive exercise provide temporary relief by shifting attention away from uncomfortable emotions. 

Furthermore, alexithymia, characterised by difficulty identifying and describing one’s own emotions, is strongly associated with ED pathology (Shank et al., 2019). Individuals with high alexithymia often struggle to differentiate emotional states from bodily sensations, contributing to behaviours such as emotional eating, eating in the absence of hunger, or rigid restriction. In BED, alexithymia is linked to binge episodes triggered by poorly understood emotional cues, while in AN and BN, alexithymia may contribute to emotional avoidance and reliance on ED behaviours for affect regulation. 

The effects of trauma are contributing factors to emotion dysregulation, and considered a risk factor for ED development. Individuals who experience sexual, physical, or emotional abuse, neglect, and bullying are likely to experience heightened emotional reactivity, threat perception, and avoidance behaviours (Calder et al., 2023). Researchers explain that trauma often results in lowered distress tolerance and increased reliance on maladaptive coping behaviours, including disordered eating. Furthermore, PTSD comorbidity is common, hence trauma‑related symptoms are hypothesised to frequently interact with ED behaviours in complex ways.  


'''Reward Processing Dysfunction'''
[[File:Striatum.gif|thumb|'''Figure 2.''' Striatum]]
[[File:Anterior cingulate gyrus animation.gif|thumb|'''Figure 3'''. Anterior Cingulate Cortex ]]
Abnormal reward valuation is understood to be a central psychological mechanism that maintains ED behaviours. Research consistently shows that individuals with eating disorders display altered neural activity response to various stimuli, as well as disruptions in reinforcement learning (Calder et al., 2023). Brain regions involved in reward processing, habit formation, and learning, such as the striatum and anterior cingulate cortex (see figures 2 &amp; 3), exhibit atypical activation patterns and differences in dopamine receptor binding across ED types. The insula (see figure 4), which integrates bodily sensations with conscious thought, emotion, and behaviour, also shows altered responses. Together, these regions have been shown to react differently to food images, taste, and social feedback compared to healthy controls, indicating that reward dysfunction extends beyond eating‑related stimuli for ED populations.
[[File:Insular cortex.gif|thumb|'''Figure 4.''' Insula. ]]
In the context of BN and BED, research shows that food is valued more highly than other types of rewards, thus shaping behaviour through its heightened influence on reward outcomes (Calder et al., 2023). Compulsive behaviours specific to each condition (e.g. bingeing, purging) are therefore more likely to occur when food is overvalued and alternative rewards are discounted or ignored. In addition to the neural changes already described, BN and BED are associated with reduced structural and functional connectivity between frontal control regions and the striatum. This combination of highly salient food rewards, and weakened fronto‑striatal pathways, reduces an individual’s ability to inhibit or modulate reward‑seeking impulses. Weak connectivity in these circuits is thought to predict compulsive reward‑seeking behaviour. As a result, even when individuals experience negative consequences from binge episodes, they may struggle to learn from these outcomes or adjust their behaviour accordingly.


Anhedonia, a global reduction in reward responsiveness, is frequently reported by people who experience AN, resulting in food and eating becoming undervalued or aversive to them (Calder et al., 2023). Researchers propose that reward contamination further contributes to this pattern, where the brain learns to associate normally punishing stimuli (e.g., starvation, excessive exercise) with reward, while normally rewarding stimuli (e.g., high‑calorie foods) become experienced as punishment. Structural reductions in the striatum and somatosensory cortex have also been observed, which accounts for distorted bodily sensations and contributes to anhedonia. These changes support maladaptive conditioning in which starvation and weight loss embody a sense of safety, achievement, and emotional relief. Restrictive and preoccupied behaviours centred on food, body shape, and exercise are therefore reinforced over time.

Consistent with affect‑regulation models, eating‑disorder behaviours also become negatively reinforced because they reduce emotional discomfort. This relief increases the likelihood that the behaviours will be repeated, further embedding them within the individual’s coping pattern.


'''Cognitive Rigidity'''

Cognitive rigidity refers to inflexible thinking and behavioural patterns, including difficulty adapting to new information and modifying behaviour. Researchers believe that individuals with EDs often exhibit rigid beliefs about food and weight which interact with a need to exert control over negative emotions. This interaction is the proposed process in which compulsive behaviours and obsessive thoughts develop (Calder et al., 2023). In AN, rigidity manifests as strict dietary rules and fear of losing control, while in BN and BED, binge episodes may feel compulsive and uncontrollable.


'''Interoceptive Awareness'''

Interoceptive awareness (IA) refers to the ability to recognise and process internal bodily states such as hunger, satiety, pain, and arousal. IA is impaired across EDs, and contributes to body mistrust, distorted hunger cues, and inappropriate responses to internal sensations (Brown et al., 2020). Individuals may ignore physical discomfort, misinterpret bodily signals, or avoid sensations altogether, reinforcing maladaptive coping.      

 &lt;blockquote&gt;'''''QUIZ: Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{What coping style do people who experience EDs tend to show?
|type=&quot;()&quot;}
+ Avoidance-oriented
- Problem-oriented

{Compulsive behaviours are more likely to occur when food is ... and alternative rewards are ...
|type=&quot;()&quot;}
- undervalued; overvalued
+ overvalued; undervalued
&lt;/quiz&gt;&lt;/blockquote&gt;

== Psychological Mechanisms of Psychedelic-Assisted Therapy ==

PAT is proposed to influence several psychological mechanisms implicated in EDs, particularly those discussed in the previous section. The next part of this chapter aims to examine the theorised therapeutic mechanisms PAT possesses and practical implications for ED treatment.  


'''Emotion Regulation''' 

Emotion dysregulation is a core mechanism implicated in EDs. Affect regulation theory proposes that ED behaviours emerge as maladaptive strategies to escape, reduce, or blunt overwhelming emotional experiences (Schaefer et al., 2020). Restriction, bingeing, purging, and compulsive exercise may temporarily alleviate distress while reinforcing avoidance-oriented coping and limiting opportunities to learn more adaptive ways of responding to difficult emotions. 

Psychedelics often evoke intense emotional experiences that may disrupt habitual avoidance patterns. Researchers propose that, during psychedelic sessions, attempts to suppress or avoid difficult emotions can intensify these experiences, creating conditions in which emotional acceptance becomes a preferred response (Calder et al., 2023). Although this shift does not occur in every individual, experiencing difficult emotions without resorting to ED behaviours may weaken the association between emotional distress and maladaptive coping, particularly when emotional acceptance becomes associated with a more positive or tolerable experience.

The therapeutic value of this process lies in its potential to reshape affective responses. When individuals experience strong emotions without engaging in maladaptive behaviours, they may begin to develop a new approach towards emotional tolerance. Integration sessions can consolidate this learning by helping individuals articulate, differentiate, and reflect on the emotions experienced during dosing. This process may support the development of more adaptive coping strategies, including task-oriented, problem-focused, and socially supported approaches, which are associated with improved ED outcomes (Fitzsimmons &amp; Bardone-Cone, 2010). In this way, PAT may strengthen emotion regulation and reduce reliance on ED behaviours as strategies for managing affect. 


'''Reward Processing''' 

Reward dysfunction may contribute to the maintenance of EDs by reinforcing maladaptive behaviours while diminishing the perceived value of adaptive rewards. Predictive coding provides a useful framework for understanding how PAT might influence these processes. Individuals with EDs may hold rigid beliefs, conceptualised as high-level priors, about themselves in relation to food, body weight, and rewarding behaviours (Calder et al., 2023; Mograbi et al., 2024). These beliefs can influence how experiences are perceived and valued, potentially reinforcing existing behavioural patterns. Psychedelics are proposed to weaken high-level priors, allowing bottom-up sensory information to exert greater influence on perception and the valuation of experiences. 

During psychedelic experiences, individuals frequently report a heightened appreciation of sensory, social, and bodily experiences. This shift may counteract anhedonia and support the revaluation of previously feared or avoided stimuli. The therapeutic opportunity lies in translating these temporary changes in perception and reward into meaningful behavioural change. Integration sessions can explore positive and negative moments experienced during dosing and connect them to concrete goals. An example of this, inspired from Calder et al.’s (2023) article, could be to clarify specific plans to nourish the body due to the participant having experienced themselves as a decaying skeleton followed by the realisation of the body being a gift. If the period following dosing provides an opportunity for increased neuroplasticity, it may also be particularly conducive to reinforcing adaptive reward learning through behavioural activation with the help of a therapist. 


'''Cognitive Flexibility''' 

Cognitive rigidity is a hallmark of EDs and is characterised by inflexible beliefs about food, weight, body shape, and control. Predictive coding provides a framework for understanding this rigidity, as EDs may involve entrenched priors that resist updating even when confronted with contradictory sensory evidence (Zanella &amp; Lee, 2022). Psychedelics are proposed to disrupt these entrenched priors by increasing neural entropy and reducing the dominance of top-down processing (Calder et al., 2023). This temporary loosening of cognitive constraints may allow individuals to consider alternative perspectives and question long-held beliefs. 

Experiences of ego dissolution may further contribute to cognitive flexibility by reducing attachment to rigid self-concepts (Peled-Avron, 2024; Mograbi et al., 2024). When the boundaries of the self become less defined, individuals may find it easier to question identity-related beliefs that sustain ED pathology. Integration sessions can harness this potential flexibility by supporting cognitive reframing, encouraging behavioural experiments, and strengthening metacognitive awareness. Through these processes, individuals may be better able to translate insights gained during psychedelic experiences into sustained changes in thinking and behaviour.


'''Reconnecting with Bodily Signals'''

Interoceptive deficits are central to ED pathology, contributing to body mistrust, distorted perceptions of hunger cues, and difficulties responding appropriately to internal sensations (Brown et al., 2020). Psychedelics may enhance interoceptive awareness by altering sensory processing and increasing sensitivity to bodily signals. This proposed mechanism is closely related to autonomic regulation, for which polyvagal theory provides a framework for understanding the relationship between bodily signals, emotional regulation, and perceived safety.

Polyvagal theory emphasises the role of the vagus nerve in interoception, emotional regulation, and the perception of safety (Porges, 2022). Vagal afferents transmit information from the body to the insula, where interoceptive signals are integrated with emotional and cognitive processes. Individuals with EDs may exhibit chronic sympathetic arousal and reduced vagal tone, potentially impairing interoceptive accuracy and contributing to emotional rigidity. Psychedelics may initially increase sympathetic activity, as reflected in physiological responses such as increased heart rate, followed by a parasympathetic shift associated with greater relaxation and an increased capacity for rest (Li et al., 2025). Within a polyvagal framework, these changes may have implications for vagal regulation, interoceptive awareness, and emotional regulation.

The therapeutic value of this proposed mechanism lies in its potential to restore trust in bodily signals. Integration sessions may support this process by helping individuals explore bodily sensations experienced during dosing, connect interoceptive cues with emotional states, and practise interoceptive exposure to hunger, fullness, and anxiety-related sensations. Incorporating mindfulness techniques may further support autonomic regulation and help individuals develop a more adaptive relationship with their bodily experiences.

 A Brief Note Concerning The Gut-Brain Interaction 
Although gut microbiome disruption is not a direct psychological mechanism in EDs, it is a relevant biological factor to consider when examining the potential effects of PAT. Restrictive or chaotic eating patterns can contribute to gut dysbiosis, which may weaken gut-barrier integrity and contribute to inflammation affecting the brain (Anton-Paduraru et al., 2024). These changes have been shown to influence mood, stress responsivity, cognitive rigidity, and interoceptive awareness through HPA-axis activation, altered neurotransmitter synthesis, and disrupted hunger–satiety signalling. 

Emerging research suggests that psychedelics may also interact with the gut–brain axis. Certain microbes can metabolise psychedelic compounds, and microbial activity has been associated with modulatory effects on behavioural outcomes. Additionally, psychedelic use may alter microbial composition towards anti-inflammatory profiles, with potential implications for neuroplasticity, neurotransmitter synthesis and signalling improvements (Caspani et al., 2024). These microbiome-related effects may therefore contribute to changes in mood, cognitive flexibility, and appetite regulation.

Although the therapeutic potential of psychedelics in EDs is considered primarily in relation to psychological mechanisms, including changes in perception, emotional processing, and reduced avoidance, microbiome-related effects may represent an additional pathway through which biological processes influence psychological outcomes. However, the extent to which these interactions contribute to therapeutic outcomes in EDs remains to be established.


&lt;blockquote&gt;'''QUIZ: ''Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{ In predictive coding terms, what are “high‑level priors” in eating disorders? 
|type=&quot;()&quot;}
+ Rigid, entrenched beliefs about food, weight, and the self that shape perception and behaviour
- Flexible beliefs that easily update with new sensory information
- Momentary emotional reactions triggered by external cues

{What is the proposed mechanism by which psychedelics support emotion regulation in PAT for EDs? 
|type=&quot;()&quot;}
- By suppressing emotional intensity to prevent distress
+ By evoking strong emotions that disrupt avoidance patterns and promote emotional acceptance
- By eliminating negative emotions through serotonin release

{What is interoceptive awareness?
|type=&quot;()&quot;}
- The ability to evaluate reward value and anticipate pleasurable outcomes
+ The capacity to sense, interpret, and respond to internal bodily signals such as hunger, fullness, and emotional arousal
- The process of weakening cognitive rigidity through ego dissolution
&lt;/quiz&gt;&lt;/blockquote&gt;

== Limitations ==
Despite the potential of PAT to influence psychological mechanisms implicated in EDs, several limitations constrain current understanding of these processes and their therapeutic relevance. Research examining emotion dysregulation in EDs illustrates broader challenges in establishing the mechanisms underlying these conditions. Although non-acceptance of emotions has been identified as a transdiagnostic risk factor across psychiatric conditions (Paulus et al., 2021), Zhou et al.’s meta-analysis (2025) highlights that the causal pathways linking emotional dysregulation and EDs remain unclear, largely because of a lack of experimental and longitudinal studies. Further limitations include restricted availability of measurement scales, insufficient cultural specificity, heterogeneity across samples, gender imbalance, and limited developmental analysis. Together, these factors constrain understanding of how specific emotional processes relate to different ED presentations across the lifespan and stages of recovery.

These limitations are also relevant when considering the proposed mechanisms of PAT. Although existing theoretical frameworks offer ways to conceptualise how psychedelic experiences may influence psychological processes responsible for EDs, the emerging nature of psychedelic therapy limits the extent to which proposed mechanisms have been tested. However, with the number of clinical trials increasing as of recently, it will be interesting to see how the theorised therapeutic mechanisms across different ED presentations and stages of recovery emerges during further warranted investigation.

Nevertheless, current limitations in the evidence highlight the need for research that clarifies the relationships between psychological processes that underscore ED behaviours, and treatment outcomes. There are several important psychological components of ED maintenance that represent meaningful targets for treatment, but they should not be considered in isolation from eachother or the neurobiological processes that influence them. A more comprehensive understanding of how these mechanisms interact may help clarify the therapeutic potential of PAT and inform the development of more targeted treatment approaches.

== Conclusion ==
PAT offers a potential framework for addressing several interconnected psychological mechanisms implicated in EDs. Through its proposed effects on emotional processing, reward valuation, cognitive flexibility, and interoceptive awareness, PAT may create opportunities to disrupt established patterns of avoidance, rigid thinking, and maladaptive behavioural reinforcement. The gut–brain interaction may represent an additional biological pathway relevant to these processes.

These mechanisms should not be understood as independent processes. Changes in emotion regulation may influence the ability to tolerate bodily sensations, while shifts in reward valuation and cognitive flexibility may create opportunities to respond differently to distress and challenge entrenched beliefs. However, the extent to which PAT produces these changes, and whether they translate into sustained improvements in ED outcomes, requires further investigation, although preliminary evidence is promising. 

The therapeutic potential of PAT lies not only in the acute psychedelic experience but also in the structured integration process that follows. Integration sessions provide an opportunity to translate emotional breakthroughs, changes in cognitive flexibility, interoceptive shifts, and reward processing into sustained behavioural change. Effective integration involves helping individuals articulate insights, connect them to ED-related patterns, and develop concrete strategies for change. These may include strengthening adaptive coping, challenging rigid beliefs, practising interoceptive awareness, reinforcing positive reward experiences, and supporting nutritional rehabilitation.

By grounding the understanding of PAT in affect regulation theory and the predictive coding framework, therapists may be better positioned to help individuals explore how psychedelic experiences could disrupt maladaptive emotional and cognitive patterns and create opportunities for new learning. Polyvagal-informed approaches may further support the development of mind–body awareness and emotional regulation through mindfulness strategies. Together, these approaches offer a multifaceted framework for translating psychedelic experiences into therapeutic change and addressing the interconnected mechanisms that maintain EDs and associated suffering. 

==See Also==
* [https://w.wiki/TsdG Ayahuasca and the brain] (Wikiversity)
* [https://w.wiki/TscF Emotional effects of psychedelics] (Wikiversity)
* [https://w.wiki/Tsdb Psilocybin and emotion] (Wikiversity)
* [https://w.wiki/TsdS Psilocibyn assisted psychotherapy] (Wikiversity)
* [https://w.wiki/Tsce Psychedelics, altered consciousness, and personal growth] (Wikiversity)
* [[Eating Disorders|Eating disorders]] (Wikiversity)

==References==
{{Hanging indent|1=

{{ic|Try &quot;Edit source&quot; and then wrapping any text to be italicised in two apostrophes e.g., ''this is italics''}}

Anton-Păduraru, D. T., Trofin, F., Nastase, E. V., Miftode, R. S., Miftode, I. L., Trandafirescu, M. F., Cojocaru, E., Țarcă, E., Mindru, D. E., &amp; Dorneanu, O. S. (2023). The Role of the Gut Microbiota in Anorexia Nervosa in Children and Adults-Systematic Review. &quot;International journal of molecular sciences, 25&quot;(1), 41. https://doi.org/10.3390/ijms25010041

Brown, T. A., Vanzhula, I. A., Reilly, E. E., Levinson, C. A., Berner, L. A., Krueger, A., Lavender, J. M., Kaye, W. H., &amp; Wierenga, C. E. (2020). Body mistrust bridges interoceptive awareness and eating disorder symptoms. &quot;Journal of abnormal psychology, 129&quot;(5), 445–456. https://doi.org/10.1037/abn0000516 

Calder, A., Mock, S., Friedli, N., Pasi, P., &amp; Hasler, G. (2023). Psychedelics in the treatment of eating disorders: Rationale and potential mechanisms. &quot;European Neuropsychopharmacology, 75&quot;, 1–14. https://doi.org/10.1016/j.euroneuro.2023.05.008 

Caspani, G., Ruffell, S. G. D., Tsang, W., Netzband, N., Rohani-Shukla, C., Swann, J. R., &amp; Jefferies, W. A. (2024). Mind over matter: the microbial mindscapes of psychedelics and the gut-brain axis. &quot;Pharmacological research, 207&quot;, 107338. https://doi.org/10.1016/j.phrs.2024.107338  

Fitzsimmons, E. E., &amp; Bardone-Cone, A. M. (2010). Differences in coping across stages of recovery from an eating disorder. &quot;The International journal of eating disorders, 43&quot;(8), 689–693. https://doi.org/10.1002/eat.20781 

Hatzipantelis, C. J., &amp; Olson, D. E. (2024). The Effects of Psychedelics on Neuronal Physiology. &quot;Annual review of physiology, 86&quot;, 27–47. https://doi.org/10.1146/annurev-physiol-042022-020923

Hay, P., Aouad, P., Le, A., Marks, P., Maloney, D., National Eating Disorder Research Consortium, Touyz, S., &amp; Maguire, S. (2023). Epidemiology of eating disorders: population, prevalence, disease burden and quality of life informing public policy in Australia-a rapid review. &quot;Journal of eating disorders, 11&quot;(1), 23. https://doi.org/10.1186/s40337-023-00738-7

Li, H., Wang, H., &amp; Wang, X. (2025). Psychedelics and the Autonomic Nervous System: A Perspective on Their Interplay and Therapeutic Potential. &quot;ACS pharmacology &amp; translational science, 8&quot;(3), 899–902. https://doi.org/10.1021/acsptsci.5c00005 

Leppanen, J., Brown, D., McLinden, H., Williams, S., &amp; Tchanturia, K. (2022). The Role of Emotion Regulation in Eating Disorders: A Network Meta-Analysis Approach. &quot;Frontiers in psychiatry, 13&quot;, 793094. https://doi.org/10.3389/fpsyt.2022.793094 

Mograbi, D. C., Rodrigues, R., Bienemann, B., &amp; Huntley, J. (2024). Brain Networks, Neurotransmitters and Psychedelics: Towards a Neurochemistry of Self-Awareness. &quot;Current neurology and neuroscience reports, 24&quot;(8), 323–340. https://doi.org/10.1007/s11910-024-01353-y

Paulus F. W., Ohmann S., Möhler E., Plener P. &amp; Popow C. (2021). Emotional Dysregulation in Children and Adolescents With Psychiatric Disorders. A Narrative Review. &quot;Frontiers in Psychiatry 12&quot;:628252. doi: 10.3389/fpsyt.2021.628252

Peled-Avron L., Aday J. Ss, Kalafateli A. L., Hamilton H. K., Woolley J. D. (2024). Editorial: Down the rabbit hole – the psychological and neural mechanisms of psychedelic compounds and their use in treating mental health and medical conditions. &quot;Frontiers in Psychiatry 15&quot;:1431389. doi: 10.3389/fpsyt.2024.1431389

Porges S. W. (2025). Polyvagal Theory: Current Status, Clinical Applications, and Future Directions. &quot;Clinical neuropsychiatry, 22&quot;(3), 169–184. https://doi.org/10.36131/cnfioritieditore20250301

Schaefer, L. M., Smith, K. E., Anderson, L. M., Cao, L., Crosby, R. D., Engel, S. G., Crow, S. J., Peterson, C. B., &amp; Wonderlich, S. A. (2020). The role of affect in the maintenance of binge-eating disorder: Evidence from an ecological momentary assessment study. &quot;Journal of abnormal psychology, 129&quot;(4), 387–396. https://doi.org/10.1037/abn0000517 

Shank, L. M., Tanofsky-Kraff, M., Kelly, N. R., Jaramillo, M., Rubin, S. G., Altman, D. R., Byrne, M. E., LeMay-Russell, S., Schvey, N. A., Broadney, M. M., Brady, S. M., Yang, S. B., Courville, A. B., Ramirez, S., Crist, A. C., Yanovski, S. Z., &amp; Yanovski, J. A. (2019). The association between alexithymia and eating behavior in children and adolescents. &quot;Appetite, 142&quot;, 104381. https://doi.org/10.1016/j.appet.2019.104381

Wolfgang, A. S., &amp; Hoge, C. W. (2023). Psychedelic-Assisted Therapy in Military and Veterans Healthcare Systems: Clinical, Legal, and Implementation Considerations. &quot;Current psychiatry reports, 25&quot;(10), 513–532. https://doi.org/10.1007/s11920-023-01446-4 

Zanella, E., &amp; Lee, E. (2022). Integrative review on psychological and social risk and prevention factors of eating disorders including anorexia nervosa and bulimia nervosa: seven major theories. &quot;Heliyon, 8&quot;(11), e11422. https://doi.org/10.1016/j.heliyon.2022.e11422 

Zhou, R., Zhang, L., Liu, Z., &amp; Cao, B. (2025). Emotion regulation difficulties and disordered eating in adolescents and young adults: a meta-analysis. &quot;Journal of eating disorders, 13&quot;(1), 25. https://doi.org/10.1186/s40337-025-01197-y

}}

==External links==
* [https://www.abct.org/fact-sheets/psychedelic-assisted-therapy/ Psychedelic-Assisted Therapy | Fact Sheet] (ABCT - Association for Behavioral and Cognitive Therapies)
* [https://podcasts.apple.com/au/podcast/can-magic-mushrooms-help-treat-anorexia/id189330872?i=1000784809236 Can magic mushrooms help treat anorexia?] (Apple Podcasts)
* [https://www.apa.org/news/podcasts/speaking-of-psychology/eating-disorder The ‘silent epidemic’ of eating disorders] (American Psychological Association)
* [https://www.apa.org/monitor/2023/04/sensations-eating-disorders-suicidal-behavior What is interoception, and how does it affect mental health]? 5 questions for April Smith (American Psychological Association)
* [https://www.cbte.co/what-is-cbte/transdiagnostic-view-eating-disorders/ Transdiagnostic view of eating disorders] (cbte.co)
* [https://psychedelic.support/resources/polyvagal-theory-mind-body-dr-erica-zelfand/ Polyvagal Theory with Dr. Erica Zelfand: Mind-Body Connection] ·(Psychedelic Support)
* [https://www.wholeselfnutrition.org/post/nervous-system-regulation-a-missing-piece-in-eating-disorder-recovery Nervous System Regulation: A Missing Piece in Eating Disorder Recovery]  (wholeselfnutrition.org)

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      <text bytes="36302" sha1="902jesrss4x236zbt8wpvhmq7ro5ssg" xml:space="preserve">{{title|Psychedelic treatment of eating disorders:&lt;br&gt;How might psychedelic-assisted therapy influence psychological mechanisms involved in eating disorders?}}
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== Overview ==
{{RoundBoxTop|theme=7}}[[File:Neural network - Midjourney and Grok.png|thumb|'''Figure 1.''' Psychedelics are thought to temporarily disrupt rigid neural communication pathways, promoting more flexible patterns of connectivity across networks involved in mood regulation, fear processing, reward learning, and cognitive adaptability. These changes may support therapeutic shifts in behaviour and emotional processing (Hatzipantelis &amp; Olson, 2025).]]Emma, a 27‑year‑old from Canberra, has lived with an eating disorder for nearly two decades. She describes her problem eating behaviours to have started at school, after being bullied about her appearance. Ever since, they have remained in her life as “a way for me to feel in control”. Although she is aware of the harm caused by restrictive eating and compulsive exercise, she feels trapped in her thought patterns characterised by a preoccupation about food and weight concerns which have become entrenched in her daily life. 

After reading an article describing emerging research suggesting that psychedelics may alter patterns of neural connectivity that shape behaviour (see Figure 1), she expressed interest in pursuing psychedelic‑assisted therapy through a provider accessible to her.

After participating in her first supervised psilocybin‑assisted therapy session, Emma reported experiencing an emotional journey that allowed her to feel “connected to my body for the first time in years”. After 3 months, she has noticed a shift in how she relates to her body, and is finding it easier to actively call into question how she responds to distress with the support of her psychotherapist. 


Her experience raises a central question: What psychological mechanisms could explain these changes?{{RoundBoxBottom|theme=3}}  

This chapter explores how psychedelic‑assisted therapy (PAT) may influence the emotional, cognitive, and neurobiological processes that underpin eating disorders (EDs).   

{{RoundBoxTop|theme=11}}'''Focus questions'''
{{ic|}}Two central questions will be addressed:
* What psychological processes underpin eating disorders, and how do they guide ED behaviour?
* How might psychedelic‑assisted therapy influence these processes to support recovery?
{{ic|}}{{ic|}}{{RoundBoxBottom}}

== Introduction ==
'''Eating Disorders'''  

[[wikipedia:Eating_disorder|Eating disorders]] (EDs) are psychiatric conditions characterised by abnormal eating behaviours that negatively affect physical and mental health. They are associated with chronic illness, disability, reduced quality of life, increased suicide risk, and are highly comorbid with [[wikipedia:Mood_disorder|mood disorders]], [[wikipedia:Post-traumatic_stress_disorder|post-traumatic stress disorder]] (PTSD), [[wikipedia:Obsessive–compulsive_disorder|obsessive-compulsive disorder]] (OCD), and [[wikipedia:Substance_use_disorder|substance use disorders]] (Calder et al., 2023). [[wikipedia:Anorexia|Anorexia nervosa]] (AN) has the highest mortality rate of any psychiatric disorder, while [[wikipedia:Bulimia|bulimia nervosa]] (BN) and [[wikipedia:Binge_eating_disorder|binge‑eating disorder]] (BED) are also highly prevalent types of eating disorders.  

In Australia, the prevalence of EDs is rising, particularly among young people. Approximately 10.46% of the population has experienced an eating disorder at some point, with an estimated economic burden of $84 billion (Hay et al., 2023). Despite decades of research, the pathogenesis of EDs remains incompletely understood (Calder et al., 2023). Current evidence suggests a complex interplay between genetic predisposition, temperament, hormonal dysregulation, cognitive abnormalities, sociocultural pressures, and traumatic experiences.

Although cognitive‑behavioural therapy (CBT‑E) combined with pharmacological treatment has demonstrated beneficial outcomes, efficacy remains limited and varies across ED types (Calder et al., 2023). Recovery is often long and difficult, with only two‑thirds of individuals with AN and BN eventually recovering, while others can remain ill for many years. This highlights the need for treatment approaches that can accelerate recovery and provide benefit for individuals who do not respond to conventional therapies.


'''Psychedelic-Assisted Therapy'''

In 2023, Australia legalised the prescription of MDMA and psilocybin under professional supervision, marking a significant shift in mental‑health treatment options. Psychedelic compounds, including [[wikipedia:LSD|LSD]], [[wikipedia:Psilocybin|psilocybin]], [[wikipedia:Dimethyltryptamine|DMT]], [[wikipedia:Ketamine|ketamine]], and [[wikipedia:MDMA|MDMA]], have demonstrated promising therapeutic effects across a wide range of psychiatric conditions. Researchers propose that psychedelics act through psychological and neural mechanisms that increase [[wikipedia:Neuroplasticity|neuroplasticity]], facilitate insight, and foster emotional acceptance (Peled‑Avron et al., 2024). At a neurobiological level, psychedelics influence processes that inform perception, emotion, and behaviour, offering a potential avenue for addressing entrenched ED mechanisms.

PAT differs from pharmacological treatment alone because the drug is administered within a structured therapeutic context designed to maximise safety and clinical benefit (Calder et al., 2023). Treatment typically involves three types of sessions. Preparatory sessions feature participants undergoing psychoeducation, where the clinician establishes rapport and clear safety protocols. Followed by supervised medication where the participant has an inward experience with the reassurance of clinicians present in the same space. Lastly, integrative sessions where individuals process and explore insights from the previous session with their psychotherapist to foster behavioural change (Wolfgang &amp; Hoge, 2023). This combination of pharmacological and psychological intervention is theorised to effectively target underlying psychological mechanisms common across various mental health disorders, illustrating PAT’s potential as a valuable transdiagnostic treatment option. 

PAT has become a subject of increasing popularity in ED research because many of the psychological mechanisms it is proposed to influence are the same ones implicated in ED maintenance and comorbidities (Calder et al., 2023; Peled-Avron et al., 2024). Early research, including case study reports, small clinical studies, meta-analyses and reviews indicate that PAT produces improvements in affect, reductions in ED symptom severity, enhanced body image, weight restoration, and reductions in comorbid symptoms. Although preliminary, these findings indicate that PAT may disrupt and promote shifts away from maladaptive coping patterns that become entrenched in treatment resistant ED populations.

== Psychological Mechanisms in Eating Disorders ==


'''Emotion Dysregulation'''

Emotion dysregulation is considered to be a significant risk factor for the onset and maintenance of EDs. It refers to difficulties recognising, assessing, and modifying emotional responses to meet situational demands (Zhou et al., 2025). 

Research consistently shows that individuals with EDs experience significant challenges in regulating emotions, increasing their vulnerability to comorbid symptoms, which contribute to the emergence of disordered eating patterns (Leppanen et al., 2022). This idea is supported by affect regulation theory which posits that eating disorders develop and are maintained as maladaptive strategies to manage, tolerate and escape from negative emotions and psychological distress (Schaefer et al., 2020; Zanella &amp; Lee, 2022). This is further exemplified in Fitzsimmons &amp; Bardone-Cone’s article examining differences in coping within eating disorder patients (2010). The authors explain that avoidance and emotion-oriented coping styles often function as maladaptive attempts to manage (di)stress. They explain that behaviours such as binge eating, purging, starvation, and/or compulsive exercise provide temporary relief by shifting attention away from uncomfortable emotions. 

Furthermore, alexithymia, characterised by difficulty identifying and describing one’s own emotions, is strongly associated with ED pathology (Shank et al., 2019). Individuals with high alexithymia often struggle to differentiate emotional states from bodily sensations, contributing to behaviours such as emotional eating, eating in the absence of hunger, or rigid restriction. In BED, alexithymia is linked to binge episodes triggered by poorly understood emotional cues, while in AN and BN, alexithymia may contribute to emotional avoidance and reliance on ED behaviours for affect regulation. 

The effects of trauma are contributing factors to emotion dysregulation, and considered a risk factor for ED development. Individuals who experience sexual, physical, or emotional abuse, neglect, and bullying are likely to experience heightened emotional reactivity, threat perception, and avoidance behaviours (Calder et al., 2023). Researchers explain that trauma often results in lowered distress tolerance and increased reliance on maladaptive coping behaviours, including disordered eating. Furthermore, PTSD comorbidity is common, hence trauma‑related symptoms are hypothesised to frequently interact with ED behaviours in complex ways.  


'''Reward Processing Dysfunction'''
[[File:Striatum.gif|thumb|'''Figure 2.''' Striatum]]
[[File:Anterior cingulate gyrus animation.gif|thumb|'''Figure 3'''. Anterior Cingulate Cortex ]]
Abnormal reward valuation is understood to be a central psychological mechanism that maintains ED behaviours. Research consistently shows that individuals with eating disorders display altered neural activity response to various stimuli, as well as disruptions in reinforcement learning (Calder et al., 2023). Brain regions involved in reward processing, habit formation, and learning, such as the striatum and anterior cingulate cortex (see figures 2 &amp; 3), exhibit atypical activation patterns and differences in dopamine receptor binding across ED types. The insula (see figure 4), which integrates bodily sensations with conscious thought, emotion, and behaviour, also shows altered responses. Together, these regions have been shown to react differently to food images, taste, and social feedback compared to healthy controls, indicating that reward dysfunction extends beyond eating‑related stimuli for ED populations.
[[File:Insular cortex.gif|thumb|'''Figure 4.''' Insula. ]]
In the context of BN and BED, research shows that food is valued more highly than other types of rewards, thus shaping behaviour through its heightened influence on reward outcomes (Calder et al., 2023). Compulsive behaviours specific to each condition (e.g. bingeing, purging) are therefore more likely to occur when food is overvalued and alternative rewards are discounted or ignored. In addition to the neural changes already described, BN and BED are associated with reduced structural and functional connectivity between frontal control regions and the striatum. This combination of highly salient food rewards, and weakened fronto‑striatal pathways, reduces an individual’s ability to inhibit or modulate reward‑seeking impulses. Weak connectivity in these circuits is thought to predict compulsive reward‑seeking behaviour. As a result, even when individuals experience negative consequences from binge episodes, they may struggle to learn from these outcomes or adjust their behaviour accordingly.


Anhedonia, a global reduction in reward responsiveness, is frequently reported by people who experience AN, resulting in food and eating becoming undervalued or aversive to them (Calder et al., 2023). Researchers propose that reward contamination further contributes to this pattern, where the brain learns to associate normally punishing stimuli (e.g., starvation, excessive exercise) with reward, while normally rewarding stimuli (e.g., high‑calorie foods) become experienced as punishment. Structural reductions in the striatum and somatosensory cortex have also been observed, which accounts for distorted bodily sensations and contributes to anhedonia. These changes support maladaptive conditioning in which starvation and weight loss embody a sense of safety, achievement, and emotional relief. Restrictive and preoccupied behaviours centred on food, body shape, and exercise are therefore reinforced over time.

Consistent with affect‑regulation models, eating‑disorder behaviours also become negatively reinforced because they reduce emotional discomfort. This relief increases the likelihood that the behaviours will be repeated, further embedding them within the individual’s coping pattern.


'''Cognitive Rigidity'''

Cognitive rigidity refers to inflexible thinking and behavioural patterns, including difficulty adapting to new information and modifying behaviour. Researchers believe that individuals with EDs often exhibit rigid beliefs about food and weight which interact with a need to exert control over negative emotions. This interaction is the proposed process in which compulsive behaviours and obsessive thoughts develop (Calder et al., 2023). In AN, rigidity manifests as strict dietary rules and fear of losing control, while in BN and BED, binge episodes may feel compulsive and uncontrollable.


'''Interoceptive Awareness'''

Interoceptive awareness (IA) refers to the ability to recognise and process internal bodily states such as hunger, satiety, pain, and arousal. IA is impaired across EDs, and contributes to body mistrust, distorted hunger cues, and inappropriate responses to internal sensations (Brown et al., 2020). Individuals may ignore physical discomfort, misinterpret bodily signals, or avoid sensations altogether, reinforcing maladaptive coping.      

 &lt;blockquote&gt;'''''QUIZ: Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{What coping style do people who experience EDs tend to show?
|type=&quot;()&quot;}
+ Avoidance-oriented
- Problem-oriented

{Compulsive behaviours are more likely to occur when food is ... and alternative rewards are ...
|type=&quot;()&quot;}
- undervalued; overvalued
+ overvalued; undervalued
&lt;/quiz&gt;&lt;/blockquote&gt;

== Psychological Mechanisms of Psychedelic-Assisted Therapy ==

PAT is proposed to influence several psychological mechanisms implicated in EDs, particularly those discussed in the previous section. The next part of this chapter aims to examine the theorised therapeutic mechanisms PAT possesses and practical implications for ED treatment.  


'''Emotion Regulation''' 

Emotion dysregulation is a core mechanism implicated in EDs. Affect regulation theory proposes that ED behaviours emerge as maladaptive strategies to escape, reduce, or blunt overwhelming emotional experiences (Schaefer et al., 2020). Restriction, bingeing, purging, and compulsive exercise may temporarily alleviate distress while reinforcing avoidance-oriented coping and limiting opportunities to learn more adaptive ways of responding to difficult emotions. 

Psychedelics often evoke intense emotional experiences that may disrupt habitual avoidance patterns. Researchers propose that, during psychedelic sessions, attempts to suppress or avoid difficult emotions can intensify these experiences, creating conditions in which emotional acceptance becomes a preferred response (Calder et al., 2023). Although this shift does not occur in every individual, experiencing difficult emotions without resorting to ED behaviours may weaken the association between emotional distress and maladaptive coping, particularly when emotional acceptance becomes associated with a more positive or tolerable experience.

The therapeutic value of this process lies in its potential to reshape affective responses. When individuals experience strong emotions without engaging in maladaptive behaviours, they may begin to develop a new approach towards emotional tolerance. Integration sessions can consolidate this learning by helping individuals articulate, differentiate, and reflect on the emotions experienced during dosing. This process may support the development of more adaptive coping strategies, including task-oriented, problem-focused, and socially supported approaches, which are associated with improved ED outcomes (Fitzsimmons &amp; Bardone-Cone, 2010). In this way, PAT may strengthen emotion regulation and reduce reliance on ED behaviours as strategies for managing affect. 


'''Reward Processing''' 

Reward dysfunction may contribute to the maintenance of EDs by reinforcing maladaptive behaviours while diminishing the perceived value of adaptive rewards. Predictive coding provides a useful framework for understanding how PAT might influence these processes. Individuals with EDs may hold rigid beliefs, conceptualised as high-level priors, about themselves in relation to food, body weight, and rewarding behaviours (Calder et al., 2023; Mograbi et al., 2024). These beliefs can influence how experiences are perceived and valued, potentially reinforcing existing behavioural patterns. Psychedelics are proposed to weaken high-level priors, allowing bottom-up sensory information to exert greater influence on perception and the valuation of experiences. 

During psychedelic experiences, individuals frequently report a heightened appreciation of sensory, social, and bodily experiences. This shift may counteract anhedonia and support the revaluation of previously feared or avoided stimuli. The therapeutic opportunity lies in translating these temporary changes in perception and reward into meaningful behavioural change. Integration sessions can explore positive and negative moments experienced during dosing and connect them to concrete goals. An example of this, inspired from Calder et al.’s (2023) article, could be to clarify specific plans to nourish the body due to the participant having experienced themselves as a decaying skeleton followed by the realisation of the body being a gift. If the period following dosing provides an opportunity for increased neuroplasticity, it may also be particularly conducive to reinforcing adaptive reward learning through behavioural activation with the help of a therapist. 


'''Cognitive Flexibility''' 

Cognitive rigidity is a hallmark of EDs and is characterised by inflexible beliefs about food, weight, body shape, and control. Predictive coding provides a framework for understanding this rigidity, as EDs may involve entrenched priors that resist updating even when confronted with contradictory sensory evidence (Zanella &amp; Lee, 2022). Psychedelics are proposed to disrupt these entrenched priors by increasing neural entropy and reducing the dominance of top-down processing (Calder et al., 2023). This temporary loosening of cognitive constraints may allow individuals to consider alternative perspectives and question long-held beliefs. 

Experiences of ego dissolution may further contribute to cognitive flexibility by reducing attachment to rigid self-concepts (Peled-Avron, 2024; Mograbi et al., 2024). When the boundaries of the self become less defined, individuals may find it easier to question identity-related beliefs that sustain ED pathology. Integration sessions can harness this potential flexibility by supporting cognitive reframing, encouraging behavioural experiments, and strengthening metacognitive awareness. Through these processes, individuals may be better able to translate insights gained during psychedelic experiences into sustained changes in thinking and behaviour.


'''Reconnecting with Bodily Signals'''

Interoceptive deficits are central to ED pathology, contributing to body mistrust, distorted perceptions of hunger cues, and difficulties responding appropriately to internal sensations (Brown et al., 2020). Psychedelics may enhance interoceptive awareness by altering sensory processing and increasing sensitivity to bodily signals. This proposed mechanism is closely related to autonomic regulation, for which polyvagal theory provides a framework for understanding the relationship between bodily signals, emotional regulation, and perceived safety.

Polyvagal theory emphasises the role of the vagus nerve in interoception, emotional regulation, and the perception of safety (Porges, 2022). Vagal afferents transmit information from the body to the insula, where interoceptive signals are integrated with emotional and cognitive processes. Individuals with EDs may exhibit chronic sympathetic arousal and reduced vagal tone, potentially impairing interoceptive accuracy and contributing to emotional rigidity. Psychedelics may initially increase sympathetic activity, as reflected in physiological responses such as increased heart rate, followed by a parasympathetic shift associated with greater relaxation and an increased capacity for rest (Li et al., 2025). Within a polyvagal framework, these changes may have implications for vagal regulation, interoceptive awareness, and emotional regulation.

The therapeutic value of this proposed mechanism lies in its potential to restore trust in bodily signals. Integration sessions may support this process by helping individuals explore bodily sensations experienced during dosing, connect interoceptive cues with emotional states, and practise interoceptive exposure to hunger, fullness, and anxiety-related sensations. Incorporating mindfulness techniques may further support autonomic regulation and help individuals develop a more adaptive relationship with their bodily experiences.

 A Brief Note Concerning The Gut-Brain Interaction 
Although gut microbiome disruption is not a direct psychological mechanism in EDs, it is a relevant biological factor to consider when examining the potential effects of PAT. Restrictive or chaotic eating patterns can contribute to gut dysbiosis, which may weaken gut-barrier integrity and contribute to inflammation affecting the brain (Anton-Paduraru et al., 2024). These changes have been shown to influence mood, stress responsivity, cognitive rigidity, and interoceptive awareness through [[wikipedia:Hypothalamic–pituitary–adrenal_axis|HPA-axis activation]], altered neurotransmitter synthesis, and disrupted hunger–satiety signalling. 

Emerging research suggests that psychedelics may also interact with the gut–brain axis. Certain microbes can metabolise psychedelic compounds, and microbial activity has been associated with modulatory effects on behavioural outcomes. Additionally, psychedelic use may alter microbial composition towards anti-inflammatory profiles, with potential implications for neuroplasticity, neurotransmitter synthesis and signalling improvements (Caspani et al., 2024). These microbiome-related effects may therefore contribute to changes in mood, cognitive flexibility, and appetite regulation.

Although the therapeutic potential of psychedelics in EDs is considered primarily in relation to psychological mechanisms, including changes in perception, emotional processing, and reduced avoidance, microbiome-related effects may represent an additional pathway through which biological processes influence psychological outcomes. However, the extent to which these interactions contribute to therapeutic outcomes in EDs remains to be established.


&lt;blockquote&gt;'''QUIZ: ''Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{ In predictive coding terms, what are “high‑level priors” in eating disorders? 
|type=&quot;()&quot;}
+ Rigid, entrenched beliefs about food, weight, and the self that shape perception and behaviour
- Flexible beliefs that easily update with new sensory information
- Momentary emotional reactions triggered by external cues

{What is the proposed mechanism by which psychedelics support emotion regulation in PAT for EDs? 
|type=&quot;()&quot;}
- By suppressing emotional intensity to prevent distress
+ By evoking strong emotions that disrupt avoidance patterns and promote emotional acceptance
- By eliminating negative emotions through serotonin release

{What is interoceptive awareness?
|type=&quot;()&quot;}
- The ability to evaluate reward value and anticipate pleasurable outcomes
+ The capacity to sense, interpret, and respond to internal bodily signals such as hunger, fullness, and emotional arousal
- The process of weakening cognitive rigidity through ego dissolution
&lt;/quiz&gt;&lt;/blockquote&gt;

== Limitations ==
Despite the potential of PAT to influence psychological mechanisms implicated in EDs, several limitations constrain current understanding of these processes and their therapeutic relevance. Research examining emotion dysregulation in EDs illustrates broader challenges in establishing the mechanisms underlying these conditions. Although non-acceptance of emotions has been identified as a transdiagnostic risk factor across psychiatric conditions (Paulus et al., 2021), Zhou et al.’s meta-analysis (2025) highlights that the causal pathways linking emotional dysregulation and EDs remain unclear, largely because of a lack of experimental and longitudinal studies. Further limitations include restricted availability of measurement scales, insufficient cultural specificity, heterogeneity across samples, gender imbalance, and limited developmental analysis. Together, these factors constrain understanding of how specific emotional processes relate to different ED presentations across the lifespan and stages of recovery.

These limitations are also relevant when considering the proposed mechanisms of PAT. Although existing theoretical frameworks offer ways to conceptualise how psychedelic experiences may influence psychological processes responsible for EDs, the emerging nature of psychedelic therapy limits the extent to which proposed mechanisms have been tested. However, with the number of clinical trials increasing as of recently, it will be interesting to see how the theorised therapeutic mechanisms across different ED presentations and stages of recovery emerges during further warranted investigation.

Nevertheless, current limitations in the evidence highlight the need for research that clarifies the relationships between psychological processes that underscore ED behaviours, and treatment outcomes. There are several important psychological components of ED maintenance that represent meaningful targets for treatment, but they should not be considered in isolation from eachother or the neurobiological processes that influence them. A more comprehensive understanding of how these mechanisms interact may help clarify the therapeutic potential of PAT and inform the development of more targeted treatment approaches.

== Conclusion ==
PAT offers a potential framework for addressing several interconnected psychological mechanisms implicated in EDs. Through its proposed effects on emotional processing, reward valuation, cognitive flexibility, and interoceptive awareness, PAT may create opportunities to disrupt established patterns of avoidance, rigid thinking, and maladaptive behavioural reinforcement. The gut–brain interaction may represent an additional biological pathway relevant to these processes.

These mechanisms should not be understood as independent processes. Changes in emotion regulation may influence the ability to tolerate bodily sensations, while shifts in reward valuation and cognitive flexibility may create opportunities to respond differently to distress and challenge entrenched beliefs. However, the extent to which PAT produces these changes, and whether they translate into sustained improvements in ED outcomes, requires further investigation, although preliminary evidence is promising. 

The therapeutic potential of PAT lies not only in the acute psychedelic experience but also in the structured integration process that follows. Integration sessions provide an opportunity to translate emotional breakthroughs, changes in cognitive flexibility, interoceptive shifts, and reward processing into sustained behavioural change. Effective integration involves helping individuals articulate insights, connect them to ED-related patterns, and develop concrete strategies for change. These may include strengthening adaptive coping, challenging rigid beliefs, practising interoceptive awareness, reinforcing positive reward experiences, and supporting nutritional rehabilitation.

By grounding the understanding of PAT in affect regulation theory and the predictive coding framework, therapists may be better positioned to help individuals explore how psychedelic experiences could disrupt maladaptive emotional and cognitive patterns and create opportunities for new learning. Polyvagal-informed approaches may further support the development of mind–body awareness and emotional regulation through mindfulness strategies. Together, these approaches offer a multifaceted framework for translating psychedelic experiences into therapeutic change and addressing the interconnected mechanisms that maintain EDs and associated suffering. 

==See Also==
* [https://w.wiki/TsdG Ayahuasca and the brain] (Wikiversity)
* [https://w.wiki/TscF Emotional effects of psychedelics] (Wikiversity)
* [https://w.wiki/Tsdb Psilocybin and emotion] (Wikiversity)
* [https://w.wiki/TsdS Psilocibyn assisted psychotherapy] (Wikiversity)
* [https://w.wiki/Tsce Psychedelics, altered consciousness, and personal growth] (Wikiversity)
* [[Eating Disorders|Eating disorders]] (Wikiversity)

==References==
{{Hanging indent|1=

{{ic|Try &quot;Edit source&quot; and then wrapping any text to be italicised in two apostrophes e.g., ''this is italics''}}

Anton-Păduraru, D. T., Trofin, F., Nastase, E. V., Miftode, R. S., Miftode, I. L., Trandafirescu, M. F., Cojocaru, E., Țarcă, E., Mindru, D. E., &amp; Dorneanu, O. S. (2023). The Role of the Gut Microbiota in Anorexia Nervosa in Children and Adults-Systematic Review. &quot;International journal of molecular sciences, 25&quot;(1), 41. https://doi.org/10.3390/ijms25010041

Brown, T. A., Vanzhula, I. A., Reilly, E. E., Levinson, C. A., Berner, L. A., Krueger, A., Lavender, J. M., Kaye, W. H., &amp; Wierenga, C. E. (2020). Body mistrust bridges interoceptive awareness and eating disorder symptoms. &quot;Journal of abnormal psychology, 129&quot;(5), 445–456. https://doi.org/10.1037/abn0000516 

Calder, A., Mock, S., Friedli, N., Pasi, P., &amp; Hasler, G. (2023). Psychedelics in the treatment of eating disorders: Rationale and potential mechanisms. &quot;European Neuropsychopharmacology, 75&quot;, 1–14. https://doi.org/10.1016/j.euroneuro.2023.05.008 

Caspani, G., Ruffell, S. G. D., Tsang, W., Netzband, N., Rohani-Shukla, C., Swann, J. R., &amp; Jefferies, W. A. (2024). Mind over matter: the microbial mindscapes of psychedelics and the gut-brain axis. &quot;Pharmacological research, 207&quot;, 107338. https://doi.org/10.1016/j.phrs.2024.107338  

Fitzsimmons, E. E., &amp; Bardone-Cone, A. M. (2010). Differences in coping across stages of recovery from an eating disorder. &quot;The International journal of eating disorders, 43&quot;(8), 689–693. https://doi.org/10.1002/eat.20781 

Hatzipantelis, C. J., &amp; Olson, D. E. (2024). The Effects of Psychedelics on Neuronal Physiology. &quot;Annual review of physiology, 86&quot;, 27–47. https://doi.org/10.1146/annurev-physiol-042022-020923

Hay, P., Aouad, P., Le, A., Marks, P., Maloney, D., National Eating Disorder Research Consortium, Touyz, S., &amp; Maguire, S. (2023). Epidemiology of eating disorders: population, prevalence, disease burden and quality of life informing public policy in Australia-a rapid review. &quot;Journal of eating disorders, 11&quot;(1), 23. https://doi.org/10.1186/s40337-023-00738-7

Li, H., Wang, H., &amp; Wang, X. (2025). Psychedelics and the Autonomic Nervous System: A Perspective on Their Interplay and Therapeutic Potential. &quot;ACS pharmacology &amp; translational science, 8&quot;(3), 899–902. https://doi.org/10.1021/acsptsci.5c00005 

Leppanen, J., Brown, D., McLinden, H., Williams, S., &amp; Tchanturia, K. (2022). The Role of Emotion Regulation in Eating Disorders: A Network Meta-Analysis Approach. &quot;Frontiers in psychiatry, 13&quot;, 793094. https://doi.org/10.3389/fpsyt.2022.793094 

Mograbi, D. C., Rodrigues, R., Bienemann, B., &amp; Huntley, J. (2024). Brain Networks, Neurotransmitters and Psychedelics: Towards a Neurochemistry of Self-Awareness. &quot;Current neurology and neuroscience reports, 24&quot;(8), 323–340. https://doi.org/10.1007/s11910-024-01353-y

Paulus F. W., Ohmann S., Möhler E., Plener P. &amp; Popow C. (2021). Emotional Dysregulation in Children and Adolescents With Psychiatric Disorders. A Narrative Review. &quot;Frontiers in Psychiatry 12&quot;:628252. doi: 10.3389/fpsyt.2021.628252

Peled-Avron L., Aday J. Ss, Kalafateli A. L., Hamilton H. K., Woolley J. D. (2024). Editorial: Down the rabbit hole – the psychological and neural mechanisms of psychedelic compounds and their use in treating mental health and medical conditions. &quot;Frontiers in Psychiatry 15&quot;:1431389. doi: 10.3389/fpsyt.2024.1431389

Porges S. W. (2025). Polyvagal Theory: Current Status, Clinical Applications, and Future Directions. &quot;Clinical neuropsychiatry, 22&quot;(3), 169–184. https://doi.org/10.36131/cnfioritieditore20250301

Schaefer, L. M., Smith, K. E., Anderson, L. M., Cao, L., Crosby, R. D., Engel, S. G., Crow, S. J., Peterson, C. B., &amp; Wonderlich, S. A. (2020). The role of affect in the maintenance of binge-eating disorder: Evidence from an ecological momentary assessment study. &quot;Journal of abnormal psychology, 129&quot;(4), 387–396. https://doi.org/10.1037/abn0000517 

Shank, L. M., Tanofsky-Kraff, M., Kelly, N. R., Jaramillo, M., Rubin, S. G., Altman, D. R., Byrne, M. E., LeMay-Russell, S., Schvey, N. A., Broadney, M. M., Brady, S. M., Yang, S. B., Courville, A. B., Ramirez, S., Crist, A. C., Yanovski, S. Z., &amp; Yanovski, J. A. (2019). The association between alexithymia and eating behavior in children and adolescents. &quot;Appetite, 142&quot;, 104381. https://doi.org/10.1016/j.appet.2019.104381

Wolfgang, A. S., &amp; Hoge, C. W. (2023). Psychedelic-Assisted Therapy in Military and Veterans Healthcare Systems: Clinical, Legal, and Implementation Considerations. &quot;Current psychiatry reports, 25&quot;(10), 513–532. https://doi.org/10.1007/s11920-023-01446-4 

Zanella, E., &amp; Lee, E. (2022). Integrative review on psychological and social risk and prevention factors of eating disorders including anorexia nervosa and bulimia nervosa: seven major theories. &quot;Heliyon, 8&quot;(11), e11422. https://doi.org/10.1016/j.heliyon.2022.e11422 

Zhou, R., Zhang, L., Liu, Z., &amp; Cao, B. (2025). Emotion regulation difficulties and disordered eating in adolescents and young adults: a meta-analysis. &quot;Journal of eating disorders, 13&quot;(1), 25. https://doi.org/10.1186/s40337-025-01197-y

}}

==External links==
* [https://www.abct.org/fact-sheets/psychedelic-assisted-therapy/ Psychedelic-Assisted Therapy | Fact Sheet] (ABCT - Association for Behavioral and Cognitive Therapies)
* [https://podcasts.apple.com/au/podcast/can-magic-mushrooms-help-treat-anorexia/id189330872?i=1000784809236 Can magic mushrooms help treat anorexia?] (Apple Podcasts)
* [https://www.apa.org/news/podcasts/speaking-of-psychology/eating-disorder The ‘silent epidemic’ of eating disorders] (American Psychological Association)
* [https://www.apa.org/monitor/2023/04/sensations-eating-disorders-suicidal-behavior What is interoception, and how does it affect mental health]? 5 questions for April Smith (American Psychological Association)
* [https://www.cbte.co/what-is-cbte/transdiagnostic-view-eating-disorders/ Transdiagnostic view of eating disorders] (cbte.co)
* [https://psychedelic.support/resources/polyvagal-theory-mind-body-dr-erica-zelfand/ Polyvagal Theory with Dr. Erica Zelfand: Mind-Body Connection] ·(Psychedelic Support)
* [https://www.wholeselfnutrition.org/post/nervous-system-regulation-a-missing-piece-in-eating-disorder-recovery Nervous System Regulation: A Missing Piece in Eating Disorder Recovery]  (wholeselfnutrition.org)

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      <text bytes="36397" sha1="sl4avj785a6ayugo0xjom91ecebfawj" xml:space="preserve">{{title|Psychedelic treatment of eating disorders:&lt;br&gt;How might psychedelic-assisted therapy influence psychological mechanisms involved in eating disorders?}}
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== Overview ==
{{RoundBoxTop|theme=7}}[[File:Neural network - Midjourney and Grok.png|thumb|'''Figure 1.''' Psychedelics are thought to temporarily disrupt rigid neural communication pathways, promoting more flexible patterns of connectivity across networks involved in mood regulation, fear processing, reward learning, and cognitive adaptability. These changes may support therapeutic shifts in behaviour and emotional processing (Hatzipantelis &amp; Olson, 2025).]]Emma, a 27‑year‑old from Canberra, has lived with an eating disorder for nearly two decades. She describes her problem eating behaviours to have started at school, after being bullied about her appearance. Ever since, they have remained in her life as “a way for me to feel in control”. Although she is aware of the harm caused by restrictive eating and compulsive exercise, she feels trapped in her thought patterns characterised by a preoccupation about food and weight concerns which have become entrenched in her daily life. 

After reading an article describing emerging research suggesting that psychedelics may alter patterns of neural connectivity that shape behaviour (see Figure 1), she expressed interest in pursuing psychedelic‑assisted therapy through a provider accessible to her.

After participating in her first supervised psilocybin‑assisted therapy session, Emma reported experiencing an emotional journey that allowed her to feel “connected to my body for the first time in years”. After 3 months, she has noticed a shift in how she relates to her body, and is finding it easier to actively call into question how she responds to distress with the support of her psychotherapist. 


Her experience raises a central question: What psychological mechanisms could explain these changes?{{RoundBoxBottom|theme=3}}  

This chapter explores how psychedelic‑assisted therapy (PAT) may influence the emotional, cognitive, and neurobiological processes that underpin eating disorders (EDs).   

{{RoundBoxTop|theme=11}}'''Focus questions'''
{{ic|}}Two central questions will be addressed:
* What psychological processes underpin eating disorders, and how do they guide ED behaviour?
* How might psychedelic‑assisted therapy influence these processes to support recovery?
{{ic|}}{{ic|}}{{RoundBoxBottom}}

== Introduction ==
'''Eating Disorders'''  

[[wikipedia:Eating_disorder|Eating disorders]] (EDs) are psychiatric conditions characterised by abnormal eating behaviours that negatively affect physical and mental health. They are associated with chronic illness, disability, reduced quality of life, increased suicide risk, and are highly comorbid with [[wikipedia:Mood_disorder|mood disorders]], [[wikipedia:Post-traumatic_stress_disorder|post-traumatic stress disorder]] (PTSD), [[wikipedia:Obsessive–compulsive_disorder|obsessive-compulsive disorder]] (OCD), and [[wikipedia:Substance_use_disorder|substance use disorders]] (Calder et al., 2023). [[wikipedia:Anorexia|Anorexia nervosa]] (AN) has the highest mortality rate of any psychiatric disorder, while [[wikipedia:Bulimia|bulimia nervosa]] (BN) and [[wikipedia:Binge_eating_disorder|binge‑eating disorder]] (BED) are also highly prevalent types of eating disorders.  

In Australia, the prevalence of EDs is rising, particularly among young people. Approximately 10.46% of the population has experienced an eating disorder at some point, with an estimated economic burden of $84 billion (Hay et al., 2023). Despite decades of research, the pathogenesis of EDs remains incompletely understood (Calder et al., 2023). Current evidence suggests a complex interplay between genetic predisposition, temperament, hormonal dysregulation, cognitive abnormalities, sociocultural pressures, and traumatic experiences.

Although cognitive‑behavioural therapy (CBT‑E) combined with pharmacological treatment has demonstrated beneficial outcomes, efficacy remains limited and varies across ED types (Calder et al., 2023). Recovery is often long and difficult, with only two‑thirds of individuals with AN and BN eventually recovering, while others can remain ill for many years. This highlights the need for treatment approaches that can accelerate recovery and provide benefit for individuals who do not respond to conventional therapies.


'''Psychedelic-Assisted Therapy'''

In 2023, Australia legalised the prescription of MDMA and psilocybin under professional supervision, marking a significant shift in mental‑health treatment options. Psychedelic compounds, including [[wikipedia:LSD|LSD]], [[wikipedia:Psilocybin|psilocybin]], [[wikipedia:Dimethyltryptamine|DMT]], [[wikipedia:Ketamine|ketamine]], and [[wikipedia:MDMA|MDMA]], have demonstrated promising therapeutic effects across a wide range of psychiatric conditions. Researchers propose that psychedelics act through psychological and neural mechanisms that increase [[wikipedia:Neuroplasticity|neuroplasticity]], facilitate insight, and foster emotional acceptance (Peled‑Avron et al., 2024). At a neurobiological level, psychedelics influence processes that inform perception, emotion, and behaviour, offering a potential avenue for addressing entrenched ED mechanisms.

PAT differs from pharmacological treatment alone because the drug is administered within a structured therapeutic context designed to maximise safety and clinical benefit (Calder et al., 2023). Treatment typically involves three types of sessions. Preparatory sessions feature participants undergoing psychoeducation, where the clinician establishes rapport and clear safety protocols. Followed by supervised medication where the participant has an inward experience with the reassurance of clinicians present in the same space. Lastly, integrative sessions where individuals process and explore insights from the previous session with their psychotherapist to foster behavioural change (Wolfgang &amp; Hoge, 2023). This combination of pharmacological and psychological intervention is theorised to effectively target underlying psychological mechanisms common across various mental health disorders, illustrating PAT’s potential as a valuable transdiagnostic treatment option. 

PAT has become a subject of increasing popularity in ED research because many of the psychological mechanisms it is proposed to influence are the same ones implicated in ED maintenance and comorbidities (Calder et al., 2023; Peled-Avron et al., 2024). Early research, including case study reports, small clinical studies, meta-analyses and reviews indicate that PAT produces improvements in affect, reductions in ED symptom severity, enhanced body image, weight restoration, and reductions in comorbid symptoms. Although preliminary, these findings indicate that PAT may disrupt and promote shifts away from maladaptive coping patterns that become entrenched in treatment resistant ED populations.

== Psychological Mechanisms in Eating Disorders ==


'''Emotion Dysregulation'''

Emotion dysregulation is considered to be a significant risk factor for the onset and maintenance of EDs. It refers to difficulties recognising, assessing, and modifying emotional responses to meet situational demands (Zhou et al., 2025). 

Research consistently shows that individuals with EDs experience significant challenges in regulating emotions, increasing their vulnerability to comorbid symptoms, which contribute to the emergence of disordered eating patterns (Leppanen et al., 2022). This idea is supported by affect regulation theory which posits that eating disorders develop and are maintained as maladaptive strategies to manage, tolerate and escape from negative emotions and psychological distress (Schaefer et al., 2020; Zanella &amp; Lee, 2022). This is further exemplified in Fitzsimmons &amp; Bardone-Cone’s article examining differences in coping within eating disorder patients (2010). The authors explain that avoidance and emotion-oriented coping styles often function as maladaptive attempts to manage (di)stress. They explain that behaviours such as binge eating, purging, starvation, and/or compulsive exercise provide temporary relief by shifting attention away from uncomfortable emotions. 

Furthermore, alexithymia, characterised by difficulty identifying and describing one’s own emotions, is strongly associated with ED pathology (Shank et al., 2019). Individuals with high alexithymia often struggle to differentiate emotional states from bodily sensations, contributing to behaviours such as emotional eating, eating in the absence of hunger, or rigid restriction. In BED, alexithymia is linked to binge episodes triggered by poorly understood emotional cues, while in AN and BN, alexithymia may contribute to emotional avoidance and reliance on ED behaviours for affect regulation. 

The effects of trauma are contributing factors to emotion dysregulation, and considered a risk factor for ED development. Individuals who experience sexual, physical, or emotional abuse, neglect, and bullying are likely to experience heightened emotional reactivity, threat perception, and avoidance behaviours (Calder et al., 2023). Researchers explain that trauma often results in lowered distress tolerance and increased reliance on maladaptive coping behaviours, including disordered eating. Furthermore, PTSD comorbidity is common, hence trauma‑related symptoms are hypothesised to frequently interact with ED behaviours in complex ways.  


'''Reward Processing Dysfunction'''
[[File:Striatum.gif|thumb|'''Figure 2.''' Striatum]]
[[File:Anterior cingulate gyrus animation.gif|thumb|'''Figure 3'''. Anterior Cingulate Cortex ]]
Abnormal reward valuation is understood to be a central psychological mechanism that maintains ED behaviours. Research consistently shows that individuals with eating disorders display altered neural activity response to various stimuli, as well as disruptions in reinforcement learning (Calder et al., 2023). Brain regions involved in reward processing, habit formation, and learning, such as the striatum and anterior cingulate cortex (see figures 2 &amp; 3), exhibit atypical activation patterns and differences in dopamine receptor binding across ED types. The insula (see figure 4), which integrates bodily sensations with conscious thought, emotion, and behaviour, also shows altered responses. Together, these regions have been shown to react differently to food images, taste, and social feedback compared to healthy controls, indicating that reward dysfunction extends beyond eating‑related stimuli for ED populations.
[[File:Insular cortex.gif|thumb|'''Figure 4.''' Insula. ]]
In the context of BN and BED, research shows that food is valued more highly than other types of rewards, thus shaping behaviour through its heightened influence on reward outcomes (Calder et al., 2023). Compulsive behaviours specific to each condition (e.g. bingeing, purging) are therefore more likely to occur when food is overvalued and alternative rewards are discounted or ignored. In addition to the neural changes already described, BN and BED are associated with reduced structural and functional connectivity between frontal control regions and the striatum. This combination of highly salient food rewards, and weakened fronto‑striatal pathways, reduces an individual’s ability to inhibit or modulate reward‑seeking impulses. Weak connectivity in these circuits is thought to predict compulsive reward‑seeking behaviour. As a result, even when individuals experience negative consequences from binge episodes, they may struggle to learn from these outcomes or adjust their behaviour accordingly.


Anhedonia, a global reduction in reward responsiveness, is frequently reported by people who experience AN, resulting in food and eating becoming undervalued or aversive to them (Calder et al., 2023). Researchers propose that reward contamination further contributes to this pattern, where the brain learns to associate normally punishing stimuli (e.g., starvation, excessive exercise) with reward, while normally rewarding stimuli (e.g., high‑calorie foods) become experienced as punishment. Structural reductions in the striatum and somatosensory cortex have also been observed, which accounts for distorted bodily sensations and contributes to anhedonia. These changes support maladaptive conditioning in which starvation and weight loss embody a sense of safety, achievement, and emotional relief. Restrictive and preoccupied behaviours centred on food, body shape, and exercise are therefore reinforced over time.

Consistent with affect‑regulation models, eating‑disorder behaviours also become negatively reinforced because they reduce emotional discomfort. This relief increases the likelihood that the behaviours will be repeated, further embedding them within the individual’s coping pattern.


'''Cognitive Rigidity'''

Cognitive rigidity refers to inflexible thinking and behavioural patterns, including difficulty adapting to new information and modifying behaviour. Researchers believe that individuals with EDs often exhibit rigid beliefs about food and weight which interact with a need to exert control over negative emotions. This interaction is the proposed process in which compulsive behaviours and obsessive thoughts develop (Calder et al., 2023). In AN, rigidity manifests as strict dietary rules and fear of losing control, while in BN and BED, binge episodes may feel compulsive and uncontrollable.


'''Interoceptive Awareness'''

Interoceptive awareness (IA) refers to the ability to recognise and process internal bodily states such as hunger, satiety, pain, and arousal. IA is impaired across EDs, and contributes to body mistrust, distorted hunger cues, and inappropriate responses to internal sensations (Brown et al., 2020). Individuals may ignore physical discomfort, misinterpret bodily signals, or avoid sensations altogether, reinforcing maladaptive coping.      

 &lt;blockquote&gt;'''''QUIZ: Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{What coping style do people who experience EDs tend to show?
|type=&quot;()&quot;}
+ Avoidance-oriented
- Problem-oriented

{Compulsive behaviours are more likely to occur when food is ... and alternative rewards are ...
|type=&quot;()&quot;}
- undervalued; overvalued
+ overvalued; undervalued
&lt;/quiz&gt;&lt;/blockquote&gt;

== Psychological Mechanisms of Psychedelic-Assisted Therapy ==

PAT is proposed to influence several psychological mechanisms implicated in EDs, particularly those discussed in the previous section. The next part of this chapter aims to examine the theorised therapeutic mechanisms PAT possesses and practical implications for ED treatment.  


'''Emotion Regulation''' 

Emotion dysregulation is a core mechanism implicated in EDs. Affect regulation theory proposes that ED behaviours emerge as maladaptive strategies to escape, reduce, or blunt overwhelming emotional experiences (Schaefer et al., 2020). Restriction, bingeing, purging, and compulsive exercise may temporarily alleviate distress while reinforcing avoidance-oriented coping and limiting opportunities to learn more adaptive ways of responding to difficult emotions. 

Psychedelics often evoke intense emotional experiences that may disrupt habitual avoidance patterns. Researchers propose that, during psychedelic sessions, attempts to suppress or avoid difficult emotions can intensify these experiences, creating conditions in which emotional acceptance becomes a preferred response (Calder et al., 2023). Although this shift does not occur in every individual, experiencing difficult emotions without resorting to ED behaviours may weaken the association between emotional distress and maladaptive coping, particularly when emotional acceptance becomes associated with a more positive or tolerable experience.

The therapeutic value of this process lies in its potential to reshape affective responses. When individuals experience strong emotions without engaging in maladaptive behaviours, they may begin to develop a new approach towards emotional tolerance. Integration sessions can consolidate this learning by helping individuals articulate, differentiate, and reflect on the emotions experienced during dosing. This process may support the development of more adaptive coping strategies, including task-oriented, problem-focused, and socially supported approaches, which are associated with improved ED outcomes (Fitzsimmons &amp; Bardone-Cone, 2010). In this way, PAT may strengthen emotion regulation and reduce reliance on ED behaviours as strategies for managing affect. 


'''Reward Processing''' 

Reward dysfunction may contribute to the maintenance of EDs by reinforcing maladaptive behaviours while diminishing the perceived value of adaptive rewards. Predictive coding provides a useful framework for understanding how PAT might influence these processes. Individuals with EDs may hold rigid beliefs, conceptualised as high-level priors, about themselves in relation to food, body weight, and rewarding behaviours (Calder et al., 2023; Mograbi et al., 2024). These beliefs can influence how experiences are perceived and valued, potentially reinforcing existing behavioural patterns. Psychedelics are proposed to weaken high-level priors, allowing bottom-up sensory information to exert greater influence on perception and the valuation of experiences. 

During psychedelic experiences, individuals frequently report a heightened appreciation of sensory, social, and bodily experiences. This shift may counteract anhedonia and support the revaluation of previously feared or avoided stimuli. The therapeutic opportunity lies in translating these temporary changes in perception and reward into meaningful behavioural change. Integration sessions can explore positive and negative moments experienced during dosing and connect them to concrete goals. An example of this, inspired from Calder et al.’s (2023) article, could be to clarify specific plans to nourish the body due to the participant having experienced themselves as a decaying skeleton followed by the realisation of the body being a gift. If the period following dosing provides an opportunity for increased neuroplasticity, it may also be particularly conducive to reinforcing adaptive reward learning through behavioural activation with the help of a therapist. 


'''Cognitive Flexibility''' 

Cognitive rigidity is a hallmark of EDs and is characterised by inflexible beliefs about food, weight, body shape, and control. Predictive coding provides a framework for understanding this rigidity, as EDs may involve entrenched priors that resist updating even when confronted with contradictory sensory evidence (Zanella &amp; Lee, 2022). Psychedelics are proposed to disrupt these entrenched priors by increasing neural entropy and reducing the dominance of top-down processing (Calder et al., 2023). This temporary loosening of cognitive constraints may allow individuals to consider alternative perspectives and question long-held beliefs. 

Experiences of ego dissolution may further contribute to cognitive flexibility by reducing attachment to rigid self-concepts (Peled-Avron, 2024; Mograbi et al., 2024). When the boundaries of the self become less defined, individuals may find it easier to question identity-related beliefs that sustain ED pathology. Integration sessions can harness this potential flexibility by supporting cognitive reframing, encouraging behavioural experiments, and strengthening metacognitive awareness. Through these processes, individuals may be better able to translate insights gained during psychedelic experiences into sustained changes in thinking and behaviour.


'''Reconnecting with Bodily Signals'''

Interoceptive deficits are central to ED pathology, contributing to body mistrust, distorted perceptions of hunger cues, and difficulties responding appropriately to internal sensations (Brown et al., 2020). Psychedelics may enhance interoceptive awareness by altering sensory processing and increasing sensitivity to bodily signals. This proposed mechanism is closely related to autonomic regulation, for which polyvagal theory provides a framework for understanding the relationship between bodily signals, emotional regulation, and perceived safety.

Polyvagal theory emphasises the role of the vagus nerve in interoception, emotional regulation, and the perception of safety (Porges, 2022). Vagal afferents transmit information from the body to the insula, where interoceptive signals are integrated with emotional and cognitive processes. Individuals with EDs may exhibit chronic sympathetic arousal and reduced vagal tone, potentially impairing interoceptive accuracy and contributing to emotional rigidity. Psychedelics may initially increase sympathetic activity, as reflected in physiological responses such as increased heart rate, followed by a parasympathetic shift associated with greater relaxation and an increased capacity for rest (Li et al., 2025). Within a polyvagal framework, these changes may have implications for vagal regulation, interoceptive awareness, and emotional regulation.

The therapeutic value of this proposed mechanism lies in its potential to restore trust in bodily signals. Integration sessions may support this process by helping individuals explore bodily sensations experienced during dosing, connect interoceptive cues with emotional states, and practise interoceptive exposure to hunger, fullness, and anxiety-related sensations. Incorporating mindfulness techniques may further support autonomic regulation and help individuals develop a more adaptive relationship with their bodily experiences.

 A Brief Note Concerning The Gut-Brain Interaction 
Although gut microbiome disruption is not a direct psychological mechanism in EDs, it is a relevant biological factor to consider when examining the potential effects of PAT. Restrictive or chaotic eating patterns can contribute to gut dysbiosis, which may weaken gut-barrier integrity and contribute to inflammation affecting the brain (Anton-Paduraru et al., 2024). These changes have been shown to influence mood, stress responsivity, cognitive rigidity, and interoceptive awareness through [[wikipedia:Hypothalamic–pituitary–adrenal_axis|HPA-axis activation]], altered neurotransmitter synthesis, and disrupted hunger–satiety signalling. 

Emerging research suggests that psychedelics may also interact with the gut–brain axis. Certain microbes can metabolise psychedelic compounds, and microbial activity has been associated with modulatory effects on behavioural outcomes. Additionally, psychedelic use may alter microbial composition towards anti-inflammatory profiles, with potential implications for neuroplasticity, neurotransmitter synthesis and signalling improvements (Caspani et al., 2024). These microbiome-related effects may therefore contribute to changes in mood, cognitive flexibility, and appetite regulation.

Although the therapeutic potential of psychedelics in EDs is considered primarily in relation to psychological mechanisms, including changes in perception, emotional processing, and reduced avoidance, microbiome-related effects may represent an additional pathway through which biological processes influence psychological outcomes. However, the extent to which these interactions contribute to therapeutic outcomes in EDs remains to be established.


&lt;blockquote&gt;'''QUIZ: ''Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{ In predictive coding terms, what are “high‑level priors” in eating disorders? 
|type=&quot;()&quot;}
+ Rigid, entrenched beliefs about food, weight, and the self that shape perception and behaviour
- Flexible beliefs that easily update with new sensory information
- Momentary emotional reactions triggered by external cues

{What is the proposed mechanism by which psychedelics support emotion regulation in PAT for EDs? 
|type=&quot;()&quot;}
- By suppressing emotional intensity to prevent distress
+ By evoking strong emotions that disrupt avoidance patterns and promote emotional acceptance
- By eliminating negative emotions through serotonin release

{What is interoceptive awareness?
|type=&quot;()&quot;}
- The ability to evaluate reward value and anticipate pleasurable outcomes
+ The capacity to sense, interpret, and respond to internal bodily signals such as hunger, fullness, and emotional arousal
- The process of weakening cognitive rigidity through ego dissolution
&lt;/quiz&gt;&lt;/blockquote&gt;

== Limitations ==
Despite the potential of PAT to influence psychological mechanisms implicated in EDs, several limitations constrain current understanding of these processes and their therapeutic relevance. Research examining emotion dysregulation in EDs illustrates broader challenges in establishing the mechanisms underlying these conditions. Although non-acceptance of emotions has been identified as a transdiagnostic risk factor across psychiatric conditions (Paulus et al., 2021), Zhou et al.’s meta-analysis (2025) highlights that the causal pathways linking emotional dysregulation and EDs remain unclear, largely because of a lack of experimental and longitudinal studies. Further limitations include restricted availability of measurement scales, insufficient cultural specificity, heterogeneity across samples, gender imbalance, and limited developmental analysis. Together, these factors constrain understanding of how specific emotional processes relate to different ED presentations across the lifespan and stages of recovery.

These limitations are also relevant when considering the proposed mechanisms of PAT. Although existing theoretical frameworks offer ways to conceptualise how psychedelic experiences may influence psychological processes responsible for EDs, the emerging nature of psychedelic therapy limits the extent to which proposed mechanisms have been tested. However, with the number of clinical trials increasing as of recently, it will be interesting to see how the theorised therapeutic mechanisms across different ED presentations and stages of recovery emerges during further warranted investigation.

Nevertheless, current limitations in the evidence highlight the need for research that clarifies the relationships between psychological processes that underscore ED behaviours, and treatment outcomes. There are several important psychological components of ED maintenance that represent meaningful targets for treatment, but they should not be considered in isolation from eachother or the neurobiological processes that influence them. A more comprehensive understanding of how these mechanisms interact may help clarify the therapeutic potential of PAT and inform the development of more targeted treatment approaches.

== Conclusion ==
PAT offers a potential framework for addressing several interconnected psychological mechanisms implicated in EDs. Through its proposed effects on emotional processing, reward valuation, cognitive flexibility, and interoceptive awareness, PAT may create opportunities to disrupt established patterns of avoidance, rigid thinking, and maladaptive behavioural reinforcement. The gut–brain interaction may represent an additional biological pathway relevant to these processes.

These mechanisms should not be understood as independent processes. Changes in emotion regulation may influence the ability to tolerate bodily sensations, while shifts in reward valuation and cognitive flexibility may create opportunities to respond differently to distress and challenge entrenched beliefs. However, the extent to which PAT produces these changes, and whether they translate into sustained improvements in ED outcomes, requires further investigation, although preliminary evidence is promising. 

The therapeutic potential of PAT lies not only in the acute psychedelic experience but also in the structured integration process that follows. Integration sessions provide an opportunity to translate emotional breakthroughs, changes in cognitive flexibility, interoceptive shifts, and reward processing into sustained behavioural change. Effective integration involves helping individuals articulate insights, connect them to ED-related patterns, and develop concrete strategies for change. These may include strengthening adaptive coping, challenging rigid beliefs, practising interoceptive awareness, reinforcing positive reward experiences, and supporting nutritional rehabilitation.

By grounding the understanding of PAT in affect regulation theory and the predictive coding framework, therapists may be better positioned to help individuals explore how psychedelic experiences could disrupt maladaptive emotional and cognitive patterns and create opportunities for new learning. Polyvagal-informed approaches may further support the development of mind–body awareness and emotional regulation through mindfulness strategies. Together, these approaches offer a multifaceted framework for translating psychedelic experiences into therapeutic change and addressing the interconnected mechanisms that maintain EDs and associated suffering. 

==See Also==
* [https://w.wiki/TsdG Ayahuasca and the brain] (Wikiversity)
* [https://w.wiki/TscF Emotional effects of psychedelics] (Wikiversity)
* [https://w.wiki/Tsdb Psilocybin and emotion] (Wikiversity)
* [https://w.wiki/TsdS Psilocibyn assisted psychotherapy] (Wikiversity)
* [https://w.wiki/Tsce Psychedelics, altered consciousness, and personal growth] (Wikiversity)
* [[Eating Disorders|Eating disorders]] (Wikiversity)

==References==
{{Hanging indent|1=

{{ic|Try &quot;Edit source&quot; and then wrapping any text to be italicised in two apostrophes e.g., ''this is italics''}}

Anton-Păduraru, D. T., Trofin, F., Nastase, E. V., Miftode, R. S., Miftode, I. L., Trandafirescu, M. F., Cojocaru, E., Țarcă, E., Mindru, D. E., &amp; Dorneanu, O. S. (2023). The Role of the Gut Microbiota in Anorexia Nervosa in Children and Adults-Systematic Review. &quot;International journal of molecular sciences, 25&quot;(1), 41. https://doi.org/10.3390/ijms25010041

Brown, T. A., Vanzhula, I. A., Reilly, E. E., Levinson, C. A., Berner, L. A., Krueger, A., Lavender, J. M., Kaye, W. H., &amp; Wierenga, C. E. (2020). Body mistrust bridges interoceptive awareness and eating disorder symptoms. &quot;Journal of abnormal psychology, 129&quot;(5), 445–456. https://doi.org/10.1037/abn0000516 

Calder, A., Mock, S., Friedli, N., Pasi, P., &amp; Hasler, G. (2023). Psychedelics in the treatment of eating disorders: Rationale and potential mechanisms. &quot;European Neuropsychopharmacology, 75&quot;, 1–14. https://doi.org/10.1016/j.euroneuro.2023.05.008 

Caspani, G., Ruffell, S. G. D., Tsang, W., Netzband, N., Rohani-Shukla, C., Swann, J. R., &amp; Jefferies, W. A. (2024). Mind over matter: the microbial mindscapes of psychedelics and the gut-brain axis. &quot;Pharmacological research, 207&quot;, 107338. https://doi.org/10.1016/j.phrs.2024.107338  

Fitzsimmons, E. E., &amp; Bardone-Cone, A. M. (2010). Differences in coping across stages of recovery from an eating disorder. &quot;The International journal of eating disorders, 43&quot;(8), 689–693. https://doi.org/10.1002/eat.20781 

Hatzipantelis, C. J., &amp; Olson, D. E. (2024). The Effects of Psychedelics on Neuronal Physiology. &quot;Annual review of physiology, 86&quot;, 27–47. https://doi.org/10.1146/annurev-physiol-042022-020923

Hay, P., Aouad, P., Le, A., Marks, P., Maloney, D., National Eating Disorder Research Consortium, Touyz, S., &amp; Maguire, S. (2023). Epidemiology of eating disorders: population, prevalence, disease burden and quality of life informing public policy in Australia-a rapid review. &quot;Journal of eating disorders, 11&quot;(1), 23. https://doi.org/10.1186/s40337-023-00738-7

Li, H., Wang, H., &amp; Wang, X. (2025). Psychedelics and the Autonomic Nervous System: A Perspective on Their Interplay and Therapeutic Potential. &quot;ACS pharmacology &amp; translational science, 8&quot;(3), 899–902. https://doi.org/10.1021/acsptsci.5c00005 

Leppanen, J., Brown, D., McLinden, H., Williams, S., &amp; Tchanturia, K. (2022). The Role of Emotion Regulation in Eating Disorders: A Network Meta-Analysis Approach. &quot;Frontiers in psychiatry, 13&quot;, 793094. https://doi.org/10.3389/fpsyt.2022.793094 

Mograbi, D. C., Rodrigues, R., Bienemann, B., &amp; Huntley, J. (2024). Brain Networks, Neurotransmitters and Psychedelics: Towards a Neurochemistry of Self-Awareness. &quot;Current neurology and neuroscience reports, 24&quot;(8), 323–340. https://doi.org/10.1007/s11910-024-01353-y

Paulus F. W., Ohmann S., Möhler E., Plener P. &amp; Popow C. (2021). Emotional Dysregulation in Children and Adolescents With Psychiatric Disorders. A Narrative Review. &quot;Frontiers in Psychiatry 12&quot;:628252. doi: 10.3389/fpsyt.2021.628252

Peled-Avron L., Aday J. Ss, Kalafateli A. L., Hamilton H. K., Woolley J. D. (2024). Editorial: Down the rabbit hole – the psychological and neural mechanisms of psychedelic compounds and their use in treating mental health and medical conditions. &quot;Frontiers in Psychiatry 15&quot;:1431389. doi: 10.3389/fpsyt.2024.1431389

Porges S. W. (2025). Polyvagal Theory: Current Status, Clinical Applications, and Future Directions. &quot;Clinical neuropsychiatry, 22&quot;(3), 169–184. https://doi.org/10.36131/cnfioritieditore20250301

Schaefer, L. M., Smith, K. E., Anderson, L. M., Cao, L., Crosby, R. D., Engel, S. G., Crow, S. J., Peterson, C. B., &amp; Wonderlich, S. A. (2020). The role of affect in the maintenance of binge-eating disorder: Evidence from an ecological momentary assessment study. &quot;Journal of abnormal psychology, 129&quot;(4), 387–396. https://doi.org/10.1037/abn0000517 

Shank, L. M., Tanofsky-Kraff, M., Kelly, N. R., Jaramillo, M., Rubin, S. G., Altman, D. R., Byrne, M. E., LeMay-Russell, S., Schvey, N. A., Broadney, M. M., Brady, S. M., Yang, S. B., Courville, A. B., Ramirez, S., Crist, A. C., Yanovski, S. Z., &amp; Yanovski, J. A. (2019). The association between alexithymia and eating behavior in children and adolescents. &quot;Appetite, 142&quot;, 104381. https://doi.org/10.1016/j.appet.2019.104381

Wolfgang, A. S., &amp; Hoge, C. W. (2023). Psychedelic-Assisted Therapy in Military and Veterans Healthcare Systems: Clinical, Legal, and Implementation Considerations. &quot;Current psychiatry reports, 25&quot;(10), 513–532. https://doi.org/10.1007/s11920-023-01446-4 

Zanella, E., &amp; Lee, E. (2022). Integrative review on psychological and social risk and prevention factors of eating disorders including anorexia nervosa and bulimia nervosa: seven major theories. &quot;Heliyon, 8&quot;(11), e11422. https://doi.org/10.1016/j.heliyon.2022.e11422 

Zhou, R., Zhang, L., Liu, Z., &amp; Cao, B. (2025). Emotion regulation difficulties and disordered eating in adolescents and young adults: a meta-analysis. &quot;Journal of eating disorders, 13&quot;(1), 25. https://doi.org/10.1186/s40337-025-01197-y

}}

==External links==
* [https://www.abct.org/fact-sheets/psychedelic-assisted-therapy/ Psychedelic-Assisted Therapy | Fact Sheet] (ABCT - Association for Behavioral and Cognitive Therapies)
* [https://podcasts.apple.com/au/podcast/can-magic-mushrooms-help-treat-anorexia/id189330872?i=1000784809236 Can magic mushrooms help treat anorexia?] (Apple Podcasts)
* [https://www.apa.org/news/podcasts/speaking-of-psychology/eating-disorder The ‘silent epidemic’ of eating disorders] (American Psychological Association)
* [https://www.apa.org/monitor/2023/04/sensations-eating-disorders-suicidal-behavior What is interoception, and how does it affect mental health]? 5 questions for April Smith (American Psychological Association)
* [https://www.cbte.co/what-is-cbte/transdiagnostic-view-eating-disorders/ Transdiagnostic view of eating disorders] (cbte.co)
* [https://psychedelic.support/resources/polyvagal-theory-mind-body-dr-erica-zelfand/ Polyvagal Theory with Dr. Erica Zelfand: Mind-Body Connection] ·(Psychedelic Support)
* [https://www.wholeselfnutrition.org/post/nervous-system-regulation-a-missing-piece-in-eating-disorder-recovery Nervous System Regulation: A Missing Piece in Eating Disorder Recovery]  (wholeselfnutrition.org)
* [https://youtu.be/RwS-CHJcCiY?si=157viTWiOGAQ-7LP Best Neural Entropy - Explainer] (Youtube)

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      <text bytes="36400" sha1="sp0fwh6kyx2p3ws7hkebh59t1mcwsyg" xml:space="preserve">{{title|Psychedelic treatment of eating disorders:&lt;br&gt;How might psychedelic-assisted therapy influence psychological mechanisms involved in eating disorders?}}
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== Overview ==
{{RoundBoxTop|theme=7}}[[File:Neural network - Midjourney and Grok.png|thumb|'''Figure 1.''' Psychedelics are thought to temporarily disrupt rigid neural communication pathways by promoting more flexible patterns of connectivity across networks involved in mood regulation, fear processing, reward learning, and cognitive adaptability. These changes may support therapeutic shifts in behaviour and emotional processing (Hatzipantelis &amp; Olson, 2025).]]Emma, a 27‑year‑old from Canberra, has lived with an eating disorder for nearly two decades. She describes her problem eating behaviours to have started at school, after being bullied about her appearance. Ever since, they have remained in her life as “a way for me to feel in control”. Although she is aware of the harm caused by restrictive eating and compulsive exercise, she feels trapped in her thought patterns characterised by a preoccupation about food and weight concerns which have become entrenched in her daily life. 

After reading an article describing emerging research suggesting that psychedelics may alter patterns of neural connectivity that shape behaviour (see Figure 1), she expressed interest in pursuing psychedelic‑assisted therapy through a provider accessible to her.

After participating in her first supervised psilocybin‑assisted therapy session, Emma reported experiencing an emotional journey that allowed her to feel “connected to my body for the first time in years”. After 3 months, she has noticed a shift in how she relates to her body, and is finding it easier to actively call into question how she responds to distress with the support of her psychotherapist. 


Her experience raises a central question: What psychological mechanisms could explain these changes?{{RoundBoxBottom|theme=3}}  

This chapter explores how psychedelic‑assisted therapy (PAT) may influence the emotional, cognitive, and neurobiological processes that underpin eating disorders (EDs).   

{{RoundBoxTop|theme=11}}'''Focus questions'''
{{ic|}}Two central questions will be addressed:
* What psychological processes underpin eating disorders, and how do they guide ED behaviour?
* How might psychedelic‑assisted therapy influence these processes and support recovery?
{{ic|}}{{ic|}}{{RoundBoxBottom}}

== Introduction ==
'''Eating Disorders'''  

[[wikipedia:Eating_disorder|Eating disorders]] (EDs) are psychiatric conditions characterised by abnormal eating behaviours that negatively affect physical and mental health. They are associated with chronic illness, disability, reduced quality of life, increased suicide risk, and are highly comorbid with [[wikipedia:Mood_disorder|mood disorders]], [[wikipedia:Post-traumatic_stress_disorder|post-traumatic stress disorder]] (PTSD), [[wikipedia:Obsessive–compulsive_disorder|obsessive-compulsive disorder]] (OCD), and [[wikipedia:Substance_use_disorder|substance use disorders]] (Calder et al., 2023). [[wikipedia:Anorexia|Anorexia nervosa]] (AN) has the highest mortality rate of any psychiatric disorder, while [[wikipedia:Bulimia|bulimia nervosa]] (BN) and [[wikipedia:Binge_eating_disorder|binge‑eating disorder]] (BED) are also highly prevalent types of eating disorders.  

In Australia, the prevalence of EDs is rising, particularly among young people. Approximately 10.46% of the population has experienced an eating disorder at some point, with an estimated economic burden of $84 billion (Hay et al., 2023). Despite decades of research, the pathogenesis of EDs remains incompletely understood (Calder et al., 2023). Current evidence suggests a complex interplay between genetic predisposition, temperament, hormonal dysregulation, cognitive abnormalities, sociocultural pressures, and traumatic experiences.

Although cognitive‑behavioural therapy (CBT‑E) combined with pharmacological treatment has demonstrated beneficial outcomes, efficacy remains limited and varies across ED types (Calder et al., 2023). Recovery is often long and difficult, with only two‑thirds of individuals with AN and BN eventually recovering, while others can remain ill for many years. This highlights the need for treatment approaches that can accelerate recovery and provide benefit for individuals who do not respond to conventional therapies.


'''Psychedelic-Assisted Therapy'''

In 2023, Australia legalised the prescription of MDMA and psilocybin under professional supervision, marking a significant shift in mental‑health treatment options. Psychedelic compounds, including [[wikipedia:LSD|LSD]], [[wikipedia:Psilocybin|psilocybin]], [[wikipedia:Dimethyltryptamine|DMT]], [[wikipedia:Ketamine|ketamine]], and [[wikipedia:MDMA|MDMA]], have demonstrated promising therapeutic effects across a wide range of psychiatric conditions. Researchers propose that psychedelics act through psychological and neural mechanisms that increase [[wikipedia:Neuroplasticity|neuroplasticity]], facilitate insight, and foster emotional acceptance (Peled‑Avron et al., 2024). At a neurobiological level, psychedelics influence processes that inform perception, emotion, and behaviour, offering a potential avenue for addressing entrenched ED mechanisms.

PAT differs from pharmacological treatment alone because the drug is administered within a structured therapeutic context designed to maximise safety and clinical benefit (Calder et al., 2023). Treatment typically involves three types of sessions. Preparatory sessions feature participants undergoing psychoeducation, where the clinician establishes rapport and clear safety protocols. Followed by supervised medication where the participant has an inward experience with the reassurance of clinicians present in the same space. Lastly, integrative sessions where individuals process and explore insights from the previous session with their psychotherapist to foster behavioural change (Wolfgang &amp; Hoge, 2023). This combination of pharmacological and psychological intervention is theorised to effectively target underlying psychological mechanisms common across various mental health disorders, illustrating PAT’s potential as a valuable transdiagnostic treatment option. 

PAT has become a subject of increasing popularity in ED research because many of the psychological mechanisms it is proposed to influence are the same ones implicated in ED maintenance and comorbidities (Calder et al., 2023; Peled-Avron et al., 2024). Early research, including case study reports, small clinical studies, meta-analyses and reviews indicate that PAT produces improvements in affect, reductions in ED symptom severity, enhanced body image, weight restoration, and reductions in comorbid symptoms. Although preliminary, these findings indicate that PAT may disrupt and promote shifts away from maladaptive coping patterns that become entrenched in treatment resistant ED populations.

== Psychological Mechanisms in Eating Disorders ==


'''Emotion Dysregulation'''

Emotion dysregulation is considered to be a significant risk factor for the onset and maintenance of EDs. It refers to difficulties recognising, assessing, and modifying emotional responses to meet situational demands (Zhou et al., 2025). 

Research consistently shows that individuals with EDs experience significant challenges in regulating emotions, increasing their vulnerability to comorbid symptoms, which contribute to the emergence of disordered eating patterns (Leppanen et al., 2022). This idea is supported by affect regulation theory which posits that eating disorders develop and are maintained as maladaptive strategies to manage, tolerate and escape from negative emotions and psychological distress (Schaefer et al., 2020; Zanella &amp; Lee, 2022). This is further exemplified in Fitzsimmons &amp; Bardone-Cone’s article examining differences in coping within eating disorder patients (2010). The authors explain that avoidance and emotion-oriented coping styles often function as maladaptive attempts to manage (di)stress. They explain that behaviours such as binge eating, purging, starvation, and/or compulsive exercise provide temporary relief by shifting attention away from uncomfortable emotions. 

Furthermore, alexithymia, characterised by difficulty identifying and describing one’s own emotions, is strongly associated with ED pathology (Shank et al., 2019). Individuals with high alexithymia often struggle to differentiate emotional states from bodily sensations, contributing to behaviours such as emotional eating, eating in the absence of hunger, or rigid restriction. In BED, alexithymia is linked to binge episodes triggered by poorly understood emotional cues, while in AN and BN, alexithymia may contribute to emotional avoidance and reliance on ED behaviours for affect regulation. 

The effects of trauma are contributing factors to emotion dysregulation, and considered a risk factor for ED development. Individuals who experience sexual, physical, or emotional abuse, neglect, and bullying are likely to experience heightened emotional reactivity, threat perception, and avoidance behaviours (Calder et al., 2023). Researchers explain that trauma often results in lowered distress tolerance and increased reliance on maladaptive coping behaviours, including disordered eating. Furthermore, PTSD comorbidity is common, hence trauma‑related symptoms are hypothesised to frequently interact with ED behaviours in complex ways.  


'''Reward Processing Dysfunction'''
[[File:Striatum.gif|thumb|'''Figure 2.''' Striatum]]
[[File:Anterior cingulate gyrus animation.gif|thumb|'''Figure 3'''. Anterior Cingulate Cortex ]]
Abnormal reward valuation is understood to be a central psychological mechanism that maintains ED behaviours. Research consistently shows that individuals with eating disorders display altered neural activity response to various stimuli, as well as disruptions in reinforcement learning (Calder et al., 2023). Brain regions involved in reward processing, habit formation, and learning, such as the striatum and anterior cingulate cortex (see figures 2 &amp; 3), exhibit atypical activation patterns and differences in dopamine receptor binding across ED types. The insula (see figure 4), which integrates bodily sensations with conscious thought, emotion, and behaviour, also shows altered responses. Together, these regions have been shown to react differently to food images, taste, and social feedback compared to healthy controls, indicating that reward dysfunction extends beyond eating‑related stimuli for ED populations.
[[File:Insular cortex.gif|thumb|'''Figure 4.''' Insula. ]]
In the context of BN and BED, research shows that food is valued more highly than other types of rewards, thus shaping behaviour through its heightened influence on reward outcomes (Calder et al., 2023). Compulsive behaviours specific to each condition (e.g. bingeing, purging) are therefore more likely to occur when food is overvalued and alternative rewards are discounted or ignored. In addition to the neural changes already described, BN and BED are associated with reduced structural and functional connectivity between frontal control regions and the striatum. This combination of highly salient food rewards, and weakened fronto‑striatal pathways, reduces an individual’s ability to inhibit or modulate reward‑seeking impulses. Weak connectivity in these circuits is thought to predict compulsive reward‑seeking behaviour. As a result, even when individuals experience negative consequences from binge episodes, they may struggle to learn from these outcomes or adjust their behaviour accordingly.


Anhedonia, a global reduction in reward responsiveness, is frequently reported by people who experience AN, resulting in food and eating becoming undervalued or aversive to them (Calder et al., 2023). Researchers propose that reward contamination further contributes to this pattern, where the brain learns to associate normally punishing stimuli (e.g., starvation, excessive exercise) with reward, while normally rewarding stimuli (e.g., high‑calorie foods) become experienced as punishment. Structural reductions in the striatum and somatosensory cortex have also been observed, which accounts for distorted bodily sensations and contributes to anhedonia. These changes support maladaptive conditioning in which starvation and weight loss embody a sense of safety, achievement, and emotional relief. Restrictive and preoccupied behaviours centred on food, body shape, and exercise are therefore reinforced over time.

Consistent with affect‑regulation models, eating‑disorder behaviours also become negatively reinforced because they reduce emotional discomfort. This relief increases the likelihood that the behaviours will be repeated, further embedding them within the individual’s coping pattern.


'''Cognitive Rigidity'''

Cognitive rigidity refers to inflexible thinking and behavioural patterns, including difficulty adapting to new information and modifying behaviour. Researchers believe that individuals with EDs often exhibit rigid beliefs about food and weight which interact with a need to exert control over negative emotions. This interaction is the proposed process in which compulsive behaviours and obsessive thoughts develop (Calder et al., 2023). In AN, rigidity manifests as strict dietary rules and fear of losing control, while in BN and BED, binge episodes may feel compulsive and uncontrollable.


'''Interoceptive Awareness'''

Interoceptive awareness (IA) refers to the ability to recognise and process internal bodily states such as hunger, satiety, pain, and arousal. IA is impaired across EDs, and contributes to body mistrust, distorted hunger cues, and inappropriate responses to internal sensations (Brown et al., 2020). Individuals may ignore physical discomfort, misinterpret bodily signals, or avoid sensations altogether, reinforcing maladaptive coping.      

 &lt;blockquote&gt;'''''QUIZ: Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{What coping style do people who experience EDs tend to show?
|type=&quot;()&quot;}
+ Avoidance-oriented
- Problem-oriented

{Compulsive behaviours are more likely to occur when food is ... and alternative rewards are ...
|type=&quot;()&quot;}
- undervalued; overvalued
+ overvalued; undervalued
&lt;/quiz&gt;&lt;/blockquote&gt;

== Psychological Mechanisms of Psychedelic-Assisted Therapy ==

PAT is proposed to influence several psychological mechanisms implicated in EDs, particularly those discussed in the previous section. The next part of this chapter aims to examine the theorised therapeutic mechanisms PAT possesses and practical implications for ED treatment.  


'''Emotion Regulation''' 

Emotion dysregulation is a core mechanism implicated in EDs. Affect regulation theory proposes that ED behaviours emerge as maladaptive strategies to escape, reduce, or blunt overwhelming emotional experiences (Schaefer et al., 2020). Restriction, bingeing, purging, and compulsive exercise may temporarily alleviate distress while reinforcing avoidance-oriented coping and limiting opportunities to learn more adaptive ways of responding to difficult emotions. 

Psychedelics often evoke intense emotional experiences that may disrupt habitual avoidance patterns. Researchers propose that, during psychedelic sessions, attempts to suppress or avoid difficult emotions can intensify these experiences, creating conditions in which emotional acceptance becomes a preferred response (Calder et al., 2023). Although this shift does not occur in every individual, experiencing difficult emotions without resorting to ED behaviours may weaken the association between emotional distress and maladaptive coping, particularly when emotional acceptance becomes associated with a more positive or tolerable experience.

The therapeutic value of this process lies in its potential to reshape affective responses. When individuals experience strong emotions without engaging in maladaptive behaviours, they may begin to develop a new approach towards emotional tolerance. Integration sessions can consolidate this learning by helping individuals articulate, differentiate, and reflect on the emotions experienced during dosing. This process may support the development of more adaptive coping strategies, including task-oriented, problem-focused, and socially supported approaches, which are associated with improved ED outcomes (Fitzsimmons &amp; Bardone-Cone, 2010). In this way, PAT may strengthen emotion regulation and reduce reliance on ED behaviours as strategies for managing affect. 


'''Reward Processing''' 

Reward dysfunction may contribute to the maintenance of EDs by reinforcing maladaptive behaviours while diminishing the perceived value of adaptive rewards. Predictive coding provides a useful framework for understanding how PAT might influence these processes. Individuals with EDs may hold rigid beliefs, conceptualised as high-level priors, about themselves in relation to food, body weight, and rewarding behaviours (Calder et al., 2023; Mograbi et al., 2024). These beliefs can influence how experiences are perceived and valued, potentially reinforcing existing behavioural patterns. Psychedelics are proposed to weaken high-level priors, allowing bottom-up sensory information to exert greater influence on perception and the valuation of experiences. 

During psychedelic experiences, individuals frequently report a heightened appreciation of sensory, social, and bodily experiences. This shift may counteract anhedonia and support the revaluation of previously feared or avoided stimuli. The therapeutic opportunity lies in translating these temporary changes in perception and reward into meaningful behavioural change. Integration sessions can explore positive and negative moments experienced during dosing and connect them to concrete goals. An example of this, inspired from Calder et al.’s (2023) article, could be to clarify specific plans to nourish the body due to the participant having experienced themselves as a decaying skeleton followed by the realisation of the body being a gift. If the period following dosing provides an opportunity for increased neuroplasticity, it may also be particularly conducive to reinforcing adaptive reward learning through behavioural activation with the help of a therapist. 


'''Cognitive Flexibility''' 

Cognitive rigidity is a hallmark of EDs and is characterised by inflexible beliefs about food, weight, body shape, and control. Predictive coding provides a framework for understanding this rigidity, as EDs may involve entrenched priors that resist updating even when confronted with contradictory sensory evidence (Zanella &amp; Lee, 2022). Psychedelics are proposed to disrupt these entrenched priors by increasing neural entropy and reducing the dominance of top-down processing (Calder et al., 2023). This temporary loosening of cognitive constraints may allow individuals to consider alternative perspectives and question long-held beliefs. 

Experiences of ego dissolution may further contribute to cognitive flexibility by reducing attachment to rigid self-concepts (Peled-Avron, 2024; Mograbi et al., 2024). When the boundaries of the self become less defined, individuals may find it easier to question identity-related beliefs that sustain ED pathology. Integration sessions can harness this potential flexibility by supporting cognitive reframing, encouraging behavioural experiments, and strengthening metacognitive awareness. Through these processes, individuals may be better able to translate insights gained during psychedelic experiences into sustained changes in thinking and behaviour.


'''Reconnecting with Bodily Signals'''

Interoceptive deficits are central to ED pathology, contributing to body mistrust, distorted perceptions of hunger cues, and difficulties responding appropriately to internal sensations (Brown et al., 2020). Psychedelics may enhance interoceptive awareness by altering sensory processing and increasing sensitivity to bodily signals. This proposed mechanism is closely related to autonomic regulation, for which polyvagal theory provides a framework for understanding the relationship between bodily signals, emotional regulation, and perceived safety.

Polyvagal theory emphasises the role of the vagus nerve in interoception, emotional regulation, and the perception of safety (Porges, 2022). Vagal afferents transmit information from the body to the insula, where interoceptive signals are integrated with emotional and cognitive processes. Individuals with EDs may exhibit chronic sympathetic arousal and reduced vagal tone, potentially impairing interoceptive accuracy and contributing to emotional rigidity. Psychedelics may initially increase sympathetic activity, as reflected in physiological responses such as increased heart rate, followed by a parasympathetic shift associated with greater relaxation and an increased capacity for rest (Li et al., 2025). Within a polyvagal framework, these changes may have implications for vagal regulation, interoceptive awareness, and emotional regulation.

The therapeutic value of this proposed mechanism lies in its potential to restore trust in bodily signals. Integration sessions may support this process by helping individuals explore bodily sensations experienced during dosing, connect interoceptive cues with emotional states, and practise interoceptive exposure to hunger, fullness, and anxiety-related sensations. Incorporating mindfulness techniques may further support autonomic regulation and help individuals develop a more adaptive relationship with their bodily experiences.

 A Brief Note Concerning The Gut-Brain Interaction 
Although gut microbiome disruption is not a direct psychological mechanism in EDs, it is a relevant biological factor to consider when examining the potential effects of PAT. Restrictive or chaotic eating patterns can contribute to gut dysbiosis, which may weaken gut-barrier integrity and contribute to inflammation affecting the brain (Anton-Paduraru et al., 2024). These changes have been shown to influence mood, stress responsivity, cognitive rigidity, and interoceptive awareness through [[wikipedia:Hypothalamic–pituitary–adrenal_axis|HPA-axis activation]], altered neurotransmitter synthesis, and disrupted hunger–satiety signalling. 

Emerging research suggests that psychedelics may also interact with the gut–brain axis. Certain microbes can metabolise psychedelic compounds, and microbial activity has been associated with modulatory effects on behavioural outcomes. Additionally, psychedelic use may alter microbial composition towards anti-inflammatory profiles, with potential implications for neuroplasticity, neurotransmitter synthesis and signalling improvements (Caspani et al., 2024). These microbiome-related effects may therefore contribute to changes in mood, cognitive flexibility, and appetite regulation.

Although the therapeutic potential of psychedelics in EDs is considered primarily in relation to psychological mechanisms, including changes in perception, emotional processing, and reduced avoidance, microbiome-related effects may represent an additional pathway through which biological processes influence psychological outcomes. However, the extent to which these interactions contribute to therapeutic outcomes in EDs remains to be established.


&lt;blockquote&gt;'''QUIZ: ''Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{ In predictive coding terms, what are “high‑level priors” in eating disorders? 
|type=&quot;()&quot;}
+ Rigid, entrenched beliefs about food, weight, and the self that shape perception and behaviour
- Flexible beliefs that easily update with new sensory information
- Momentary emotional reactions triggered by external cues

{What is the proposed mechanism by which psychedelics support emotion regulation in PAT for EDs? 
|type=&quot;()&quot;}
- By suppressing emotional intensity to prevent distress
+ By evoking strong emotions that disrupt avoidance patterns and promote emotional acceptance
- By eliminating negative emotions through serotonin release

{What is interoceptive awareness?
|type=&quot;()&quot;}
- The ability to evaluate reward value and anticipate pleasurable outcomes
+ The capacity to sense, interpret, and respond to internal bodily signals such as hunger, fullness, and emotional arousal
- The process of weakening cognitive rigidity through ego dissolution
&lt;/quiz&gt;&lt;/blockquote&gt;

== Limitations ==
Despite the potential of PAT to influence psychological mechanisms implicated in EDs, several limitations constrain current understanding of these processes and their therapeutic relevance. Research examining emotion dysregulation in EDs illustrates broader challenges in establishing the mechanisms underlying these conditions. Although non-acceptance of emotions has been identified as a transdiagnostic risk factor across psychiatric conditions (Paulus et al., 2021), Zhou et al.’s meta-analysis (2025) highlights that the causal pathways linking emotional dysregulation and EDs remain unclear, largely because of a lack of experimental and longitudinal studies. Further limitations include restricted availability of measurement scales, insufficient cultural specificity, heterogeneity across samples, gender imbalance, and limited developmental analysis. Together, these factors constrain understanding of how specific emotional processes relate to different ED presentations across the lifespan and stages of recovery.

These limitations are also relevant when considering the proposed mechanisms of PAT. Although existing theoretical frameworks offer ways to conceptualise how psychedelic experiences may influence psychological processes responsible for EDs, the emerging nature of psychedelic therapy limits the extent to which proposed mechanisms have been tested. However, with the number of clinical trials increasing as of recently, it will be interesting to see how the theorised therapeutic mechanisms across different ED presentations and stages of recovery emerges during further warranted investigation.

Nevertheless, current limitations in the evidence highlight the need for research that clarifies the relationships between psychological processes that underscore ED behaviours, and treatment outcomes. There are several important psychological components of ED maintenance that represent meaningful targets for treatment, but they should not be considered in isolation from eachother or the neurobiological processes that influence them. A more comprehensive understanding of how these mechanisms interact may help clarify the therapeutic potential of PAT and inform the development of more targeted treatment approaches.

== Conclusion ==
PAT offers a potential framework for addressing several interconnected psychological mechanisms implicated in EDs. Through its proposed effects on emotional processing, reward valuation, cognitive flexibility, and interoceptive awareness, PAT may create opportunities to disrupt established patterns of avoidance, rigid thinking, and maladaptive behavioural reinforcement. The gut–brain interaction may represent an additional biological pathway relevant to these processes.

These mechanisms should not be understood as independent processes. Changes in emotion regulation may influence the ability to tolerate bodily sensations, while shifts in reward valuation and cognitive flexibility may create opportunities to respond differently to distress and challenge entrenched beliefs. However, the extent to which PAT produces these changes, and whether they translate into sustained improvements in ED outcomes, requires further investigation, although preliminary evidence is promising. 

The therapeutic potential of PAT lies not only in the acute psychedelic experience but also in the structured integration process that follows. Integration sessions provide an opportunity to translate emotional breakthroughs, changes in cognitive flexibility, interoceptive shifts, and reward processing into sustained behavioural change. Effective integration involves helping individuals articulate insights, connect them to ED-related patterns, and develop concrete strategies for change. These may include strengthening adaptive coping, challenging rigid beliefs, practising interoceptive awareness, reinforcing positive reward experiences, and supporting nutritional rehabilitation.

By grounding the understanding of PAT in affect regulation theory and the predictive coding framework, therapists may be better positioned to help individuals explore how psychedelic experiences could disrupt maladaptive emotional and cognitive patterns and create opportunities for new learning. Polyvagal-informed approaches may further support the development of mind–body awareness and emotional regulation through mindfulness strategies. Together, these approaches offer a multifaceted framework for translating psychedelic experiences into therapeutic change and addressing the interconnected mechanisms that maintain EDs and associated suffering. 

==See Also==
* [https://w.wiki/TsdG Ayahuasca and the brain] (Wikiversity)
* [https://w.wiki/TscF Emotional effects of psychedelics] (Wikiversity)
* [https://w.wiki/Tsdb Psilocybin and emotion] (Wikiversity)
* [https://w.wiki/TsdS Psilocibyn assisted psychotherapy] (Wikiversity)
* [https://w.wiki/Tsce Psychedelics, altered consciousness, and personal growth] (Wikiversity)
* [[Eating Disorders|Eating disorders]] (Wikiversity)

==References==
{{Hanging indent|1=

{{ic|Try &quot;Edit source&quot; and then wrapping any text to be italicised in two apostrophes e.g., ''this is italics''}}

Anton-Păduraru, D. T., Trofin, F., Nastase, E. V., Miftode, R. S., Miftode, I. L., Trandafirescu, M. F., Cojocaru, E., Țarcă, E., Mindru, D. E., &amp; Dorneanu, O. S. (2023). The Role of the Gut Microbiota in Anorexia Nervosa in Children and Adults-Systematic Review. &quot;International journal of molecular sciences, 25&quot;(1), 41. https://doi.org/10.3390/ijms25010041

Brown, T. A., Vanzhula, I. A., Reilly, E. E., Levinson, C. A., Berner, L. A., Krueger, A., Lavender, J. M., Kaye, W. H., &amp; Wierenga, C. E. (2020). Body mistrust bridges interoceptive awareness and eating disorder symptoms. &quot;Journal of abnormal psychology, 129&quot;(5), 445–456. https://doi.org/10.1037/abn0000516 

Calder, A., Mock, S., Friedli, N., Pasi, P., &amp; Hasler, G. (2023). Psychedelics in the treatment of eating disorders: Rationale and potential mechanisms. &quot;European Neuropsychopharmacology, 75&quot;, 1–14. https://doi.org/10.1016/j.euroneuro.2023.05.008 

Caspani, G., Ruffell, S. G. D., Tsang, W., Netzband, N., Rohani-Shukla, C., Swann, J. R., &amp; Jefferies, W. A. (2024). Mind over matter: the microbial mindscapes of psychedelics and the gut-brain axis. &quot;Pharmacological research, 207&quot;, 107338. https://doi.org/10.1016/j.phrs.2024.107338  

Fitzsimmons, E. E., &amp; Bardone-Cone, A. M. (2010). Differences in coping across stages of recovery from an eating disorder. &quot;The International journal of eating disorders, 43&quot;(8), 689–693. https://doi.org/10.1002/eat.20781 

Hatzipantelis, C. J., &amp; Olson, D. E. (2024). The Effects of Psychedelics on Neuronal Physiology. &quot;Annual review of physiology, 86&quot;, 27–47. https://doi.org/10.1146/annurev-physiol-042022-020923

Hay, P., Aouad, P., Le, A., Marks, P., Maloney, D., National Eating Disorder Research Consortium, Touyz, S., &amp; Maguire, S. (2023). Epidemiology of eating disorders: population, prevalence, disease burden and quality of life informing public policy in Australia-a rapid review. &quot;Journal of eating disorders, 11&quot;(1), 23. https://doi.org/10.1186/s40337-023-00738-7

Li, H., Wang, H., &amp; Wang, X. (2025). Psychedelics and the Autonomic Nervous System: A Perspective on Their Interplay and Therapeutic Potential. &quot;ACS pharmacology &amp; translational science, 8&quot;(3), 899–902. https://doi.org/10.1021/acsptsci.5c00005 

Leppanen, J., Brown, D., McLinden, H., Williams, S., &amp; Tchanturia, K. (2022). The Role of Emotion Regulation in Eating Disorders: A Network Meta-Analysis Approach. &quot;Frontiers in psychiatry, 13&quot;, 793094. https://doi.org/10.3389/fpsyt.2022.793094 

Mograbi, D. C., Rodrigues, R., Bienemann, B., &amp; Huntley, J. (2024). Brain Networks, Neurotransmitters and Psychedelics: Towards a Neurochemistry of Self-Awareness. &quot;Current neurology and neuroscience reports, 24&quot;(8), 323–340. https://doi.org/10.1007/s11910-024-01353-y

Paulus F. W., Ohmann S., Möhler E., Plener P. &amp; Popow C. (2021). Emotional Dysregulation in Children and Adolescents With Psychiatric Disorders. A Narrative Review. &quot;Frontiers in Psychiatry 12&quot;:628252. doi: 10.3389/fpsyt.2021.628252

Peled-Avron L., Aday J. Ss, Kalafateli A. L., Hamilton H. K., Woolley J. D. (2024). Editorial: Down the rabbit hole – the psychological and neural mechanisms of psychedelic compounds and their use in treating mental health and medical conditions. &quot;Frontiers in Psychiatry 15&quot;:1431389. doi: 10.3389/fpsyt.2024.1431389

Porges S. W. (2025). Polyvagal Theory: Current Status, Clinical Applications, and Future Directions. &quot;Clinical neuropsychiatry, 22&quot;(3), 169–184. https://doi.org/10.36131/cnfioritieditore20250301

Schaefer, L. M., Smith, K. E., Anderson, L. M., Cao, L., Crosby, R. D., Engel, S. G., Crow, S. J., Peterson, C. B., &amp; Wonderlich, S. A. (2020). The role of affect in the maintenance of binge-eating disorder: Evidence from an ecological momentary assessment study. &quot;Journal of abnormal psychology, 129&quot;(4), 387–396. https://doi.org/10.1037/abn0000517 

Shank, L. M., Tanofsky-Kraff, M., Kelly, N. R., Jaramillo, M., Rubin, S. G., Altman, D. R., Byrne, M. E., LeMay-Russell, S., Schvey, N. A., Broadney, M. M., Brady, S. M., Yang, S. B., Courville, A. B., Ramirez, S., Crist, A. C., Yanovski, S. Z., &amp; Yanovski, J. A. (2019). The association between alexithymia and eating behavior in children and adolescents. &quot;Appetite, 142&quot;, 104381. https://doi.org/10.1016/j.appet.2019.104381

Wolfgang, A. S., &amp; Hoge, C. W. (2023). Psychedelic-Assisted Therapy in Military and Veterans Healthcare Systems: Clinical, Legal, and Implementation Considerations. &quot;Current psychiatry reports, 25&quot;(10), 513–532. https://doi.org/10.1007/s11920-023-01446-4 

Zanella, E., &amp; Lee, E. (2022). Integrative review on psychological and social risk and prevention factors of eating disorders including anorexia nervosa and bulimia nervosa: seven major theories. &quot;Heliyon, 8&quot;(11), e11422. https://doi.org/10.1016/j.heliyon.2022.e11422 

Zhou, R., Zhang, L., Liu, Z., &amp; Cao, B. (2025). Emotion regulation difficulties and disordered eating in adolescents and young adults: a meta-analysis. &quot;Journal of eating disorders, 13&quot;(1), 25. https://doi.org/10.1186/s40337-025-01197-y

}}

==External links==
* [https://www.abct.org/fact-sheets/psychedelic-assisted-therapy/ Psychedelic-Assisted Therapy | Fact Sheet] (ABCT - Association for Behavioral and Cognitive Therapies)
* [https://podcasts.apple.com/au/podcast/can-magic-mushrooms-help-treat-anorexia/id189330872?i=1000784809236 Can magic mushrooms help treat anorexia?] (Apple Podcasts)
* [https://www.apa.org/news/podcasts/speaking-of-psychology/eating-disorder The ‘silent epidemic’ of eating disorders] (American Psychological Association)
* [https://www.apa.org/monitor/2023/04/sensations-eating-disorders-suicidal-behavior What is interoception, and how does it affect mental health]? 5 questions for April Smith (American Psychological Association)
* [https://www.cbte.co/what-is-cbte/transdiagnostic-view-eating-disorders/ Transdiagnostic view of eating disorders] (cbte.co)
* [https://psychedelic.support/resources/polyvagal-theory-mind-body-dr-erica-zelfand/ Polyvagal Theory with Dr. Erica Zelfand: Mind-Body Connection] ·(Psychedelic Support)
* [https://www.wholeselfnutrition.org/post/nervous-system-regulation-a-missing-piece-in-eating-disorder-recovery Nervous System Regulation: A Missing Piece in Eating Disorder Recovery]  (wholeselfnutrition.org)
* [https://youtu.be/RwS-CHJcCiY?si=157viTWiOGAQ-7LP Best Neural Entropy - Explainer] (Youtube)

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      <text bytes="37488" sha1="3gbk0shuspaaz32fj6ru3zixak6w999" xml:space="preserve">{{title|Psychedelic treatment of eating disorders:&lt;br&gt;How might psychedelic-assisted therapy influence psychological mechanisms involved in eating disorders?}}
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== Overview ==
{{RoundBoxTop|theme=7}}[[File:Neural network - Midjourney and Grok.png|thumb|'''Figure 1.''' Psychedelics are thought to temporarily disrupt rigid neural communication pathways by promoting more flexible patterns of connectivity across networks involved in mood regulation, fear processing, reward learning, and cognitive adaptability. These changes may support therapeutic shifts in behaviour and emotional processing (Hatzipantelis &amp; Olson, 2025).]]Emma, a 27‑year‑old from Canberra, has lived with an eating disorder for nearly two decades. She describes her problem eating behaviours to have started at school, after being bullied about her appearance. Ever since, they have remained in her life as “a way for me to feel in control”. Although she is aware of the harm caused by restrictive eating and compulsive exercise, she feels trapped in her thought patterns characterised by a preoccupation about food and weight concerns which have become entrenched in her daily life. 

After reading an article describing emerging research suggesting that psychedelics may alter patterns of neural connectivity that shape behaviour (see Figure 1), she expressed interest in pursuing psychedelic‑assisted therapy through a provider accessible to her.

After participating in her first supervised psilocybin‑assisted therapy session, Emma reported experiencing an emotional journey that allowed her to feel “connected to my body for the first time in years”. After 3 months, she has noticed a shift in how she relates to her body, and is finding it easier to actively call into question how she responds to distress with the support of her psychotherapist. 


Her experience raises a central question: What psychological mechanisms could explain these changes?{{RoundBoxBottom|theme=3}}  

This chapter explores how psychedelic‑assisted therapy (PAT) may influence the emotional, cognitive, and neurobiological processes that underpin eating disorders (EDs).   

{{RoundBoxTop|theme=11}}'''Focus questions'''
{{ic|}}Two central questions will be addressed:
* What psychological processes underpin eating disorders, and how do they guide ED behaviour?
* How might psychedelic‑assisted therapy influence these processes and support recovery?
{{ic|}}{{ic|}}{{RoundBoxBottom}}

== Introduction ==
'''Eating Disorders'''  

[[wikipedia:Eating_disorder|Eating disorders]] (EDs) are psychiatric conditions characterised by abnormal eating behaviours that negatively affect physical and mental health. In Australia, the prevalence of EDs is rising particularly among young people. The economic burden is estimated to cost the nation $84 billion, with approximately 10.46% of the population having experienced an ED at some point in their lives (Hay et al., 2023). Although other forms of disordered eating exist, this chapter will focus on only three of them (see table 1), as [[wikipedia:Anorexia|Anorexia Nervosa]] (AN) has the highest mortality rate of any psychiatric disorder, while [[wikipedia:Bulimia|Bulimia Nervosa]] (BN) and [[wikipedia:Binge_eating_disorder|Binge‑Eating Disorder]] (BED) are also highly prevalent. The EDs mentioned are most associated with chronic illness, disability, reduced quality of life, increased suicide risk, and are highly comorbid with [[wikipedia:Mood_disorder|mood disorders]], [[wikipedia:Post-traumatic_stress_disorder|post-traumatic stress disorder]] (PTSD), [[wikipedia:Obsessive–compulsive_disorder|obsessive-compulsive disorder]] (OCD), and [[wikipedia:Substance_use_disorder|substance use disorders]] (Calder et al., 2023).  Despite decades of research, the pathogenesis of EDs remains incompletely understood. Current evidence suggests a complex interplay between genetic predisposition, temperament, hormonal dysregulation, cognitive abnormalities, sociocultural pressures, and traumatic experiences (Calder et al., 2023).  
{| class=&quot;wikitable&quot;
|+Table 1. Eating Disorders and Associated Symptoms 
!Eating Disorder
!Primary Symptoms
|-
|Anorexia Nervosa
|Severe caloric restriction, fear of gaining weight, distorted body image, preoccupation with weight loss.
|-
|Bullimia Nervosa
|Intense windows of food intake (binge eating) followed by inappropriate compensatory behaviours also known as 'purging' (eg. vomiting, laxative use), feelings of guilt and loss of control.
|-
|Binge-Eating Disorder
|Recurrent episodes of binge eating not followed by inappropriate compensatory behaviours, feelings of distress and loss of control.
(Wanderlich &amp; Attia., 2024)
|}


Although cognitive‑behavioural therapy (CBT‑E) combined with pharmacological treatment has demonstrated beneficial outcomes, efficacy remains limited and varies across ED types (Calder et al., 2023). Recovery is often long and difficult, with only two‑thirds of individuals with AN and BN eventually recovering, while others can remain ill for many years. This highlights the need for treatment approaches that can accelerate recovery and provide benefit for individuals who do not respond to conventional therapies.


'''Psychedelic-Assisted Therapy'''

In 2023, Australia legalised the prescription of MDMA and psilocybin under professional supervision, marking a significant shift in mental‑health treatment options. Psychedelic compounds, including [[wikipedia:LSD|LSD]], [[wikipedia:Psilocybin|psilocybin]], [[wikipedia:Dimethyltryptamine|DMT]], [[wikipedia:Ketamine|ketamine]], and [[wikipedia:MDMA|MDMA]], have demonstrated promising therapeutic effects across a wide range of psychiatric conditions. Researchers propose that psychedelics act through psychological and neural mechanisms that increase [[wikipedia:Neuroplasticity|neuroplasticity]], facilitate insight, and foster emotional acceptance (Peled‑Avron et al., 2024). At a neurobiological level, psychedelics influence processes that inform perception, emotion, and behaviour, offering a potential avenue for addressing entrenched ED mechanisms.

PAT differs from pharmacological treatment alone because the drug is administered within a structured therapeutic context designed to maximise safety and clinical benefit (Calder et al., 2023). Treatment typically involves three types of sessions. Preparatory sessions feature participants undergoing psychoeducation, where the clinician establishes rapport and clear safety protocols. Followed by supervised medication where the participant has an inward experience with the reassurance of clinicians present in the same space. Lastly, integrative sessions where individuals process and explore insights from the previous session with their psychotherapist to foster behavioural change (Wolfgang &amp; Hoge, 2023). This combination of pharmacological and psychological intervention is theorised to effectively target underlying psychological mechanisms common across various mental health disorders, illustrating PAT’s potential as a valuable transdiagnostic treatment option. 

PAT has become a subject of increasing popularity in ED research because many of the psychological mechanisms it is proposed to influence are the same ones implicated in ED maintenance and comorbidities (Calder et al., 2023; Peled-Avron et al., 2024). Early research, including case study reports, small clinical studies, meta-analyses and reviews indicate that PAT produces improvements in affect, reductions in ED symptom severity, enhanced body image, weight restoration, and reductions in comorbid symptoms. Although preliminary, these findings indicate that PAT may disrupt and promote shifts away from maladaptive coping patterns that become entrenched in treatment resistant ED populations.

== Psychological Mechanisms in Eating Disorders ==


'''Emotion Dysregulation'''

Emotion dysregulation is considered to be a significant risk factor for the onset and maintenance of EDs. It refers to difficulties recognising, assessing, and modifying emotional responses to meet situational demands (Zhou et al., 2025). 

Research consistently shows that individuals with EDs experience significant challenges in regulating emotions, increasing their vulnerability to comorbid symptoms, which contribute to the emergence of disordered eating patterns (Leppanen et al., 2022). This idea is supported by affect regulation theory which posits that eating disorders develop and are maintained as maladaptive strategies to manage, tolerate and escape from negative emotions and psychological distress (Schaefer et al., 2020; Zanella &amp; Lee, 2022). This is further exemplified in Fitzsimmons &amp; Bardone-Cone’s article examining differences in coping within eating disorder patients (2010). The authors explain that avoidance and emotion-oriented coping styles often function as maladaptive attempts to manage (di)stress. They explain that behaviours such as binge eating, purging, starvation, and/or compulsive exercise provide temporary relief by shifting attention away from uncomfortable emotions. 

Furthermore, alexithymia, characterised by difficulty identifying and describing one’s own emotions, is strongly associated with ED pathology (Shank et al., 2019). Individuals with high alexithymia often struggle to differentiate emotional states from bodily sensations, contributing to behaviours such as emotional eating, eating in the absence of hunger, or rigid restriction. In BED, alexithymia is linked to binge episodes triggered by poorly understood emotional cues, while in AN and BN, alexithymia may contribute to emotional avoidance and reliance on ED behaviours for affect regulation. 

The effects of trauma are contributing factors to emotion dysregulation, and considered a risk factor for ED development. Individuals who experience sexual, physical, or emotional abuse, neglect, and bullying are likely to experience heightened emotional reactivity, threat perception, and avoidance behaviours (Calder et al., 2023). Researchers explain that trauma often results in lowered distress tolerance and increased reliance on maladaptive coping behaviours, including disordered eating. Furthermore, PTSD comorbidity is common, hence trauma‑related symptoms are hypothesised to frequently interact with ED behaviours in complex ways.  


'''Reward Processing Dysfunction'''
[[File:Striatum.gif|thumb|'''Figure 2.''' Striatum]]
[[File:Anterior cingulate gyrus animation.gif|thumb|'''Figure 3'''. Anterior Cingulate Cortex ]]
Abnormal reward valuation is understood to be a central psychological mechanism that maintains ED behaviours. Research consistently shows that individuals with eating disorders display altered neural activity response to various stimuli, as well as disruptions in reinforcement learning (Calder et al., 2023). Brain regions involved in reward processing, habit formation, and learning, such as the striatum and anterior cingulate cortex (see figures 2 &amp; 3), exhibit atypical activation patterns and differences in dopamine receptor binding across ED types. The insula (see figure 4), which integrates bodily sensations with conscious thought, emotion, and behaviour, also shows altered responses. Together, these regions have been shown to react differently to food images, taste, and social feedback compared to healthy controls, indicating that reward dysfunction extends beyond eating‑related stimuli for ED populations.
[[File:Insular cortex.gif|thumb|'''Figure 4.''' Insula. ]]
In the context of BN and BED, research shows that food is valued more highly than other types of rewards, thus shaping behaviour through its heightened influence on reward outcomes (Calder et al., 2023). Compulsive behaviours specific to each condition (e.g. bingeing, purging) are therefore more likely to occur when food is overvalued and alternative rewards are discounted or ignored. In addition to the neural changes already described, BN and BED are associated with reduced structural and functional connectivity between frontal control regions and the striatum. This combination of highly salient food rewards, and weakened fronto‑striatal pathways, reduces an individual’s ability to inhibit or modulate reward‑seeking impulses. Weak connectivity in these circuits is thought to predict compulsive reward‑seeking behaviour. As a result, even when individuals experience negative consequences from binge episodes, they may struggle to learn from these outcomes or adjust their behaviour accordingly.


Anhedonia, a global reduction in reward responsiveness, is frequently reported by people who experience AN, resulting in food and eating becoming undervalued or aversive to them (Calder et al., 2023). Researchers propose that reward contamination further contributes to this pattern, where the brain learns to associate normally punishing stimuli (e.g., starvation, excessive exercise) with reward, while normally rewarding stimuli (e.g., high‑calorie foods) become experienced as punishment. Structural reductions in the striatum and somatosensory cortex have also been observed, which accounts for distorted bodily sensations and contributes to anhedonia. These changes support maladaptive conditioning in which starvation and weight loss embody a sense of safety, achievement, and emotional relief. Restrictive and preoccupied behaviours centred on food, body shape, and exercise are therefore reinforced over time.

Consistent with affect‑regulation models, eating‑disorder behaviours also become negatively reinforced because they reduce emotional discomfort. This relief increases the likelihood that the behaviours will be repeated, further embedding them within the individual’s coping pattern.


'''Cognitive Rigidity'''

Cognitive rigidity refers to inflexible thinking and behavioural patterns, including difficulty adapting to new information and modifying behaviour. Researchers believe that individuals with EDs often exhibit rigid beliefs about food and weight which interact with a need to exert control over negative emotions. This interaction is the proposed process in which compulsive behaviours and obsessive thoughts develop (Calder et al., 2023). In AN, rigidity manifests as strict dietary rules and fear of losing control, while in BN and BED, binge episodes may feel compulsive and uncontrollable.


'''Interoceptive Awareness'''

Interoceptive awareness (IA) refers to the ability to recognise and process internal bodily states such as hunger, satiety, pain, and arousal. IA is impaired across EDs, and contributes to body mistrust, distorted hunger cues, and inappropriate responses to internal sensations (Brown et al., 2020). Individuals may ignore physical discomfort, misinterpret bodily signals, or avoid sensations altogether, reinforcing maladaptive coping.      

 &lt;blockquote&gt;'''''QUIZ: Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{What coping style do people who experience EDs tend to show?
|type=&quot;()&quot;}
+ Avoidance-oriented
- Problem-oriented

{Compulsive behaviours are more likely to occur when food is ... and alternative rewards are ...
|type=&quot;()&quot;}
- undervalued; overvalued
+ overvalued; undervalued
&lt;/quiz&gt;&lt;/blockquote&gt;

== Psychological Mechanisms of Psychedelic-Assisted Therapy ==

PAT is proposed to influence several psychological mechanisms implicated in EDs, particularly those discussed in the previous section. The next part of this chapter aims to examine the theorised therapeutic mechanisms PAT possesses and practical implications for ED treatment.  


'''Emotion Regulation''' 

Emotion dysregulation is a core mechanism implicated in EDs. Affect regulation theory proposes that ED behaviours emerge as maladaptive strategies to escape, reduce, or blunt overwhelming emotional experiences (Schaefer et al., 2020). Restriction, bingeing, purging, and compulsive exercise may temporarily alleviate distress while reinforcing avoidance-oriented coping and limiting opportunities to learn more adaptive ways of responding to difficult emotions. 

Psychedelics often evoke intense emotional experiences that may disrupt habitual avoidance patterns. Researchers propose that, during psychedelic sessions, attempts to suppress or avoid difficult emotions can intensify these experiences, creating conditions in which emotional acceptance becomes a preferred response (Calder et al., 2023). Although this shift does not occur in every individual, experiencing difficult emotions without resorting to ED behaviours may weaken the association between emotional distress and maladaptive coping, particularly when emotional acceptance becomes associated with a more positive or tolerable experience.

The therapeutic value of this process lies in its potential to reshape affective responses. When individuals experience strong emotions without engaging in maladaptive behaviours, they may begin to develop a new approach towards emotional tolerance. Integration sessions can consolidate this learning by helping individuals articulate, differentiate, and reflect on the emotions experienced during dosing. This process may support the development of more adaptive coping strategies, including task-oriented, problem-focused, and socially supported approaches, which are associated with improved ED outcomes (Fitzsimmons &amp; Bardone-Cone, 2010). In this way, PAT may strengthen emotion regulation and reduce reliance on ED behaviours as strategies for managing affect. 


'''Reward Processing''' 

Reward dysfunction may contribute to the maintenance of EDs by reinforcing maladaptive behaviours while diminishing the perceived value of adaptive rewards. Predictive coding provides a useful framework for understanding how PAT might influence these processes. Individuals with EDs may hold rigid beliefs, conceptualised as high-level priors, about themselves in relation to food, body weight, and rewarding behaviours (Calder et al., 2023; Mograbi et al., 2024). These beliefs can influence how experiences are perceived and valued, potentially reinforcing existing behavioural patterns. Psychedelics are proposed to weaken high-level priors, allowing bottom-up sensory information to exert greater influence on perception and the valuation of experiences. 

During psychedelic experiences, individuals frequently report a heightened appreciation of sensory, social, and bodily experiences. This shift may counteract anhedonia and support the revaluation of previously feared or avoided stimuli. The therapeutic opportunity lies in translating these temporary changes in perception and reward into meaningful behavioural change. Integration sessions can explore positive and negative moments experienced during dosing and connect them to concrete goals. An example of this, inspired from Calder et al.’s (2023) article, could be to clarify specific plans to nourish the body due to the participant having experienced themselves as a decaying skeleton followed by the realisation of the body being a gift. If the period following dosing provides an opportunity for increased neuroplasticity, it may also be particularly conducive to reinforcing adaptive reward learning through behavioural activation with the help of a therapist. 


'''Cognitive Flexibility''' 

Cognitive rigidity is a hallmark of EDs and is characterised by inflexible beliefs about food, weight, body shape, and control. Predictive coding provides a framework for understanding this rigidity, as EDs may involve entrenched priors that resist updating even when confronted with contradictory sensory evidence (Zanella &amp; Lee, 2022). Psychedelics are proposed to disrupt these entrenched priors by increasing neural entropy and reducing the dominance of top-down processing (Calder et al., 2023). This temporary loosening of cognitive constraints may allow individuals to consider alternative perspectives and question long-held beliefs. 

Experiences of ego dissolution may further contribute to cognitive flexibility by reducing attachment to rigid self-concepts (Peled-Avron, 2024; Mograbi et al., 2024). When the boundaries of the self become less defined, individuals may find it easier to question identity-related beliefs that sustain ED pathology. Integration sessions can harness this potential flexibility by supporting cognitive reframing, encouraging behavioural experiments, and strengthening metacognitive awareness. Through these processes, individuals may be better able to translate insights gained during psychedelic experiences into sustained changes in thinking and behaviour.


'''Reconnecting with Bodily Signals'''

Interoceptive deficits are central to ED pathology, contributing to body mistrust, distorted perceptions of hunger cues, and difficulties responding appropriately to internal sensations (Brown et al., 2020). Psychedelics may enhance interoceptive awareness by altering sensory processing and increasing sensitivity to bodily signals. This proposed mechanism is closely related to autonomic regulation, for which polyvagal theory provides a framework for understanding the relationship between bodily signals, emotional regulation, and perceived safety.

Polyvagal theory emphasises the role of the vagus nerve in interoception, emotional regulation, and the perception of safety (Porges, 2022). Vagal afferents transmit information from the body to the insula, where interoceptive signals are integrated with emotional and cognitive processes. Individuals with EDs may exhibit chronic sympathetic arousal and reduced vagal tone, potentially impairing interoceptive accuracy and contributing to emotional rigidity. Psychedelics may initially increase sympathetic activity, as reflected in physiological responses such as increased heart rate, followed by a parasympathetic shift associated with greater relaxation and an increased capacity for rest (Li et al., 2025). Within a polyvagal framework, these changes may have implications for vagal regulation, interoceptive awareness, and emotional regulation.

The therapeutic value of this proposed mechanism lies in its potential to restore trust in bodily signals. Integration sessions may support this process by helping individuals explore bodily sensations experienced during dosing, connect interoceptive cues with emotional states, and practise interoceptive exposure to hunger, fullness, and anxiety-related sensations. Incorporating mindfulness techniques may further support autonomic regulation and help individuals develop a more adaptive relationship with their bodily experiences.

 A Brief Note Concerning The Gut-Brain Interaction 
Although gut microbiome disruption is not a direct psychological mechanism in EDs, it is a relevant biological factor to consider when examining the potential effects of PAT. Restrictive or chaotic eating patterns can contribute to gut dysbiosis, which may weaken gut-barrier integrity and contribute to inflammation affecting the brain (Anton-Paduraru et al., 2024). These changes have been shown to influence mood, stress responsivity, cognitive rigidity, and interoceptive awareness through [[wikipedia:Hypothalamic–pituitary–adrenal_axis|HPA-axis activation]], altered neurotransmitter synthesis, and disrupted hunger–satiety signalling. 

Emerging research suggests that psychedelics may also interact with the gut–brain axis. Certain microbes can metabolise psychedelic compounds, and microbial activity has been associated with modulatory effects on behavioural outcomes. Additionally, psychedelic use may alter microbial composition towards anti-inflammatory profiles, with potential implications for neuroplasticity, neurotransmitter synthesis and signalling improvements (Caspani et al., 2024). These microbiome-related effects may therefore contribute to changes in mood, cognitive flexibility, and appetite regulation.

Although the therapeutic potential of psychedelics in EDs is considered primarily in relation to psychological mechanisms, including changes in perception, emotional processing, and reduced avoidance, microbiome-related effects may represent an additional pathway through which biological processes influence psychological outcomes. However, the extent to which these interactions contribute to therapeutic outcomes in EDs remains to be established.


&lt;blockquote&gt;'''QUIZ: ''Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{ In predictive coding terms, what are “high‑level priors” in eating disorders? 
|type=&quot;()&quot;}
+ Rigid, entrenched beliefs about food, weight, and the self that shape perception and behaviour
- Flexible beliefs that easily update with new sensory information
- Momentary emotional reactions triggered by external cues

{What is the proposed mechanism by which psychedelics support emotion regulation in PAT for EDs? 
|type=&quot;()&quot;}
- By suppressing emotional intensity to prevent distress
+ By evoking strong emotions that disrupt avoidance patterns and promote emotional acceptance
- By eliminating negative emotions through serotonin release

{What is interoceptive awareness?
|type=&quot;()&quot;}
- The ability to evaluate reward value and anticipate pleasurable outcomes
+ The capacity to sense, interpret, and respond to internal bodily signals such as hunger, fullness, and emotional arousal
- The process of weakening cognitive rigidity through ego dissolution
&lt;/quiz&gt;&lt;/blockquote&gt;

== Limitations ==
Despite the potential of PAT to influence psychological mechanisms implicated in EDs, several limitations constrain current understanding of these processes and their therapeutic relevance. Research examining emotion dysregulation in EDs illustrates broader challenges in establishing the mechanisms underlying these conditions. Although non-acceptance of emotions has been identified as a transdiagnostic risk factor across psychiatric conditions (Paulus et al., 2021), Zhou et al.’s meta-analysis (2025) highlights that the causal pathways linking emotional dysregulation and EDs remain unclear, largely because of a lack of experimental and longitudinal studies. Further limitations include restricted availability of measurement scales, insufficient cultural specificity, heterogeneity across samples, gender imbalance, and limited developmental analysis. Together, these factors constrain understanding of how specific emotional processes relate to different ED presentations across the lifespan and stages of recovery.

These limitations are also relevant when considering the proposed mechanisms of PAT. Although existing theoretical frameworks offer ways to conceptualise how psychedelic experiences may influence psychological processes responsible for EDs, the emerging nature of psychedelic therapy limits the extent to which proposed mechanisms have been tested. However, with the number of clinical trials increasing as of recently, it will be interesting to see how the theorised therapeutic mechanisms across different ED presentations and stages of recovery emerges during further warranted investigation.

Nevertheless, current limitations in the evidence highlight the need for research that clarifies the relationships between psychological processes that underscore ED behaviours, and treatment outcomes. There are several important psychological components of ED maintenance that represent meaningful targets for treatment, but they should not be considered in isolation from eachother or the neurobiological processes that influence them. A more comprehensive understanding of how these mechanisms interact may help clarify the therapeutic potential of PAT and inform the development of more targeted treatment approaches.

== Conclusion ==
PAT offers a potential framework for addressing several interconnected psychological mechanisms implicated in EDs. Through its proposed effects on emotional processing, reward valuation, cognitive flexibility, and interoceptive awareness, PAT may create opportunities to disrupt established patterns of avoidance, rigid thinking, and maladaptive behavioural reinforcement. The gut–brain interaction may represent an additional biological pathway relevant to these processes.

These mechanisms should not be understood as independent processes. Changes in emotion regulation may influence the ability to tolerate bodily sensations, while shifts in reward valuation and cognitive flexibility may create opportunities to respond differently to distress and challenge entrenched beliefs. However, the extent to which PAT produces these changes, and whether they translate into sustained improvements in ED outcomes, requires further investigation, although preliminary evidence is promising. 

The therapeutic potential of PAT lies not only in the acute psychedelic experience but also in the structured integration process that follows. Integration sessions provide an opportunity to translate emotional breakthroughs, changes in cognitive flexibility, interoceptive shifts, and reward processing into sustained behavioural change. Effective integration involves helping individuals articulate insights, connect them to ED-related patterns, and develop concrete strategies for change. These may include strengthening adaptive coping, challenging rigid beliefs, practising interoceptive awareness, reinforcing positive reward experiences, and supporting nutritional rehabilitation.

By grounding the understanding of PAT in affect regulation theory and the predictive coding framework, therapists may be better positioned to help individuals explore how psychedelic experiences could disrupt maladaptive emotional and cognitive patterns and create opportunities for new learning. Polyvagal-informed approaches may further support the development of mind–body awareness and emotional regulation through mindfulness strategies. Together, these approaches offer a multifaceted framework for translating psychedelic experiences into therapeutic change and addressing the interconnected mechanisms that maintain EDs and associated suffering. 

==See Also==
* [https://w.wiki/TsdG Ayahuasca and the brain] (Wikiversity)
* [https://w.wiki/TscF Emotional effects of psychedelics] (Wikiversity)
* [https://w.wiki/Tsdb Psilocybin and emotion] (Wikiversity)
* [https://w.wiki/TsdS Psilocibyn assisted psychotherapy] (Wikiversity)
* [https://w.wiki/Tsce Psychedelics, altered consciousness, and personal growth] (Wikiversity)
* [[Eating Disorders|Eating disorders]] (Wikiversity)

==References==
{{Hanging indent|1=

{{ic|Try &quot;Edit source&quot; and then wrapping any text to be italicised in two apostrophes e.g., ''this is italics''}}

Anton-Păduraru, D. T., Trofin, F., Nastase, E. V., Miftode, R. S., Miftode, I. L., Trandafirescu, M. F., Cojocaru, E., Țarcă, E., Mindru, D. E., &amp; Dorneanu, O. S. (2023). The Role of the Gut Microbiota in Anorexia Nervosa in Children and Adults-Systematic Review. &quot;International journal of molecular sciences, 25&quot;(1), 41. https://doi.org/10.3390/ijms25010041

Brown, T. A., Vanzhula, I. A., Reilly, E. E., Levinson, C. A., Berner, L. A., Krueger, A., Lavender, J. M., Kaye, W. H., &amp; Wierenga, C. E. (2020). Body mistrust bridges interoceptive awareness and eating disorder symptoms. &quot;Journal of abnormal psychology, 129&quot;(5), 445–456. https://doi.org/10.1037/abn0000516 

Calder, A., Mock, S., Friedli, N., Pasi, P., &amp; Hasler, G. (2023). Psychedelics in the treatment of eating disorders: Rationale and potential mechanisms. &quot;European Neuropsychopharmacology, 75&quot;, 1–14. https://doi.org/10.1016/j.euroneuro.2023.05.008 

Caspani, G., Ruffell, S. G. D., Tsang, W., Netzband, N., Rohani-Shukla, C., Swann, J. R., &amp; Jefferies, W. A. (2024). Mind over matter: the microbial mindscapes of psychedelics and the gut-brain axis. &quot;Pharmacological research, 207&quot;, 107338. https://doi.org/10.1016/j.phrs.2024.107338  

Fitzsimmons, E. E., &amp; Bardone-Cone, A. M. (2010). Differences in coping across stages of recovery from an eating disorder. &quot;The International journal of eating disorders, 43&quot;(8), 689–693. https://doi.org/10.1002/eat.20781 

Hatzipantelis, C. J., &amp; Olson, D. E. (2024). The Effects of Psychedelics on Neuronal Physiology. &quot;Annual review of physiology, 86&quot;, 27–47. https://doi.org/10.1146/annurev-physiol-042022-020923

Hay, P., Aouad, P., Le, A., Marks, P., Maloney, D., National Eating Disorder Research Consortium, Touyz, S., &amp; Maguire, S. (2023). Epidemiology of eating disorders: population, prevalence, disease burden and quality of life informing public policy in Australia-a rapid review. &quot;Journal of eating disorders, 11&quot;(1), 23. https://doi.org/10.1186/s40337-023-00738-7

Li, H., Wang, H., &amp; Wang, X. (2025). Psychedelics and the Autonomic Nervous System: A Perspective on Their Interplay and Therapeutic Potential. &quot;ACS pharmacology &amp; translational science, 8&quot;(3), 899–902. https://doi.org/10.1021/acsptsci.5c00005 

Leppanen, J., Brown, D., McLinden, H., Williams, S., &amp; Tchanturia, K. (2022). The Role of Emotion Regulation in Eating Disorders: A Network Meta-Analysis Approach. &quot;Frontiers in psychiatry, 13&quot;, 793094. https://doi.org/10.3389/fpsyt.2022.793094 

Mograbi, D. C., Rodrigues, R., Bienemann, B., &amp; Huntley, J. (2024). Brain Networks, Neurotransmitters and Psychedelics: Towards a Neurochemistry of Self-Awareness. &quot;Current neurology and neuroscience reports, 24&quot;(8), 323–340. https://doi.org/10.1007/s11910-024-01353-y

Paulus F. W., Ohmann S., Möhler E., Plener P. &amp; Popow C. (2021). Emotional Dysregulation in Children and Adolescents With Psychiatric Disorders. A Narrative Review. &quot;Frontiers in Psychiatry 12&quot;:628252. doi: 10.3389/fpsyt.2021.628252

Peled-Avron L., Aday J. Ss, Kalafateli A. L., Hamilton H. K., Woolley J. D. (2024). Editorial: Down the rabbit hole – the psychological and neural mechanisms of psychedelic compounds and their use in treating mental health and medical conditions. &quot;Frontiers in Psychiatry 15&quot;:1431389. doi: 10.3389/fpsyt.2024.1431389

Porges S. W. (2025). Polyvagal Theory: Current Status, Clinical Applications, and Future Directions. &quot;Clinical neuropsychiatry, 22&quot;(3), 169–184. https://doi.org/10.36131/cnfioritieditore20250301

Schaefer, L. M., Smith, K. E., Anderson, L. M., Cao, L., Crosby, R. D., Engel, S. G., Crow, S. J., Peterson, C. B., &amp; Wonderlich, S. A. (2020). The role of affect in the maintenance of binge-eating disorder: Evidence from an ecological momentary assessment study. &quot;Journal of abnormal psychology, 129&quot;(4), 387–396. https://doi.org/10.1037/abn0000517 

Shank, L. M., Tanofsky-Kraff, M., Kelly, N. R., Jaramillo, M., Rubin, S. G., Altman, D. R., Byrne, M. E., LeMay-Russell, S., Schvey, N. A., Broadney, M. M., Brady, S. M., Yang, S. B., Courville, A. B., Ramirez, S., Crist, A. C., Yanovski, S. Z., &amp; Yanovski, J. A. (2019). The association between alexithymia and eating behavior in children and adolescents. &quot;Appetite, 142&quot;, 104381. https://doi.org/10.1016/j.appet.2019.104381

Wonderlich, J., &amp; Attia, E. (2024). Eating disorders in the DSM-5. In P. Robinson, T. Wade, B. Herpertz-Dahlmann, F. Fernandez-Aranda, J. Treasure, &amp; S. Wonderlich (Eds.), Eating disorders: An international comprehensive view (pp. 7–18). &quot;Springer Nature Switzerland AG&quot;. https://doi.org/10.1007/978-3-031-46096-8_9

Wolfgang, A. S., &amp; Hoge, C. W. (2023). Psychedelic-Assisted Therapy in Military and Veterans Healthcare Systems: Clinical, Legal, and Implementation Considerations. &quot;Current psychiatry reports, 25&quot;(10), 513–532. https://doi.org/10.1007/s11920-023-01446-4 

Zanella, E., &amp; Lee, E. (2022). Integrative review on psychological and social risk and prevention factors of eating disorders including anorexia nervosa and bulimia nervosa: seven major theories. &quot;Heliyon, 8&quot;(11), e11422. https://doi.org/10.1016/j.heliyon.2022.e11422 

Zhou, R., Zhang, L., Liu, Z., &amp; Cao, B. (2025). Emotion regulation difficulties and disordered eating in adolescents and young adults: a meta-analysis. &quot;Journal of eating disorders, 13&quot;(1), 25. https://doi.org/10.1186/s40337-025-01197-y

}}

==External links==
* [https://www.abct.org/fact-sheets/psychedelic-assisted-therapy/ Psychedelic-Assisted Therapy | Fact Sheet] (ABCT - Association for Behavioral and Cognitive Therapies)
* [https://podcasts.apple.com/au/podcast/can-magic-mushrooms-help-treat-anorexia/id189330872?i=1000784809236 Can magic mushrooms help treat anorexia?] (Apple Podcasts)
* [https://www.apa.org/news/podcasts/speaking-of-psychology/eating-disorder The ‘silent epidemic’ of eating disorders] (American Psychological Association)
* [https://www.apa.org/monitor/2023/04/sensations-eating-disorders-suicidal-behavior What is interoception, and how does it affect mental health]? 5 questions for April Smith (American Psychological Association)
* [https://www.cbte.co/what-is-cbte/transdiagnostic-view-eating-disorders/ Transdiagnostic view of eating disorders] (cbte.co)
* [https://psychedelic.support/resources/polyvagal-theory-mind-body-dr-erica-zelfand/ Polyvagal Theory with Dr. Erica Zelfand: Mind-Body Connection] ·(Psychedelic Support)
* [https://www.wholeselfnutrition.org/post/nervous-system-regulation-a-missing-piece-in-eating-disorder-recovery Nervous System Regulation: A Missing Piece in Eating Disorder Recovery]  (wholeselfnutrition.org)
* [https://youtu.be/RwS-CHJcCiY?si=157viTWiOGAQ-7LP Best Neural Entropy - Explainer] (Youtube)

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== Overview ==
{{RoundBoxTop|theme=7}}[[File:Neural network - Midjourney and Grok.png|thumb|'''Figure 1.''' Psychedelics are thought to temporarily disrupt rigid neural communication pathways by promoting more flexible patterns of connectivity across networks involved in mood regulation, fear processing, reward learning, and cognitive adaptability. These changes may support therapeutic shifts in behaviour and emotional processing (Hatzipantelis &amp; Olson, 2025).]]Emma, a 27‑year‑old from Canberra, has lived with an eating disorder for nearly two decades. She describes her problem eating behaviours to have started at school, after being bullied about her appearance and experiencing an unsteady home life. Ever since, they have remained in her life as “a way for me to feel in control”. Although she is aware of the harm caused by restrictive eating and compulsive exercise, she feels trapped in her thought patterns characterised by a preoccupation about food and weight concerns which have become entrenched in her daily life. 

After reading an article describing emerging research suggesting that psychedelics may alter patterns of neural connectivity that shape behaviour (see Figure 1), she expressed interest in pursuing psychedelic‑assisted therapy through a provider accessible to her.

After participating in her first supervised psilocybin‑assisted therapy session, Emma reported experiencing an emotional journey that allowed her to feel “connected to my body for the first time in years”. After 3 months, she has noticed a shift in how she relates to her body, and is finding it easier to actively call into question how she responds to distress with the support of her psychotherapist. 


Her experience raises a central question: What psychological mechanisms could explain these changes?{{RoundBoxBottom|theme=3}}  

This chapter explores how psychedelic‑assisted therapy (PAT) may influence the emotional, cognitive, and neurobiological processes that underpin eating disorders (EDs).   

{{RoundBoxTop|theme=11}}'''Focus questions'''
{{ic|}}Two central questions will be addressed:
* What psychological processes underpin eating disorders, and how do they guide ED behaviour?
* How might psychedelic‑assisted therapy influence these processes and support recovery?
{{ic|}}{{ic|}}{{RoundBoxBottom}}

== Introduction ==
'''Eating Disorders'''  

[[wikipedia:Eating_disorder|Eating disorders]] (EDs) are psychiatric conditions characterised by abnormal eating behaviours that negatively affect physical and mental health. In Australia, the prevalence of EDs is rising particularly among young people. The economic burden is estimated to cost the nation $84 billion, with approximately 10.46% of the population having experienced an ED at some point in their lives (Hay et al., 2023). Although other forms of disordered eating exist, this chapter will focus on only three of them (see table 1), as [[wikipedia:Anorexia|Anorexia Nervosa]] (AN) has the highest mortality rate of any psychiatric disorder, while [[wikipedia:Bulimia|Bulimia Nervosa]] (BN) and [[wikipedia:Binge_eating_disorder|Binge‑Eating Disorder]] (BED) are also highly prevalent. The EDs mentioned are most associated with chronic illness, disability, reduced quality of life, increased suicide risk, and are highly comorbid with [[wikipedia:Mood_disorder|mood disorders]], [[wikipedia:Post-traumatic_stress_disorder|post-traumatic stress disorder]] (PTSD), [[wikipedia:Obsessive–compulsive_disorder|obsessive-compulsive disorder]] (OCD), and [[wikipedia:Substance_use_disorder|substance use disorders]] (Calder et al., 2023).  Despite decades of research, the pathogenesis of EDs remains incompletely understood. Current evidence suggests a complex interplay between genetic predisposition, temperament, hormonal dysregulation, cognitive abnormalities, sociocultural pressures, and traumatic experiences (Calder et al., 2023).  
{| class=&quot;wikitable&quot;
|+Table 1. Eating Disorders and Associated Symptoms 
!Eating Disorder
!Primary Symptoms
|-
|Anorexia Nervosa
|Severe caloric restriction, fear of gaining weight, distorted body image, preoccupation with weight loss.
|-
|Bullimia Nervosa
|Intense windows of food intake (binge eating) followed by inappropriate compensatory behaviours also known as 'purging' (eg. vomiting, laxative use), feelings of guilt and loss of control.
|-
|Binge-Eating Disorder
|Recurrent episodes of binge eating not followed by inappropriate compensatory behaviours, feelings of distress and loss of control.
(Wanderlich &amp; Attia., 2024)
|}


Although cognitive‑behavioural therapy (CBT‑E) combined with pharmacological treatment has demonstrated beneficial outcomes, efficacy remains limited and varies across ED types (Calder et al., 2023). Recovery is often long and difficult, with only two‑thirds of individuals with AN and BN eventually recovering, while others can remain ill for many years. This highlights the need for treatment approaches that can accelerate recovery and provide benefit for individuals who do not respond to conventional therapies.


'''Psychedelic-Assisted Therapy'''

In 2023, Australia legalised the prescription of MDMA and psilocybin under professional supervision, marking a significant shift in mental‑health treatment options. Psychedelic compounds, including [[wikipedia:LSD|LSD]], [[wikipedia:Psilocybin|psilocybin]], [[wikipedia:Dimethyltryptamine|DMT]], [[wikipedia:Ketamine|ketamine]], and [[wikipedia:MDMA|MDMA]], have demonstrated promising therapeutic effects across a wide range of psychiatric conditions. Researchers propose that psychedelics act through psychological and neural mechanisms that increase [[wikipedia:Neuroplasticity|neuroplasticity]], facilitate insight, and foster emotional acceptance (Peled‑Avron et al., 2024). At a neurobiological level, psychedelics influence processes that inform perception, emotion, and behaviour, offering a potential avenue for addressing entrenched ED mechanisms.

PAT differs from pharmacological treatment alone because the drug is administered within a structured therapeutic context designed to maximise safety and clinical benefit (Calder et al., 2023). Treatment typically involves three types of sessions. Preparatory sessions feature participants undergoing psychoeducation, where the clinician establishes rapport and clear safety protocols. Followed by supervised medication where the participant has an inward experience with the reassurance of clinicians present in the same space. Lastly, integrative sessions where individuals process and explore insights from the previous session with their psychotherapist to foster behavioural change (Wolfgang &amp; Hoge, 2023). This combination of pharmacological and psychological intervention is theorised to effectively target underlying psychological mechanisms common across various mental health disorders, illustrating PAT’s potential as a valuable transdiagnostic treatment option. 

PAT has become a subject of increasing popularity in ED research because many of the psychological mechanisms it is proposed to influence are the same ones implicated in ED maintenance and comorbidities (Calder et al., 2023; Peled-Avron et al., 2024). Early research, including case study reports, small clinical studies, meta-analyses and reviews indicate that PAT produces improvements in affect, reductions in ED symptom severity, enhanced body image, weight restoration, and reductions in comorbid symptoms. Although preliminary, these findings indicate that PAT may disrupt and promote shifts away from maladaptive coping patterns that become entrenched in treatment resistant ED populations.

== Psychological Mechanisms in Eating Disorders ==


'''Emotion Dysregulation'''

Emotion dysregulation is considered to be a significant risk factor for the onset and maintenance of EDs. It refers to difficulties recognising, assessing, and modifying emotional responses to meet situational demands (Zhou et al., 2025). 

Research consistently shows that individuals with EDs experience significant challenges in regulating emotions, increasing their vulnerability to comorbid symptoms, which contribute to the emergence of disordered eating patterns (Leppanen et al., 2022). This idea is supported by affect regulation theory which posits that eating disorders develop and are maintained as maladaptive strategies to manage, tolerate and escape from negative emotions and psychological distress (Schaefer et al., 2020; Zanella &amp; Lee, 2022). This is further exemplified in Fitzsimmons &amp; Bardone-Cone’s article examining differences in coping within eating disorder patients (2010). The authors explain that avoidance and emotion-oriented coping styles often function as maladaptive attempts to manage (di)stress. They explain that behaviours such as binge eating, purging, starvation, and/or compulsive exercise provide temporary relief by shifting attention away from uncomfortable emotions. 

Furthermore, alexithymia, characterised by difficulty identifying and describing one’s own emotions, is strongly associated with ED pathology (Shank et al., 2019). Individuals with high alexithymia often struggle to differentiate emotional states from bodily sensations, contributing to behaviours such as emotional eating, eating in the absence of hunger, or rigid restriction. In BED, alexithymia is linked to binge episodes triggered by poorly understood emotional cues, while in AN and BN, alexithymia may contribute to emotional avoidance and reliance on ED behaviours for affect regulation. 

The effects of trauma are contributing factors to emotion dysregulation, and considered a risk factor for ED development. Individuals who experience sexual, physical, or emotional abuse, neglect, and bullying are likely to experience heightened emotional reactivity, threat perception, and avoidance behaviours (Calder et al., 2023). Researchers explain that trauma often results in lowered distress tolerance and increased reliance on maladaptive coping behaviours, including disordered eating. Furthermore, PTSD comorbidity is common, hence trauma‑related symptoms are hypothesised to frequently interact with ED behaviours in complex ways.  


'''Reward Processing Dysfunction'''
[[File:Striatum.gif|thumb|'''Figure 2.''' Striatum]]
[[File:Anterior cingulate gyrus animation.gif|thumb|'''Figure 3'''. Anterior Cingulate Cortex ]]
Abnormal reward valuation is understood to be a central psychological mechanism that maintains ED behaviours. Research consistently shows that individuals with eating disorders display altered neural activity response to various stimuli, as well as disruptions in reinforcement learning (Calder et al., 2023). Brain regions involved in reward processing, habit formation, and learning, such as the striatum and anterior cingulate cortex (see figures 2 &amp; 3), exhibit atypical activation patterns and differences in dopamine receptor binding across ED types. The insula (see figure 4), which integrates bodily sensations with conscious thought, emotion, and behaviour, also shows altered responses. Together, these regions have been shown to react differently to food images, taste, and social feedback compared to healthy controls, indicating that reward dysfunction extends beyond eating‑related stimuli for ED populations.
[[File:Insular cortex.gif|thumb|'''Figure 4.''' Insula. ]]
In the context of BN and BED, research shows that food is valued more highly than other types of rewards, thus shaping behaviour through its heightened influence on reward outcomes (Calder et al., 2023). Compulsive behaviours specific to each condition (e.g. bingeing, purging) are therefore more likely to occur when food is overvalued and alternative rewards are discounted or ignored. In addition to the neural changes already described, BN and BED are associated with reduced structural and functional connectivity between frontal control regions and the striatum. This combination of highly salient food rewards, and weakened fronto‑striatal pathways, reduces an individual’s ability to inhibit or modulate reward‑seeking impulses. Weak connectivity in these circuits is thought to predict compulsive reward‑seeking behaviour. As a result, even when individuals experience negative consequences from binge episodes, they may struggle to learn from these outcomes or adjust their behaviour accordingly.


Anhedonia, a global reduction in reward responsiveness, is frequently reported by people who experience AN, resulting in food and eating becoming undervalued or aversive to them (Calder et al., 2023). Researchers propose that reward contamination further contributes to this pattern, where the brain learns to associate normally punishing stimuli (e.g., starvation, excessive exercise) with reward, while normally rewarding stimuli (e.g., high‑calorie foods) become experienced as punishment. Structural reductions in the striatum and somatosensory cortex have also been observed, which accounts for distorted bodily sensations and contributes to anhedonia. These changes support maladaptive conditioning in which starvation and weight loss embody a sense of safety, achievement, and emotional relief. Restrictive and preoccupied behaviours centred on food, body shape, and exercise are therefore reinforced over time.

Consistent with affect‑regulation models, eating‑disorder behaviours also become negatively reinforced because they reduce emotional discomfort. This relief increases the likelihood that the behaviours will be repeated, further embedding them within the individual’s coping pattern.


'''Cognitive Rigidity'''

Cognitive rigidity refers to inflexible thinking and behavioural patterns, including difficulty adapting to new information and modifying behaviour. Researchers believe that individuals with EDs often exhibit rigid beliefs about food and weight which interact with a need to exert control over negative emotions. This interaction is the proposed process in which compulsive behaviours and obsessive thoughts develop (Calder et al., 2023). In AN, rigidity manifests as strict dietary rules and fear of losing control, while in BN and BED, binge episodes may feel compulsive and uncontrollable.


'''Interoceptive Awareness'''

Interoceptive awareness (IA) refers to the ability to recognise and process internal bodily states such as hunger, satiety, pain, and arousal. IA is impaired across EDs, and contributes to body mistrust, distorted hunger cues, and inappropriate responses to internal sensations (Brown et al., 2020). Individuals may ignore physical discomfort, misinterpret bodily signals, or avoid sensations altogether, reinforcing maladaptive coping.      

 &lt;blockquote&gt;'''''QUIZ: Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{What coping style do people who experience EDs tend to show?
|type=&quot;()&quot;}
+ Avoidance-oriented
- Problem-oriented

{Compulsive behaviours are more likely to occur when food is ... and alternative rewards are ...
|type=&quot;()&quot;}
- undervalued; overvalued
+ overvalued; undervalued
&lt;/quiz&gt;&lt;/blockquote&gt;

== Psychological Mechanisms of Psychedelic-Assisted Therapy ==

PAT is proposed to influence several psychological mechanisms implicated in EDs, particularly those discussed in the previous section. The next part of this chapter aims to examine the theorised therapeutic mechanisms PAT possesses and practical implications for ED treatment.  


'''Emotion Regulation''' 

Emotion dysregulation is a core mechanism implicated in EDs. Affect regulation theory proposes that ED behaviours emerge as maladaptive strategies to escape, reduce, or blunt overwhelming emotional experiences (Schaefer et al., 2020). Restriction, bingeing, purging, and compulsive exercise may temporarily alleviate distress while reinforcing avoidance-oriented coping and limiting opportunities to learn more adaptive ways of responding to difficult emotions. 

Psychedelics often evoke intense emotional experiences that may disrupt habitual avoidance patterns. Researchers propose that, during psychedelic sessions, attempts to suppress or avoid difficult emotions can intensify these experiences, creating conditions in which emotional acceptance becomes a preferred response (Calder et al., 2023). Although this shift does not occur in every individual, experiencing difficult emotions without resorting to ED behaviours may weaken the association between emotional distress and maladaptive coping, particularly when emotional acceptance becomes associated with a more positive or tolerable experience.

The therapeutic value of this process lies in its potential to reshape affective responses. When individuals experience strong emotions without engaging in maladaptive behaviours, they may begin to develop a new approach towards emotional tolerance. Integration sessions can consolidate this learning by helping individuals articulate, differentiate, and reflect on the emotions experienced during dosing. This process may support the development of more adaptive coping strategies, including task-oriented, problem-focused, and socially supported approaches, which are associated with improved ED outcomes (Fitzsimmons &amp; Bardone-Cone, 2010). In this way, PAT may strengthen emotion regulation and reduce reliance on ED behaviours as strategies for managing affect. 


'''Reward Processing''' 

Reward dysfunction may contribute to the maintenance of EDs by reinforcing maladaptive behaviours while diminishing the perceived value of adaptive rewards. Predictive coding provides a useful framework for understanding how PAT might influence these processes. Individuals with EDs may hold rigid beliefs, conceptualised as high-level priors, about themselves in relation to food, body weight, and rewarding behaviours (Calder et al., 2023; Mograbi et al., 2024). These beliefs can influence how experiences are perceived and valued, potentially reinforcing existing behavioural patterns. Psychedelics are proposed to weaken high-level priors, allowing bottom-up sensory information to exert greater influence on perception and the valuation of experiences. 

During psychedelic experiences, individuals frequently report a heightened appreciation of sensory, social, and bodily experiences. This shift may counteract anhedonia and support the revaluation of previously feared or avoided stimuli. The therapeutic opportunity lies in translating these temporary changes in perception and reward into meaningful behavioural change. Integration sessions can explore positive and negative moments experienced during dosing and connect them to concrete goals. An example of this, inspired from Calder et al.’s (2023) article, could be to clarify specific plans to nourish the body due to the participant having experienced themselves as a decaying skeleton followed by the realisation of the body being a gift. If the period following dosing provides an opportunity for increased neuroplasticity, it may also be particularly conducive to reinforcing adaptive reward learning through behavioural activation with the help of a therapist. 


'''Cognitive Flexibility''' 

Cognitive rigidity is a hallmark of EDs and is characterised by inflexible beliefs about food, weight, body shape, and control. Predictive coding provides a framework for understanding this rigidity, as EDs may involve entrenched priors that resist updating even when confronted with contradictory sensory evidence (Zanella &amp; Lee, 2022). Psychedelics are proposed to disrupt these entrenched priors by increasing neural entropy and reducing the dominance of top-down processing (Calder et al., 2023). This temporary loosening of cognitive constraints may allow individuals to consider alternative perspectives and question long-held beliefs. 

Experiences of ego dissolution may further contribute to cognitive flexibility by reducing attachment to rigid self-concepts (Peled-Avron, 2024; Mograbi et al., 2024). When the boundaries of the self become less defined, individuals may find it easier to question identity-related beliefs that sustain ED pathology. Integration sessions can harness this potential flexibility by supporting cognitive reframing, encouraging behavioural experiments, and strengthening metacognitive awareness. Through these processes, individuals may be better able to translate insights gained during psychedelic experiences into sustained changes in thinking and behaviour.


'''Reconnecting with Bodily Signals'''

Interoceptive deficits are central to ED pathology, contributing to body mistrust, distorted perceptions of hunger cues, and difficulties responding appropriately to internal sensations (Brown et al., 2020). Psychedelics may enhance interoceptive awareness by altering sensory processing and increasing sensitivity to bodily signals. This proposed mechanism is closely related to autonomic regulation, for which polyvagal theory provides a framework for understanding the relationship between bodily signals, emotional regulation, and perceived safety.

Polyvagal theory emphasises the role of the vagus nerve in interoception, emotional regulation, and the perception of safety (Porges, 2022). Vagal afferents transmit information from the body to the insula, where interoceptive signals are integrated with emotional and cognitive processes. Individuals with EDs may exhibit chronic sympathetic arousal and reduced vagal tone, potentially impairing interoceptive accuracy and contributing to emotional rigidity. Psychedelics may initially increase sympathetic activity, as reflected in physiological responses such as increased heart rate, followed by a parasympathetic shift associated with greater relaxation and an increased capacity for rest (Li et al., 2025). Within a polyvagal framework, these changes may have implications for vagal regulation, interoceptive awareness, and emotional regulation.

The therapeutic value of this proposed mechanism lies in its potential to restore trust in bodily signals. Integration sessions may support this process by helping individuals explore bodily sensations experienced during dosing, connect interoceptive cues with emotional states, and practise interoceptive exposure to hunger, fullness, and anxiety-related sensations. Incorporating mindfulness techniques may further support autonomic regulation and help individuals develop a more adaptive relationship with their bodily experiences.

 A Brief Note Concerning The Gut-Brain Interaction 
Although gut microbiome disruption is not a direct psychological mechanism in EDs, it is a relevant biological factor to consider when examining the potential effects of PAT. Restrictive or chaotic eating patterns can contribute to gut dysbiosis, which may weaken gut-barrier integrity and contribute to inflammation affecting the brain (Anton-Paduraru et al., 2024). These changes have been shown to influence mood, stress responsivity, cognitive rigidity, and interoceptive awareness through [[wikipedia:Hypothalamic–pituitary–adrenal_axis|HPA-axis activation]], altered neurotransmitter synthesis, and disrupted hunger–satiety signalling. 

Emerging research suggests that psychedelics may also interact with the gut–brain axis. Certain microbes can metabolise psychedelic compounds, and microbial activity has been associated with modulatory effects on behavioural outcomes. Additionally, psychedelic use may alter microbial composition towards anti-inflammatory profiles, with potential implications for neuroplasticity, neurotransmitter synthesis and signalling improvements (Caspani et al., 2024). These microbiome-related effects may therefore contribute to changes in mood, cognitive flexibility, and appetite regulation.

Although the therapeutic potential of psychedelics in EDs is considered primarily in relation to psychological mechanisms, including changes in perception, emotional processing, and reduced avoidance, microbiome-related effects may represent an additional pathway through which biological processes influence psychological outcomes. However, the extent to which these interactions contribute to therapeutic outcomes in EDs remains to be established.


&lt;blockquote&gt;'''QUIZ: ''Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{ In predictive coding terms, what are “high‑level priors” in eating disorders? 
|type=&quot;()&quot;}
+ Rigid, entrenched beliefs about food, weight, and the self that shape perception and behaviour
- Flexible beliefs that easily update with new sensory information
- Momentary emotional reactions triggered by external cues

{What is the proposed mechanism by which psychedelics support emotion regulation in PAT for EDs? 
|type=&quot;()&quot;}
- By suppressing emotional intensity to prevent distress
+ By evoking strong emotions that disrupt avoidance patterns and promote emotional acceptance
- By eliminating negative emotions through serotonin release

{What is interoceptive awareness?
|type=&quot;()&quot;}
- The ability to evaluate reward value and anticipate pleasurable outcomes
+ The capacity to sense, interpret, and respond to internal bodily signals such as hunger, fullness, and emotional arousal
- The process of weakening cognitive rigidity through ego dissolution
&lt;/quiz&gt;&lt;/blockquote&gt;

== Limitations ==
Despite the potential of PAT to influence psychological mechanisms implicated in EDs, several limitations constrain current understanding of these processes and their therapeutic relevance. Research examining emotion dysregulation in EDs illustrates broader challenges in establishing the mechanisms underlying these conditions. Although non-acceptance of emotions has been identified as a transdiagnostic risk factor across psychiatric conditions (Paulus et al., 2021), Zhou et al.’s meta-analysis (2025) highlights that the causal pathways linking emotional dysregulation and EDs remain unclear, largely because of a lack of experimental and longitudinal studies. Further limitations include restricted availability of measurement scales, insufficient cultural specificity, heterogeneity across samples, gender imbalance, and limited developmental analysis. Together, these factors constrain understanding of how specific emotional processes relate to different ED presentations across the lifespan and stages of recovery.

These limitations are also relevant when considering the proposed mechanisms of PAT. Although existing theoretical frameworks offer ways to conceptualise how psychedelic experiences may influence psychological processes responsible for EDs, the emerging nature of psychedelic therapy limits the extent to which proposed mechanisms have been tested. However, with the number of clinical trials increasing as of recently, it will be interesting to see how the theorised therapeutic mechanisms across different ED presentations and stages of recovery emerges during further warranted investigation.

Nevertheless, current limitations in the evidence highlight the need for research that clarifies the relationships between psychological processes that underscore ED behaviours, and treatment outcomes. There are several important psychological components of ED maintenance that represent meaningful targets for treatment, but they should not be considered in isolation from eachother or the neurobiological processes that influence them. A more comprehensive understanding of how these mechanisms interact may help clarify the therapeutic potential of PAT and inform the development of more targeted treatment approaches.

== Conclusion ==
PAT offers a potential framework for addressing several interconnected psychological mechanisms implicated in EDs. Through its proposed effects on emotional processing, reward valuation, cognitive flexibility, and interoceptive awareness, PAT may create opportunities to disrupt established patterns of avoidance, rigid thinking, and maladaptive behavioural reinforcement. The gut–brain interaction may represent an additional biological pathway relevant to these processes.

These mechanisms should not be understood as independent processes. Changes in emotion regulation may influence the ability to tolerate bodily sensations, while shifts in reward valuation and cognitive flexibility may create opportunities to respond differently to distress and challenge entrenched beliefs. However, the extent to which PAT produces these changes, and whether they translate into sustained improvements in ED outcomes, requires further investigation, although preliminary evidence is promising. 

The therapeutic potential of PAT lies not only in the acute psychedelic experience but also in the structured integration process that follows. Integration sessions provide an opportunity to translate emotional breakthroughs, changes in cognitive flexibility, interoceptive shifts, and reward processing into sustained behavioural change. Effective integration involves helping individuals articulate insights, connect them to ED-related patterns, and develop concrete strategies for change. These may include strengthening adaptive coping, challenging rigid beliefs, practising interoceptive awareness, reinforcing positive reward experiences, and supporting nutritional rehabilitation.

By grounding the understanding of PAT in affect regulation theory and the predictive coding framework, therapists may be better positioned to help individuals explore how psychedelic experiences could disrupt maladaptive emotional and cognitive patterns and create opportunities for new learning. Polyvagal-informed approaches may further support the development of mind–body awareness and emotional regulation through mindfulness strategies. Together, these approaches offer a multifaceted framework for translating psychedelic experiences into therapeutic change and addressing the interconnected mechanisms that maintain EDs and associated suffering. 

==See Also==
* [https://w.wiki/TsdG Ayahuasca and the brain] (Wikiversity)
* [https://w.wiki/TscF Emotional effects of psychedelics] (Wikiversity)
* [https://w.wiki/Tsdb Psilocybin and emotion] (Wikiversity)
* [https://w.wiki/TsdS Psilocibyn assisted psychotherapy] (Wikiversity)
* [https://w.wiki/Tsce Psychedelics, altered consciousness, and personal growth] (Wikiversity)
* [[Eating Disorders|Eating disorders]] (Wikiversity)

==References==
{{Hanging indent|1=

{{ic|Try &quot;Edit source&quot; and then wrapping any text to be italicised in two apostrophes e.g., ''this is italics''}}

Anton-Păduraru, D. T., Trofin, F., Nastase, E. V., Miftode, R. S., Miftode, I. L., Trandafirescu, M. F., Cojocaru, E., Țarcă, E., Mindru, D. E., &amp; Dorneanu, O. S. (2023). The Role of the Gut Microbiota in Anorexia Nervosa in Children and Adults-Systematic Review. &quot;International journal of molecular sciences, 25&quot;(1), 41. https://doi.org/10.3390/ijms25010041

Brown, T. A., Vanzhula, I. A., Reilly, E. E., Levinson, C. A., Berner, L. A., Krueger, A., Lavender, J. M., Kaye, W. H., &amp; Wierenga, C. E. (2020). Body mistrust bridges interoceptive awareness and eating disorder symptoms. &quot;Journal of abnormal psychology, 129&quot;(5), 445–456. https://doi.org/10.1037/abn0000516 

Calder, A., Mock, S., Friedli, N., Pasi, P., &amp; Hasler, G. (2023). Psychedelics in the treatment of eating disorders: Rationale and potential mechanisms. &quot;European Neuropsychopharmacology, 75&quot;, 1–14. https://doi.org/10.1016/j.euroneuro.2023.05.008 

Caspani, G., Ruffell, S. G. D., Tsang, W., Netzband, N., Rohani-Shukla, C., Swann, J. R., &amp; Jefferies, W. A. (2024). Mind over matter: the microbial mindscapes of psychedelics and the gut-brain axis. &quot;Pharmacological research, 207&quot;, 107338. https://doi.org/10.1016/j.phrs.2024.107338  

Fitzsimmons, E. E., &amp; Bardone-Cone, A. M. (2010). Differences in coping across stages of recovery from an eating disorder. &quot;The International journal of eating disorders, 43&quot;(8), 689–693. https://doi.org/10.1002/eat.20781 

Hatzipantelis, C. J., &amp; Olson, D. E. (2024). The Effects of Psychedelics on Neuronal Physiology. &quot;Annual review of physiology, 86&quot;, 27–47. https://doi.org/10.1146/annurev-physiol-042022-020923

Hay, P., Aouad, P., Le, A., Marks, P., Maloney, D., National Eating Disorder Research Consortium, Touyz, S., &amp; Maguire, S. (2023). Epidemiology of eating disorders: population, prevalence, disease burden and quality of life informing public policy in Australia-a rapid review. &quot;Journal of eating disorders, 11&quot;(1), 23. https://doi.org/10.1186/s40337-023-00738-7

Li, H., Wang, H., &amp; Wang, X. (2025). Psychedelics and the Autonomic Nervous System: A Perspective on Their Interplay and Therapeutic Potential. &quot;ACS pharmacology &amp; translational science, 8&quot;(3), 899–902. https://doi.org/10.1021/acsptsci.5c00005 

Leppanen, J., Brown, D., McLinden, H., Williams, S., &amp; Tchanturia, K. (2022). The Role of Emotion Regulation in Eating Disorders: A Network Meta-Analysis Approach. &quot;Frontiers in psychiatry, 13&quot;, 793094. https://doi.org/10.3389/fpsyt.2022.793094 

Mograbi, D. C., Rodrigues, R., Bienemann, B., &amp; Huntley, J. (2024). Brain Networks, Neurotransmitters and Psychedelics: Towards a Neurochemistry of Self-Awareness. &quot;Current neurology and neuroscience reports, 24&quot;(8), 323–340. https://doi.org/10.1007/s11910-024-01353-y

Paulus F. W., Ohmann S., Möhler E., Plener P. &amp; Popow C. (2021). Emotional Dysregulation in Children and Adolescents With Psychiatric Disorders. A Narrative Review. &quot;Frontiers in Psychiatry 12&quot;:628252. doi: 10.3389/fpsyt.2021.628252

Peled-Avron L., Aday J. Ss, Kalafateli A. L., Hamilton H. K., Woolley J. D. (2024). Editorial: Down the rabbit hole – the psychological and neural mechanisms of psychedelic compounds and their use in treating mental health and medical conditions. &quot;Frontiers in Psychiatry 15&quot;:1431389. doi: 10.3389/fpsyt.2024.1431389

Porges S. W. (2025). Polyvagal Theory: Current Status, Clinical Applications, and Future Directions. &quot;Clinical neuropsychiatry, 22&quot;(3), 169–184. https://doi.org/10.36131/cnfioritieditore20250301

Schaefer, L. M., Smith, K. E., Anderson, L. M., Cao, L., Crosby, R. D., Engel, S. G., Crow, S. J., Peterson, C. B., &amp; Wonderlich, S. A. (2020). The role of affect in the maintenance of binge-eating disorder: Evidence from an ecological momentary assessment study. &quot;Journal of abnormal psychology, 129&quot;(4), 387–396. https://doi.org/10.1037/abn0000517 

Shank, L. M., Tanofsky-Kraff, M., Kelly, N. R., Jaramillo, M., Rubin, S. G., Altman, D. R., Byrne, M. E., LeMay-Russell, S., Schvey, N. A., Broadney, M. M., Brady, S. M., Yang, S. B., Courville, A. B., Ramirez, S., Crist, A. C., Yanovski, S. Z., &amp; Yanovski, J. A. (2019). The association between alexithymia and eating behavior in children and adolescents. &quot;Appetite, 142&quot;, 104381. https://doi.org/10.1016/j.appet.2019.104381

Wonderlich, J., &amp; Attia, E. (2024). Eating disorders in the DSM-5. In P. Robinson, T. Wade, B. Herpertz-Dahlmann, F. Fernandez-Aranda, J. Treasure, &amp; S. Wonderlich (Eds.), Eating disorders: An international comprehensive view (pp. 7–18). &quot;Springer Nature Switzerland AG&quot;. https://doi.org/10.1007/978-3-031-46096-8_9

Wolfgang, A. S., &amp; Hoge, C. W. (2023). Psychedelic-Assisted Therapy in Military and Veterans Healthcare Systems: Clinical, Legal, and Implementation Considerations. &quot;Current psychiatry reports, 25&quot;(10), 513–532. https://doi.org/10.1007/s11920-023-01446-4 

Zanella, E., &amp; Lee, E. (2022). Integrative review on psychological and social risk and prevention factors of eating disorders including anorexia nervosa and bulimia nervosa: seven major theories. &quot;Heliyon, 8&quot;(11), e11422. https://doi.org/10.1016/j.heliyon.2022.e11422 

Zhou, R., Zhang, L., Liu, Z., &amp; Cao, B. (2025). Emotion regulation difficulties and disordered eating in adolescents and young adults: a meta-analysis. &quot;Journal of eating disorders, 13&quot;(1), 25. https://doi.org/10.1186/s40337-025-01197-y

}}

==External links==
* [https://www.abct.org/fact-sheets/psychedelic-assisted-therapy/ Psychedelic-Assisted Therapy | Fact Sheet] (ABCT - Association for Behavioral and Cognitive Therapies)
* [https://podcasts.apple.com/au/podcast/can-magic-mushrooms-help-treat-anorexia/id189330872?i=1000784809236 Can magic mushrooms help treat anorexia?] (Apple Podcasts)
* [https://www.apa.org/news/podcasts/speaking-of-psychology/eating-disorder The ‘silent epidemic’ of eating disorders] (American Psychological Association)
* [https://www.apa.org/monitor/2023/04/sensations-eating-disorders-suicidal-behavior What is interoception, and how does it affect mental health]? 5 questions for April Smith (American Psychological Association)
* [https://www.cbte.co/what-is-cbte/transdiagnostic-view-eating-disorders/ Transdiagnostic view of eating disorders] (cbte.co)
* [https://psychedelic.support/resources/polyvagal-theory-mind-body-dr-erica-zelfand/ Polyvagal Theory with Dr. Erica Zelfand: Mind-Body Connection] ·(Psychedelic Support)
* [https://www.wholeselfnutrition.org/post/nervous-system-regulation-a-missing-piece-in-eating-disorder-recovery Nervous System Regulation: A Missing Piece in Eating Disorder Recovery]  (wholeselfnutrition.org)
* [https://youtu.be/RwS-CHJcCiY?si=157viTWiOGAQ-7LP Best Neural Entropy - Explainer] (Youtube)

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      <text bytes="37528" sha1="chn901ygoiis8eskz5dnoh6zb6ylyau" xml:space="preserve">{{title|Psychedelic treatment of eating disorders:&lt;br&gt;How might psychedelic-assisted therapy influence psychological mechanisms involved in eating disorders?}}
__TOC__

== Overview ==
{{RoundBoxTop|theme=7}}[[File:Neural network - Midjourney and Grok.png|thumb|'''Figure 1.''' Psychedelics are thought to temporarily disrupt rigid neural communication pathways by promoting more flexible patterns of connectivity across networks involved in mood regulation, fear processing, reward learning, and cognitive adaptability. These changes may support therapeutic shifts in behaviour and emotional processing (Hatzipantelis &amp; Olson, 2025).]]Emma, a 27‑year‑old from Canberra, has lived with an eating disorder for nearly two decades. She describes her problem eating behaviours to have started at school, after being bullied about her appearance and experiencing an unsteady home life. Ever since, they have remained in her life as “a way for me to feel in control”. Although she is aware of the harm caused by restrictive eating and compulsive exercise, she feels trapped in her thought patterns characterised by a preoccupation about food and weight concerns, as they've become entrenched in her daily life. 

After reading an article describing emerging research suggesting that psychedelics may alter patterns of neural connectivity that shape behaviour (see Figure 1), she expressed interest in pursuing psychedelic‑assisted therapy through a provider accessible to her.

After participating in her first supervised psilocybin‑assisted therapy session, Emma reported experiencing an emotional journey that allowed her to feel “connected to my body for the first time in years”. After 3 months, she has noticed a shift in how she relates to her body, and is finding it easier to actively call into question how she responds to distress with the support of her psychotherapist. 


Her experience raises a central question: What psychological mechanisms could explain these changes?{{RoundBoxBottom|theme=3}}  

This chapter explores how psychedelic‑assisted therapy (PAT) may influence the emotional, cognitive, and neurobiological processes that underpin eating disorders (EDs).   

{{RoundBoxTop|theme=11}}'''Focus questions'''
{{ic|}}Two central questions will be addressed:
* What psychological processes underpin eating disorders, and how do they guide ED behaviour?
* How might psychedelic‑assisted therapy influence these processes and support recovery?
{{ic|}}{{ic|}}{{RoundBoxBottom}}

== Introduction ==
'''Eating Disorders'''  

[[wikipedia:Eating_disorder|Eating disorders]] (EDs) are psychiatric conditions characterised by abnormal eating behaviours that negatively affect physical and mental health. In Australia, the prevalence of EDs is rising particularly among young people. The economic burden is estimated to cost the nation $84 billion, with approximately 10.46% of the population having experienced an ED at some point in their lives (Hay et al., 2023). Although other forms of disordered eating exist, this chapter will focus on only three of them (see table 1), as [[wikipedia:Anorexia|Anorexia Nervosa]] (AN) has the highest mortality rate of any psychiatric disorder, while [[wikipedia:Bulimia|Bulimia Nervosa]] (BN) and [[wikipedia:Binge_eating_disorder|Binge‑Eating Disorder]] (BED) are also highly prevalent. The EDs mentioned are most associated with chronic illness, disability, reduced quality of life, increased suicide risk, and are highly comorbid with [[wikipedia:Mood_disorder|mood disorders]], [[wikipedia:Post-traumatic_stress_disorder|post-traumatic stress disorder]] (PTSD), [[wikipedia:Obsessive–compulsive_disorder|obsessive-compulsive disorder]] (OCD), and [[wikipedia:Substance_use_disorder|substance use disorders]] (Calder et al., 2023).  Despite decades of research, the pathogenesis of EDs remains incompletely understood. Current evidence suggests a complex interplay between genetic predisposition, temperament, hormonal dysregulation, cognitive abnormalities, sociocultural pressures, and traumatic experiences (Calder et al., 2023).  
{| class=&quot;wikitable&quot;
|+Table 1. Eating Disorders and Associated Symptoms 
!Eating Disorder
!Primary Symptoms
|-
|Anorexia Nervosa
|Severe caloric restriction, fear of gaining weight, distorted body image, preoccupation with weight loss.
|-
|Bullimia Nervosa
|Intense windows of food intake (binge eating) followed by inappropriate compensatory behaviours also known as 'purging' (eg. vomiting, laxative use), feelings of guilt and loss of control.
|-
|Binge-Eating Disorder
|Recurrent episodes of binge eating not followed by inappropriate compensatory behaviours, feelings of distress and loss of control.
(Wanderlich &amp; Attia., 2024)
|}


Although cognitive‑behavioural therapy (CBT‑E) combined with pharmacological treatment has demonstrated beneficial outcomes, efficacy remains limited and varies across ED types (Calder et al., 2023). Recovery is often long and difficult, with only two‑thirds of individuals with AN and BN eventually recovering, while others can remain ill for many years. This highlights the need for treatment approaches that can accelerate recovery and provide benefit for individuals who do not respond to conventional therapies.


'''Psychedelic-Assisted Therapy'''

In 2023, Australia legalised the prescription of MDMA and psilocybin under professional supervision, marking a significant shift in mental‑health treatment options. Psychedelic compounds, including [[wikipedia:LSD|LSD]], [[wikipedia:Psilocybin|psilocybin]], [[wikipedia:Dimethyltryptamine|DMT]], [[wikipedia:Ketamine|ketamine]], and [[wikipedia:MDMA|MDMA]], have demonstrated promising therapeutic effects across a wide range of psychiatric conditions. Researchers propose that psychedelics act through psychological and neural mechanisms that increase [[wikipedia:Neuroplasticity|neuroplasticity]], facilitate insight, and foster emotional acceptance (Peled‑Avron et al., 2024). At a neurobiological level, psychedelics influence processes that inform perception, emotion, and behaviour, offering a potential avenue for addressing entrenched ED mechanisms.

PAT differs from pharmacological treatment alone because the drug is administered within a structured therapeutic context designed to maximise safety and clinical benefit (Calder et al., 2023). Treatment typically involves three types of sessions. Preparatory sessions feature participants undergoing psychoeducation, where the clinician establishes rapport and clear safety protocols. Followed by supervised medication where the participant has an inward experience with the reassurance of clinicians present in the same space. Lastly, integrative sessions where individuals process and explore insights from the previous session with their psychotherapist to foster behavioural change (Wolfgang &amp; Hoge, 2023). This combination of pharmacological and psychological intervention is theorised to effectively target underlying psychological mechanisms common across various mental health disorders, illustrating PAT’s potential as a valuable transdiagnostic treatment option. 

PAT has become a subject of increasing popularity in ED research because many of the psychological mechanisms it is proposed to influence are the same ones implicated in ED maintenance and comorbidities (Calder et al., 2023; Peled-Avron et al., 2024). Early research, including case study reports, small clinical studies, meta-analyses and reviews indicate that PAT produces improvements in affect, reductions in ED symptom severity, enhanced body image, weight restoration, and reductions in comorbid symptoms. Although preliminary, these findings indicate that PAT may disrupt and promote shifts away from maladaptive coping patterns that become entrenched in treatment resistant ED populations.

== Psychological Mechanisms in Eating Disorders ==


'''Emotion Dysregulation'''

Emotion dysregulation is considered to be a significant risk factor for the onset and maintenance of EDs. It refers to difficulties recognising, assessing, and modifying emotional responses to meet situational demands (Zhou et al., 2025). 

Research consistently shows that individuals with EDs experience significant challenges in regulating emotions, increasing their vulnerability to comorbid symptoms, which contribute to the emergence of disordered eating patterns (Leppanen et al., 2022). This idea is supported by affect regulation theory which posits that eating disorders develop and are maintained as maladaptive strategies to manage, tolerate and escape from negative emotions and psychological distress (Schaefer et al., 2020; Zanella &amp; Lee, 2022). This is further exemplified in Fitzsimmons &amp; Bardone-Cone’s article examining differences in coping within eating disorder patients (2010). The authors explain that avoidance and emotion-oriented coping styles often function as maladaptive attempts to manage (di)stress. They explain that behaviours such as binge eating, purging, starvation, and/or compulsive exercise provide temporary relief by shifting attention away from uncomfortable emotions. 

Furthermore, alexithymia, characterised by difficulty identifying and describing one’s own emotions, is strongly associated with ED pathology (Shank et al., 2019). Individuals with high alexithymia often struggle to differentiate emotional states from bodily sensations, contributing to behaviours such as emotional eating, eating in the absence of hunger, or rigid restriction. In BED, alexithymia is linked to binge episodes triggered by poorly understood emotional cues, while in AN and BN, alexithymia may contribute to emotional avoidance and reliance on ED behaviours for affect regulation. 

The effects of trauma are contributing factors to emotion dysregulation, and considered a risk factor for ED development. Individuals who experience sexual, physical, or emotional abuse, neglect, and bullying are likely to experience heightened emotional reactivity, threat perception, and avoidance behaviours (Calder et al., 2023). Researchers explain that trauma often results in lowered distress tolerance and increased reliance on maladaptive coping behaviours, including disordered eating. Furthermore, PTSD comorbidity is common, hence trauma‑related symptoms are hypothesised to frequently interact with ED behaviours in complex ways.  


'''Reward Processing Dysfunction'''
[[File:Striatum.gif|thumb|'''Figure 2.''' Striatum]]
[[File:Anterior cingulate gyrus animation.gif|thumb|'''Figure 3'''. Anterior Cingulate Cortex ]]
Abnormal reward valuation is understood to be a central psychological mechanism that maintains ED behaviours. Research consistently shows that individuals with eating disorders display altered neural activity response to various stimuli, as well as disruptions in reinforcement learning (Calder et al., 2023). Brain regions involved in reward processing, habit formation, and learning, such as the striatum and anterior cingulate cortex (see figures 2 &amp; 3), exhibit atypical activation patterns and differences in dopamine receptor binding across ED types. The insula (see figure 4), which integrates bodily sensations with conscious thought, emotion, and behaviour, also shows altered responses. Together, these regions have been shown to react differently to food images, taste, and social feedback compared to healthy controls, indicating that reward dysfunction extends beyond eating‑related stimuli for ED populations.
[[File:Insular cortex.gif|thumb|'''Figure 4.''' Insula. ]]
In the context of BN and BED, research shows that food is valued more highly than other types of rewards, thus shaping behaviour through its heightened influence on reward outcomes (Calder et al., 2023). Compulsive behaviours specific to each condition (e.g. bingeing, purging) are therefore more likely to occur when food is overvalued and alternative rewards are discounted or ignored. In addition to the neural changes already described, BN and BED are associated with reduced structural and functional connectivity between frontal control regions and the striatum. This combination of highly salient food rewards, and weakened fronto‑striatal pathways, reduces an individual’s ability to inhibit or modulate reward‑seeking impulses. Weak connectivity in these circuits is thought to predict compulsive reward‑seeking behaviour. As a result, even when individuals experience negative consequences from binge episodes, they may struggle to learn from these outcomes or adjust their behaviour accordingly.


Anhedonia, a global reduction in reward responsiveness, is frequently reported by people who experience AN, resulting in food and eating becoming undervalued or aversive to them (Calder et al., 2023). Researchers propose that reward contamination further contributes to this pattern, where the brain learns to associate normally punishing stimuli (e.g., starvation, excessive exercise) with reward, while normally rewarding stimuli (e.g., high‑calorie foods) become experienced as punishment. Structural reductions in the striatum and somatosensory cortex have also been observed, which accounts for distorted bodily sensations and contributes to anhedonia. These changes support maladaptive conditioning in which starvation and weight loss embody a sense of safety, achievement, and emotional relief. Restrictive and preoccupied behaviours centred on food, body shape, and exercise are therefore reinforced over time.

Consistent with affect‑regulation models, eating‑disorder behaviours also become negatively reinforced because they reduce emotional discomfort. This relief increases the likelihood that the behaviours will be repeated, further embedding them within the individual’s coping pattern.


'''Cognitive Rigidity'''

Cognitive rigidity refers to inflexible thinking and behavioural patterns, including difficulty adapting to new information and modifying behaviour. Researchers believe that individuals with EDs often exhibit rigid beliefs about food and weight which interact with a need to exert control over negative emotions. This interaction is the proposed process in which compulsive behaviours and obsessive thoughts develop (Calder et al., 2023). In AN, rigidity manifests as strict dietary rules and fear of losing control, while in BN and BED, binge episodes may feel compulsive and uncontrollable.


'''Interoceptive Awareness'''

Interoceptive awareness (IA) refers to the ability to recognise and process internal bodily states such as hunger, satiety, pain, and arousal. IA is impaired across EDs, and contributes to body mistrust, distorted hunger cues, and inappropriate responses to internal sensations (Brown et al., 2020). Individuals may ignore physical discomfort, misinterpret bodily signals, or avoid sensations altogether, reinforcing maladaptive coping.      

 &lt;blockquote&gt;'''''QUIZ: Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{What coping style do people who experience EDs tend to show?
|type=&quot;()&quot;}
+ Avoidance-oriented
- Problem-oriented

{Compulsive behaviours are more likely to occur when food is ... and alternative rewards are ...
|type=&quot;()&quot;}
- undervalued; overvalued
+ overvalued; undervalued
&lt;/quiz&gt;&lt;/blockquote&gt;

== Psychological Mechanisms of Psychedelic-Assisted Therapy ==

PAT is proposed to influence several psychological mechanisms implicated in EDs, particularly those discussed in the previous section. The next part of this chapter aims to examine the theorised therapeutic mechanisms PAT possesses and practical implications for ED treatment.  


'''Emotion Regulation''' 

Emotion dysregulation is a core mechanism implicated in EDs. Affect regulation theory proposes that ED behaviours emerge as maladaptive strategies to escape, reduce, or blunt overwhelming emotional experiences (Schaefer et al., 2020). Restriction, bingeing, purging, and compulsive exercise may temporarily alleviate distress while reinforcing avoidance-oriented coping and limiting opportunities to learn more adaptive ways of responding to difficult emotions. 

Psychedelics often evoke intense emotional experiences that may disrupt habitual avoidance patterns. Researchers propose that, during psychedelic sessions, attempts to suppress or avoid difficult emotions can intensify these experiences, creating conditions in which emotional acceptance becomes a preferred response (Calder et al., 2023). Although this shift does not occur in every individual, experiencing difficult emotions without resorting to ED behaviours may weaken the association between emotional distress and maladaptive coping, particularly when emotional acceptance becomes associated with a more positive or tolerable experience.

The therapeutic value of this process lies in its potential to reshape affective responses. When individuals experience strong emotions without engaging in maladaptive behaviours, they may begin to develop a new approach towards emotional tolerance. Integration sessions can consolidate this learning by helping individuals articulate, differentiate, and reflect on the emotions experienced during dosing. This process may support the development of more adaptive coping strategies, including task-oriented, problem-focused, and socially supported approaches, which are associated with improved ED outcomes (Fitzsimmons &amp; Bardone-Cone, 2010). In this way, PAT may strengthen emotion regulation and reduce reliance on ED behaviours as strategies for managing affect. 


'''Reward Processing''' 

Reward dysfunction may contribute to the maintenance of EDs by reinforcing maladaptive behaviours while diminishing the perceived value of adaptive rewards. Predictive coding provides a useful framework for understanding how PAT might influence these processes. Individuals with EDs may hold rigid beliefs, conceptualised as high-level priors, about themselves in relation to food, body weight, and rewarding behaviours (Calder et al., 2023; Mograbi et al., 2024). These beliefs can influence how experiences are perceived and valued, potentially reinforcing existing behavioural patterns. Psychedelics are proposed to weaken high-level priors, allowing bottom-up sensory information to exert greater influence on perception and the valuation of experiences. 

During psychedelic experiences, individuals frequently report a heightened appreciation of sensory, social, and bodily experiences. This shift may counteract anhedonia and support the revaluation of previously feared or avoided stimuli. The therapeutic opportunity lies in translating these temporary changes in perception and reward into meaningful behavioural change. Integration sessions can explore positive and negative moments experienced during dosing and connect them to concrete goals. An example of this, inspired from Calder et al.’s (2023) article, could be to clarify specific plans to nourish the body due to the participant having experienced themselves as a decaying skeleton followed by the realisation of the body being a gift. If the period following dosing provides an opportunity for increased neuroplasticity, it may also be particularly conducive to reinforcing adaptive reward learning through behavioural activation with the help of a therapist. 


'''Cognitive Flexibility''' 

Cognitive rigidity is a hallmark of EDs and is characterised by inflexible beliefs about food, weight, body shape, and control. Predictive coding provides a framework for understanding this rigidity, as EDs may involve entrenched priors that resist updating even when confronted with contradictory sensory evidence (Zanella &amp; Lee, 2022). Psychedelics are proposed to disrupt these entrenched priors by increasing neural entropy and reducing the dominance of top-down processing (Calder et al., 2023). This temporary loosening of cognitive constraints may allow individuals to consider alternative perspectives and question long-held beliefs. 

Experiences of ego dissolution may further contribute to cognitive flexibility by reducing attachment to rigid self-concepts (Peled-Avron, 2024; Mograbi et al., 2024). When the boundaries of the self become less defined, individuals may find it easier to question identity-related beliefs that sustain ED pathology. Integration sessions can harness this potential flexibility by supporting cognitive reframing, encouraging behavioural experiments, and strengthening metacognitive awareness. Through these processes, individuals may be better able to translate insights gained during psychedelic experiences into sustained changes in thinking and behaviour.


'''Reconnecting with Bodily Signals'''

Interoceptive deficits are central to ED pathology, contributing to body mistrust, distorted perceptions of hunger cues, and difficulties responding appropriately to internal sensations (Brown et al., 2020). Psychedelics may enhance interoceptive awareness by altering sensory processing and increasing sensitivity to bodily signals. This proposed mechanism is closely related to autonomic regulation, for which polyvagal theory provides a framework for understanding the relationship between bodily signals, emotional regulation, and perceived safety.

Polyvagal theory emphasises the role of the vagus nerve in interoception, emotional regulation, and the perception of safety (Porges, 2022). Vagal afferents transmit information from the body to the insula, where interoceptive signals are integrated with emotional and cognitive processes. Individuals with EDs may exhibit chronic sympathetic arousal and reduced vagal tone, potentially impairing interoceptive accuracy and contributing to emotional rigidity. Psychedelics may initially increase sympathetic activity, as reflected in physiological responses such as increased heart rate, followed by a parasympathetic shift associated with greater relaxation and an increased capacity for rest (Li et al., 2025). Within a polyvagal framework, these changes may have implications for vagal regulation, interoceptive awareness, and emotional regulation.

The therapeutic value of this proposed mechanism lies in its potential to restore trust in bodily signals. Integration sessions may support this process by helping individuals explore bodily sensations experienced during dosing, connect interoceptive cues with emotional states, and practise interoceptive exposure to hunger, fullness, and anxiety-related sensations. Incorporating mindfulness techniques may further support autonomic regulation and help individuals develop a more adaptive relationship with their bodily experiences.

 A Brief Note Concerning The Gut-Brain Interaction 
Although gut microbiome disruption is not a direct psychological mechanism in EDs, it is a relevant biological factor to consider when examining the potential effects of PAT. Restrictive or chaotic eating patterns can contribute to gut dysbiosis, which may weaken gut-barrier integrity and contribute to inflammation affecting the brain (Anton-Paduraru et al., 2024). These changes have been shown to influence mood, stress responsivity, cognitive rigidity, and interoceptive awareness through [[wikipedia:Hypothalamic–pituitary–adrenal_axis|HPA-axis activation]], altered neurotransmitter synthesis, and disrupted hunger–satiety signalling. 

Emerging research suggests that psychedelics may also interact with the gut–brain axis. Certain microbes can metabolise psychedelic compounds, and microbial activity has been associated with modulatory effects on behavioural outcomes. Additionally, psychedelic use may alter microbial composition towards anti-inflammatory profiles, with potential implications for neuroplasticity, neurotransmitter synthesis and signalling improvements (Caspani et al., 2024). These microbiome-related effects may therefore contribute to changes in mood, cognitive flexibility, and appetite regulation.

Although the therapeutic potential of psychedelics in EDs is considered primarily in relation to psychological mechanisms, including changes in perception, emotional processing, and reduced avoidance, microbiome-related effects may represent an additional pathway through which biological processes influence psychological outcomes. However, the extent to which these interactions contribute to therapeutic outcomes in EDs remains to be established.


&lt;blockquote&gt;'''QUIZ: ''Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{ In predictive coding terms, what are “high‑level priors” in eating disorders? 
|type=&quot;()&quot;}
+ Rigid, entrenched beliefs about food, weight, and the self that shape perception and behaviour
- Flexible beliefs that easily update with new sensory information
- Momentary emotional reactions triggered by external cues

{What is the proposed mechanism by which psychedelics support emotion regulation in PAT for EDs? 
|type=&quot;()&quot;}
- By suppressing emotional intensity to prevent distress
+ By evoking strong emotions that disrupt avoidance patterns and promote emotional acceptance
- By eliminating negative emotions through serotonin release

{What is interoceptive awareness?
|type=&quot;()&quot;}
- The ability to evaluate reward value and anticipate pleasurable outcomes
+ The capacity to sense, interpret, and respond to internal bodily signals such as hunger, fullness, and emotional arousal
- The process of weakening cognitive rigidity through ego dissolution
&lt;/quiz&gt;&lt;/blockquote&gt;

== Limitations ==
Despite the potential of PAT to influence psychological mechanisms implicated in EDs, several limitations constrain current understanding of these processes and their therapeutic relevance. Research examining emotion dysregulation in EDs illustrates broader challenges in establishing the mechanisms underlying these conditions. Although non-acceptance of emotions has been identified as a transdiagnostic risk factor across psychiatric conditions (Paulus et al., 2021), Zhou et al.’s meta-analysis (2025) highlights that the causal pathways linking emotional dysregulation and EDs remain unclear, largely because of a lack of experimental and longitudinal studies. Further limitations include restricted availability of measurement scales, insufficient cultural specificity, heterogeneity across samples, gender imbalance, and limited developmental analysis. Together, these factors constrain understanding of how specific emotional processes relate to different ED presentations across the lifespan and stages of recovery.

These limitations are also relevant when considering the proposed mechanisms of PAT. Although existing theoretical frameworks offer ways to conceptualise how psychedelic experiences may influence psychological processes responsible for EDs, the emerging nature of psychedelic therapy limits the extent to which proposed mechanisms have been tested. However, with the number of clinical trials increasing as of recently, it will be interesting to see how the theorised therapeutic mechanisms across different ED presentations and stages of recovery emerges during further warranted investigation.

Nevertheless, current limitations in the evidence highlight the need for research that clarifies the relationships between psychological processes that underscore ED behaviours, and treatment outcomes. There are several important psychological components of ED maintenance that represent meaningful targets for treatment, but they should not be considered in isolation from eachother or the neurobiological processes that influence them. A more comprehensive understanding of how these mechanisms interact may help clarify the therapeutic potential of PAT and inform the development of more targeted treatment approaches.

== Conclusion ==
PAT offers a potential framework for addressing several interconnected psychological mechanisms implicated in EDs. Through its proposed effects on emotional processing, reward valuation, cognitive flexibility, and interoceptive awareness, PAT may create opportunities to disrupt established patterns of avoidance, rigid thinking, and maladaptive behavioural reinforcement. The gut–brain interaction may represent an additional biological pathway relevant to these processes.

These mechanisms should not be understood as independent processes. Changes in emotion regulation may influence the ability to tolerate bodily sensations, while shifts in reward valuation and cognitive flexibility may create opportunities to respond differently to distress and challenge entrenched beliefs. However, the extent to which PAT produces these changes, and whether they translate into sustained improvements in ED outcomes, requires further investigation, although preliminary evidence is promising. 

The therapeutic potential of PAT lies not only in the acute psychedelic experience but also in the structured integration process that follows. Integration sessions provide an opportunity to translate emotional breakthroughs, changes in cognitive flexibility, interoceptive shifts, and reward processing into sustained behavioural change. Effective integration involves helping individuals articulate insights, connect them to ED-related patterns, and develop concrete strategies for change. These may include strengthening adaptive coping, challenging rigid beliefs, practising interoceptive awareness, reinforcing positive reward experiences, and supporting nutritional rehabilitation.

By grounding the understanding of PAT in affect regulation theory and the predictive coding framework, therapists may be better positioned to help individuals explore how psychedelic experiences could disrupt maladaptive emotional and cognitive patterns and create opportunities for new learning. Polyvagal-informed approaches may further support the development of mind–body awareness and emotional regulation through mindfulness strategies. Together, these approaches offer a multifaceted framework for translating psychedelic experiences into therapeutic change and addressing the interconnected mechanisms that maintain EDs and associated suffering. 

==See Also==
* [https://w.wiki/TsdG Ayahuasca and the brain] (Wikiversity)
* [https://w.wiki/TscF Emotional effects of psychedelics] (Wikiversity)
* [https://w.wiki/Tsdb Psilocybin and emotion] (Wikiversity)
* [https://w.wiki/TsdS Psilocibyn assisted psychotherapy] (Wikiversity)
* [https://w.wiki/Tsce Psychedelics, altered consciousness, and personal growth] (Wikiversity)
* [[Eating Disorders|Eating disorders]] (Wikiversity)

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}}

==External links==
* [https://www.abct.org/fact-sheets/psychedelic-assisted-therapy/ Psychedelic-Assisted Therapy | Fact Sheet] (ABCT - Association for Behavioral and Cognitive Therapies)
* [https://podcasts.apple.com/au/podcast/can-magic-mushrooms-help-treat-anorexia/id189330872?i=1000784809236 Can magic mushrooms help treat anorexia?] (Apple Podcasts)
* [https://www.apa.org/news/podcasts/speaking-of-psychology/eating-disorder The ‘silent epidemic’ of eating disorders] (American Psychological Association)
* [https://www.apa.org/monitor/2023/04/sensations-eating-disorders-suicidal-behavior What is interoception, and how does it affect mental health]? 5 questions for April Smith (American Psychological Association)
* [https://www.cbte.co/what-is-cbte/transdiagnostic-view-eating-disorders/ Transdiagnostic view of eating disorders] (cbte.co)
* [https://psychedelic.support/resources/polyvagal-theory-mind-body-dr-erica-zelfand/ Polyvagal Theory with Dr. Erica Zelfand: Mind-Body Connection] ·(Psychedelic Support)
* [https://www.wholeselfnutrition.org/post/nervous-system-regulation-a-missing-piece-in-eating-disorder-recovery Nervous System Regulation: A Missing Piece in Eating Disorder Recovery]  (wholeselfnutrition.org)
* [https://youtu.be/RwS-CHJcCiY?si=157viTWiOGAQ-7LP Best Neural Entropy - Explainer] (Youtube)

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      <text bytes="37549" sha1="mqpaj9kydhb9tiwz70oqq0bierng4cr" xml:space="preserve">{{title|Psychedelic treatment of eating disorders:&lt;br&gt;How might psychedelic-assisted therapy influence psychological mechanisms involved in eating disorders?}}
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== Overview ==
{{RoundBoxTop|theme=7}}[[File:Neural network - Midjourney and Grok.png|thumb|'''Figure 1.''' Psychedelics are thought to temporarily disrupt rigid neural communication pathways by promoting more flexible patterns of connectivity across networks involved in mood regulation, fear processing, reward learning, and cognitive adaptability. These changes may support therapeutic shifts in behaviour and emotional processing (Hatzipantelis &amp; Olson, 2025).]]Emma, a 27‑year‑old from Canberra, has lived with an eating disorder for nearly two decades. She describes her problem eating behaviours to have started at school, after being bullied about her appearance and experiencing an unsteady home life. Ever since, they have remained in her life as “a way for me to feel in control”. Although she is aware of the harm caused by restrictive eating and compulsive exercise, she feels trapped in her thought patterns characterised by a preoccupation about food and weight concerns, as they've become entrenched in her daily life. 

After reading an article describing emerging research suggesting that psychedelics may alter patterns of neural connectivity that shape behaviour (see Figure 1), she expressed interest in pursuing psychedelic‑assisted therapy through a provider accessible to her.

After participating in her first supervised psilocybin‑assisted therapy session, Emma reported experiencing an emotional journey that allowed her to feel “connected to my body for the first time in years”. After 3 months, she has noticed a shift in how she relates to her body, and is finding it easier to actively call into question how she responds to distress with the support of her psychotherapist. 


Her experience raises a central question: What psychological mechanisms could explain these changes?{{RoundBoxBottom|theme=3}}  

This chapter explores how psychedelic‑assisted therapy (PAT) may influence the emotional, cognitive, and neurobiological processes that underpin eating disorders (EDs).   

{{RoundBoxTop|theme=11}}'''Focus questions'''
{{ic|}}Two central questions will be addressed:
* What psychological processes underpin eating disorders, and how do they guide ED behaviour?
* How might psychedelic‑assisted therapy influence these processes and support recovery?
{{ic|}}{{ic|}}{{RoundBoxBottom}}

== Introduction ==
'''Eating Disorders'''  

[[wikipedia:Eating_disorder|Eating disorders]] (EDs) are psychiatric conditions characterised by abnormal eating behaviours that negatively affect physical and mental health. In Australia, the prevalence of EDs is rising particularly among young people. The economic burden is estimated to cost the nation $84 billion, with approximately 10.46% of the population having experienced an ED at some point in their lives (Hay et al., 2023). Although other forms of disordered eating exist, this chapter will focus on only three of them (see table 1), as [[wikipedia:Anorexia|Anorexia Nervosa]] (AN) has the highest mortality rate of any psychiatric disorder, while [[wikipedia:Bulimia|Bulimia Nervosa]] (BN) and [[wikipedia:Binge_eating_disorder|Binge‑Eating Disorder]] (BED) are also highly prevalent. The EDs mentioned are most associated with chronic illness, disability, reduced quality of life, increased suicide risk, and are highly comorbid with [[wikipedia:Mood_disorder|mood disorders]], [[wikipedia:Post-traumatic_stress_disorder|post-traumatic stress disorder]] (PTSD), [[wikipedia:Obsessive–compulsive_disorder|obsessive-compulsive disorder]] (OCD), and [[wikipedia:Substance_use_disorder|substance use disorders]] (Calder et al., 2023).  Despite decades of research, the pathogenesis of EDs remains incompletely understood. Current evidence suggests a complex interplay between genetic predisposition, temperament, hormonal dysregulation, cognitive abnormalities, sociocultural pressures, and traumatic experiences (Calder et al., 2023).  
{| class=&quot;wikitable&quot;
|+Table 1. Eating Disorders and Associated Symptoms 
!Eating Disorder
!Primary Symptoms
|-
|Anorexia Nervosa
|Severe caloric restriction, fear of gaining weight, distorted body image, preoccupation with weight loss, compulsive exercise.
|-
|Bullimia Nervosa
|Intense windows of food intake (binge eating) followed by inappropriate compensatory behaviours also known as 'purging' (eg. vomiting, laxative use), feelings of guilt and loss of control.
|-
|Binge-Eating Disorder
|Recurrent episodes of binge eating not followed by inappropriate compensatory behaviours, feelings of distress and loss of control.
(Wanderlich &amp; Attia., 2024)
|}


Although cognitive‑behavioural therapy (CBT‑E) combined with pharmacological treatment has demonstrated beneficial outcomes, efficacy remains limited and varies across ED types (Calder et al., 2023). Recovery is often long and difficult, with only two‑thirds of individuals with AN and BN eventually recovering, while others can remain ill for many years. This highlights the need for treatment approaches that can accelerate recovery and provide benefit for individuals who do not respond to conventional therapies.


'''Psychedelic-Assisted Therapy'''

In 2023, Australia legalised the prescription of MDMA and psilocybin under professional supervision, marking a significant shift in mental‑health treatment options. Psychedelic compounds, including [[wikipedia:LSD|LSD]], [[wikipedia:Psilocybin|psilocybin]], [[wikipedia:Dimethyltryptamine|DMT]], [[wikipedia:Ketamine|ketamine]], and [[wikipedia:MDMA|MDMA]], have demonstrated promising therapeutic effects across a wide range of psychiatric conditions. Researchers propose that psychedelics act through psychological and neural mechanisms that increase [[wikipedia:Neuroplasticity|neuroplasticity]], facilitate insight, and foster emotional acceptance (Peled‑Avron et al., 2024). At a neurobiological level, psychedelics influence processes that inform perception, emotion, and behaviour, offering a potential avenue for addressing entrenched ED mechanisms.

PAT differs from pharmacological treatment alone because the drug is administered within a structured therapeutic context designed to maximise safety and clinical benefit (Calder et al., 2023). Treatment typically involves three types of sessions. Preparatory sessions feature participants undergoing psychoeducation, where the clinician establishes rapport and clear safety protocols. Followed by supervised medication where the participant has an inward experience with the reassurance of clinicians present in the same space. Lastly, integrative sessions where individuals process and explore insights from the previous session with their psychotherapist to foster behavioural change (Wolfgang &amp; Hoge, 2023). This combination of pharmacological and psychological intervention is theorised to effectively target underlying psychological mechanisms common across various mental health disorders, illustrating PAT’s potential as a valuable transdiagnostic treatment option. 

PAT has become a subject of increasing popularity in ED research because many of the psychological mechanisms it is proposed to influence are the same ones implicated in ED maintenance and comorbidities (Calder et al., 2023; Peled-Avron et al., 2024). Early research, including case study reports, small clinical studies, meta-analyses and reviews indicate that PAT produces improvements in affect, reductions in ED symptom severity, enhanced body image, weight restoration, and reductions in comorbid symptoms. Although preliminary, these findings indicate that PAT may disrupt and promote shifts away from maladaptive coping patterns that become entrenched in treatment resistant ED populations.

== Psychological Mechanisms in Eating Disorders ==


'''Emotion Dysregulation'''

Emotion dysregulation is considered to be a significant risk factor for the onset and maintenance of EDs. It refers to difficulties recognising, assessing, and modifying emotional responses to meet situational demands (Zhou et al., 2025). 

Research consistently shows that individuals with EDs experience significant challenges in regulating emotions, increasing their vulnerability to comorbid symptoms, which contribute to the emergence of disordered eating patterns (Leppanen et al., 2022). This idea is supported by affect regulation theory which posits that eating disorders develop and are maintained as maladaptive strategies to manage, tolerate and escape from negative emotions and psychological distress (Schaefer et al., 2020; Zanella &amp; Lee, 2022). This is further exemplified in Fitzsimmons &amp; Bardone-Cone’s article examining differences in coping within eating disorder patients (2010). The authors explain that avoidance and emotion-oriented coping styles often function as maladaptive attempts to manage (di)stress. They explain that behaviours such as binge eating, purging, starvation, and/or compulsive exercise provide temporary relief by shifting attention away from uncomfortable emotions. 

Furthermore, alexithymia, characterised by difficulty identifying and describing one’s own emotions, is strongly associated with ED pathology (Shank et al., 2019). Individuals with high alexithymia often struggle to differentiate emotional states from bodily sensations, contributing to behaviours such as emotional eating, eating in the absence of hunger, or rigid restriction. In BED, alexithymia is linked to binge episodes triggered by poorly understood emotional cues, while in AN and BN, alexithymia may contribute to emotional avoidance and reliance on ED behaviours for affect regulation. 

The effects of trauma are contributing factors to emotion dysregulation, and considered a risk factor for ED development. Individuals who experience sexual, physical, or emotional abuse, neglect, and bullying are likely to experience heightened emotional reactivity, threat perception, and avoidance behaviours (Calder et al., 2023). Researchers explain that trauma often results in lowered distress tolerance and increased reliance on maladaptive coping behaviours, including disordered eating. Furthermore, PTSD comorbidity is common, hence trauma‑related symptoms are hypothesised to frequently interact with ED behaviours in complex ways.  


'''Reward Processing Dysfunction'''
[[File:Striatum.gif|thumb|'''Figure 2.''' Striatum]]
[[File:Anterior cingulate gyrus animation.gif|thumb|'''Figure 3'''. Anterior Cingulate Cortex ]]
Abnormal reward valuation is understood to be a central psychological mechanism that maintains ED behaviours. Research consistently shows that individuals with eating disorders display altered neural activity response to various stimuli, as well as disruptions in reinforcement learning (Calder et al., 2023). Brain regions involved in reward processing, habit formation, and learning, such as the striatum and anterior cingulate cortex (see figures 2 &amp; 3), exhibit atypical activation patterns and differences in dopamine receptor binding across ED types. The insula (see figure 4), which integrates bodily sensations with conscious thought, emotion, and behaviour, also shows altered responses. Together, these regions have been shown to react differently to food images, taste, and social feedback compared to healthy controls, indicating that reward dysfunction extends beyond eating‑related stimuli for ED populations.
[[File:Insular cortex.gif|thumb|'''Figure 4.''' Insula. ]]
In the context of BN and BED, research shows that food is valued more highly than other types of rewards, thus shaping behaviour through its heightened influence on reward outcomes (Calder et al., 2023). Compulsive behaviours specific to each condition (e.g. bingeing, purging) are therefore more likely to occur when food is overvalued and alternative rewards are discounted or ignored. In addition to the neural changes already described, BN and BED are associated with reduced structural and functional connectivity between frontal control regions and the striatum. This combination of highly salient food rewards, and weakened fronto‑striatal pathways, reduces an individual’s ability to inhibit or modulate reward‑seeking impulses. Weak connectivity in these circuits is thought to predict compulsive reward‑seeking behaviour. As a result, even when individuals experience negative consequences from binge episodes, they may struggle to learn from these outcomes or adjust their behaviour accordingly.


Anhedonia, a global reduction in reward responsiveness, is frequently reported by people who experience AN, resulting in food and eating becoming undervalued or aversive to them (Calder et al., 2023). Researchers propose that reward contamination further contributes to this pattern, where the brain learns to associate normally punishing stimuli (e.g., starvation, excessive exercise) with reward, while normally rewarding stimuli (e.g., high‑calorie foods) become experienced as punishment. Structural reductions in the striatum and somatosensory cortex have also been observed, which accounts for distorted bodily sensations and contributes to anhedonia. These changes support maladaptive conditioning in which starvation and weight loss embody a sense of safety, achievement, and emotional relief. Restrictive and preoccupied behaviours centred on food, body shape, and exercise are therefore reinforced over time.

Consistent with affect‑regulation models, eating‑disorder behaviours also become negatively reinforced because they reduce emotional discomfort. This relief increases the likelihood that the behaviours will be repeated, further embedding them within the individual’s coping pattern.


'''Cognitive Rigidity'''

Cognitive rigidity refers to inflexible thinking and behavioural patterns, including difficulty adapting to new information and modifying behaviour. Researchers believe that individuals with EDs often exhibit rigid beliefs about food and weight which interact with a need to exert control over negative emotions. This interaction is the proposed process in which compulsive behaviours and obsessive thoughts develop (Calder et al., 2023). In AN, rigidity manifests as strict dietary rules and fear of losing control, while in BN and BED, binge episodes may feel compulsive and uncontrollable.


'''Interoceptive Awareness'''

Interoceptive awareness (IA) refers to the ability to recognise and process internal bodily states such as hunger, satiety, pain, and arousal. IA is impaired across EDs, and contributes to body mistrust, distorted hunger cues, and inappropriate responses to internal sensations (Brown et al., 2020). Individuals may ignore physical discomfort, misinterpret bodily signals, or avoid sensations altogether, reinforcing maladaptive coping.      

 &lt;blockquote&gt;'''''QUIZ: Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{What coping style do people who experience EDs tend to show?
|type=&quot;()&quot;}
+ Avoidance-oriented
- Problem-oriented

{Compulsive behaviours are more likely to occur when food is ... and alternative rewards are ...
|type=&quot;()&quot;}
- undervalued; overvalued
+ overvalued; undervalued
&lt;/quiz&gt;&lt;/blockquote&gt;

== Psychological Mechanisms of Psychedelic-Assisted Therapy ==

PAT is proposed to influence several psychological mechanisms implicated in EDs, particularly those discussed in the previous section. The next part of this chapter aims to examine the theorised therapeutic mechanisms PAT possesses and practical implications for ED treatment.  


'''Emotion Regulation''' 

Emotion dysregulation is a core mechanism implicated in EDs. Affect regulation theory proposes that ED behaviours emerge as maladaptive strategies to escape, reduce, or blunt overwhelming emotional experiences (Schaefer et al., 2020). Restriction, bingeing, purging, and compulsive exercise may temporarily alleviate distress while reinforcing avoidance-oriented coping and limiting opportunities to learn more adaptive ways of responding to difficult emotions. 

Psychedelics often evoke intense emotional experiences that may disrupt habitual avoidance patterns. Researchers propose that, during psychedelic sessions, attempts to suppress or avoid difficult emotions can intensify these experiences, creating conditions in which emotional acceptance becomes a preferred response (Calder et al., 2023). Although this shift does not occur in every individual, experiencing difficult emotions without resorting to ED behaviours may weaken the association between emotional distress and maladaptive coping, particularly when emotional acceptance becomes associated with a more positive or tolerable experience.

The therapeutic value of this process lies in its potential to reshape affective responses. When individuals experience strong emotions without engaging in maladaptive behaviours, they may begin to develop a new approach towards emotional tolerance. Integration sessions can consolidate this learning by helping individuals articulate, differentiate, and reflect on the emotions experienced during dosing. This process may support the development of more adaptive coping strategies, including task-oriented, problem-focused, and socially supported approaches, which are associated with improved ED outcomes (Fitzsimmons &amp; Bardone-Cone, 2010). In this way, PAT may strengthen emotion regulation and reduce reliance on ED behaviours as strategies for managing affect. 


'''Reward Processing''' 

Reward dysfunction may contribute to the maintenance of EDs by reinforcing maladaptive behaviours while diminishing the perceived value of adaptive rewards. Predictive coding provides a useful framework for understanding how PAT might influence these processes. Individuals with EDs may hold rigid beliefs, conceptualised as high-level priors, about themselves in relation to food, body weight, and rewarding behaviours (Calder et al., 2023; Mograbi et al., 2024). These beliefs can influence how experiences are perceived and valued, potentially reinforcing existing behavioural patterns. Psychedelics are proposed to weaken high-level priors, allowing bottom-up sensory information to exert greater influence on perception and the valuation of experiences. 

During psychedelic experiences, individuals frequently report a heightened appreciation of sensory, social, and bodily experiences. This shift may counteract anhedonia and support the revaluation of previously feared or avoided stimuli. The therapeutic opportunity lies in translating these temporary changes in perception and reward into meaningful behavioural change. Integration sessions can explore positive and negative moments experienced during dosing and connect them to concrete goals. An example of this, inspired from Calder et al.’s (2023) article, could be to clarify specific plans to nourish the body due to the participant having experienced themselves as a decaying skeleton followed by the realisation of the body being a gift. If the period following dosing provides an opportunity for increased neuroplasticity, it may also be particularly conducive to reinforcing adaptive reward learning through behavioural activation with the help of a therapist. 


'''Cognitive Flexibility''' 

Cognitive rigidity is a hallmark of EDs and is characterised by inflexible beliefs about food, weight, body shape, and control. Predictive coding provides a framework for understanding this rigidity, as EDs may involve entrenched priors that resist updating even when confronted with contradictory sensory evidence (Zanella &amp; Lee, 2022). Psychedelics are proposed to disrupt these entrenched priors by increasing neural entropy and reducing the dominance of top-down processing (Calder et al., 2023). This temporary loosening of cognitive constraints may allow individuals to consider alternative perspectives and question long-held beliefs. 

Experiences of ego dissolution may further contribute to cognitive flexibility by reducing attachment to rigid self-concepts (Peled-Avron, 2024; Mograbi et al., 2024). When the boundaries of the self become less defined, individuals may find it easier to question identity-related beliefs that sustain ED pathology. Integration sessions can harness this potential flexibility by supporting cognitive reframing, encouraging behavioural experiments, and strengthening metacognitive awareness. Through these processes, individuals may be better able to translate insights gained during psychedelic experiences into sustained changes in thinking and behaviour.


'''Reconnecting with Bodily Signals'''

Interoceptive deficits are central to ED pathology, contributing to body mistrust, distorted perceptions of hunger cues, and difficulties responding appropriately to internal sensations (Brown et al., 2020). Psychedelics may enhance interoceptive awareness by altering sensory processing and increasing sensitivity to bodily signals. This proposed mechanism is closely related to autonomic regulation, for which polyvagal theory provides a framework for understanding the relationship between bodily signals, emotional regulation, and perceived safety.

Polyvagal theory emphasises the role of the vagus nerve in interoception, emotional regulation, and the perception of safety (Porges, 2022). Vagal afferents transmit information from the body to the insula, where interoceptive signals are integrated with emotional and cognitive processes. Individuals with EDs may exhibit chronic sympathetic arousal and reduced vagal tone, potentially impairing interoceptive accuracy and contributing to emotional rigidity. Psychedelics may initially increase sympathetic activity, as reflected in physiological responses such as increased heart rate, followed by a parasympathetic shift associated with greater relaxation and an increased capacity for rest (Li et al., 2025). Within a polyvagal framework, these changes may have implications for vagal regulation, interoceptive awareness, and emotional regulation.

The therapeutic value of this proposed mechanism lies in its potential to restore trust in bodily signals. Integration sessions may support this process by helping individuals explore bodily sensations experienced during dosing, connect interoceptive cues with emotional states, and practise interoceptive exposure to hunger, fullness, and anxiety-related sensations. Incorporating mindfulness techniques may further support autonomic regulation and help individuals develop a more adaptive relationship with their bodily experiences.

 A Brief Note Concerning The Gut-Brain Interaction 
Although gut microbiome disruption is not a direct psychological mechanism in EDs, it is a relevant biological factor to consider when examining the potential effects of PAT. Restrictive or chaotic eating patterns can contribute to gut dysbiosis, which may weaken gut-barrier integrity and contribute to inflammation affecting the brain (Anton-Paduraru et al., 2024). These changes have been shown to influence mood, stress responsivity, cognitive rigidity, and interoceptive awareness through [[wikipedia:Hypothalamic–pituitary–adrenal_axis|HPA-axis activation]], altered neurotransmitter synthesis, and disrupted hunger–satiety signalling. 

Emerging research suggests that psychedelics may also interact with the gut–brain axis. Certain microbes can metabolise psychedelic compounds, and microbial activity has been associated with modulatory effects on behavioural outcomes. Additionally, psychedelic use may alter microbial composition towards anti-inflammatory profiles, with potential implications for neuroplasticity, neurotransmitter synthesis and signalling improvements (Caspani et al., 2024). These microbiome-related effects may therefore contribute to changes in mood, cognitive flexibility, and appetite regulation.

Although the therapeutic potential of psychedelics in EDs is considered primarily in relation to psychological mechanisms, including changes in perception, emotional processing, and reduced avoidance, microbiome-related effects may represent an additional pathway through which biological processes influence psychological outcomes. However, the extent to which these interactions contribute to therapeutic outcomes in EDs remains to be established.


&lt;blockquote&gt;'''QUIZ: ''Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{ In predictive coding terms, what are “high‑level priors” in eating disorders? 
|type=&quot;()&quot;}
+ Rigid, entrenched beliefs about food, weight, and the self that shape perception and behaviour
- Flexible beliefs that easily update with new sensory information
- Momentary emotional reactions triggered by external cues

{What is the proposed mechanism by which psychedelics support emotion regulation in PAT for EDs? 
|type=&quot;()&quot;}
- By suppressing emotional intensity to prevent distress
+ By evoking strong emotions that disrupt avoidance patterns and promote emotional acceptance
- By eliminating negative emotions through serotonin release

{What is interoceptive awareness?
|type=&quot;()&quot;}
- The ability to evaluate reward value and anticipate pleasurable outcomes
+ The capacity to sense, interpret, and respond to internal bodily signals such as hunger, fullness, and emotional arousal
- The process of weakening cognitive rigidity through ego dissolution
&lt;/quiz&gt;&lt;/blockquote&gt;

== Limitations ==
Despite the potential of PAT to influence psychological mechanisms implicated in EDs, several limitations constrain current understanding of these processes and their therapeutic relevance. Research examining emotion dysregulation in EDs illustrates broader challenges in establishing the mechanisms underlying these conditions. Although non-acceptance of emotions has been identified as a transdiagnostic risk factor across psychiatric conditions (Paulus et al., 2021), Zhou et al.’s meta-analysis (2025) highlights that the causal pathways linking emotional dysregulation and EDs remain unclear, largely because of a lack of experimental and longitudinal studies. Further limitations include restricted availability of measurement scales, insufficient cultural specificity, heterogeneity across samples, gender imbalance, and limited developmental analysis. Together, these factors constrain understanding of how specific emotional processes relate to different ED presentations across the lifespan and stages of recovery.

These limitations are also relevant when considering the proposed mechanisms of PAT. Although existing theoretical frameworks offer ways to conceptualise how psychedelic experiences may influence psychological processes responsible for EDs, the emerging nature of psychedelic therapy limits the extent to which proposed mechanisms have been tested. However, with the number of clinical trials increasing as of recently, it will be interesting to see how the theorised therapeutic mechanisms across different ED presentations and stages of recovery emerges during further warranted investigation.

Nevertheless, current limitations in the evidence highlight the need for research that clarifies the relationships between psychological processes that underscore ED behaviours, and treatment outcomes. There are several important psychological components of ED maintenance that represent meaningful targets for treatment, but they should not be considered in isolation from eachother or the neurobiological processes that influence them. A more comprehensive understanding of how these mechanisms interact may help clarify the therapeutic potential of PAT and inform the development of more targeted treatment approaches.

== Conclusion ==
PAT offers a potential framework for addressing several interconnected psychological mechanisms implicated in EDs. Through its proposed effects on emotional processing, reward valuation, cognitive flexibility, and interoceptive awareness, PAT may create opportunities to disrupt established patterns of avoidance, rigid thinking, and maladaptive behavioural reinforcement. The gut–brain interaction may represent an additional biological pathway relevant to these processes.

These mechanisms should not be understood as independent processes. Changes in emotion regulation may influence the ability to tolerate bodily sensations, while shifts in reward valuation and cognitive flexibility may create opportunities to respond differently to distress and challenge entrenched beliefs. However, the extent to which PAT produces these changes, and whether they translate into sustained improvements in ED outcomes, requires further investigation, although preliminary evidence is promising. 

The therapeutic potential of PAT lies not only in the acute psychedelic experience but also in the structured integration process that follows. Integration sessions provide an opportunity to translate emotional breakthroughs, changes in cognitive flexibility, interoceptive shifts, and reward processing into sustained behavioural change. Effective integration involves helping individuals articulate insights, connect them to ED-related patterns, and develop concrete strategies for change. These may include strengthening adaptive coping, challenging rigid beliefs, practising interoceptive awareness, reinforcing positive reward experiences, and supporting nutritional rehabilitation.

By grounding the understanding of PAT in affect regulation theory and the predictive coding framework, therapists may be better positioned to help individuals explore how psychedelic experiences could disrupt maladaptive emotional and cognitive patterns and create opportunities for new learning. Polyvagal-informed approaches may further support the development of mind–body awareness and emotional regulation through mindfulness strategies. Together, these approaches offer a multifaceted framework for translating psychedelic experiences into therapeutic change and addressing the interconnected mechanisms that maintain EDs and associated suffering. 

==See Also==
* [https://w.wiki/TsdG Ayahuasca and the brain] (Wikiversity)
* [https://w.wiki/TscF Emotional effects of psychedelics] (Wikiversity)
* [https://w.wiki/Tsdb Psilocybin and emotion] (Wikiversity)
* [https://w.wiki/TsdS Psilocibyn assisted psychotherapy] (Wikiversity)
* [https://w.wiki/Tsce Psychedelics, altered consciousness, and personal growth] (Wikiversity)
* [[Eating Disorders|Eating disorders]] (Wikiversity)

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{{Hanging indent|1=

{{ic|Try &quot;Edit source&quot; and then wrapping any text to be italicised in two apostrophes e.g., ''this is italics''}}

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Peled-Avron L., Aday J. Ss, Kalafateli A. L., Hamilton H. K., Woolley J. D. (2024). Editorial: Down the rabbit hole – the psychological and neural mechanisms of psychedelic compounds and their use in treating mental health and medical conditions. &quot;Frontiers in Psychiatry 15&quot;:1431389. doi: 10.3389/fpsyt.2024.1431389

Porges S. W. (2025). Polyvagal Theory: Current Status, Clinical Applications, and Future Directions. &quot;Clinical neuropsychiatry, 22&quot;(3), 169–184. https://doi.org/10.36131/cnfioritieditore20250301

Schaefer, L. M., Smith, K. E., Anderson, L. M., Cao, L., Crosby, R. D., Engel, S. G., Crow, S. J., Peterson, C. B., &amp; Wonderlich, S. A. (2020). The role of affect in the maintenance of binge-eating disorder: Evidence from an ecological momentary assessment study. &quot;Journal of abnormal psychology, 129&quot;(4), 387–396. https://doi.org/10.1037/abn0000517 

Shank, L. M., Tanofsky-Kraff, M., Kelly, N. R., Jaramillo, M., Rubin, S. G., Altman, D. R., Byrne, M. E., LeMay-Russell, S., Schvey, N. A., Broadney, M. M., Brady, S. M., Yang, S. B., Courville, A. B., Ramirez, S., Crist, A. C., Yanovski, S. Z., &amp; Yanovski, J. A. (2019). The association between alexithymia and eating behavior in children and adolescents. &quot;Appetite, 142&quot;, 104381. https://doi.org/10.1016/j.appet.2019.104381

Wonderlich, J., &amp; Attia, E. (2024). Eating disorders in the DSM-5. In P. Robinson, T. Wade, B. Herpertz-Dahlmann, F. Fernandez-Aranda, J. Treasure, &amp; S. Wonderlich (Eds.), Eating disorders: An international comprehensive view (pp. 7–18). &quot;Springer Nature Switzerland AG&quot;. https://doi.org/10.1007/978-3-031-46096-8_9

Wolfgang, A. S., &amp; Hoge, C. W. (2023). Psychedelic-Assisted Therapy in Military and Veterans Healthcare Systems: Clinical, Legal, and Implementation Considerations. &quot;Current psychiatry reports, 25&quot;(10), 513–532. https://doi.org/10.1007/s11920-023-01446-4 

Zanella, E., &amp; Lee, E. (2022). Integrative review on psychological and social risk and prevention factors of eating disorders including anorexia nervosa and bulimia nervosa: seven major theories. &quot;Heliyon, 8&quot;(11), e11422. https://doi.org/10.1016/j.heliyon.2022.e11422 

Zhou, R., Zhang, L., Liu, Z., &amp; Cao, B. (2025). Emotion regulation difficulties and disordered eating in adolescents and young adults: a meta-analysis. &quot;Journal of eating disorders, 13&quot;(1), 25. https://doi.org/10.1186/s40337-025-01197-y

}}

==External links==
* [https://www.abct.org/fact-sheets/psychedelic-assisted-therapy/ Psychedelic-Assisted Therapy | Fact Sheet] (ABCT - Association for Behavioral and Cognitive Therapies)
* [https://podcasts.apple.com/au/podcast/can-magic-mushrooms-help-treat-anorexia/id189330872?i=1000784809236 Can magic mushrooms help treat anorexia?] (Apple Podcasts)
* [https://www.apa.org/news/podcasts/speaking-of-psychology/eating-disorder The ‘silent epidemic’ of eating disorders] (American Psychological Association)
* [https://www.apa.org/monitor/2023/04/sensations-eating-disorders-suicidal-behavior What is interoception, and how does it affect mental health]? 5 questions for April Smith (American Psychological Association)
* [https://www.cbte.co/what-is-cbte/transdiagnostic-view-eating-disorders/ Transdiagnostic view of eating disorders] (cbte.co)
* [https://psychedelic.support/resources/polyvagal-theory-mind-body-dr-erica-zelfand/ Polyvagal Theory with Dr. Erica Zelfand: Mind-Body Connection] ·(Psychedelic Support)
* [https://www.wholeselfnutrition.org/post/nervous-system-regulation-a-missing-piece-in-eating-disorder-recovery Nervous System Regulation: A Missing Piece in Eating Disorder Recovery]  (wholeselfnutrition.org)
* [https://youtu.be/RwS-CHJcCiY?si=157viTWiOGAQ-7LP Best Neural Entropy - Explainer] (Youtube)

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      <text bytes="37648" sha1="2q2l700t3h0tsayzzs4f2y7dmq1ag08" xml:space="preserve">{{title|Psychedelic treatment of eating disorders:&lt;br&gt;How might psychedelic-assisted therapy influence psychological mechanisms involved in eating disorders?}}
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== Overview ==
{{RoundBoxTop|theme=7}}[[File:Neural network - Midjourney and Grok.png|thumb|'''Figure 1.''' Psychedelics are thought to temporarily disrupt rigid neural communication pathways by promoting more flexible patterns of connectivity across networks involved in mood regulation, fear processing, reward learning, and cognitive adaptability. These changes may support therapeutic shifts in behaviour and emotional processing (Hatzipantelis &amp; Olson, 2025).]]Emma, a 27‑year‑old from Canberra, has lived with an eating disorder for nearly two decades. She describes her problem eating behaviours to have started at school, after being bullied about her appearance and experiencing an unsteady home life. Ever since, they have remained in her life as “a way for me to feel in control”. Although she is aware of the harm caused by restrictive eating and compulsive exercise, she feels trapped in her thought patterns characterised by a preoccupation about food and weight concerns, as they've become entrenched in her daily life. 

After reading an article describing emerging research suggesting that psychedelics may alter patterns of neural connectivity that shape behaviour (see Figure 1), she expressed interest in pursuing psychedelic‑assisted therapy through a provider accessible to her.

After participating in her first supervised psilocybin‑assisted therapy session, Emma reported experiencing an emotional journey that allowed her to feel “connected to my body for the first time in years”. After 3 months, she has noticed a shift in how she relates to her body, and is finding it easier to actively call into question how she responds to distress with the support of her psychotherapist. 


Her experience raises a central question: What psychological mechanisms could explain these changes?{{RoundBoxBottom|theme=3}}  

This chapter explores how psychedelic‑assisted therapy (PAT) may influence the emotional, cognitive, and neurobiological processes that underpin eating disorders (EDs).   

{{RoundBoxTop|theme=11}}'''Focus questions'''
{{ic|}}Two central questions will be addressed:
* What psychological processes underpin eating disorders, and how do they guide ED behaviour?
* How might psychedelic‑assisted therapy influence these processes and support recovery?
{{ic|}}{{ic|}}{{RoundBoxBottom}}

== Introduction ==
'''Eating Disorders'''  

[[wikipedia:Eating_disorder|Eating disorders]] (EDs) are psychiatric conditions characterised by abnormal eating behaviours that negatively affect physical and mental health. In Australia, the prevalence of EDs is rising particularly among young people. The economic burden is estimated to cost the nation $84 billion, with approximately 10.46% of the population having experienced an ED at some point in their lives (Hay et al., 2023). Although other forms of disordered eating exist, this chapter will focus on only three of them (see table 1), as [[wikipedia:Anorexia|Anorexia Nervosa]] (AN) has the highest mortality rate of any psychiatric disorder, while [[wikipedia:Bulimia|Bulimia Nervosa]] (BN) and [[wikipedia:Binge_eating_disorder|Binge‑Eating Disorder]] (BED) are also highly prevalent. The EDs mentioned are most associated with chronic illness, disability, reduced quality of life, increased suicide risk, and are highly comorbid with [[wikipedia:Mood_disorder|mood disorders]], [[wikipedia:Post-traumatic_stress_disorder|post-traumatic stress disorder]] (PTSD), [[wikipedia:Obsessive–compulsive_disorder|obsessive-compulsive disorder]] (OCD), and [[wikipedia:Substance_use_disorder|substance use disorders]] (Calder et al., 2023).  Despite decades of research, the pathogenesis of EDs remains incompletely understood. Current evidence suggests a complex interplay between genetic predisposition, temperament, hormonal dysregulation, cognitive abnormalities, sociocultural pressures, and traumatic experiences (Calder et al., 2023).  
{| class=&quot;wikitable&quot;
|+Table 1. Eating Disorders and Associated Symptoms 
!Eating Disorder
!Primary Symptoms
|-
|Anorexia Nervosa
|Severe caloric restriction, fear of gaining weight, distorted body image, preoccupation with weight loss, compulsive exercise.
|-
|Bullimia Nervosa
|Intense windows of food intake (binge eating) followed by inappropriate compensatory behaviours also known as 'purging' (eg. vomiting, laxative use), feelings of guilt and loss of control.
|-
|Binge-Eating Disorder
|Recurrent episodes of binge eating not followed by inappropriate compensatory behaviours, feelings of distress and loss of control.
(Wanderlich &amp; Attia., 2024)
|}


Although cognitive‑behavioural therapy (CBT‑E) combined with pharmacological treatment has demonstrated beneficial outcomes, efficacy remains limited and varies across ED types (Calder et al., 2023). Recovery is often long and difficult, with only two‑thirds of individuals with AN and BN eventually recovering, while others can remain ill for many years. This highlights the need for treatment approaches that can accelerate recovery and provide benefit for individuals who do not respond to conventional therapies.


'''Psychedelic-Assisted Therapy'''

In 2023, Australia legalised the prescription of MDMA and psilocybin under professional supervision, marking a significant shift in mental‑health treatment options. Psychedelic compounds, including [[wikipedia:LSD|LSD]], [[wikipedia:Psilocybin|psilocybin]], [[wikipedia:Dimethyltryptamine|DMT]], [[wikipedia:Ketamine|ketamine]], and [[wikipedia:MDMA|MDMA]], have demonstrated promising therapeutic effects across a wide range of psychiatric conditions. Researchers propose that psychedelics act through psychological and neural mechanisms that increase [[wikipedia:Neuroplasticity|neuroplasticity]], facilitate insight, and foster emotional acceptance (Peled‑Avron et al., 2024). At a neurobiological level, psychedelics influence processes that inform perception, emotion, and behaviour, offering a potential avenue for addressing entrenched ED mechanisms.

PAT differs from pharmacological treatment alone because the drug is administered within a structured therapeutic context designed to maximise safety and clinical benefit (Calder et al., 2023). Treatment typically involves three types of sessions undertaken numerous times across several months. Preparatory sessions feature participants undergoing psychoeducation, where a psychotherapist establishes rapport and clear safety protocols. Followed by supervised medication sessions, where the participant has an inward experience with the reassurance of clinicians present in the same space. Lastly, integrative sessions led by the psychotherapist provide an opportunity for individuals to process and explore insights from the previous session, in aims to facilitate behavioural change (Wolfgang &amp; Hoge, 2023). This combination of pharmacological and psychological intervention is theorised to effectively target underlying psychological mechanisms common across various mental health disorders, illustrating PAT’s potential as a valuable transdiagnostic treatment option. 

PAT has become a subject of increasing popularity in ED research because many of the psychological mechanisms it is proposed to influence are the same ones implicated in ED maintenance and comorbidities (Calder et al., 2023; Peled-Avron et al., 2024). Early research, including case study reports, small clinical studies, meta-analyses and reviews indicate that PAT produces improvements in affect, reductions in ED symptom severity, enhanced body image, weight restoration, and reductions in comorbid symptoms. Although preliminary, these findings indicate that PAT may disrupt and promote shifts away from maladaptive coping patterns that become entrenched in treatment resistant ED populations.

== Psychological Mechanisms in Eating Disorders ==


'''Emotion Dysregulation'''

Emotion dysregulation is considered to be a significant risk factor for the onset and maintenance of EDs. It refers to difficulties recognising, assessing, and modifying emotional responses to meet situational demands (Zhou et al., 2025). 

Research consistently shows that individuals with EDs experience significant challenges in regulating emotions, increasing their vulnerability to comorbid symptoms, which contribute to the emergence of disordered eating patterns (Leppanen et al., 2022). This idea is supported by affect regulation theory which posits that eating disorders develop and are maintained as maladaptive strategies to manage, tolerate and escape from negative emotions and psychological distress (Schaefer et al., 2020; Zanella &amp; Lee, 2022). This is further exemplified in Fitzsimmons &amp; Bardone-Cone’s article examining differences in coping within eating disorder patients (2010). The authors explain that avoidance and emotion-oriented coping styles often function as maladaptive attempts to manage (di)stress. They explain that behaviours such as binge eating, purging, starvation, and/or compulsive exercise provide temporary relief by shifting attention away from uncomfortable emotions. 

Furthermore, alexithymia, characterised by difficulty identifying and describing one’s own emotions, is strongly associated with ED pathology (Shank et al., 2019). Individuals with high alexithymia often struggle to differentiate emotional states from bodily sensations, contributing to behaviours such as emotional eating, eating in the absence of hunger, or rigid restriction. In BED, alexithymia is linked to binge episodes triggered by poorly understood emotional cues, while in AN and BN, alexithymia may contribute to emotional avoidance and reliance on ED behaviours for affect regulation. 

The effects of trauma are contributing factors to emotion dysregulation, and considered a risk factor for ED development. Individuals who experience sexual, physical, or emotional abuse, neglect, and bullying are likely to experience heightened emotional reactivity, threat perception, and avoidance behaviours (Calder et al., 2023). Researchers explain that trauma often results in lowered distress tolerance and increased reliance on maladaptive coping behaviours, including disordered eating. Furthermore, PTSD comorbidity is common, hence trauma‑related symptoms are hypothesised to frequently interact with ED behaviours in complex ways.  


'''Reward Processing Dysfunction'''
[[File:Striatum.gif|thumb|'''Figure 2.''' Striatum]]
[[File:Anterior cingulate gyrus animation.gif|thumb|'''Figure 3'''. Anterior Cingulate Cortex ]]
Abnormal reward valuation is understood to be a central psychological mechanism that maintains ED behaviours. Research consistently shows that individuals with eating disorders display altered neural activity response to various stimuli, as well as disruptions in reinforcement learning (Calder et al., 2023). Brain regions involved in reward processing, habit formation, and learning, such as the striatum and anterior cingulate cortex (see figures 2 &amp; 3), exhibit atypical activation patterns and differences in dopamine receptor binding across ED types. The insula (see figure 4), which integrates bodily sensations with conscious thought, emotion, and behaviour, also shows altered responses. Together, these regions have been shown to react differently to food images, taste, and social feedback compared to healthy controls, indicating that reward dysfunction extends beyond eating‑related stimuli for ED populations.
[[File:Insular cortex.gif|thumb|'''Figure 4.''' Insula. ]]
In the context of BN and BED, research shows that food is valued more highly than other types of rewards, thus shaping behaviour through its heightened influence on reward outcomes (Calder et al., 2023). Compulsive behaviours specific to each condition (e.g. bingeing, purging) are therefore more likely to occur when food is overvalued and alternative rewards are discounted or ignored. In addition to the neural changes already described, BN and BED are associated with reduced structural and functional connectivity between frontal control regions and the striatum. This combination of highly salient food rewards, and weakened fronto‑striatal pathways, reduces an individual’s ability to inhibit or modulate reward‑seeking impulses. Weak connectivity in these circuits is thought to predict compulsive reward‑seeking behaviour. As a result, even when individuals experience negative consequences from binge episodes, they may struggle to learn from these outcomes or adjust their behaviour accordingly.


Anhedonia, a global reduction in reward responsiveness, is frequently reported by people who experience AN, resulting in food and eating becoming undervalued or aversive to them (Calder et al., 2023). Researchers propose that reward contamination further contributes to this pattern, where the brain learns to associate normally punishing stimuli (e.g., starvation, excessive exercise) with reward, while normally rewarding stimuli (e.g., high‑calorie foods) become experienced as punishment. Structural reductions in the striatum and somatosensory cortex have also been observed, which accounts for distorted bodily sensations and contributes to anhedonia. These changes support maladaptive conditioning in which starvation and weight loss embody a sense of safety, achievement, and emotional relief. Restrictive and preoccupied behaviours centred on food, body shape, and exercise are therefore reinforced over time.

Consistent with affect‑regulation models, eating‑disorder behaviours also become negatively reinforced because they reduce emotional discomfort. This relief increases the likelihood that the behaviours will be repeated, further embedding them within the individual’s coping pattern.


'''Cognitive Rigidity'''

Cognitive rigidity refers to inflexible thinking and behavioural patterns, including difficulty adapting to new information and modifying behaviour. Researchers believe that individuals with EDs often exhibit rigid beliefs about food and weight which interact with a need to exert control over negative emotions. This interaction is the proposed process in which compulsive behaviours and obsessive thoughts develop (Calder et al., 2023). In AN, rigidity manifests as strict dietary rules and fear of losing control, while in BN and BED, binge episodes may feel compulsive and uncontrollable.


'''Interoceptive Awareness'''

Interoceptive awareness (IA) refers to the ability to recognise and process internal bodily states such as hunger, satiety, pain, and arousal. IA is impaired across EDs, and contributes to body mistrust, distorted hunger cues, and inappropriate responses to internal sensations (Brown et al., 2020). Individuals may ignore physical discomfort, misinterpret bodily signals, or avoid sensations altogether, reinforcing maladaptive coping.      

 &lt;blockquote&gt;'''''QUIZ: Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{What coping style do people who experience EDs tend to show?
|type=&quot;()&quot;}
+ Avoidance-oriented
- Problem-oriented

{Compulsive behaviours are more likely to occur when food is ... and alternative rewards are ...
|type=&quot;()&quot;}
- undervalued; overvalued
+ overvalued; undervalued
&lt;/quiz&gt;&lt;/blockquote&gt;

== Psychological Mechanisms of Psychedelic-Assisted Therapy ==

PAT is proposed to influence several psychological mechanisms implicated in EDs, particularly those discussed in the previous section. The next part of this chapter aims to examine the theorised therapeutic mechanisms PAT possesses and practical implications for ED treatment.  


'''Emotion Regulation''' 

Emotion dysregulation is a core mechanism implicated in EDs. Affect regulation theory proposes that ED behaviours emerge as maladaptive strategies to escape, reduce, or blunt overwhelming emotional experiences (Schaefer et al., 2020). Restriction, bingeing, purging, and compulsive exercise may temporarily alleviate distress while reinforcing avoidance-oriented coping and limiting opportunities to learn more adaptive ways of responding to difficult emotions. 

Psychedelics often evoke intense emotional experiences that may disrupt habitual avoidance patterns. Researchers propose that, during psychedelic sessions, attempts to suppress or avoid difficult emotions can intensify these experiences, creating conditions in which emotional acceptance becomes a preferred response (Calder et al., 2023). Although this shift does not occur in every individual, experiencing difficult emotions without resorting to ED behaviours may weaken the association between emotional distress and maladaptive coping, particularly when emotional acceptance becomes associated with a more positive or tolerable experience.

The therapeutic value of this process lies in its potential to reshape affective responses. When individuals experience strong emotions without engaging in maladaptive behaviours, they may begin to develop a new approach towards emotional tolerance. Integration sessions can consolidate this learning by helping individuals articulate, differentiate, and reflect on the emotions experienced during dosing. This process may support the development of more adaptive coping strategies, including task-oriented, problem-focused, and socially supported approaches, which are associated with improved ED outcomes (Fitzsimmons &amp; Bardone-Cone, 2010). In this way, PAT may strengthen emotion regulation and reduce reliance on ED behaviours as strategies for managing affect. 


'''Reward Processing''' 

Reward dysfunction may contribute to the maintenance of EDs by reinforcing maladaptive behaviours while diminishing the perceived value of adaptive rewards. Predictive coding provides a useful framework for understanding how PAT might influence these processes. Individuals with EDs may hold rigid beliefs, conceptualised as high-level priors, about themselves in relation to food, body weight, and rewarding behaviours (Calder et al., 2023; Mograbi et al., 2024). These beliefs can influence how experiences are perceived and valued, potentially reinforcing existing behavioural patterns. Psychedelics are proposed to weaken high-level priors, allowing bottom-up sensory information to exert greater influence on perception and the valuation of experiences. 

During psychedelic experiences, individuals frequently report a heightened appreciation of sensory, social, and bodily experiences. This shift may counteract anhedonia and support the revaluation of previously feared or avoided stimuli. The therapeutic opportunity lies in translating these temporary changes in perception and reward into meaningful behavioural change. Integration sessions can explore positive and negative moments experienced during dosing and connect them to concrete goals. An example of this, inspired from Calder et al.’s (2023) article, could be to clarify specific plans to nourish the body due to the participant having experienced themselves as a decaying skeleton followed by the realisation of the body being a gift. If the period following dosing provides an opportunity for increased neuroplasticity, it may also be particularly conducive to reinforcing adaptive reward learning through behavioural activation with the help of a therapist. 


'''Cognitive Flexibility''' 

Cognitive rigidity is a hallmark of EDs and is characterised by inflexible beliefs about food, weight, body shape, and control. Predictive coding provides a framework for understanding this rigidity, as EDs may involve entrenched priors that resist updating even when confronted with contradictory sensory evidence (Zanella &amp; Lee, 2022). Psychedelics are proposed to disrupt these entrenched priors by increasing neural entropy and reducing the dominance of top-down processing (Calder et al., 2023). This temporary loosening of cognitive constraints may allow individuals to consider alternative perspectives and question long-held beliefs. 

Experiences of ego dissolution may further contribute to cognitive flexibility by reducing attachment to rigid self-concepts (Peled-Avron, 2024; Mograbi et al., 2024). When the boundaries of the self become less defined, individuals may find it easier to question identity-related beliefs that sustain ED pathology. Integration sessions can harness this potential flexibility by supporting cognitive reframing, encouraging behavioural experiments, and strengthening metacognitive awareness. Through these processes, individuals may be better able to translate insights gained during psychedelic experiences into sustained changes in thinking and behaviour.


'''Reconnecting with Bodily Signals'''

Interoceptive deficits are central to ED pathology, contributing to body mistrust, distorted perceptions of hunger cues, and difficulties responding appropriately to internal sensations (Brown et al., 2020). Psychedelics may enhance interoceptive awareness by altering sensory processing and increasing sensitivity to bodily signals. This proposed mechanism is closely related to autonomic regulation, for which polyvagal theory provides a framework for understanding the relationship between bodily signals, emotional regulation, and perceived safety.

Polyvagal theory emphasises the role of the vagus nerve in interoception, emotional regulation, and the perception of safety (Porges, 2022). Vagal afferents transmit information from the body to the insula, where interoceptive signals are integrated with emotional and cognitive processes. Individuals with EDs may exhibit chronic sympathetic arousal and reduced vagal tone, potentially impairing interoceptive accuracy and contributing to emotional rigidity. Psychedelics may initially increase sympathetic activity, as reflected in physiological responses such as increased heart rate, followed by a parasympathetic shift associated with greater relaxation and an increased capacity for rest (Li et al., 2025). Within a polyvagal framework, these changes may have implications for vagal regulation, interoceptive awareness, and emotional regulation.

The therapeutic value of this proposed mechanism lies in its potential to restore trust in bodily signals. Integration sessions may support this process by helping individuals explore bodily sensations experienced during dosing, connect interoceptive cues with emotional states, and practise interoceptive exposure to hunger, fullness, and anxiety-related sensations. Incorporating mindfulness techniques may further support autonomic regulation and help individuals develop a more adaptive relationship with their bodily experiences.

 A Brief Note Concerning The Gut-Brain Interaction 
Although gut microbiome disruption is not a direct psychological mechanism in EDs, it is a relevant biological factor to consider when examining the potential effects of PAT. Restrictive or chaotic eating patterns can contribute to gut dysbiosis, which may weaken gut-barrier integrity and contribute to inflammation affecting the brain (Anton-Paduraru et al., 2024). These changes have been shown to influence mood, stress responsivity, cognitive rigidity, and interoceptive awareness through [[wikipedia:Hypothalamic–pituitary–adrenal_axis|HPA-axis activation]], altered neurotransmitter synthesis, and disrupted hunger–satiety signalling. 

Emerging research suggests that psychedelics may also interact with the gut–brain axis. Certain microbes can metabolise psychedelic compounds, and microbial activity has been associated with modulatory effects on behavioural outcomes. Additionally, psychedelic use may alter microbial composition towards anti-inflammatory profiles, with potential implications for neuroplasticity, neurotransmitter synthesis and signalling improvements (Caspani et al., 2024). These microbiome-related effects may therefore contribute to changes in mood, cognitive flexibility, and appetite regulation.

Although the therapeutic potential of psychedelics in EDs is considered primarily in relation to psychological mechanisms, including changes in perception, emotional processing, and reduced avoidance, microbiome-related effects may represent an additional pathway through which biological processes influence psychological outcomes. However, the extent to which these interactions contribute to therapeutic outcomes in EDs remains to be established.


&lt;blockquote&gt;'''QUIZ: ''Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{ In predictive coding terms, what are “high‑level priors” in eating disorders? 
|type=&quot;()&quot;}
+ Rigid, entrenched beliefs about food, weight, and the self that shape perception and behaviour
- Flexible beliefs that easily update with new sensory information
- Momentary emotional reactions triggered by external cues

{What is the proposed mechanism by which psychedelics support emotion regulation in PAT for EDs? 
|type=&quot;()&quot;}
- By suppressing emotional intensity to prevent distress
+ By evoking strong emotions that disrupt avoidance patterns and promote emotional acceptance
- By eliminating negative emotions through serotonin release

{What is interoceptive awareness?
|type=&quot;()&quot;}
- The ability to evaluate reward value and anticipate pleasurable outcomes
+ The capacity to sense, interpret, and respond to internal bodily signals such as hunger, fullness, and emotional arousal
- The process of weakening cognitive rigidity through ego dissolution
&lt;/quiz&gt;&lt;/blockquote&gt;

== Limitations ==
Despite the potential of PAT to influence psychological mechanisms implicated in EDs, several limitations constrain current understanding of these processes and their therapeutic relevance. Research examining emotion dysregulation in EDs illustrates broader challenges in establishing the mechanisms underlying these conditions. Although non-acceptance of emotions has been identified as a transdiagnostic risk factor across psychiatric conditions (Paulus et al., 2021), Zhou et al.’s meta-analysis (2025) highlights that the causal pathways linking emotional dysregulation and EDs remain unclear, largely because of a lack of experimental and longitudinal studies. Further limitations include restricted availability of measurement scales, insufficient cultural specificity, heterogeneity across samples, gender imbalance, and limited developmental analysis. Together, these factors constrain understanding of how specific emotional processes relate to different ED presentations across the lifespan and stages of recovery.

These limitations are also relevant when considering the proposed mechanisms of PAT. Although existing theoretical frameworks offer ways to conceptualise how psychedelic experiences may influence psychological processes responsible for EDs, the emerging nature of psychedelic therapy limits the extent to which proposed mechanisms have been tested. However, with the number of clinical trials increasing as of recently, it will be interesting to see how the theorised therapeutic mechanisms across different ED presentations and stages of recovery emerges during further warranted investigation.

Nevertheless, current limitations in the evidence highlight the need for research that clarifies the relationships between psychological processes that underscore ED behaviours, and treatment outcomes. There are several important psychological components of ED maintenance that represent meaningful targets for treatment, but they should not be considered in isolation from eachother or the neurobiological processes that influence them. A more comprehensive understanding of how these mechanisms interact may help clarify the therapeutic potential of PAT and inform the development of more targeted treatment approaches.

== Conclusion ==
PAT offers a potential framework for addressing several interconnected psychological mechanisms implicated in EDs. Through its proposed effects on emotional processing, reward valuation, cognitive flexibility, and interoceptive awareness, PAT may create opportunities to disrupt established patterns of avoidance, rigid thinking, and maladaptive behavioural reinforcement. The gut–brain interaction may represent an additional biological pathway relevant to these processes.

These mechanisms should not be understood as independent processes. Changes in emotion regulation may influence the ability to tolerate bodily sensations, while shifts in reward valuation and cognitive flexibility may create opportunities to respond differently to distress and challenge entrenched beliefs. However, the extent to which PAT produces these changes, and whether they translate into sustained improvements in ED outcomes, requires further investigation, although preliminary evidence is promising. 

The therapeutic potential of PAT lies not only in the acute psychedelic experience but also in the structured integration process that follows. Integration sessions provide an opportunity to translate emotional breakthroughs, changes in cognitive flexibility, interoceptive shifts, and reward processing into sustained behavioural change. Effective integration involves helping individuals articulate insights, connect them to ED-related patterns, and develop concrete strategies for change. These may include strengthening adaptive coping, challenging rigid beliefs, practising interoceptive awareness, reinforcing positive reward experiences, and supporting nutritional rehabilitation.

By grounding the understanding of PAT in affect regulation theory and the predictive coding framework, therapists may be better positioned to help individuals explore how psychedelic experiences could disrupt maladaptive emotional and cognitive patterns and create opportunities for new learning. Polyvagal-informed approaches may further support the development of mind–body awareness and emotional regulation through mindfulness strategies. Together, these approaches offer a multifaceted framework for translating psychedelic experiences into therapeutic change and addressing the interconnected mechanisms that maintain EDs and associated suffering. 

==See Also==
* [https://w.wiki/TsdG Ayahuasca and the brain] (Wikiversity)
* [https://w.wiki/TscF Emotional effects of psychedelics] (Wikiversity)
* [https://w.wiki/Tsdb Psilocybin and emotion] (Wikiversity)
* [https://w.wiki/TsdS Psilocibyn assisted psychotherapy] (Wikiversity)
* [https://w.wiki/Tsce Psychedelics, altered consciousness, and personal growth] (Wikiversity)
* [[Eating Disorders|Eating disorders]] (Wikiversity)

==References==
{{Hanging indent|1=

{{ic|Try &quot;Edit source&quot; and then wrapping any text to be italicised in two apostrophes e.g., ''this is italics''}}

Anton-Păduraru, D. T., Trofin, F., Nastase, E. V., Miftode, R. S., Miftode, I. L., Trandafirescu, M. F., Cojocaru, E., Țarcă, E., Mindru, D. E., &amp; Dorneanu, O. S. (2023). The Role of the Gut Microbiota in Anorexia Nervosa in Children and Adults-Systematic Review. &quot;International journal of molecular sciences, 25&quot;(1), 41. https://doi.org/10.3390/ijms25010041

Brown, T. A., Vanzhula, I. A., Reilly, E. E., Levinson, C. A., Berner, L. A., Krueger, A., Lavender, J. M., Kaye, W. H., &amp; Wierenga, C. E. (2020). Body mistrust bridges interoceptive awareness and eating disorder symptoms. &quot;Journal of abnormal psychology, 129&quot;(5), 445–456. https://doi.org/10.1037/abn0000516 

Calder, A., Mock, S., Friedli, N., Pasi, P., &amp; Hasler, G. (2023). Psychedelics in the treatment of eating disorders: Rationale and potential mechanisms. &quot;European Neuropsychopharmacology, 75&quot;, 1–14. https://doi.org/10.1016/j.euroneuro.2023.05.008 

Caspani, G., Ruffell, S. G. D., Tsang, W., Netzband, N., Rohani-Shukla, C., Swann, J. R., &amp; Jefferies, W. A. (2024). Mind over matter: the microbial mindscapes of psychedelics and the gut-brain axis. &quot;Pharmacological research, 207&quot;, 107338. https://doi.org/10.1016/j.phrs.2024.107338  

Fitzsimmons, E. E., &amp; Bardone-Cone, A. M. (2010). Differences in coping across stages of recovery from an eating disorder. &quot;The International journal of eating disorders, 43&quot;(8), 689–693. https://doi.org/10.1002/eat.20781 

Hatzipantelis, C. J., &amp; Olson, D. E. (2024). The Effects of Psychedelics on Neuronal Physiology. &quot;Annual review of physiology, 86&quot;, 27–47. https://doi.org/10.1146/annurev-physiol-042022-020923

Hay, P., Aouad, P., Le, A., Marks, P., Maloney, D., National Eating Disorder Research Consortium, Touyz, S., &amp; Maguire, S. (2023). Epidemiology of eating disorders: population, prevalence, disease burden and quality of life informing public policy in Australia-a rapid review. &quot;Journal of eating disorders, 11&quot;(1), 23. https://doi.org/10.1186/s40337-023-00738-7

Li, H., Wang, H., &amp; Wang, X. (2025). Psychedelics and the Autonomic Nervous System: A Perspective on Their Interplay and Therapeutic Potential. &quot;ACS pharmacology &amp; translational science, 8&quot;(3), 899–902. https://doi.org/10.1021/acsptsci.5c00005 

Leppanen, J., Brown, D., McLinden, H., Williams, S., &amp; Tchanturia, K. (2022). The Role of Emotion Regulation in Eating Disorders: A Network Meta-Analysis Approach. &quot;Frontiers in psychiatry, 13&quot;, 793094. https://doi.org/10.3389/fpsyt.2022.793094 

Mograbi, D. C., Rodrigues, R., Bienemann, B., &amp; Huntley, J. (2024). Brain Networks, Neurotransmitters and Psychedelics: Towards a Neurochemistry of Self-Awareness. &quot;Current neurology and neuroscience reports, 24&quot;(8), 323–340. https://doi.org/10.1007/s11910-024-01353-y

Paulus F. W., Ohmann S., Möhler E., Plener P. &amp; Popow C. (2021). Emotional Dysregulation in Children and Adolescents With Psychiatric Disorders. A Narrative Review. &quot;Frontiers in Psychiatry 12&quot;:628252. doi: 10.3389/fpsyt.2021.628252

Peled-Avron L., Aday J. Ss, Kalafateli A. L., Hamilton H. K., Woolley J. D. (2024). Editorial: Down the rabbit hole – the psychological and neural mechanisms of psychedelic compounds and their use in treating mental health and medical conditions. &quot;Frontiers in Psychiatry 15&quot;:1431389. doi: 10.3389/fpsyt.2024.1431389

Porges S. W. (2025). Polyvagal Theory: Current Status, Clinical Applications, and Future Directions. &quot;Clinical neuropsychiatry, 22&quot;(3), 169–184. https://doi.org/10.36131/cnfioritieditore20250301

Schaefer, L. M., Smith, K. E., Anderson, L. M., Cao, L., Crosby, R. D., Engel, S. G., Crow, S. J., Peterson, C. B., &amp; Wonderlich, S. A. (2020). The role of affect in the maintenance of binge-eating disorder: Evidence from an ecological momentary assessment study. &quot;Journal of abnormal psychology, 129&quot;(4), 387–396. https://doi.org/10.1037/abn0000517 

Shank, L. M., Tanofsky-Kraff, M., Kelly, N. R., Jaramillo, M., Rubin, S. G., Altman, D. R., Byrne, M. E., LeMay-Russell, S., Schvey, N. A., Broadney, M. M., Brady, S. M., Yang, S. B., Courville, A. B., Ramirez, S., Crist, A. C., Yanovski, S. Z., &amp; Yanovski, J. A. (2019). The association between alexithymia and eating behavior in children and adolescents. &quot;Appetite, 142&quot;, 104381. https://doi.org/10.1016/j.appet.2019.104381

Wonderlich, J., &amp; Attia, E. (2024). Eating disorders in the DSM-5. In P. Robinson, T. Wade, B. Herpertz-Dahlmann, F. Fernandez-Aranda, J. Treasure, &amp; S. Wonderlich (Eds.), Eating disorders: An international comprehensive view (pp. 7–18). &quot;Springer Nature Switzerland AG&quot;. https://doi.org/10.1007/978-3-031-46096-8_9

Wolfgang, A. S., &amp; Hoge, C. W. (2023). Psychedelic-Assisted Therapy in Military and Veterans Healthcare Systems: Clinical, Legal, and Implementation Considerations. &quot;Current psychiatry reports, 25&quot;(10), 513–532. https://doi.org/10.1007/s11920-023-01446-4 

Zanella, E., &amp; Lee, E. (2022). Integrative review on psychological and social risk and prevention factors of eating disorders including anorexia nervosa and bulimia nervosa: seven major theories. &quot;Heliyon, 8&quot;(11), e11422. https://doi.org/10.1016/j.heliyon.2022.e11422 

Zhou, R., Zhang, L., Liu, Z., &amp; Cao, B. (2025). Emotion regulation difficulties and disordered eating in adolescents and young adults: a meta-analysis. &quot;Journal of eating disorders, 13&quot;(1), 25. https://doi.org/10.1186/s40337-025-01197-y

}}

==External links==
* [https://www.abct.org/fact-sheets/psychedelic-assisted-therapy/ Psychedelic-Assisted Therapy | Fact Sheet] (ABCT - Association for Behavioral and Cognitive Therapies)
* [https://podcasts.apple.com/au/podcast/can-magic-mushrooms-help-treat-anorexia/id189330872?i=1000784809236 Can magic mushrooms help treat anorexia?] (Apple Podcasts)
* [https://www.apa.org/news/podcasts/speaking-of-psychology/eating-disorder The ‘silent epidemic’ of eating disorders] (American Psychological Association)
* [https://www.apa.org/monitor/2023/04/sensations-eating-disorders-suicidal-behavior What is interoception, and how does it affect mental health]? 5 questions for April Smith (American Psychological Association)
* [https://www.cbte.co/what-is-cbte/transdiagnostic-view-eating-disorders/ Transdiagnostic view of eating disorders] (cbte.co)
* [https://psychedelic.support/resources/polyvagal-theory-mind-body-dr-erica-zelfand/ Polyvagal Theory with Dr. Erica Zelfand: Mind-Body Connection] ·(Psychedelic Support)
* [https://www.wholeselfnutrition.org/post/nervous-system-regulation-a-missing-piece-in-eating-disorder-recovery Nervous System Regulation: A Missing Piece in Eating Disorder Recovery]  (wholeselfnutrition.org)
* [https://youtu.be/RwS-CHJcCiY?si=157viTWiOGAQ-7LP Best Neural Entropy - Explainer] (Youtube)

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      <text bytes="37650" sha1="0xinkztx8zlyqc8fb80vb1dfqoulwrt" xml:space="preserve">{{title|Psychedelic treatment of eating disorders:&lt;br&gt;How might psychedelic-assisted therapy influence psychological mechanisms involved in eating disorders?}}
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== Overview ==
{{RoundBoxTop|theme=7}}[[File:Neural network - Midjourney and Grok.png|thumb|'''Figure 1.''' Psychedelics are thought to temporarily disrupt rigid neural communication pathways by promoting more flexible patterns of connectivity across networks involved in mood regulation, fear processing, reward learning, and cognitive adaptability. These changes may support therapeutic shifts in behaviour and emotional processing (Hatzipantelis &amp; Olson, 2025).]]Emma, a 27‑year‑old from Canberra, has lived with an eating disorder for nearly two decades. She describes her problem eating behaviours to have started at school, after being bullied about her appearance and experiencing an unsteady home life. Ever since, they have remained in her life as “a way for me to feel in control”. Although she is aware of the harm caused by restrictive eating and compulsive exercise, she feels trapped in her thought patterns characterised by a preoccupation about food and weight concerns, as they've become entrenched in her daily life. 

After reading an article describing emerging research suggesting that psychedelics may alter patterns of neural connectivity that shape behaviour (see Figure 1), she expressed interest in pursuing psychedelic‑assisted therapy through a provider accessible to her.

After participating in her first supervised psilocybin‑assisted therapy session, Emma reported experiencing an emotional journey that allowed her to feel “connected to my body for the first time in years”. After 3 months, she has noticed a shift in how she relates to her body, and is finding it easier to actively call into question how she responds to distress with the support of her psychotherapist. 


Her experience raises a central question: What psychological mechanisms could explain these changes?{{RoundBoxBottom|theme=3}}  

This chapter explores how psychedelic‑assisted therapy (PAT) may influence the emotional, cognitive, and neurobiological processes that underpin eating disorders (EDs).   

{{RoundBoxTop|theme=11}}'''Focus questions'''
{{ic|}}Two central questions will be addressed:
* What psychological processes underpin eating disorders, and how do they guide ED behaviour?
* How might psychedelic‑assisted therapy influence these processes and support recovery?
{{ic|}}{{ic|}}{{RoundBoxBottom}}

== Introduction ==
'''Eating Disorders'''  

[[wikipedia:Eating_disorder|Eating disorders]] (EDs) are psychiatric conditions characterised by abnormal eating behaviours that negatively affect physical and mental health. In Australia, the prevalence of EDs is rising particularly among young people. The economic burden is estimated to cost the nation $84 billion, with approximately 10.46% of the population having experienced an ED at some point in their lives (Hay et al., 2023). Although other forms of disordered eating exist, this chapter will focus on only three of them (see table 1), as [[wikipedia:Anorexia|Anorexia Nervosa]] (AN) has the highest mortality rate of any psychiatric disorder, while [[wikipedia:Bulimia|Bulimia Nervosa]] (BN) and [[wikipedia:Binge_eating_disorder|Binge‑Eating Disorder]] (BED) are also highly prevalent. The EDs mentioned are most associated with chronic illness, disability, reduced quality of life, increased suicide risk, and are highly comorbid with [[wikipedia:Mood_disorder|mood disorders]], [[wikipedia:Post-traumatic_stress_disorder|post-traumatic stress disorder]] (PTSD), [[wikipedia:Obsessive–compulsive_disorder|obsessive-compulsive disorder]] (OCD), and [[wikipedia:Substance_use_disorder|substance use disorders]] (Calder et al., 2023).  Despite decades of research, the pathogenesis of EDs remains incompletely understood. Current evidence suggests a complex interplay between genetic predisposition, temperament, hormonal dysregulation, cognitive abnormalities, sociocultural pressures, and traumatic experiences (Calder et al., 2023).  
{| class=&quot;wikitable&quot;
|+Table 1. Eating Disorders and Associated Symptoms 
!Eating Disorder
!Primary Symptoms
|-
|Anorexia Nervosa
|Severe caloric restriction, fear of gaining weight, distorted body image, preoccupation with weight loss, compulsive exercise.
|-
|Bullimia Nervosa
|Intense windows of food intake (binge eating) followed by inappropriate compensatory behaviours also known as 'purging' (eg. vomiting, laxative use), feelings of guilt and loss of control.
|-
|Binge-Eating Disorder
|Recurrent episodes of binge eating not followed by inappropriate compensatory behaviours, feelings of distress and loss of control.
(Wanderlich &amp; Attia., 2024)
|}


Although cognitive‑behavioural therapy (CBT‑E) combined with pharmacological treatment has demonstrated beneficial outcomes, efficacy remains limited and varies across ED types (Calder et al., 2023). Recovery is often long and difficult, with only two‑thirds of individuals with AN and BN eventually recovering, while others can remain ill for many years. This highlights the need for treatment approaches that can accelerate recovery and provide benefit for individuals who do not respond to conventional therapies.


'''Psychedelic-Assisted Therapy'''

In 2023, Australia legalised the prescription of MDMA and psilocybin under professional supervision, marking a significant shift in mental‑health treatment options. Psychedelic compounds, including [[wikipedia:LSD|LSD]], [[wikipedia:Psilocybin|psilocybin]], [[wikipedia:Dimethyltryptamine|DMT]], [[wikipedia:Ketamine|ketamine]], and [[wikipedia:MDMA|MDMA]], have demonstrated promising therapeutic effects across a wide range of psychiatric conditions. Researchers propose that psychedelics act through psychological and neural mechanisms that increase [[wikipedia:Neuroplasticity|neuroplasticity]], facilitate insight, and foster emotional acceptance (Peled‑Avron et al., 2024). At a neurobiological level, psychedelics influence processes that inform perception, emotion, and behaviour, offering a potential avenue for addressing entrenched ED mechanisms.

PAT differs from pharmacological treatment alone because the drug is administered within a structured therapeutic context designed to maximise safety and clinical benefit (Calder et al., 2023). Treatment typically involves three types of sessions, undertaken numerous times, across several months. Preparatory sessions feature participants undergoing psychoeducation, where a psychotherapist establishes rapport and clear safety protocols. Followed by supervised medication sessions, where the participant has an inward experience with the reassurance of clinicians present in the same space. Lastly, integrative sessions led by the psychotherapist provide an opportunity for individuals to process and explore insights from the previous session, in aims to facilitate behavioural change (Wolfgang &amp; Hoge, 2023). This combination of pharmacological and psychological intervention is theorised to effectively target underlying psychological mechanisms common across various mental health disorders, illustrating PAT’s potential as a valuable transdiagnostic treatment option. 

PAT has become a subject of increasing popularity in ED research because many of the psychological mechanisms it is proposed to influence are the same ones implicated in ED maintenance and comorbidities (Calder et al., 2023; Peled-Avron et al., 2024). Early research, including case study reports, small clinical studies, meta-analyses and reviews indicate that PAT produces improvements in affect, reductions in ED symptom severity, enhanced body image, weight restoration, and reductions in comorbid symptoms. Although preliminary, these findings indicate that PAT may disrupt and promote shifts away from maladaptive coping patterns that become entrenched in treatment resistant ED populations.

== Psychological Mechanisms in Eating Disorders ==


'''Emotion Dysregulation'''

Emotion dysregulation is considered to be a significant risk factor for the onset and maintenance of EDs. It refers to difficulties recognising, assessing, and modifying emotional responses to meet situational demands (Zhou et al., 2025). 

Research consistently shows that individuals with EDs experience significant challenges in regulating emotions, increasing their vulnerability to comorbid symptoms, which contribute to the emergence of disordered eating patterns (Leppanen et al., 2022). This idea is supported by affect regulation theory which posits that eating disorders develop and are maintained as maladaptive strategies to manage, tolerate and escape from negative emotions and psychological distress (Schaefer et al., 2020; Zanella &amp; Lee, 2022). This is further exemplified in Fitzsimmons &amp; Bardone-Cone’s article examining differences in coping within eating disorder patients (2010). The authors explain that avoidance and emotion-oriented coping styles often function as maladaptive attempts to manage (di)stress. They explain that behaviours such as binge eating, purging, starvation, and/or compulsive exercise provide temporary relief by shifting attention away from uncomfortable emotions. 

Furthermore, alexithymia, characterised by difficulty identifying and describing one’s own emotions, is strongly associated with ED pathology (Shank et al., 2019). Individuals with high alexithymia often struggle to differentiate emotional states from bodily sensations, contributing to behaviours such as emotional eating, eating in the absence of hunger, or rigid restriction. In BED, alexithymia is linked to binge episodes triggered by poorly understood emotional cues, while in AN and BN, alexithymia may contribute to emotional avoidance and reliance on ED behaviours for affect regulation. 

The effects of trauma are contributing factors to emotion dysregulation, and considered a risk factor for ED development. Individuals who experience sexual, physical, or emotional abuse, neglect, and bullying are likely to experience heightened emotional reactivity, threat perception, and avoidance behaviours (Calder et al., 2023). Researchers explain that trauma often results in lowered distress tolerance and increased reliance on maladaptive coping behaviours, including disordered eating. Furthermore, PTSD comorbidity is common, hence trauma‑related symptoms are hypothesised to frequently interact with ED behaviours in complex ways.  


'''Reward Processing Dysfunction'''
[[File:Striatum.gif|thumb|'''Figure 2.''' Striatum]]
[[File:Anterior cingulate gyrus animation.gif|thumb|'''Figure 3'''. Anterior Cingulate Cortex ]]
Abnormal reward valuation is understood to be a central psychological mechanism that maintains ED behaviours. Research consistently shows that individuals with eating disorders display altered neural activity response to various stimuli, as well as disruptions in reinforcement learning (Calder et al., 2023). Brain regions involved in reward processing, habit formation, and learning, such as the striatum and anterior cingulate cortex (see figures 2 &amp; 3), exhibit atypical activation patterns and differences in dopamine receptor binding across ED types. The insula (see figure 4), which integrates bodily sensations with conscious thought, emotion, and behaviour, also shows altered responses. Together, these regions have been shown to react differently to food images, taste, and social feedback compared to healthy controls, indicating that reward dysfunction extends beyond eating‑related stimuli for ED populations.
[[File:Insular cortex.gif|thumb|'''Figure 4.''' Insula. ]]
In the context of BN and BED, research shows that food is valued more highly than other types of rewards, thus shaping behaviour through its heightened influence on reward outcomes (Calder et al., 2023). Compulsive behaviours specific to each condition (e.g. bingeing, purging) are therefore more likely to occur when food is overvalued and alternative rewards are discounted or ignored. In addition to the neural changes already described, BN and BED are associated with reduced structural and functional connectivity between frontal control regions and the striatum. This combination of highly salient food rewards, and weakened fronto‑striatal pathways, reduces an individual’s ability to inhibit or modulate reward‑seeking impulses. Weak connectivity in these circuits is thought to predict compulsive reward‑seeking behaviour. As a result, even when individuals experience negative consequences from binge episodes, they may struggle to learn from these outcomes or adjust their behaviour accordingly.


Anhedonia, a global reduction in reward responsiveness, is frequently reported by people who experience AN, resulting in food and eating becoming undervalued or aversive to them (Calder et al., 2023). Researchers propose that reward contamination further contributes to this pattern, where the brain learns to associate normally punishing stimuli (e.g., starvation, excessive exercise) with reward, while normally rewarding stimuli (e.g., high‑calorie foods) become experienced as punishment. Structural reductions in the striatum and somatosensory cortex have also been observed, which accounts for distorted bodily sensations and contributes to anhedonia. These changes support maladaptive conditioning in which starvation and weight loss embody a sense of safety, achievement, and emotional relief. Restrictive and preoccupied behaviours centred on food, body shape, and exercise are therefore reinforced over time.

Consistent with affect‑regulation models, eating‑disorder behaviours also become negatively reinforced because they reduce emotional discomfort. This relief increases the likelihood that the behaviours will be repeated, further embedding them within the individual’s coping pattern.


'''Cognitive Rigidity'''

Cognitive rigidity refers to inflexible thinking and behavioural patterns, including difficulty adapting to new information and modifying behaviour. Researchers believe that individuals with EDs often exhibit rigid beliefs about food and weight which interact with a need to exert control over negative emotions. This interaction is the proposed process in which compulsive behaviours and obsessive thoughts develop (Calder et al., 2023). In AN, rigidity manifests as strict dietary rules and fear of losing control, while in BN and BED, binge episodes may feel compulsive and uncontrollable.


'''Interoceptive Awareness'''

Interoceptive awareness (IA) refers to the ability to recognise and process internal bodily states such as hunger, satiety, pain, and arousal. IA is impaired across EDs, and contributes to body mistrust, distorted hunger cues, and inappropriate responses to internal sensations (Brown et al., 2020). Individuals may ignore physical discomfort, misinterpret bodily signals, or avoid sensations altogether, reinforcing maladaptive coping.      

 &lt;blockquote&gt;'''''QUIZ: Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{What coping style do people who experience EDs tend to show?
|type=&quot;()&quot;}
+ Avoidance-oriented
- Problem-oriented

{Compulsive behaviours are more likely to occur when food is ... and alternative rewards are ...
|type=&quot;()&quot;}
- undervalued; overvalued
+ overvalued; undervalued
&lt;/quiz&gt;&lt;/blockquote&gt;

== Psychological Mechanisms of Psychedelic-Assisted Therapy ==

PAT is proposed to influence several psychological mechanisms implicated in EDs, particularly those discussed in the previous section. The next part of this chapter aims to examine the theorised therapeutic mechanisms PAT possesses and practical implications for ED treatment.  


'''Emotion Regulation''' 

Emotion dysregulation is a core mechanism implicated in EDs. Affect regulation theory proposes that ED behaviours emerge as maladaptive strategies to escape, reduce, or blunt overwhelming emotional experiences (Schaefer et al., 2020). Restriction, bingeing, purging, and compulsive exercise may temporarily alleviate distress while reinforcing avoidance-oriented coping and limiting opportunities to learn more adaptive ways of responding to difficult emotions. 

Psychedelics often evoke intense emotional experiences that may disrupt habitual avoidance patterns. Researchers propose that, during psychedelic sessions, attempts to suppress or avoid difficult emotions can intensify these experiences, creating conditions in which emotional acceptance becomes a preferred response (Calder et al., 2023). Although this shift does not occur in every individual, experiencing difficult emotions without resorting to ED behaviours may weaken the association between emotional distress and maladaptive coping, particularly when emotional acceptance becomes associated with a more positive or tolerable experience.

The therapeutic value of this process lies in its potential to reshape affective responses. When individuals experience strong emotions without engaging in maladaptive behaviours, they may begin to develop a new approach towards emotional tolerance. Integration sessions can consolidate this learning by helping individuals articulate, differentiate, and reflect on the emotions experienced during dosing. This process may support the development of more adaptive coping strategies, including task-oriented, problem-focused, and socially supported approaches, which are associated with improved ED outcomes (Fitzsimmons &amp; Bardone-Cone, 2010). In this way, PAT may strengthen emotion regulation and reduce reliance on ED behaviours as strategies for managing affect. 


'''Reward Processing''' 

Reward dysfunction may contribute to the maintenance of EDs by reinforcing maladaptive behaviours while diminishing the perceived value of adaptive rewards. Predictive coding provides a useful framework for understanding how PAT might influence these processes. Individuals with EDs may hold rigid beliefs, conceptualised as high-level priors, about themselves in relation to food, body weight, and rewarding behaviours (Calder et al., 2023; Mograbi et al., 2024). These beliefs can influence how experiences are perceived and valued, potentially reinforcing existing behavioural patterns. Psychedelics are proposed to weaken high-level priors, allowing bottom-up sensory information to exert greater influence on perception and the valuation of experiences. 

During psychedelic experiences, individuals frequently report a heightened appreciation of sensory, social, and bodily experiences. This shift may counteract anhedonia and support the revaluation of previously feared or avoided stimuli. The therapeutic opportunity lies in translating these temporary changes in perception and reward into meaningful behavioural change. Integration sessions can explore positive and negative moments experienced during dosing and connect them to concrete goals. An example of this, inspired from Calder et al.’s (2023) article, could be to clarify specific plans to nourish the body due to the participant having experienced themselves as a decaying skeleton followed by the realisation of the body being a gift. If the period following dosing provides an opportunity for increased neuroplasticity, it may also be particularly conducive to reinforcing adaptive reward learning through behavioural activation with the help of a therapist. 


'''Cognitive Flexibility''' 

Cognitive rigidity is a hallmark of EDs and is characterised by inflexible beliefs about food, weight, body shape, and control. Predictive coding provides a framework for understanding this rigidity, as EDs may involve entrenched priors that resist updating even when confronted with contradictory sensory evidence (Zanella &amp; Lee, 2022). Psychedelics are proposed to disrupt these entrenched priors by increasing neural entropy and reducing the dominance of top-down processing (Calder et al., 2023). This temporary loosening of cognitive constraints may allow individuals to consider alternative perspectives and question long-held beliefs. 

Experiences of ego dissolution may further contribute to cognitive flexibility by reducing attachment to rigid self-concepts (Peled-Avron, 2024; Mograbi et al., 2024). When the boundaries of the self become less defined, individuals may find it easier to question identity-related beliefs that sustain ED pathology. Integration sessions can harness this potential flexibility by supporting cognitive reframing, encouraging behavioural experiments, and strengthening metacognitive awareness. Through these processes, individuals may be better able to translate insights gained during psychedelic experiences into sustained changes in thinking and behaviour.


'''Reconnecting with Bodily Signals'''

Interoceptive deficits are central to ED pathology, contributing to body mistrust, distorted perceptions of hunger cues, and difficulties responding appropriately to internal sensations (Brown et al., 2020). Psychedelics may enhance interoceptive awareness by altering sensory processing and increasing sensitivity to bodily signals. This proposed mechanism is closely related to autonomic regulation, for which polyvagal theory provides a framework for understanding the relationship between bodily signals, emotional regulation, and perceived safety.

Polyvagal theory emphasises the role of the vagus nerve in interoception, emotional regulation, and the perception of safety (Porges, 2022). Vagal afferents transmit information from the body to the insula, where interoceptive signals are integrated with emotional and cognitive processes. Individuals with EDs may exhibit chronic sympathetic arousal and reduced vagal tone, potentially impairing interoceptive accuracy and contributing to emotional rigidity. Psychedelics may initially increase sympathetic activity, as reflected in physiological responses such as increased heart rate, followed by a parasympathetic shift associated with greater relaxation and an increased capacity for rest (Li et al., 2025). Within a polyvagal framework, these changes may have implications for vagal regulation, interoceptive awareness, and emotional regulation.

The therapeutic value of this proposed mechanism lies in its potential to restore trust in bodily signals. Integration sessions may support this process by helping individuals explore bodily sensations experienced during dosing, connect interoceptive cues with emotional states, and practise interoceptive exposure to hunger, fullness, and anxiety-related sensations. Incorporating mindfulness techniques may further support autonomic regulation and help individuals develop a more adaptive relationship with their bodily experiences.

 A Brief Note Concerning The Gut-Brain Interaction 
Although gut microbiome disruption is not a direct psychological mechanism in EDs, it is a relevant biological factor to consider when examining the potential effects of PAT. Restrictive or chaotic eating patterns can contribute to gut dysbiosis, which may weaken gut-barrier integrity and contribute to inflammation affecting the brain (Anton-Paduraru et al., 2024). These changes have been shown to influence mood, stress responsivity, cognitive rigidity, and interoceptive awareness through [[wikipedia:Hypothalamic–pituitary–adrenal_axis|HPA-axis activation]], altered neurotransmitter synthesis, and disrupted hunger–satiety signalling. 

Emerging research suggests that psychedelics may also interact with the gut–brain axis. Certain microbes can metabolise psychedelic compounds, and microbial activity has been associated with modulatory effects on behavioural outcomes. Additionally, psychedelic use may alter microbial composition towards anti-inflammatory profiles, with potential implications for neuroplasticity, neurotransmitter synthesis and signalling improvements (Caspani et al., 2024). These microbiome-related effects may therefore contribute to changes in mood, cognitive flexibility, and appetite regulation.

Although the therapeutic potential of psychedelics in EDs is considered primarily in relation to psychological mechanisms, including changes in perception, emotional processing, and reduced avoidance, microbiome-related effects may represent an additional pathway through which biological processes influence psychological outcomes. However, the extent to which these interactions contribute to therapeutic outcomes in EDs remains to be established.


&lt;blockquote&gt;'''QUIZ: ''Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{ In predictive coding terms, what are “high‑level priors” in eating disorders? 
|type=&quot;()&quot;}
+ Rigid, entrenched beliefs about food, weight, and the self that shape perception and behaviour
- Flexible beliefs that easily update with new sensory information
- Momentary emotional reactions triggered by external cues

{What is the proposed mechanism by which psychedelics support emotion regulation in PAT for EDs? 
|type=&quot;()&quot;}
- By suppressing emotional intensity to prevent distress
+ By evoking strong emotions that disrupt avoidance patterns and promote emotional acceptance
- By eliminating negative emotions through serotonin release

{What is interoceptive awareness?
|type=&quot;()&quot;}
- The ability to evaluate reward value and anticipate pleasurable outcomes
+ The capacity to sense, interpret, and respond to internal bodily signals such as hunger, fullness, and emotional arousal
- The process of weakening cognitive rigidity through ego dissolution
&lt;/quiz&gt;&lt;/blockquote&gt;

== Limitations ==
Despite the potential of PAT to influence psychological mechanisms implicated in EDs, several limitations constrain current understanding of these processes and their therapeutic relevance. Research examining emotion dysregulation in EDs illustrates broader challenges in establishing the mechanisms underlying these conditions. Although non-acceptance of emotions has been identified as a transdiagnostic risk factor across psychiatric conditions (Paulus et al., 2021), Zhou et al.’s meta-analysis (2025) highlights that the causal pathways linking emotional dysregulation and EDs remain unclear, largely because of a lack of experimental and longitudinal studies. Further limitations include restricted availability of measurement scales, insufficient cultural specificity, heterogeneity across samples, gender imbalance, and limited developmental analysis. Together, these factors constrain understanding of how specific emotional processes relate to different ED presentations across the lifespan and stages of recovery.

These limitations are also relevant when considering the proposed mechanisms of PAT. Although existing theoretical frameworks offer ways to conceptualise how psychedelic experiences may influence psychological processes responsible for EDs, the emerging nature of psychedelic therapy limits the extent to which proposed mechanisms have been tested. However, with the number of clinical trials increasing as of recently, it will be interesting to see how the theorised therapeutic mechanisms across different ED presentations and stages of recovery emerges during further warranted investigation.

Nevertheless, current limitations in the evidence highlight the need for research that clarifies the relationships between psychological processes that underscore ED behaviours, and treatment outcomes. There are several important psychological components of ED maintenance that represent meaningful targets for treatment, but they should not be considered in isolation from eachother or the neurobiological processes that influence them. A more comprehensive understanding of how these mechanisms interact may help clarify the therapeutic potential of PAT and inform the development of more targeted treatment approaches.

== Conclusion ==
PAT offers a potential framework for addressing several interconnected psychological mechanisms implicated in EDs. Through its proposed effects on emotional processing, reward valuation, cognitive flexibility, and interoceptive awareness, PAT may create opportunities to disrupt established patterns of avoidance, rigid thinking, and maladaptive behavioural reinforcement. The gut–brain interaction may represent an additional biological pathway relevant to these processes.

These mechanisms should not be understood as independent processes. Changes in emotion regulation may influence the ability to tolerate bodily sensations, while shifts in reward valuation and cognitive flexibility may create opportunities to respond differently to distress and challenge entrenched beliefs. However, the extent to which PAT produces these changes, and whether they translate into sustained improvements in ED outcomes, requires further investigation, although preliminary evidence is promising. 

The therapeutic potential of PAT lies not only in the acute psychedelic experience but also in the structured integration process that follows. Integration sessions provide an opportunity to translate emotional breakthroughs, changes in cognitive flexibility, interoceptive shifts, and reward processing into sustained behavioural change. Effective integration involves helping individuals articulate insights, connect them to ED-related patterns, and develop concrete strategies for change. These may include strengthening adaptive coping, challenging rigid beliefs, practising interoceptive awareness, reinforcing positive reward experiences, and supporting nutritional rehabilitation.

By grounding the understanding of PAT in affect regulation theory and the predictive coding framework, therapists may be better positioned to help individuals explore how psychedelic experiences could disrupt maladaptive emotional and cognitive patterns and create opportunities for new learning. Polyvagal-informed approaches may further support the development of mind–body awareness and emotional regulation through mindfulness strategies. Together, these approaches offer a multifaceted framework for translating psychedelic experiences into therapeutic change and addressing the interconnected mechanisms that maintain EDs and associated suffering. 

==See Also==
* [https://w.wiki/TsdG Ayahuasca and the brain] (Wikiversity)
* [https://w.wiki/TscF Emotional effects of psychedelics] (Wikiversity)
* [https://w.wiki/Tsdb Psilocybin and emotion] (Wikiversity)
* [https://w.wiki/TsdS Psilocibyn assisted psychotherapy] (Wikiversity)
* [https://w.wiki/Tsce Psychedelics, altered consciousness, and personal growth] (Wikiversity)
* [[Eating Disorders|Eating disorders]] (Wikiversity)

==References==
{{Hanging indent|1=

{{ic|Try &quot;Edit source&quot; and then wrapping any text to be italicised in two apostrophes e.g., ''this is italics''}}

Anton-Păduraru, D. T., Trofin, F., Nastase, E. V., Miftode, R. S., Miftode, I. L., Trandafirescu, M. F., Cojocaru, E., Țarcă, E., Mindru, D. E., &amp; Dorneanu, O. S. (2023). The Role of the Gut Microbiota in Anorexia Nervosa in Children and Adults-Systematic Review. &quot;International journal of molecular sciences, 25&quot;(1), 41. https://doi.org/10.3390/ijms25010041

Brown, T. A., Vanzhula, I. A., Reilly, E. E., Levinson, C. A., Berner, L. A., Krueger, A., Lavender, J. M., Kaye, W. H., &amp; Wierenga, C. E. (2020). Body mistrust bridges interoceptive awareness and eating disorder symptoms. &quot;Journal of abnormal psychology, 129&quot;(5), 445–456. https://doi.org/10.1037/abn0000516 

Calder, A., Mock, S., Friedli, N., Pasi, P., &amp; Hasler, G. (2023). Psychedelics in the treatment of eating disorders: Rationale and potential mechanisms. &quot;European Neuropsychopharmacology, 75&quot;, 1–14. https://doi.org/10.1016/j.euroneuro.2023.05.008 

Caspani, G., Ruffell, S. G. D., Tsang, W., Netzband, N., Rohani-Shukla, C., Swann, J. R., &amp; Jefferies, W. A. (2024). Mind over matter: the microbial mindscapes of psychedelics and the gut-brain axis. &quot;Pharmacological research, 207&quot;, 107338. https://doi.org/10.1016/j.phrs.2024.107338  

Fitzsimmons, E. E., &amp; Bardone-Cone, A. M. (2010). Differences in coping across stages of recovery from an eating disorder. &quot;The International journal of eating disorders, 43&quot;(8), 689–693. https://doi.org/10.1002/eat.20781 

Hatzipantelis, C. J., &amp; Olson, D. E. (2024). The Effects of Psychedelics on Neuronal Physiology. &quot;Annual review of physiology, 86&quot;, 27–47. https://doi.org/10.1146/annurev-physiol-042022-020923

Hay, P., Aouad, P., Le, A., Marks, P., Maloney, D., National Eating Disorder Research Consortium, Touyz, S., &amp; Maguire, S. (2023). Epidemiology of eating disorders: population, prevalence, disease burden and quality of life informing public policy in Australia-a rapid review. &quot;Journal of eating disorders, 11&quot;(1), 23. https://doi.org/10.1186/s40337-023-00738-7

Li, H., Wang, H., &amp; Wang, X. (2025). Psychedelics and the Autonomic Nervous System: A Perspective on Their Interplay and Therapeutic Potential. &quot;ACS pharmacology &amp; translational science, 8&quot;(3), 899–902. https://doi.org/10.1021/acsptsci.5c00005 

Leppanen, J., Brown, D., McLinden, H., Williams, S., &amp; Tchanturia, K. (2022). The Role of Emotion Regulation in Eating Disorders: A Network Meta-Analysis Approach. &quot;Frontiers in psychiatry, 13&quot;, 793094. https://doi.org/10.3389/fpsyt.2022.793094 

Mograbi, D. C., Rodrigues, R., Bienemann, B., &amp; Huntley, J. (2024). Brain Networks, Neurotransmitters and Psychedelics: Towards a Neurochemistry of Self-Awareness. &quot;Current neurology and neuroscience reports, 24&quot;(8), 323–340. https://doi.org/10.1007/s11910-024-01353-y

Paulus F. W., Ohmann S., Möhler E., Plener P. &amp; Popow C. (2021). Emotional Dysregulation in Children and Adolescents With Psychiatric Disorders. A Narrative Review. &quot;Frontiers in Psychiatry 12&quot;:628252. doi: 10.3389/fpsyt.2021.628252

Peled-Avron L., Aday J. Ss, Kalafateli A. L., Hamilton H. K., Woolley J. D. (2024). Editorial: Down the rabbit hole – the psychological and neural mechanisms of psychedelic compounds and their use in treating mental health and medical conditions. &quot;Frontiers in Psychiatry 15&quot;:1431389. doi: 10.3389/fpsyt.2024.1431389

Porges S. W. (2025). Polyvagal Theory: Current Status, Clinical Applications, and Future Directions. &quot;Clinical neuropsychiatry, 22&quot;(3), 169–184. https://doi.org/10.36131/cnfioritieditore20250301

Schaefer, L. M., Smith, K. E., Anderson, L. M., Cao, L., Crosby, R. D., Engel, S. G., Crow, S. J., Peterson, C. B., &amp; Wonderlich, S. A. (2020). The role of affect in the maintenance of binge-eating disorder: Evidence from an ecological momentary assessment study. &quot;Journal of abnormal psychology, 129&quot;(4), 387–396. https://doi.org/10.1037/abn0000517 

Shank, L. M., Tanofsky-Kraff, M., Kelly, N. R., Jaramillo, M., Rubin, S. G., Altman, D. R., Byrne, M. E., LeMay-Russell, S., Schvey, N. A., Broadney, M. M., Brady, S. M., Yang, S. B., Courville, A. B., Ramirez, S., Crist, A. C., Yanovski, S. Z., &amp; Yanovski, J. A. (2019). The association between alexithymia and eating behavior in children and adolescents. &quot;Appetite, 142&quot;, 104381. https://doi.org/10.1016/j.appet.2019.104381

Wonderlich, J., &amp; Attia, E. (2024). Eating disorders in the DSM-5. In P. Robinson, T. Wade, B. Herpertz-Dahlmann, F. Fernandez-Aranda, J. Treasure, &amp; S. Wonderlich (Eds.), Eating disorders: An international comprehensive view (pp. 7–18). &quot;Springer Nature Switzerland AG&quot;. https://doi.org/10.1007/978-3-031-46096-8_9

Wolfgang, A. S., &amp; Hoge, C. W. (2023). Psychedelic-Assisted Therapy in Military and Veterans Healthcare Systems: Clinical, Legal, and Implementation Considerations. &quot;Current psychiatry reports, 25&quot;(10), 513–532. https://doi.org/10.1007/s11920-023-01446-4 

Zanella, E., &amp; Lee, E. (2022). Integrative review on psychological and social risk and prevention factors of eating disorders including anorexia nervosa and bulimia nervosa: seven major theories. &quot;Heliyon, 8&quot;(11), e11422. https://doi.org/10.1016/j.heliyon.2022.e11422 

Zhou, R., Zhang, L., Liu, Z., &amp; Cao, B. (2025). Emotion regulation difficulties and disordered eating in adolescents and young adults: a meta-analysis. &quot;Journal of eating disorders, 13&quot;(1), 25. https://doi.org/10.1186/s40337-025-01197-y

}}

==External links==
* [https://www.abct.org/fact-sheets/psychedelic-assisted-therapy/ Psychedelic-Assisted Therapy | Fact Sheet] (ABCT - Association for Behavioral and Cognitive Therapies)
* [https://podcasts.apple.com/au/podcast/can-magic-mushrooms-help-treat-anorexia/id189330872?i=1000784809236 Can magic mushrooms help treat anorexia?] (Apple Podcasts)
* [https://www.apa.org/news/podcasts/speaking-of-psychology/eating-disorder The ‘silent epidemic’ of eating disorders] (American Psychological Association)
* [https://www.apa.org/monitor/2023/04/sensations-eating-disorders-suicidal-behavior What is interoception, and how does it affect mental health]? 5 questions for April Smith (American Psychological Association)
* [https://www.cbte.co/what-is-cbte/transdiagnostic-view-eating-disorders/ Transdiagnostic view of eating disorders] (cbte.co)
* [https://psychedelic.support/resources/polyvagal-theory-mind-body-dr-erica-zelfand/ Polyvagal Theory with Dr. Erica Zelfand: Mind-Body Connection] ·(Psychedelic Support)
* [https://www.wholeselfnutrition.org/post/nervous-system-regulation-a-missing-piece-in-eating-disorder-recovery Nervous System Regulation: A Missing Piece in Eating Disorder Recovery]  (wholeselfnutrition.org)
* [https://youtu.be/RwS-CHJcCiY?si=157viTWiOGAQ-7LP Best Neural Entropy - Explainer] (Youtube)

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      <text bytes="37657" sha1="qqqnyj9zz2l38z2ivfh1p07otvdpxep" xml:space="preserve">{{title|Psychedelic treatment of eating disorders:&lt;br&gt;How might psychedelic-assisted therapy influence psychological mechanisms involved in eating disorders?}}
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== Overview ==
{{RoundBoxTop|theme=7}}[[File:Neural network - Midjourney and Grok.png|thumb|'''Figure 1.''' Psychedelics are thought to temporarily disrupt rigid neural communication pathways by promoting more flexible patterns of connectivity across networks involved in mood regulation, fear processing, reward learning, and cognitive adaptability. These changes may support therapeutic shifts in behaviour and emotional processing (Hatzipantelis &amp; Olson, 2025).]]Emma, a 27‑year‑old from Canberra, has lived with an eating disorder for nearly two decades. She describes her problem eating behaviours to have started at school, after being bullied about her appearance and experiencing an unsteady home life. Ever since, they have remained in her life as “a way for me to feel in control”. Although she is aware of the harm caused by restrictive eating and compulsive exercise, she feels trapped in her thought patterns characterised by a preoccupation about food and weight concerns, as they've become entrenched in her daily life. 

After reading an article describing emerging research suggesting that psychedelics may alter patterns of neural connectivity that shape behaviour (see Figure 1), she expressed interest in pursuing psychedelic‑assisted therapy through a provider accessible to her.

After participating in her first supervised psilocybin‑assisted therapy session, Emma reported experiencing an emotional journey that allowed her to feel “connected to my body for the first time in years”. After 3 months, she has noticed a shift in how she relates to her body, and is finding it easier to actively call into question how she responds to distress with the support of her psychotherapist. 


Her experience raises a central question: What psychological mechanisms could explain these changes?{{RoundBoxBottom|theme=3}}  

This chapter explores how psychedelic‑assisted therapy (PAT) may influence the emotional, cognitive, and neurobiological processes that underpin eating disorders (EDs).   

{{RoundBoxTop|theme=11}}'''Focus questions'''
{{ic|}}Two central questions will be addressed:
* What psychological processes underpin eating disorders, and how do they guide ED behaviour?
* How might psychedelic‑assisted therapy influence these processes and support recovery?
{{ic|}}{{ic|}}{{RoundBoxBottom}}

== Introduction ==
'''Eating Disorders'''  

[[wikipedia:Eating_disorder|Eating disorders]] (EDs) are psychiatric conditions characterised by abnormal eating behaviours that negatively affect physical and mental health. In Australia, the prevalence of EDs is rising particularly among young people. The economic burden is estimated to cost the nation $84 billion, with approximately 10.46% of the population having experienced an ED at some point in their lives (Hay et al., 2023). Although other forms of disordered eating exist, this chapter will focus on only three of them (see table 1), as [[wikipedia:Anorexia|Anorexia Nervosa]] (AN) has the highest mortality rate of any psychiatric disorder, while [[wikipedia:Bulimia|Bulimia Nervosa]] (BN) and [[wikipedia:Binge_eating_disorder|Binge‑Eating Disorder]] (BED) are also highly prevalent. The EDs mentioned are most associated with chronic illness, disability, reduced quality of life, increased suicide risk, and are highly comorbid with [[wikipedia:Mood_disorder|mood disorders]], [[wikipedia:Post-traumatic_stress_disorder|post-traumatic stress disorder]] (PTSD), [[wikipedia:Obsessive–compulsive_disorder|obsessive-compulsive disorder]] (OCD), and [[wikipedia:Substance_use_disorder|substance use disorders]] (Calder et al., 2023).  Despite decades of research, the pathogenesis of EDs remains incompletely understood. Current evidence suggests a complex interplay between genetic predisposition, temperament, hormonal dysregulation, cognitive abnormalities, sociocultural pressures, and traumatic experiences (Calder et al., 2023).  
{| class=&quot;wikitable&quot;
|+Table 1. Eating Disorders and Associated Symptoms 
!Eating Disorder
!Primary Symptoms
|-
|Anorexia Nervosa
|Severe caloric restriction, fear of gaining weight, distorted body image, preoccupation with weight loss, compulsive exercise.
|-
|Bullimia Nervosa
|Intense windows of food intake (binge eating) followed by inappropriate compensatory behaviours also known as 'purging' (eg. vomiting, laxative use), feelings of guilt and loss of control.
|-
|Binge-Eating Disorder
|Recurrent episodes of binge eating not followed by inappropriate compensatory behaviours, feelings of distress and loss of control.
(Wanderlich &amp; Attia., 2024)
|}


Although cognitive‑behavioural therapy (CBT‑E) combined with pharmacological treatment has demonstrated beneficial outcomes, efficacy remains limited and varies across ED types (Calder et al., 2023). Recovery is often long and difficult, with only two‑thirds of individuals with AN and BN eventually recovering, while others can remain ill for many years. This highlights the need for treatment approaches that can accelerate recovery and provide benefit for individuals who do not respond to conventional therapies.


'''Psychedelic-Assisted Therapy'''

In 2023, Australia legalised the prescription of MDMA and psilocybin under professional supervision, marking a significant shift in mental‑health treatment options. Psychedelic compounds, including [[wikipedia:LSD|LSD]], [[wikipedia:Psilocybin|psilocybin]], [[wikipedia:Dimethyltryptamine|DMT]], [[wikipedia:Ketamine|ketamine]], and [[wikipedia:MDMA|MDMA]], have demonstrated promising therapeutic effects across a wide range of psychiatric conditions. Researchers propose that psychedelics act through psychological and neural mechanisms that increase [[wikipedia:Neuroplasticity|neuroplasticity]], facilitate insight, and foster emotional acceptance (Peled‑Avron et al., 2024). At a neurobiological level, psychedelics influence processes that inform perception, emotion, and behaviour, offering a potential avenue for addressing entrenched ED mechanisms.

PAT differs from pharmacological treatment alone because the drug is administered within a structured therapeutic context designed to maximise safety and clinical benefit (Calder et al., 2023). Treatment typically involves three types of sessions, undertaken numerous times, across several months. Preparatory sessions feature participants undergoing psychoeducation, where a psychotherapist establishes rapport and clear safety protocols. Followed by supervised medication sessions, where the participant undergoes the inward experience with the reassurance of clinicians present in the same space. Lastly, integrative sessions led by the psychotherapist provide an opportunity for individuals to process and explore insights from the previous session, in aims to facilitate behavioural change (Wolfgang &amp; Hoge, 2023). This combination of pharmacological and psychological intervention is theorised to effectively target underlying psychological mechanisms common across various mental health disorders, illustrating PAT’s potential as a valuable transdiagnostic treatment option. 

PAT has become a subject of increasing popularity in ED research because many of the psychological mechanisms it is proposed to influence are the same ones implicated in ED maintenance and comorbidities (Calder et al., 2023; Peled-Avron et al., 2024). Early research, including case study reports, small clinical studies, meta-analyses and reviews indicate that PAT produces improvements in affect, reductions in ED symptom severity, enhanced body image, weight restoration, and reductions in comorbid symptoms. Although preliminary, these findings indicate that PAT may disrupt and promote shifts away from maladaptive coping patterns that become entrenched in treatment resistant ED populations.

== Psychological Mechanisms in Eating Disorders ==


'''Emotion Dysregulation'''

Emotion dysregulation is considered to be a significant risk factor for the onset and maintenance of EDs. It refers to difficulties recognising, assessing, and modifying emotional responses to meet situational demands (Zhou et al., 2025). 

Research consistently shows that individuals with EDs experience significant challenges in regulating emotions, increasing their vulnerability to comorbid symptoms, which contribute to the emergence of disordered eating patterns (Leppanen et al., 2022). This idea is supported by affect regulation theory which posits that eating disorders develop and are maintained as maladaptive strategies to manage, tolerate and escape from negative emotions and psychological distress (Schaefer et al., 2020; Zanella &amp; Lee, 2022). This is further exemplified in Fitzsimmons &amp; Bardone-Cone’s article examining differences in coping within eating disorder patients (2010). The authors explain that avoidance and emotion-oriented coping styles often function as maladaptive attempts to manage (di)stress. They explain that behaviours such as binge eating, purging, starvation, and/or compulsive exercise provide temporary relief by shifting attention away from uncomfortable emotions. 

Furthermore, alexithymia, characterised by difficulty identifying and describing one’s own emotions, is strongly associated with ED pathology (Shank et al., 2019). Individuals with high alexithymia often struggle to differentiate emotional states from bodily sensations, contributing to behaviours such as emotional eating, eating in the absence of hunger, or rigid restriction. In BED, alexithymia is linked to binge episodes triggered by poorly understood emotional cues, while in AN and BN, alexithymia may contribute to emotional avoidance and reliance on ED behaviours for affect regulation. 

The effects of trauma are contributing factors to emotion dysregulation, and considered a risk factor for ED development. Individuals who experience sexual, physical, or emotional abuse, neglect, and bullying are likely to experience heightened emotional reactivity, threat perception, and avoidance behaviours (Calder et al., 2023). Researchers explain that trauma often results in lowered distress tolerance and increased reliance on maladaptive coping behaviours, including disordered eating. Furthermore, PTSD comorbidity is common, hence trauma‑related symptoms are hypothesised to frequently interact with ED behaviours in complex ways.  


'''Reward Processing Dysfunction'''
[[File:Striatum.gif|thumb|'''Figure 2.''' Striatum]]
[[File:Anterior cingulate gyrus animation.gif|thumb|'''Figure 3'''. Anterior Cingulate Cortex ]]
Abnormal reward valuation is understood to be a central psychological mechanism that maintains ED behaviours. Research consistently shows that individuals with eating disorders display altered neural activity response to various stimuli, as well as disruptions in reinforcement learning (Calder et al., 2023). Brain regions involved in reward processing, habit formation, and learning, such as the striatum and anterior cingulate cortex (see figures 2 &amp; 3), exhibit atypical activation patterns and differences in dopamine receptor binding across ED types. The insula (see figure 4), which integrates bodily sensations with conscious thought, emotion, and behaviour, also shows altered responses. Together, these regions have been shown to react differently to food images, taste, and social feedback compared to healthy controls, indicating that reward dysfunction extends beyond eating‑related stimuli for ED populations.
[[File:Insular cortex.gif|thumb|'''Figure 4.''' Insula. ]]
In the context of BN and BED, research shows that food is valued more highly than other types of rewards, thus shaping behaviour through its heightened influence on reward outcomes (Calder et al., 2023). Compulsive behaviours specific to each condition (e.g. bingeing, purging) are therefore more likely to occur when food is overvalued and alternative rewards are discounted or ignored. In addition to the neural changes already described, BN and BED are associated with reduced structural and functional connectivity between frontal control regions and the striatum. This combination of highly salient food rewards, and weakened fronto‑striatal pathways, reduces an individual’s ability to inhibit or modulate reward‑seeking impulses. Weak connectivity in these circuits is thought to predict compulsive reward‑seeking behaviour. As a result, even when individuals experience negative consequences from binge episodes, they may struggle to learn from these outcomes or adjust their behaviour accordingly.


Anhedonia, a global reduction in reward responsiveness, is frequently reported by people who experience AN, resulting in food and eating becoming undervalued or aversive to them (Calder et al., 2023). Researchers propose that reward contamination further contributes to this pattern, where the brain learns to associate normally punishing stimuli (e.g., starvation, excessive exercise) with reward, while normally rewarding stimuli (e.g., high‑calorie foods) become experienced as punishment. Structural reductions in the striatum and somatosensory cortex have also been observed, which accounts for distorted bodily sensations and contributes to anhedonia. These changes support maladaptive conditioning in which starvation and weight loss embody a sense of safety, achievement, and emotional relief. Restrictive and preoccupied behaviours centred on food, body shape, and exercise are therefore reinforced over time.

Consistent with affect‑regulation models, eating‑disorder behaviours also become negatively reinforced because they reduce emotional discomfort. This relief increases the likelihood that the behaviours will be repeated, further embedding them within the individual’s coping pattern.


'''Cognitive Rigidity'''

Cognitive rigidity refers to inflexible thinking and behavioural patterns, including difficulty adapting to new information and modifying behaviour. Researchers believe that individuals with EDs often exhibit rigid beliefs about food and weight which interact with a need to exert control over negative emotions. This interaction is the proposed process in which compulsive behaviours and obsessive thoughts develop (Calder et al., 2023). In AN, rigidity manifests as strict dietary rules and fear of losing control, while in BN and BED, binge episodes may feel compulsive and uncontrollable.


'''Interoceptive Awareness'''

Interoceptive awareness (IA) refers to the ability to recognise and process internal bodily states such as hunger, satiety, pain, and arousal. IA is impaired across EDs, and contributes to body mistrust, distorted hunger cues, and inappropriate responses to internal sensations (Brown et al., 2020). Individuals may ignore physical discomfort, misinterpret bodily signals, or avoid sensations altogether, reinforcing maladaptive coping.      

 &lt;blockquote&gt;'''''QUIZ: Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{What coping style do people who experience EDs tend to show?
|type=&quot;()&quot;}
+ Avoidance-oriented
- Problem-oriented

{Compulsive behaviours are more likely to occur when food is ... and alternative rewards are ...
|type=&quot;()&quot;}
- undervalued; overvalued
+ overvalued; undervalued
&lt;/quiz&gt;&lt;/blockquote&gt;

== Psychological Mechanisms of Psychedelic-Assisted Therapy ==

PAT is proposed to influence several psychological mechanisms implicated in EDs, particularly those discussed in the previous section. The next part of this chapter aims to examine the theorised therapeutic mechanisms PAT possesses and practical implications for ED treatment.  


'''Emotion Regulation''' 

Emotion dysregulation is a core mechanism implicated in EDs. Affect regulation theory proposes that ED behaviours emerge as maladaptive strategies to escape, reduce, or blunt overwhelming emotional experiences (Schaefer et al., 2020). Restriction, bingeing, purging, and compulsive exercise may temporarily alleviate distress while reinforcing avoidance-oriented coping and limiting opportunities to learn more adaptive ways of responding to difficult emotions. 

Psychedelics often evoke intense emotional experiences that may disrupt habitual avoidance patterns. Researchers propose that, during psychedelic sessions, attempts to suppress or avoid difficult emotions can intensify these experiences, creating conditions in which emotional acceptance becomes a preferred response (Calder et al., 2023). Although this shift does not occur in every individual, experiencing difficult emotions without resorting to ED behaviours may weaken the association between emotional distress and maladaptive coping, particularly when emotional acceptance becomes associated with a more positive or tolerable experience.

The therapeutic value of this process lies in its potential to reshape affective responses. When individuals experience strong emotions without engaging in maladaptive behaviours, they may begin to develop a new approach towards emotional tolerance. Integration sessions can consolidate this learning by helping individuals articulate, differentiate, and reflect on the emotions experienced during dosing. This process may support the development of more adaptive coping strategies, including task-oriented, problem-focused, and socially supported approaches, which are associated with improved ED outcomes (Fitzsimmons &amp; Bardone-Cone, 2010). In this way, PAT may strengthen emotion regulation and reduce reliance on ED behaviours as strategies for managing affect. 


'''Reward Processing''' 

Reward dysfunction may contribute to the maintenance of EDs by reinforcing maladaptive behaviours while diminishing the perceived value of adaptive rewards. Predictive coding provides a useful framework for understanding how PAT might influence these processes. Individuals with EDs may hold rigid beliefs, conceptualised as high-level priors, about themselves in relation to food, body weight, and rewarding behaviours (Calder et al., 2023; Mograbi et al., 2024). These beliefs can influence how experiences are perceived and valued, potentially reinforcing existing behavioural patterns. Psychedelics are proposed to weaken high-level priors, allowing bottom-up sensory information to exert greater influence on perception and the valuation of experiences. 

During psychedelic experiences, individuals frequently report a heightened appreciation of sensory, social, and bodily experiences. This shift may counteract anhedonia and support the revaluation of previously feared or avoided stimuli. The therapeutic opportunity lies in translating these temporary changes in perception and reward into meaningful behavioural change. Integration sessions can explore positive and negative moments experienced during dosing and connect them to concrete goals. An example of this, inspired from Calder et al.’s (2023) article, could be to clarify specific plans to nourish the body due to the participant having experienced themselves as a decaying skeleton followed by the realisation of the body being a gift. If the period following dosing provides an opportunity for increased neuroplasticity, it may also be particularly conducive to reinforcing adaptive reward learning through behavioural activation with the help of a therapist. 


'''Cognitive Flexibility''' 

Cognitive rigidity is a hallmark of EDs and is characterised by inflexible beliefs about food, weight, body shape, and control. Predictive coding provides a framework for understanding this rigidity, as EDs may involve entrenched priors that resist updating even when confronted with contradictory sensory evidence (Zanella &amp; Lee, 2022). Psychedelics are proposed to disrupt these entrenched priors by increasing neural entropy and reducing the dominance of top-down processing (Calder et al., 2023). This temporary loosening of cognitive constraints may allow individuals to consider alternative perspectives and question long-held beliefs. 

Experiences of ego dissolution may further contribute to cognitive flexibility by reducing attachment to rigid self-concepts (Peled-Avron, 2024; Mograbi et al., 2024). When the boundaries of the self become less defined, individuals may find it easier to question identity-related beliefs that sustain ED pathology. Integration sessions can harness this potential flexibility by supporting cognitive reframing, encouraging behavioural experiments, and strengthening metacognitive awareness. Through these processes, individuals may be better able to translate insights gained during psychedelic experiences into sustained changes in thinking and behaviour.


'''Reconnecting with Bodily Signals'''

Interoceptive deficits are central to ED pathology, contributing to body mistrust, distorted perceptions of hunger cues, and difficulties responding appropriately to internal sensations (Brown et al., 2020). Psychedelics may enhance interoceptive awareness by altering sensory processing and increasing sensitivity to bodily signals. This proposed mechanism is closely related to autonomic regulation, for which polyvagal theory provides a framework for understanding the relationship between bodily signals, emotional regulation, and perceived safety.

Polyvagal theory emphasises the role of the vagus nerve in interoception, emotional regulation, and the perception of safety (Porges, 2022). Vagal afferents transmit information from the body to the insula, where interoceptive signals are integrated with emotional and cognitive processes. Individuals with EDs may exhibit chronic sympathetic arousal and reduced vagal tone, potentially impairing interoceptive accuracy and contributing to emotional rigidity. Psychedelics may initially increase sympathetic activity, as reflected in physiological responses such as increased heart rate, followed by a parasympathetic shift associated with greater relaxation and an increased capacity for rest (Li et al., 2025). Within a polyvagal framework, these changes may have implications for vagal regulation, interoceptive awareness, and emotional regulation.

The therapeutic value of this proposed mechanism lies in its potential to restore trust in bodily signals. Integration sessions may support this process by helping individuals explore bodily sensations experienced during dosing, connect interoceptive cues with emotional states, and practise interoceptive exposure to hunger, fullness, and anxiety-related sensations. Incorporating mindfulness techniques may further support autonomic regulation and help individuals develop a more adaptive relationship with their bodily experiences.

 A Brief Note Concerning The Gut-Brain Interaction 
Although gut microbiome disruption is not a direct psychological mechanism in EDs, it is a relevant biological factor to consider when examining the potential effects of PAT. Restrictive or chaotic eating patterns can contribute to gut dysbiosis, which may weaken gut-barrier integrity and contribute to inflammation affecting the brain (Anton-Paduraru et al., 2024). These changes have been shown to influence mood, stress responsivity, cognitive rigidity, and interoceptive awareness through [[wikipedia:Hypothalamic–pituitary–adrenal_axis|HPA-axis activation]], altered neurotransmitter synthesis, and disrupted hunger–satiety signalling. 

Emerging research suggests that psychedelics may also interact with the gut–brain axis. Certain microbes can metabolise psychedelic compounds, and microbial activity has been associated with modulatory effects on behavioural outcomes. Additionally, psychedelic use may alter microbial composition towards anti-inflammatory profiles, with potential implications for neuroplasticity, neurotransmitter synthesis and signalling improvements (Caspani et al., 2024). These microbiome-related effects may therefore contribute to changes in mood, cognitive flexibility, and appetite regulation.

Although the therapeutic potential of psychedelics in EDs is considered primarily in relation to psychological mechanisms, including changes in perception, emotional processing, and reduced avoidance, microbiome-related effects may represent an additional pathway through which biological processes influence psychological outcomes. However, the extent to which these interactions contribute to therapeutic outcomes in EDs remains to be established.


&lt;blockquote&gt;'''QUIZ: ''Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{ In predictive coding terms, what are “high‑level priors” in eating disorders? 
|type=&quot;()&quot;}
+ Rigid, entrenched beliefs about food, weight, and the self that shape perception and behaviour
- Flexible beliefs that easily update with new sensory information
- Momentary emotional reactions triggered by external cues

{What is the proposed mechanism by which psychedelics support emotion regulation in PAT for EDs? 
|type=&quot;()&quot;}
- By suppressing emotional intensity to prevent distress
+ By evoking strong emotions that disrupt avoidance patterns and promote emotional acceptance
- By eliminating negative emotions through serotonin release

{What is interoceptive awareness?
|type=&quot;()&quot;}
- The ability to evaluate reward value and anticipate pleasurable outcomes
+ The capacity to sense, interpret, and respond to internal bodily signals such as hunger, fullness, and emotional arousal
- The process of weakening cognitive rigidity through ego dissolution
&lt;/quiz&gt;&lt;/blockquote&gt;

== Limitations ==
Despite the potential of PAT to influence psychological mechanisms implicated in EDs, several limitations constrain current understanding of these processes and their therapeutic relevance. Research examining emotion dysregulation in EDs illustrates broader challenges in establishing the mechanisms underlying these conditions. Although non-acceptance of emotions has been identified as a transdiagnostic risk factor across psychiatric conditions (Paulus et al., 2021), Zhou et al.’s meta-analysis (2025) highlights that the causal pathways linking emotional dysregulation and EDs remain unclear, largely because of a lack of experimental and longitudinal studies. Further limitations include restricted availability of measurement scales, insufficient cultural specificity, heterogeneity across samples, gender imbalance, and limited developmental analysis. Together, these factors constrain understanding of how specific emotional processes relate to different ED presentations across the lifespan and stages of recovery.

These limitations are also relevant when considering the proposed mechanisms of PAT. Although existing theoretical frameworks offer ways to conceptualise how psychedelic experiences may influence psychological processes responsible for EDs, the emerging nature of psychedelic therapy limits the extent to which proposed mechanisms have been tested. However, with the number of clinical trials increasing as of recently, it will be interesting to see how the theorised therapeutic mechanisms across different ED presentations and stages of recovery emerges during further warranted investigation.

Nevertheless, current limitations in the evidence highlight the need for research that clarifies the relationships between psychological processes that underscore ED behaviours, and treatment outcomes. There are several important psychological components of ED maintenance that represent meaningful targets for treatment, but they should not be considered in isolation from eachother or the neurobiological processes that influence them. A more comprehensive understanding of how these mechanisms interact may help clarify the therapeutic potential of PAT and inform the development of more targeted treatment approaches.

== Conclusion ==
PAT offers a potential framework for addressing several interconnected psychological mechanisms implicated in EDs. Through its proposed effects on emotional processing, reward valuation, cognitive flexibility, and interoceptive awareness, PAT may create opportunities to disrupt established patterns of avoidance, rigid thinking, and maladaptive behavioural reinforcement. The gut–brain interaction may represent an additional biological pathway relevant to these processes.

These mechanisms should not be understood as independent processes. Changes in emotion regulation may influence the ability to tolerate bodily sensations, while shifts in reward valuation and cognitive flexibility may create opportunities to respond differently to distress and challenge entrenched beliefs. However, the extent to which PAT produces these changes, and whether they translate into sustained improvements in ED outcomes, requires further investigation, although preliminary evidence is promising. 

The therapeutic potential of PAT lies not only in the acute psychedelic experience but also in the structured integration process that follows. Integration sessions provide an opportunity to translate emotional breakthroughs, changes in cognitive flexibility, interoceptive shifts, and reward processing into sustained behavioural change. Effective integration involves helping individuals articulate insights, connect them to ED-related patterns, and develop concrete strategies for change. These may include strengthening adaptive coping, challenging rigid beliefs, practising interoceptive awareness, reinforcing positive reward experiences, and supporting nutritional rehabilitation.

By grounding the understanding of PAT in affect regulation theory and the predictive coding framework, therapists may be better positioned to help individuals explore how psychedelic experiences could disrupt maladaptive emotional and cognitive patterns and create opportunities for new learning. Polyvagal-informed approaches may further support the development of mind–body awareness and emotional regulation through mindfulness strategies. Together, these approaches offer a multifaceted framework for translating psychedelic experiences into therapeutic change and addressing the interconnected mechanisms that maintain EDs and associated suffering. 

==See Also==
* [https://w.wiki/TsdG Ayahuasca and the brain] (Wikiversity)
* [https://w.wiki/TscF Emotional effects of psychedelics] (Wikiversity)
* [https://w.wiki/Tsdb Psilocybin and emotion] (Wikiversity)
* [https://w.wiki/TsdS Psilocibyn assisted psychotherapy] (Wikiversity)
* [https://w.wiki/Tsce Psychedelics, altered consciousness, and personal growth] (Wikiversity)
* [[Eating Disorders|Eating disorders]] (Wikiversity)

==References==
{{Hanging indent|1=

{{ic|Try &quot;Edit source&quot; and then wrapping any text to be italicised in two apostrophes e.g., ''this is italics''}}

Anton-Păduraru, D. T., Trofin, F., Nastase, E. V., Miftode, R. S., Miftode, I. L., Trandafirescu, M. F., Cojocaru, E., Țarcă, E., Mindru, D. E., &amp; Dorneanu, O. S. (2023). The Role of the Gut Microbiota in Anorexia Nervosa in Children and Adults-Systematic Review. &quot;International journal of molecular sciences, 25&quot;(1), 41. https://doi.org/10.3390/ijms25010041

Brown, T. A., Vanzhula, I. A., Reilly, E. E., Levinson, C. A., Berner, L. A., Krueger, A., Lavender, J. M., Kaye, W. H., &amp; Wierenga, C. E. (2020). Body mistrust bridges interoceptive awareness and eating disorder symptoms. &quot;Journal of abnormal psychology, 129&quot;(5), 445–456. https://doi.org/10.1037/abn0000516 

Calder, A., Mock, S., Friedli, N., Pasi, P., &amp; Hasler, G. (2023). Psychedelics in the treatment of eating disorders: Rationale and potential mechanisms. &quot;European Neuropsychopharmacology, 75&quot;, 1–14. https://doi.org/10.1016/j.euroneuro.2023.05.008 

Caspani, G., Ruffell, S. G. D., Tsang, W., Netzband, N., Rohani-Shukla, C., Swann, J. R., &amp; Jefferies, W. A. (2024). Mind over matter: the microbial mindscapes of psychedelics and the gut-brain axis. &quot;Pharmacological research, 207&quot;, 107338. https://doi.org/10.1016/j.phrs.2024.107338  

Fitzsimmons, E. E., &amp; Bardone-Cone, A. M. (2010). Differences in coping across stages of recovery from an eating disorder. &quot;The International journal of eating disorders, 43&quot;(8), 689–693. https://doi.org/10.1002/eat.20781 

Hatzipantelis, C. J., &amp; Olson, D. E. (2024). The Effects of Psychedelics on Neuronal Physiology. &quot;Annual review of physiology, 86&quot;, 27–47. https://doi.org/10.1146/annurev-physiol-042022-020923

Hay, P., Aouad, P., Le, A., Marks, P., Maloney, D., National Eating Disorder Research Consortium, Touyz, S., &amp; Maguire, S. (2023). Epidemiology of eating disorders: population, prevalence, disease burden and quality of life informing public policy in Australia-a rapid review. &quot;Journal of eating disorders, 11&quot;(1), 23. https://doi.org/10.1186/s40337-023-00738-7

Li, H., Wang, H., &amp; Wang, X. (2025). Psychedelics and the Autonomic Nervous System: A Perspective on Their Interplay and Therapeutic Potential. &quot;ACS pharmacology &amp; translational science, 8&quot;(3), 899–902. https://doi.org/10.1021/acsptsci.5c00005 

Leppanen, J., Brown, D., McLinden, H., Williams, S., &amp; Tchanturia, K. (2022). The Role of Emotion Regulation in Eating Disorders: A Network Meta-Analysis Approach. &quot;Frontiers in psychiatry, 13&quot;, 793094. https://doi.org/10.3389/fpsyt.2022.793094 

Mograbi, D. C., Rodrigues, R., Bienemann, B., &amp; Huntley, J. (2024). Brain Networks, Neurotransmitters and Psychedelics: Towards a Neurochemistry of Self-Awareness. &quot;Current neurology and neuroscience reports, 24&quot;(8), 323–340. https://doi.org/10.1007/s11910-024-01353-y

Paulus F. W., Ohmann S., Möhler E., Plener P. &amp; Popow C. (2021). Emotional Dysregulation in Children and Adolescents With Psychiatric Disorders. A Narrative Review. &quot;Frontiers in Psychiatry 12&quot;:628252. doi: 10.3389/fpsyt.2021.628252

Peled-Avron L., Aday J. Ss, Kalafateli A. L., Hamilton H. K., Woolley J. D. (2024). Editorial: Down the rabbit hole – the psychological and neural mechanisms of psychedelic compounds and their use in treating mental health and medical conditions. &quot;Frontiers in Psychiatry 15&quot;:1431389. doi: 10.3389/fpsyt.2024.1431389

Porges S. W. (2025). Polyvagal Theory: Current Status, Clinical Applications, and Future Directions. &quot;Clinical neuropsychiatry, 22&quot;(3), 169–184. https://doi.org/10.36131/cnfioritieditore20250301

Schaefer, L. M., Smith, K. E., Anderson, L. M., Cao, L., Crosby, R. D., Engel, S. G., Crow, S. J., Peterson, C. B., &amp; Wonderlich, S. A. (2020). The role of affect in the maintenance of binge-eating disorder: Evidence from an ecological momentary assessment study. &quot;Journal of abnormal psychology, 129&quot;(4), 387–396. https://doi.org/10.1037/abn0000517 

Shank, L. M., Tanofsky-Kraff, M., Kelly, N. R., Jaramillo, M., Rubin, S. G., Altman, D. R., Byrne, M. E., LeMay-Russell, S., Schvey, N. A., Broadney, M. M., Brady, S. M., Yang, S. B., Courville, A. B., Ramirez, S., Crist, A. C., Yanovski, S. Z., &amp; Yanovski, J. A. (2019). The association between alexithymia and eating behavior in children and adolescents. &quot;Appetite, 142&quot;, 104381. https://doi.org/10.1016/j.appet.2019.104381

Wonderlich, J., &amp; Attia, E. (2024). Eating disorders in the DSM-5. In P. Robinson, T. Wade, B. Herpertz-Dahlmann, F. Fernandez-Aranda, J. Treasure, &amp; S. Wonderlich (Eds.), Eating disorders: An international comprehensive view (pp. 7–18). &quot;Springer Nature Switzerland AG&quot;. https://doi.org/10.1007/978-3-031-46096-8_9

Wolfgang, A. S., &amp; Hoge, C. W. (2023). Psychedelic-Assisted Therapy in Military and Veterans Healthcare Systems: Clinical, Legal, and Implementation Considerations. &quot;Current psychiatry reports, 25&quot;(10), 513–532. https://doi.org/10.1007/s11920-023-01446-4 

Zanella, E., &amp; Lee, E. (2022). Integrative review on psychological and social risk and prevention factors of eating disorders including anorexia nervosa and bulimia nervosa: seven major theories. &quot;Heliyon, 8&quot;(11), e11422. https://doi.org/10.1016/j.heliyon.2022.e11422 

Zhou, R., Zhang, L., Liu, Z., &amp; Cao, B. (2025). Emotion regulation difficulties and disordered eating in adolescents and young adults: a meta-analysis. &quot;Journal of eating disorders, 13&quot;(1), 25. https://doi.org/10.1186/s40337-025-01197-y

}}

==External links==
* [https://www.abct.org/fact-sheets/psychedelic-assisted-therapy/ Psychedelic-Assisted Therapy | Fact Sheet] (ABCT - Association for Behavioral and Cognitive Therapies)
* [https://podcasts.apple.com/au/podcast/can-magic-mushrooms-help-treat-anorexia/id189330872?i=1000784809236 Can magic mushrooms help treat anorexia?] (Apple Podcasts)
* [https://www.apa.org/news/podcasts/speaking-of-psychology/eating-disorder The ‘silent epidemic’ of eating disorders] (American Psychological Association)
* [https://www.apa.org/monitor/2023/04/sensations-eating-disorders-suicidal-behavior What is interoception, and how does it affect mental health]? 5 questions for April Smith (American Psychological Association)
* [https://www.cbte.co/what-is-cbte/transdiagnostic-view-eating-disorders/ Transdiagnostic view of eating disorders] (cbte.co)
* [https://psychedelic.support/resources/polyvagal-theory-mind-body-dr-erica-zelfand/ Polyvagal Theory with Dr. Erica Zelfand: Mind-Body Connection] ·(Psychedelic Support)
* [https://www.wholeselfnutrition.org/post/nervous-system-regulation-a-missing-piece-in-eating-disorder-recovery Nervous System Regulation: A Missing Piece in Eating Disorder Recovery]  (wholeselfnutrition.org)
* [https://youtu.be/RwS-CHJcCiY?si=157viTWiOGAQ-7LP Best Neural Entropy - Explainer] (Youtube)

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      <text bytes="37624" sha1="pxlyhb4weohe0ygvq08xws9xrhony1j" xml:space="preserve">{{title|Psychedelic treatment of eating disorders:&lt;br&gt;How might psychedelic-assisted therapy influence psychological mechanisms involved in eating disorders?}}
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== Overview ==
{{RoundBoxTop|theme=7}}[[File:Neural network - Midjourney and Grok.png|thumb|'''Figure 1.''' Psychedelics are thought to temporarily disrupt rigid neural communication pathways by promoting more flexible patterns of connectivity across networks involved in mood regulation, fear processing, reward learning, and cognitive adaptability. These changes may support therapeutic shifts in behaviour and emotional processing (Hatzipantelis &amp; Olson, 2025).]]Emma, a 27‑year‑old from Canberra, has lived with an eating disorder for nearly two decades. She describes her problem eating behaviours to have started at school, after being bullied about her appearance and experiencing an unsteady home life. Ever since, they have remained in her life as “a way for me to feel in control”. Although she is aware of the harm caused by restrictive eating and compulsive exercise, she feels trapped in her thought patterns characterised by a preoccupation about food and weight concerns, as they've become entrenched in her daily life. 

After reading an article describing emerging research suggesting that psychedelics may alter patterns of neural connectivity that shape behaviour (see Figure 1), she expressed interest in pursuing psychedelic‑assisted therapy through a provider accessible to her.

After participating in her first supervised psilocybin‑assisted therapy session, Emma reported experiencing an emotional journey that allowed her to feel “connected to my body for the first time in years”. After 3 months, she has noticed a shift in how she relates to her body, and is finding it easier to actively call into question how she responds to distress with the support of her psychotherapist. 


Her experience raises a central question: What psychological mechanisms could explain these changes?{{RoundBoxBottom|theme=3}}  

This chapter explores how psychedelic‑assisted therapy (PAT) may influence the emotional, cognitive, and neurobiological processes that underpin eating disorders (EDs).   

{{RoundBoxTop|theme=11}}'''Focus questions'''
{{ic|}}Two central questions will be addressed:
* What psychological processes underpin eating disorders, and how do they guide ED behaviour?
* How might psychedelic‑assisted therapy influence these processes and support recovery?
{{ic|}}{{ic|}}{{RoundBoxBottom}}

== Introduction ==
'''Eating disorders'''  

[[wikipedia:Eating_disorder|Eating disorders]] (EDs) are psychiatric conditions characterised by abnormal eating behaviours that negatively affect physical and mental health. In Australia, the prevalence of EDs is rising particularly among young people. The economic burden is estimated to cost the nation $84 billion, with approximately 10.46% of the population having experienced an ED at some point in their lives (Hay et al., 2023). Although other forms of disordered eating exist, this chapter will focus on only three of them (see table 1), as [[wikipedia:Anorexia|Anorexia Nervosa]] (AN) has the highest mortality rate of any psychiatric disorder, while [[wikipedia:Bulimia|Bulimia Nervosa]] (BN) and [[wikipedia:Binge_eating_disorder|Binge‑Eating Disorder]] (BED) are also highly prevalent. The EDs mentioned are most associated with chronic illness, disability, reduced quality of life, increased suicide risk, and are highly comorbid with [[wikipedia:Mood_disorder|mood disorders]], [[wikipedia:Post-traumatic_stress_disorder|post-traumatic stress disorder]] (PTSD), [[wikipedia:Obsessive–compulsive_disorder|obsessive-compulsive disorder]] (OCD), and [[wikipedia:Substance_use_disorder|substance use disorders]] (Calder et al., 2023).  Despite decades of research, the pathogenesis of EDs remains incompletely understood. Current evidence suggests a complex interplay between genetic predisposition, temperament, hormonal dysregulation, cognitive abnormalities, sociocultural pressures, and traumatic experiences (Calder et al., 2023).  
{| class=&quot;wikitable&quot;
|+Table 1. Eating disorders and associated symptoms
!Eating disorder
!Primary symptoms
|-
|Anorexia Nervosa
|Severe caloric restriction, fear of gaining weight, distorted body image, preoccupation with weight loss, compulsive exercise.
|-
|Bullimia Nervosa
|Intense windows of food intake (binge eating) followed by inappropriate compensatory behaviours also known as 'purging' (eg. vomiting, laxative use), feelings of guilt and loss of control.
|-
|Binge-Eating Disorder
|Recurrent episodes of binge eating not followed by inappropriate compensatory behaviours, feelings of distress and loss of control.
(Wanderlich &amp; Attia., 2024)
|}


Although cognitive‑behavioural therapy (CBT‑E) combined with pharmacological treatment has demonstrated beneficial outcomes, efficacy remains limited and varies across ED types (Calder et al., 2023). Recovery is often long and difficult, with only two‑thirds of individuals with AN and BN eventually recovering, while others can remain ill for many years. This highlights the need for treatment approaches that can accelerate recovery and provide benefit for individuals who do not respond to conventional therapies.


'''Psychedelic-assisted therapy'''

In 2023, Australia legalised the prescription of MDMA and psilocybin under professional supervision, marking a significant shift in mental‑health treatment options. Psychedelic compounds, including [[wikipedia:LSD|LSD]], [[wikipedia:Psilocybin|psilocybin]], [[wikipedia:Dimethyltryptamine|DMT]], [[wikipedia:Ketamine|ketamine]], and [[wikipedia:MDMA|MDMA]], have demonstrated promising therapeutic effects across a wide range of psychiatric conditions. Researchers propose that psychedelics act through psychological and neural mechanisms that increase [[wikipedia:Neuroplasticity|neuroplasticity]], facilitate insight, and foster emotional acceptance (Peled‑Avron et al., 2024). At a neurobiological level, psychedelics influence processes that inform perception, emotion, and behaviour, offering a potential avenue for addressing entrenched ED mechanisms.

PAT differs from pharmacological treatment alone because the drug is administered within a structured therapeutic context designed to maximise safety and clinical benefit (Calder et al., 2023). Treatment typically involves three types of sessions, undertaken numerous times, across several months. Preparatory sessions feature participants undergoing psychoeducation, where a psychotherapist establishes rapport and clear safety protocols. Followed by supervised medication sessions, where the participant undergoes the inward experience with the reassurance of clinicians present in the same space. Lastly, integrative sessions led by the psychotherapist provide an opportunity for individuals to process and explore insights from the previous session, in aims to facilitate behavioural change (Wolfgang &amp; Hoge, 2023). This combination of pharmacological and psychological intervention is theorised to effectively target underlying psychological mechanisms common across various mental health disorders, illustrating PAT’s potential as a valuable transdiagnostic treatment option. 

PAT has become a subject of increasing popularity in ED research because many of the psychological mechanisms it is proposed to influence are the same ones implicated in ED maintenance and comorbidities (Calder et al., 2023; Peled-Avron et al., 2024). Early research, including case study reports, small clinical studies, meta-analyses and reviews indicate that PAT produces improvements in affect, reductions in ED symptom severity, enhanced body image, weight restoration, and reductions in comorbid symptoms. Although preliminary, these findings indicate that PAT may disrupt and promote shifts away from maladaptive coping patterns that become entrenched in treatment resistant ED populations.

== Psychological mechanisms in eating disorders ==


'''Emotion dysregulation'''

Emotion dysregulation is considered to be a significant risk factor for the onset and maintenance of EDs. It refers to difficulties recognising, assessing, and modifying emotional responses to meet situational demands (Zhou et al., 2025). 

Research consistently shows that individuals with EDs experience significant challenges in regulating emotions, increasing their vulnerability to comorbid symptoms, which contribute to the emergence of disordered eating patterns (Leppanen et al., 2022). This idea is supported by affect regulation theory which posits that eating disorders develop and are maintained as maladaptive strategies to manage, tolerate and escape from negative emotions and psychological distress (Schaefer et al., 2020; Zanella &amp; Lee, 2022). This is further exemplified in Fitzsimmons &amp; Bardone-Cone’s article examining differences in coping within eating disorder patients (2010). The authors explain that avoidance and emotion-oriented coping styles often function as maladaptive attempts to manage (di)stress. They explain that behaviours such as binge eating, purging, starvation, and/or compulsive exercise provide temporary relief by shifting attention away from uncomfortable emotions. 

Furthermore, alexithymia, characterised by difficulty identifying and describing one’s own emotions, is strongly associated with ED pathology (Shank et al., 2019). Individuals with high alexithymia often struggle to differentiate emotional states from bodily sensations, contributing to behaviours such as emotional eating, eating in the absence of hunger, or rigid restriction. In BED, alexithymia is linked to binge episodes triggered by poorly understood emotional cues, while in AN and BN, alexithymia may contribute to emotional avoidance and reliance on ED behaviours for affect regulation. 

The effects of trauma are contributing factors to emotion dysregulation, and considered a risk factor for ED development. Individuals who experience sexual, physical, or emotional abuse, neglect, and bullying are likely to experience heightened emotional reactivity, threat perception, and avoidance behaviours (Calder et al., 2023). Researchers explain that trauma often results in lowered distress tolerance and increased reliance on maladaptive coping behaviours, including disordered eating. Furthermore, PTSD comorbidity is common, hence trauma‑related symptoms are hypothesised to frequently interact with ED behaviours in complex ways.  


'''Reward processing dysfunction'''
[[File:Striatum.gif|thumb|'''Figure 2.''' Striatum]]
[[File:Anterior cingulate gyrus animation.gif|thumb|'''Figure 3'''. Anterior Cingulate Cortex ]]
Abnormal reward valuation is understood to be a central psychological mechanism that maintains ED behaviours. Research consistently shows that individuals with eating disorders display altered neural activity response to various stimuli, as well as disruptions in reinforcement learning (Calder et al., 2023). Brain regions involved in reward processing, habit formation, and learning, such as the striatum and anterior cingulate cortex (see figures 2 &amp; 3), exhibit atypical activation patterns and differences in dopamine receptor binding across ED types. The insula (see figure 4), which integrates bodily sensations with conscious thought, emotion, and behaviour, also shows altered responses. Together, these regions have been shown to react differently to food images, taste, and social feedback compared to healthy controls, indicating that reward dysfunction extends beyond eating‑related stimuli for ED populations.
[[File:Insular cortex.gif|thumb|'''Figure 4.''' Insula. ]]
In the context of BN and BED, research shows that food is valued more highly than other types of rewards, thus shaping behaviour through its heightened influence on reward outcomes (Calder et al., 2023). Compulsive behaviours specific to each condition (e.g. bingeing, purging) are therefore more likely to occur when food is overvalued and alternative rewards are discounted or ignored. In addition to the neural changes already described, BN and BED are associated with reduced structural and functional connectivity between frontal control regions and the striatum. This combination of highly salient food rewards, and weakened fronto‑striatal pathways, reduces an individual’s ability to inhibit or modulate reward‑seeking impulses. Weak connectivity in these circuits is thought to predict compulsive reward‑seeking behaviour. As a result, even when individuals experience negative consequences from binge episodes, they may struggle to learn from these outcomes or adjust their behaviour accordingly.


Anhedonia, a global reduction in reward responsiveness, is frequently reported by people who experience AN, resulting in food and eating becoming undervalued or aversive to them (Calder et al., 2023). Researchers propose that reward contamination further contributes to this pattern, where the brain learns to associate normally punishing stimuli (e.g., starvation, excessive exercise) with reward, while normally rewarding stimuli (e.g., high‑calorie foods) become experienced as punishment. Structural reductions in the striatum and somatosensory cortex have also been observed, which accounts for distorted bodily sensations and contributes to anhedonia. These changes support maladaptive conditioning in which starvation and weight loss embody a sense of safety, achievement, and emotional relief. Restrictive and preoccupied behaviours centred on food, body shape, and exercise are therefore reinforced over time.

Consistent with affect‑regulation models, eating‑disorder behaviours also become negatively reinforced because they reduce emotional discomfort. This relief increases the likelihood that the behaviours will be repeated, further embedding them within the individual’s coping pattern.


'''Cognitive rigidity'''

Cognitive rigidity refers to inflexible thinking and behavioural patterns, including difficulty adapting to new information and modifying behaviour. Researchers believe that individuals with EDs often exhibit rigid beliefs about food and weight which interact with a need to exert control over negative emotions. This interaction is the proposed process in which compulsive behaviours and obsessive thoughts develop (Calder et al., 2023). In AN, rigidity manifests as strict dietary rules and fear of losing control, while in BN and BED, binge episodes may feel compulsive and uncontrollable.


'''Interoceptive awareness'''

Interoceptive awareness (IA) refers to the ability to recognise and process internal bodily states such as hunger, satiety, pain, and arousal. IA is impaired across EDs, and contributes to body mistrust, distorted hunger cues, and inappropriate responses to internal sensations (Brown et al., 2020). Individuals may ignore physical discomfort, misinterpret bodily signals, or avoid sensations altogether, reinforcing maladaptive coping.      

 &lt;blockquote&gt;'''''QUIZ: Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{What coping style do people who experience EDs tend to show?
|type=&quot;()&quot;}
+ Avoidance-oriented
- Problem-oriented

{Compulsive behaviours are more likely to occur when food is ... and alternative rewards are ...
|type=&quot;()&quot;}
- undervalued; overvalued
+ overvalued; undervalued
&lt;/quiz&gt;&lt;/blockquote&gt;

== PAT's influence on ED mechanisms ==

PAT is proposed to influence several psychological mechanisms implicated in EDs, particularly those discussed in the previous section. The next part of this chapter aims to examine the theorised therapeutic mechanisms PAT possesses and practical implications for ED treatment.  


'''Emotion regulation''' 

Emotion dysregulation is a core mechanism implicated in EDs. Affect regulation theory proposes that ED behaviours emerge as maladaptive strategies to escape, reduce, or blunt overwhelming emotional experiences (Schaefer et al., 2020). Restriction, bingeing, purging, and compulsive exercise may temporarily alleviate distress while reinforcing avoidance-oriented coping and limiting opportunities to learn more adaptive ways of responding to difficult emotions. 

Psychedelics often evoke intense emotional experiences that may disrupt habitual avoidance patterns. Researchers propose that, during psychedelic sessions, attempts to suppress or avoid difficult emotions can intensify these experiences, creating conditions in which emotional acceptance becomes a preferred response (Calder et al., 2023). Although this shift does not occur in every individual, experiencing difficult emotions without resorting to ED behaviours may weaken the association between emotional distress and maladaptive coping, particularly when emotional acceptance becomes associated with a more positive or tolerable experience.

The therapeutic value of this process lies in its potential to reshape affective responses. When individuals experience strong emotions without engaging in maladaptive behaviours, they may begin to develop a new approach towards emotional tolerance. Integration sessions can consolidate this learning by helping individuals articulate, differentiate, and reflect on the emotions experienced during dosing. This process may support the development of more adaptive coping strategies, including task-oriented, problem-focused, and socially supported approaches, which are associated with improved ED outcomes (Fitzsimmons &amp; Bardone-Cone, 2010). In this way, PAT may strengthen emotion regulation and reduce reliance on ED behaviours as strategies for managing affect. 


'''Reward processing''' 

Reward dysfunction may contribute to the maintenance of EDs by reinforcing maladaptive behaviours while diminishing the perceived value of adaptive rewards. Predictive coding provides a useful framework for understanding how PAT might influence these processes. Individuals with EDs may hold rigid beliefs, conceptualised as high-level priors, about themselves in relation to food, body weight, and rewarding behaviours (Calder et al., 2023; Mograbi et al., 2024). These beliefs can influence how experiences are perceived and valued, potentially reinforcing existing behavioural patterns. Psychedelics are proposed to weaken high-level priors, allowing bottom-up sensory information to exert greater influence on perception and the valuation of experiences. 

During psychedelic experiences, individuals frequently report a heightened appreciation of sensory, social, and bodily experiences. This shift may counteract anhedonia and support the revaluation of previously feared or avoided stimuli. The therapeutic opportunity lies in translating these temporary changes in perception and reward into meaningful behavioural change. Integration sessions can explore positive and negative moments experienced during dosing and connect them to concrete goals. An example of this, inspired from Calder et al.’s (2023) article, could be to clarify specific plans to nourish the body due to the participant having experienced themselves as a decaying skeleton followed by the realisation of the body being a gift. If the period following dosing provides an opportunity for increased neuroplasticity, it may also be particularly conducive to reinforcing adaptive reward learning through behavioural activation with the help of a therapist. 


'''Cognitive flexibility''' 

Cognitive rigidity is a hallmark of EDs and is characterised by inflexible beliefs about food, weight, body shape, and control. Predictive coding provides a framework for understanding this rigidity, as EDs may involve entrenched priors that resist updating even when confronted with contradictory sensory evidence (Zanella &amp; Lee, 2022). Psychedelics are proposed to disrupt these entrenched priors by increasing neural entropy and reducing the dominance of top-down processing (Calder et al., 2023). This temporary loosening of cognitive constraints may allow individuals to consider alternative perspectives and question long-held beliefs. 

Experiences of ego dissolution may further contribute to cognitive flexibility by reducing attachment to rigid self-concepts (Peled-Avron, 2024; Mograbi et al., 2024). When the boundaries of the self become less defined, individuals may find it easier to question identity-related beliefs that sustain ED pathology. Integration sessions can harness this potential flexibility by supporting cognitive reframing, encouraging behavioural experiments, and strengthening metacognitive awareness. Through these processes, individuals may be better able to translate insights gained during psychedelic experiences into sustained changes in thinking and behaviour.


'''Reconnecting with bodily signals'''

Interoceptive deficits are central to ED pathology, contributing to body mistrust, distorted perceptions of hunger cues, and difficulties responding appropriately to internal sensations (Brown et al., 2020). Psychedelics may enhance interoceptive awareness by altering sensory processing and increasing sensitivity to bodily signals. This proposed mechanism is closely related to autonomic regulation, for which polyvagal theory provides a framework for understanding the relationship between bodily signals, emotional regulation, and perceived safety.

Polyvagal theory emphasises the role of the vagus nerve in interoception, emotional regulation, and the perception of safety (Porges, 2022). Vagal afferents transmit information from the body to the insula, where interoceptive signals are integrated with emotional and cognitive processes. Individuals with EDs may exhibit chronic sympathetic arousal and reduced vagal tone, potentially impairing interoceptive accuracy and contributing to emotional rigidity. Psychedelics may initially increase sympathetic activity, as reflected in physiological responses such as increased heart rate, followed by a parasympathetic shift associated with greater relaxation and an increased capacity for rest (Li et al., 2025). Within a polyvagal framework, these changes may have implications for vagal regulation, interoceptive awareness, and emotional regulation.

The therapeutic value of this proposed mechanism lies in its potential to restore trust in bodily signals. Integration sessions may support this process by helping individuals explore bodily sensations experienced during dosing, connect interoceptive cues with emotional states, and practise interoceptive exposure to hunger, fullness, and anxiety-related sensations. Incorporating mindfulness techniques may further support autonomic regulation and help individuals develop a more adaptive relationship with their bodily experiences.

 A brief note concerning the gut-brain axis
Although gut microbiome disruption is not a direct psychological mechanism in EDs, it is a relevant biological factor to consider when examining the potential effects of PAT. Restrictive or chaotic eating patterns can contribute to gut dysbiosis, which may weaken gut-barrier integrity and contribute to inflammation affecting the brain (Anton-Paduraru et al., 2024). These changes have been shown to influence mood, stress responsivity, cognitive rigidity, and interoceptive awareness through [[wikipedia:Hypothalamic–pituitary–adrenal_axis|HPA-axis activation]], altered neurotransmitter synthesis, and disrupted hunger–satiety signalling. 

Emerging research suggests that psychedelics may also interact with the gut–brain axis. Certain microbes can metabolise psychedelic compounds, and microbial activity has been associated with modulatory effects on behavioural outcomes. Additionally, psychedelic use may alter microbial composition towards anti-inflammatory profiles, with potential implications for neuroplasticity, neurotransmitter synthesis and signalling improvements (Caspani et al., 2024). These microbiome-related effects may therefore contribute to changes in mood, cognitive flexibility, and appetite regulation.

Although the therapeutic potential of psychedelics in EDs is considered primarily in relation to psychological mechanisms, including changes in perception, emotional processing, and reduced avoidance, microbiome-related effects may represent an additional pathway through which biological processes influence psychological outcomes. However, the extent to which these interactions contribute to therapeutic outcomes in EDs remains to be established.


&lt;blockquote&gt;'''QUIZ: ''Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{ In predictive coding terms, what are “high‑level priors” in eating disorders? 
|type=&quot;()&quot;}
+ Rigid, entrenched beliefs about food, weight, and the self that shape perception and behaviour
- Flexible beliefs that easily update with new sensory information
- Momentary emotional reactions triggered by external cues

{What is the proposed mechanism by which psychedelics support emotion regulation in PAT for EDs? 
|type=&quot;()&quot;}
- By suppressing emotional intensity to prevent distress
+ By evoking strong emotions that disrupt avoidance patterns and promote emotional acceptance
- By eliminating negative emotions through serotonin release

{What is interoceptive awareness?
|type=&quot;()&quot;}
- The ability to evaluate reward value and anticipate pleasurable outcomes
+ The capacity to sense, interpret, and respond to internal bodily signals such as hunger, fullness, and emotional arousal
- The process of weakening cognitive rigidity through ego dissolution
&lt;/quiz&gt;&lt;/blockquote&gt;

== Limitations ==
Despite the potential of PAT to influence psychological mechanisms implicated in EDs, several limitations constrain current understanding of these processes and their therapeutic relevance. Research examining emotion dysregulation in EDs illustrates broader challenges in establishing the mechanisms underlying these conditions. Although non-acceptance of emotions has been identified as a transdiagnostic risk factor across psychiatric conditions (Paulus et al., 2021), Zhou et al.’s meta-analysis (2025) highlights that the causal pathways linking emotional dysregulation and EDs remain unclear, largely because of a lack of experimental and longitudinal studies. Further limitations include restricted availability of measurement scales, insufficient cultural specificity, heterogeneity across samples, gender imbalance, and limited developmental analysis. Together, these factors constrain understanding of how specific emotional processes relate to different ED presentations across the lifespan and stages of recovery.

These limitations are also relevant when considering the proposed mechanisms of PAT. Although existing theoretical frameworks offer ways to conceptualise how psychedelic experiences may influence psychological processes responsible for EDs, the emerging nature of psychedelic therapy limits the extent to which proposed mechanisms have been tested. However, with the number of clinical trials increasing as of recently, it will be interesting to see how the theorised therapeutic mechanisms across different ED presentations and stages of recovery emerges during further warranted investigation.

Nevertheless, current limitations in the evidence highlight the need for research that clarifies the relationships between psychological processes that underscore ED behaviours, and treatment outcomes. There are several important psychological components of ED maintenance that represent meaningful targets for treatment, but they should not be considered in isolation from eachother or the neurobiological processes that influence them. A more comprehensive understanding of how these mechanisms interact may help clarify the therapeutic potential of PAT and inform the development of more targeted treatment approaches.

== Conclusion ==
PAT offers a potential framework for addressing several interconnected psychological mechanisms implicated in EDs. Through its proposed effects on emotional processing, reward valuation, cognitive flexibility, and interoceptive awareness, PAT may create opportunities to disrupt established patterns of avoidance, rigid thinking, and maladaptive behavioural reinforcement. The gut–brain interaction may represent an additional biological pathway relevant to these processes.

These mechanisms should not be understood as independent processes. Changes in emotion regulation may influence the ability to tolerate bodily sensations, while shifts in reward valuation and cognitive flexibility may create opportunities to respond differently to distress and challenge entrenched beliefs. However, the extent to which PAT produces these changes, and whether they translate into sustained improvements in ED outcomes, requires further investigation, although preliminary evidence is promising. 

The therapeutic potential of PAT lies not only in the acute psychedelic experience but also in the structured integration process that follows. Integration sessions provide an opportunity to translate emotional breakthroughs, changes in cognitive flexibility, interoceptive shifts, and reward processing into sustained behavioural change. Effective integration involves helping individuals articulate insights, connect them to ED-related patterns, and develop concrete strategies for change. These may include strengthening adaptive coping, challenging rigid beliefs, practising interoceptive awareness, reinforcing positive reward experiences, and supporting nutritional rehabilitation.

By grounding the understanding of PAT in affect regulation theory and the predictive coding framework, therapists may be better positioned to help individuals explore how psychedelic experiences could disrupt maladaptive emotional and cognitive patterns and create opportunities for new learning. Polyvagal-informed approaches may further support the development of mind–body awareness and emotional regulation through mindfulness strategies. Together, these approaches offer a multifaceted framework for translating psychedelic experiences into therapeutic change and addressing the interconnected mechanisms that maintain EDs and associated suffering. 

==See Also==
* [https://w.wiki/TsdG Ayahuasca and the brain] (Wikiversity)
* [https://w.wiki/TscF Emotional effects of psychedelics] (Wikiversity)
* [https://w.wiki/Tsdb Psilocybin and emotion] (Wikiversity)
* [https://w.wiki/TsdS Psilocibyn assisted psychotherapy] (Wikiversity)
* [https://w.wiki/Tsce Psychedelics, altered consciousness, and personal growth] (Wikiversity)
* [[Eating Disorders|Eating disorders]] (Wikiversity)

==References==
{{Hanging indent|1=

{{ic|Try &quot;Edit source&quot; and then wrapping any text to be italicised in two apostrophes e.g., ''this is italics''}}

Anton-Păduraru, D. T., Trofin, F., Nastase, E. V., Miftode, R. S., Miftode, I. L., Trandafirescu, M. F., Cojocaru, E., Țarcă, E., Mindru, D. E., &amp; Dorneanu, O. S. (2023). The Role of the Gut Microbiota in Anorexia Nervosa in Children and Adults-Systematic Review. &quot;International journal of molecular sciences, 25&quot;(1), 41. https://doi.org/10.3390/ijms25010041

Brown, T. A., Vanzhula, I. A., Reilly, E. E., Levinson, C. A., Berner, L. A., Krueger, A., Lavender, J. M., Kaye, W. H., &amp; Wierenga, C. E. (2020). Body mistrust bridges interoceptive awareness and eating disorder symptoms. &quot;Journal of abnormal psychology, 129&quot;(5), 445–456. https://doi.org/10.1037/abn0000516 

Calder, A., Mock, S., Friedli, N., Pasi, P., &amp; Hasler, G. (2023). Psychedelics in the treatment of eating disorders: Rationale and potential mechanisms. &quot;European Neuropsychopharmacology, 75&quot;, 1–14. https://doi.org/10.1016/j.euroneuro.2023.05.008 

Caspani, G., Ruffell, S. G. D., Tsang, W., Netzband, N., Rohani-Shukla, C., Swann, J. R., &amp; Jefferies, W. A. (2024). Mind over matter: the microbial mindscapes of psychedelics and the gut-brain axis. &quot;Pharmacological research, 207&quot;, 107338. https://doi.org/10.1016/j.phrs.2024.107338  

Fitzsimmons, E. E., &amp; Bardone-Cone, A. M. (2010). Differences in coping across stages of recovery from an eating disorder. &quot;The International journal of eating disorders, 43&quot;(8), 689–693. https://doi.org/10.1002/eat.20781 

Hatzipantelis, C. J., &amp; Olson, D. E. (2024). The Effects of Psychedelics on Neuronal Physiology. &quot;Annual review of physiology, 86&quot;, 27–47. https://doi.org/10.1146/annurev-physiol-042022-020923

Hay, P., Aouad, P., Le, A., Marks, P., Maloney, D., National Eating Disorder Research Consortium, Touyz, S., &amp; Maguire, S. (2023). Epidemiology of eating disorders: population, prevalence, disease burden and quality of life informing public policy in Australia-a rapid review. &quot;Journal of eating disorders, 11&quot;(1), 23. https://doi.org/10.1186/s40337-023-00738-7

Li, H., Wang, H., &amp; Wang, X. (2025). Psychedelics and the Autonomic Nervous System: A Perspective on Their Interplay and Therapeutic Potential. &quot;ACS pharmacology &amp; translational science, 8&quot;(3), 899–902. https://doi.org/10.1021/acsptsci.5c00005 

Leppanen, J., Brown, D., McLinden, H., Williams, S., &amp; Tchanturia, K. (2022). The Role of Emotion Regulation in Eating Disorders: A Network Meta-Analysis Approach. &quot;Frontiers in psychiatry, 13&quot;, 793094. https://doi.org/10.3389/fpsyt.2022.793094 

Mograbi, D. C., Rodrigues, R., Bienemann, B., &amp; Huntley, J. (2024). Brain Networks, Neurotransmitters and Psychedelics: Towards a Neurochemistry of Self-Awareness. &quot;Current neurology and neuroscience reports, 24&quot;(8), 323–340. https://doi.org/10.1007/s11910-024-01353-y

Paulus F. W., Ohmann S., Möhler E., Plener P. &amp; Popow C. (2021). Emotional Dysregulation in Children and Adolescents With Psychiatric Disorders. A Narrative Review. &quot;Frontiers in Psychiatry 12&quot;:628252. doi: 10.3389/fpsyt.2021.628252

Peled-Avron L., Aday J. Ss, Kalafateli A. L., Hamilton H. K., Woolley J. D. (2024). Editorial: Down the rabbit hole – the psychological and neural mechanisms of psychedelic compounds and their use in treating mental health and medical conditions. &quot;Frontiers in Psychiatry 15&quot;:1431389. doi: 10.3389/fpsyt.2024.1431389

Porges S. W. (2025). Polyvagal Theory: Current Status, Clinical Applications, and Future Directions. &quot;Clinical neuropsychiatry, 22&quot;(3), 169–184. https://doi.org/10.36131/cnfioritieditore20250301

Schaefer, L. M., Smith, K. E., Anderson, L. M., Cao, L., Crosby, R. D., Engel, S. G., Crow, S. J., Peterson, C. B., &amp; Wonderlich, S. A. (2020). The role of affect in the maintenance of binge-eating disorder: Evidence from an ecological momentary assessment study. &quot;Journal of abnormal psychology, 129&quot;(4), 387–396. https://doi.org/10.1037/abn0000517 

Shank, L. M., Tanofsky-Kraff, M., Kelly, N. R., Jaramillo, M., Rubin, S. G., Altman, D. R., Byrne, M. E., LeMay-Russell, S., Schvey, N. A., Broadney, M. M., Brady, S. M., Yang, S. B., Courville, A. B., Ramirez, S., Crist, A. C., Yanovski, S. Z., &amp; Yanovski, J. A. (2019). The association between alexithymia and eating behavior in children and adolescents. &quot;Appetite, 142&quot;, 104381. https://doi.org/10.1016/j.appet.2019.104381

Wonderlich, J., &amp; Attia, E. (2024). Eating disorders in the DSM-5. In P. Robinson, T. Wade, B. Herpertz-Dahlmann, F. Fernandez-Aranda, J. Treasure, &amp; S. Wonderlich (Eds.), Eating disorders: An international comprehensive view (pp. 7–18). &quot;Springer Nature Switzerland AG&quot;. https://doi.org/10.1007/978-3-031-46096-8_9

Wolfgang, A. S., &amp; Hoge, C. W. (2023). Psychedelic-Assisted Therapy in Military and Veterans Healthcare Systems: Clinical, Legal, and Implementation Considerations. &quot;Current psychiatry reports, 25&quot;(10), 513–532. https://doi.org/10.1007/s11920-023-01446-4 

Zanella, E., &amp; Lee, E. (2022). Integrative review on psychological and social risk and prevention factors of eating disorders including anorexia nervosa and bulimia nervosa: seven major theories. &quot;Heliyon, 8&quot;(11), e11422. https://doi.org/10.1016/j.heliyon.2022.e11422 

Zhou, R., Zhang, L., Liu, Z., &amp; Cao, B. (2025). Emotion regulation difficulties and disordered eating in adolescents and young adults: a meta-analysis. &quot;Journal of eating disorders, 13&quot;(1), 25. https://doi.org/10.1186/s40337-025-01197-y

}}

==External links==
* [https://www.abct.org/fact-sheets/psychedelic-assisted-therapy/ Psychedelic-Assisted Therapy | Fact Sheet] (ABCT - Association for Behavioral and Cognitive Therapies)
* [https://podcasts.apple.com/au/podcast/can-magic-mushrooms-help-treat-anorexia/id189330872?i=1000784809236 Can magic mushrooms help treat anorexia?] (Apple Podcasts)
* [https://www.apa.org/news/podcasts/speaking-of-psychology/eating-disorder The ‘silent epidemic’ of eating disorders] (American Psychological Association)
* [https://www.apa.org/monitor/2023/04/sensations-eating-disorders-suicidal-behavior What is interoception, and how does it affect mental health]? 5 questions for April Smith (American Psychological Association)
* [https://www.cbte.co/what-is-cbte/transdiagnostic-view-eating-disorders/ Transdiagnostic view of eating disorders] (cbte.co)
* [https://psychedelic.support/resources/polyvagal-theory-mind-body-dr-erica-zelfand/ Polyvagal Theory with Dr. Erica Zelfand: Mind-Body Connection] ·(Psychedelic Support)
* [https://www.wholeselfnutrition.org/post/nervous-system-regulation-a-missing-piece-in-eating-disorder-recovery Nervous System Regulation: A Missing Piece in Eating Disorder Recovery]  (wholeselfnutrition.org)
* [https://youtu.be/RwS-CHJcCiY?si=157viTWiOGAQ-7LP Best Neural Entropy - Explainer] (Youtube)

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      <text bytes="37635" sha1="h77fbaemgwg5oya3p99iux9k13tfflb" xml:space="preserve">{{title|Psychedelic treatment of eating disorders:&lt;br&gt;How might psychedelic-assisted therapy influence psychological mechanisms involved in eating disorders?}}
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== Overview ==
{{RoundBoxTop|theme=7}}[[File:Neural network - Midjourney and Grok.png|thumb|'''Figure 1.''' Psychedelics are thought to temporarily disrupt rigid neural communication pathways by promoting more flexible patterns of connectivity across networks involved in mood regulation, fear processing, reward learning, and cognitive adaptability. These changes may support therapeutic shifts in behaviour and emotional processing (Hatzipantelis &amp; Olson, 2025).]]Emma, a 27‑year‑old from Canberra, has lived with an eating disorder for nearly two decades. She describes her problem eating behaviours to have started at school, after being bullied about her appearance and experiencing an unsteady home life. Ever since, they have remained in her life as “a way for me to feel in control”. Although she is aware of the harm caused by restrictive eating and compulsive exercise, she feels trapped in her thought patterns characterised by a preoccupation about food and weight concerns, as they've become entrenched in her daily life. 

After reading an article describing emerging research suggesting that psychedelics may alter patterns of neural connectivity that shape behaviour (see Figure 1), she expressed interest in pursuing psychedelic‑assisted therapy through a provider accessible to her.

After participating in her first supervised psilocybin‑assisted therapy session, Emma reported experiencing an emotional journey that allowed her to feel “connected to my body for the first time in years”. After 3 months, she has noticed a shift in how she relates to her body, and is finding it easier to actively call into question how she responds to distress with the support of her psychotherapist. 


Her experience raises a central question: What psychological mechanisms could explain these changes?{{RoundBoxBottom|theme=3}}  

This chapter explores how psychedelic‑assisted therapy (PAT) may influence the emotional, cognitive, and neurobiological processes that underpin eating disorders (EDs).   

{{RoundBoxTop|theme=11}}'''Focus questions'''
{{ic|}}Two central questions will be addressed:
* What psychological processes underpin eating disorders, and how do they guide ED behaviour?
* How might psychedelic‑assisted therapy influence these processes and support recovery?
{{ic|}}{{ic|}}{{RoundBoxBottom}}

== Introduction ==
'''Eating disorders'''  

[[wikipedia:Eating_disorder|Eating disorders]] (EDs) are psychiatric conditions characterised by abnormal eating behaviours that negatively affect physical and mental health. In Australia, the prevalence of EDs is rising particularly among young people. The economic burden is estimated to cost the nation $84 billion, with approximately 10.46% of the population having experienced an ED at some point in their lives (Hay et al., 2023). Although other forms of disordered eating exist, this chapter will focus on only three of them (see table 1), as [[wikipedia:Anorexia|Anorexia Nervosa]] (AN) has the highest mortality rate of any psychiatric disorder, while [[wikipedia:Bulimia|Bulimia Nervosa]] (BN) and [[wikipedia:Binge_eating_disorder|Binge‑Eating Disorder]] (BED) are also highly prevalent. The EDs mentioned are most associated with chronic illness, disability, reduced quality of life, increased suicide risk, and are highly comorbid with [[wikipedia:Mood_disorder|mood disorders]], [[wikipedia:Post-traumatic_stress_disorder|post-traumatic stress disorder]] (PTSD), [[wikipedia:Obsessive–compulsive_disorder|obsessive-compulsive disorder]] (OCD), and [[wikipedia:Substance_use_disorder|substance use disorders]] (Calder et al., 2023).  Despite decades of research, the pathogenesis of EDs remains incompletely understood. Current evidence suggests a complex interplay between genetic predisposition, temperament, hormonal dysregulation, cognitive abnormalities, sociocultural pressures, and traumatic experiences (Calder et al., 2023).  
{| class=&quot;wikitable&quot;
|+Table 1. Eating disorders and associated symptoms
!Eating disorder
!Primary symptoms
|-
|Anorexia Nervosa
|Severe caloric restriction, fear of gaining weight, distorted body image, preoccupation with weight loss, compulsive exercise.
|-
|Bullimia Nervosa
|Intense windows of food intake (binge eating) followed by inappropriate compensatory behaviours also known as 'purging' (eg. vomiting, laxative use), feelings of guilt and loss of control.
|-
|Binge-Eating Disorder
|Recurrent episodes of binge eating not followed by inappropriate compensatory behaviours, feelings of distress and loss of control.
(Wanderlich &amp; Attia., 2024)
|}


Although cognitive‑behavioural therapy (CBT‑E) combined with pharmacological treatment has demonstrated beneficial outcomes, efficacy remains limited and varies across ED types (Calder et al., 2023). Recovery is often long and difficult, with only two‑thirds of individuals with AN and BN eventually recovering, while others can remain ill for many years. This highlights the need for treatment approaches that can accelerate recovery and provide benefit for individuals who do not respond to conventional therapies.


'''Psychedelic-assisted therapy'''

In 2023, Australia legalised the prescription of MDMA and psilocybin under professional supervision, marking a significant shift in mental‑health treatment options. Psychedelic compounds, including [[wikipedia:LSD|LSD]], [[wikipedia:Psilocybin|psilocybin]], [[wikipedia:Dimethyltryptamine|DMT]], [[wikipedia:Ketamine|ketamine]], and [[wikipedia:MDMA|MDMA]], have demonstrated promising therapeutic effects across a wide range of psychiatric conditions. Researchers propose that psychedelics act through psychological and neural mechanisms that increase [[wikipedia:Neuroplasticity|neuroplasticity]], facilitate insight, and foster emotional acceptance (Peled‑Avron et al., 2024). At a neurobiological level, psychedelics influence processes that inform perception, emotion, and behaviour, offering a potential avenue for addressing entrenched ED mechanisms.

PAT differs from pharmacological treatment alone because the drug is administered within a structured therapeutic context designed to maximise safety and clinical benefit (Calder et al., 2023). Treatment typically involves three types of sessions, undertaken numerous times, across several months. Preparatory sessions feature participants undergoing psychoeducation, where a psychotherapist establishes rapport and clear safety protocols. Followed by supervised medication sessions, where the participant undergoes the inward experience with the reassurance of clinicians present in the same space. Lastly, integrative sessions led by the psychotherapist provide an opportunity for individuals to process and explore insights from the previous session, in aims to facilitate behavioural change (Wolfgang &amp; Hoge, 2023). This combination of pharmacological and psychological intervention is theorised to effectively target underlying psychological mechanisms common across various mental health disorders, illustrating PAT’s potential as a valuable transdiagnostic treatment option. 

PAT has become a subject of increasing popularity in ED research because many of the psychological mechanisms it is proposed to influence are the same ones implicated in ED maintenance and comorbidities (Calder et al., 2023; Peled-Avron et al., 2024). Early research, including case study reports, small clinical studies, meta-analyses and reviews indicate that PAT produces improvements in affect, reductions in ED symptom severity, enhanced body image, weight restoration, and reductions in comorbid symptoms. Although preliminary, these findings indicate that PAT may disrupt and promote shifts away from maladaptive coping patterns that become entrenched in treatment resistant ED populations.

== Psychological mechanisms in eating disorders ==


'''Emotion dysregulation'''

Emotion dysregulation is considered to be a significant risk factor for the onset and maintenance of EDs. It refers to difficulties recognising, assessing, and modifying emotional responses to meet situational demands (Zhou et al., 2025). 

Research consistently shows that individuals with EDs experience significant challenges in regulating emotions, increasing their vulnerability to comorbid symptoms, which contribute to the emergence of disordered eating patterns (Leppanen et al., 2022). This idea is supported by affect regulation theory which posits that eating disorders develop and are maintained as maladaptive strategies to manage, tolerate and escape from negative emotions and psychological distress (Schaefer et al., 2020; Zanella &amp; Lee, 2022). This is further exemplified in Fitzsimmons &amp; Bardone-Cone’s article examining differences in coping within eating disorder patients (2010). The authors explain that avoidance and emotion-oriented coping styles often function as maladaptive attempts to manage (di)stress. They explain that behaviours such as binge eating, purging, starvation, and/or compulsive exercise provide temporary relief by shifting attention away from uncomfortable emotions. 

Furthermore, alexithymia, characterised by difficulty identifying and describing one’s own emotions, is strongly associated with ED pathology (Shank et al., 2019). Individuals with high alexithymia often struggle to differentiate emotional states from bodily sensations, contributing to behaviours such as emotional eating, eating in the absence of hunger, or rigid restriction. In BED, alexithymia is linked to binge episodes triggered by poorly understood emotional cues, while in AN and BN, alexithymia may contribute to emotional avoidance and reliance on ED behaviours for affect regulation. 

The effects of trauma are contributing factors to emotion dysregulation, and considered a risk factor for ED development. Individuals who experience sexual, physical, or emotional abuse, neglect, and bullying are likely to experience heightened emotional reactivity, threat perception, and avoidance behaviours (Calder et al., 2023). Researchers explain that trauma often results in lowered distress tolerance and increased reliance on maladaptive coping behaviours, including disordered eating. Furthermore, PTSD comorbidity is common, hence trauma‑related symptoms are hypothesised to frequently interact with ED behaviours in complex ways.  


'''Reward processing dysfunction'''
[[File:Striatum.gif|thumb|'''Figure 2.''' Striatum]]
[[File:Anterior cingulate gyrus animation.gif|thumb|'''Figure 3'''. Anterior Cingulate Cortex ]]
Abnormal reward valuation is understood to be a central psychological mechanism that maintains ED behaviours. Research consistently shows that individuals with eating disorders display altered neural activity response to various stimuli, as well as disruptions in reinforcement learning (Calder et al., 2023). Brain regions involved in reward processing, habit formation, and learning, such as the striatum and anterior cingulate cortex (see figures 2 &amp; 3), exhibit atypical activation patterns and differences in dopamine receptor binding across ED types. The insula (see figure 4), which integrates bodily sensations with conscious thought, emotion, and behaviour, also shows altered responses. Together, these regions have been shown to react differently to food images, taste, and social feedback compared to healthy controls, indicating that reward dysfunction extends beyond eating‑related stimuli for ED populations.
[[File:Insular cortex.gif|thumb|'''Figure 4.''' Insula. ]]
In the context of BN and BED, research shows that food is valued more highly than other types of rewards, thus shaping behaviour through its heightened influence on reward outcomes (Calder et al., 2023). Compulsive behaviours specific to each condition (e.g. bingeing, purging) are therefore more likely to occur when food is overvalued and alternative rewards are discounted or ignored. In addition to the neural changes already described, BN and BED are associated with reduced structural and functional connectivity between frontal control regions and the striatum. This combination of highly salient food rewards, and weakened fronto‑striatal pathways, reduces an individual’s ability to inhibit or modulate reward‑seeking impulses. Weak connectivity in these circuits is thought to predict compulsive reward‑seeking behaviour. As a result, even when individuals experience negative consequences from binge episodes, they may struggle to learn from these outcomes or adjust their behaviour accordingly.


Anhedonia, a global reduction in reward responsiveness, is frequently reported by people who experience AN, resulting in food and eating becoming undervalued or aversive to them (Calder et al., 2023). Researchers propose that reward contamination further contributes to this pattern, where the brain learns to associate normally punishing stimuli (e.g., starvation, excessive exercise) with reward, while normally rewarding stimuli (e.g., high‑calorie foods) become experienced as punishment. Structural reductions in the striatum and somatosensory cortex have also been observed, which accounts for distorted bodily sensations and contributes to anhedonia. These changes support maladaptive conditioning in which starvation and weight loss embody a sense of safety, achievement, and emotional relief. Restrictive and preoccupied behaviours centred on food, body shape, and exercise are therefore reinforced over time.

Consistent with affect‑regulation models, eating‑disorder behaviours also become negatively reinforced because they reduce emotional discomfort. This relief increases the likelihood that the behaviours will be repeated, further embedding them within the individual’s coping pattern.


'''Cognitive rigidity'''

Cognitive rigidity refers to inflexible thinking and behavioural patterns, including difficulty adapting to new information and modifying behaviour. Researchers believe that individuals with EDs often exhibit rigid beliefs about food and weight which interact with a need to exert control over negative emotions. This interaction is the proposed process in which compulsive behaviours and obsessive thoughts develop (Calder et al., 2023). In AN, rigidity manifests as strict dietary rules and fear of losing control, while in BN and BED, binge episodes may feel compulsive and uncontrollable.


'''Interoceptive awareness'''

Interoceptive awareness (IA) refers to the ability to recognise and process internal bodily states such as hunger, satiety, pain, and arousal. IA is impaired across EDs, and contributes to body mistrust, distorted hunger cues, and inappropriate responses to internal sensations (Brown et al., 2020). Individuals may ignore physical discomfort, misinterpret bodily signals, or avoid sensations altogether, reinforcing maladaptive coping.      

 &lt;blockquote&gt;'''''QUIZ: Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{What coping style do people who experience EDs tend to show?
|type=&quot;()&quot;}
+ Avoidance-oriented
- Problem-oriented

{Compulsive behaviours are more likely to occur when food is ... and alternative rewards are ...
|type=&quot;()&quot;}
- undervalued; overvalued
+ overvalued; undervalued
&lt;/quiz&gt;&lt;/blockquote&gt;

== PAT's influence on psychological mechanisms ==

PAT is proposed to influence several psychological mechanisms implicated in EDs, particularly those discussed in the previous section. The next part of this chapter aims to examine the theorised therapeutic mechanisms PAT possesses and practical implications for ED treatment.  


'''Emotion regulation''' 

Emotion dysregulation is a core mechanism implicated in EDs. Affect regulation theory proposes that ED behaviours emerge as maladaptive strategies to escape, reduce, or blunt overwhelming emotional experiences (Schaefer et al., 2020). Restriction, bingeing, purging, and compulsive exercise may temporarily alleviate distress while reinforcing avoidance-oriented coping and limiting opportunities to learn more adaptive ways of responding to difficult emotions. 

Psychedelics often evoke intense emotional experiences that may disrupt habitual avoidance patterns. Researchers propose that, during psychedelic sessions, attempts to suppress or avoid difficult emotions can intensify these experiences, creating conditions in which emotional acceptance becomes a preferred response (Calder et al., 2023). Although this shift does not occur in every individual, experiencing difficult emotions without resorting to ED behaviours may weaken the association between emotional distress and maladaptive coping, particularly when emotional acceptance becomes associated with a more positive or tolerable experience.

The therapeutic value of this process lies in its potential to reshape affective responses. When individuals experience strong emotions without engaging in maladaptive behaviours, they may begin to develop a new approach towards emotional tolerance. Integration sessions can consolidate this learning by helping individuals articulate, differentiate, and reflect on the emotions experienced during dosing. This process may support the development of more adaptive coping strategies, including task-oriented, problem-focused, and socially supported approaches, which are associated with improved ED outcomes (Fitzsimmons &amp; Bardone-Cone, 2010). In this way, PAT may strengthen emotion regulation and reduce reliance on ED behaviours as strategies for managing affect. 


'''Reward processing''' 

Reward dysfunction may contribute to the maintenance of EDs by reinforcing maladaptive behaviours while diminishing the perceived value of adaptive rewards. Predictive coding provides a useful framework for understanding how PAT might influence these processes. Individuals with EDs may hold rigid beliefs, conceptualised as high-level priors, about themselves in relation to food, body weight, and rewarding behaviours (Calder et al., 2023; Mograbi et al., 2024). These beliefs can influence how experiences are perceived and valued, potentially reinforcing existing behavioural patterns. Psychedelics are proposed to weaken high-level priors, allowing bottom-up sensory information to exert greater influence on perception and the valuation of experiences. 

During psychedelic experiences, individuals frequently report a heightened appreciation of sensory, social, and bodily experiences. This shift may counteract anhedonia and support the revaluation of previously feared or avoided stimuli. The therapeutic opportunity lies in translating these temporary changes in perception and reward into meaningful behavioural change. Integration sessions can explore positive and negative moments experienced during dosing and connect them to concrete goals. An example of this, inspired from Calder et al.’s (2023) article, could be to clarify specific plans to nourish the body due to the participant having experienced themselves as a decaying skeleton followed by the realisation of the body being a gift. If the period following dosing provides an opportunity for increased neuroplasticity, it may also be particularly conducive to reinforcing adaptive reward learning through behavioural activation with the help of a therapist. 


'''Cognitive flexibility''' 

Cognitive rigidity is a hallmark of EDs and is characterised by inflexible beliefs about food, weight, body shape, and control. Predictive coding provides a framework for understanding this rigidity, as EDs may involve entrenched priors that resist updating even when confronted with contradictory sensory evidence (Zanella &amp; Lee, 2022). Psychedelics are proposed to disrupt these entrenched priors by increasing neural entropy and reducing the dominance of top-down processing (Calder et al., 2023). This temporary loosening of cognitive constraints may allow individuals to consider alternative perspectives and question long-held beliefs. 

Experiences of ego dissolution may further contribute to cognitive flexibility by reducing attachment to rigid self-concepts (Peled-Avron, 2024; Mograbi et al., 2024). When the boundaries of the self become less defined, individuals may find it easier to question identity-related beliefs that sustain ED pathology. Integration sessions can harness this potential flexibility by supporting cognitive reframing, encouraging behavioural experiments, and strengthening metacognitive awareness. Through these processes, individuals may be better able to translate insights gained during psychedelic experiences into sustained changes in thinking and behaviour.


'''Reconnecting with bodily signals'''

Interoceptive deficits are central to ED pathology, contributing to body mistrust, distorted perceptions of hunger cues, and difficulties responding appropriately to internal sensations (Brown et al., 2020). Psychedelics may enhance interoceptive awareness by altering sensory processing and increasing sensitivity to bodily signals. This proposed mechanism is closely related to autonomic regulation, for which polyvagal theory provides a framework for understanding the relationship between bodily signals, emotional regulation, and perceived safety.

Polyvagal theory emphasises the role of the vagus nerve in interoception, emotional regulation, and the perception of safety (Porges, 2022). Vagal afferents transmit information from the body to the insula, where interoceptive signals are integrated with emotional and cognitive processes. Individuals with EDs may exhibit chronic sympathetic arousal and reduced vagal tone, potentially impairing interoceptive accuracy and contributing to emotional rigidity. Psychedelics may initially increase sympathetic activity, as reflected in physiological responses such as increased heart rate, followed by a parasympathetic shift associated with greater relaxation and an increased capacity for rest (Li et al., 2025). Within a polyvagal framework, these changes may have implications for vagal regulation, interoceptive awareness, and emotional regulation.

The therapeutic value of this proposed mechanism lies in its potential to restore trust in bodily signals. Integration sessions may support this process by helping individuals explore bodily sensations experienced during dosing, connect interoceptive cues with emotional states, and practise interoceptive exposure to hunger, fullness, and anxiety-related sensations. Incorporating mindfulness techniques may further support autonomic regulation and help individuals develop a more adaptive relationship with their bodily experiences.

 A brief note concerning the gut-brain axis
Although gut microbiome disruption is not a direct psychological mechanism in EDs, it is a relevant biological factor to consider when examining the potential effects of PAT. Restrictive or chaotic eating patterns can contribute to gut dysbiosis, which may weaken gut-barrier integrity and contribute to inflammation affecting the brain (Anton-Paduraru et al., 2024). These changes have been shown to influence mood, stress responsivity, cognitive rigidity, and interoceptive awareness through [[wikipedia:Hypothalamic–pituitary–adrenal_axis|HPA-axis activation]], altered neurotransmitter synthesis, and disrupted hunger–satiety signalling. 

Emerging research suggests that psychedelics may also interact with the gut–brain axis. Certain microbes can metabolise psychedelic compounds, and microbial activity has been associated with modulatory effects on behavioural outcomes. Additionally, psychedelic use may alter microbial composition towards anti-inflammatory profiles, with potential implications for neuroplasticity, neurotransmitter synthesis and signalling improvements (Caspani et al., 2024). These microbiome-related effects may therefore contribute to changes in mood, cognitive flexibility, and appetite regulation.

Although the therapeutic potential of psychedelics in EDs is considered primarily in relation to psychological mechanisms, including changes in perception, emotional processing, and reduced avoidance, microbiome-related effects may represent an additional pathway through which biological processes influence psychological outcomes. However, the extent to which these interactions contribute to therapeutic outcomes in EDs remains to be established.


&lt;blockquote&gt;'''QUIZ: ''Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{ In predictive coding terms, what are “high‑level priors” in eating disorders? 
|type=&quot;()&quot;}
+ Rigid, entrenched beliefs about food, weight, and the self that shape perception and behaviour
- Flexible beliefs that easily update with new sensory information
- Momentary emotional reactions triggered by external cues

{What is the proposed mechanism by which psychedelics support emotion regulation in PAT for EDs? 
|type=&quot;()&quot;}
- By suppressing emotional intensity to prevent distress
+ By evoking strong emotions that disrupt avoidance patterns and promote emotional acceptance
- By eliminating negative emotions through serotonin release

{What is interoceptive awareness?
|type=&quot;()&quot;}
- The ability to evaluate reward value and anticipate pleasurable outcomes
+ The capacity to sense, interpret, and respond to internal bodily signals such as hunger, fullness, and emotional arousal
- The process of weakening cognitive rigidity through ego dissolution
&lt;/quiz&gt;&lt;/blockquote&gt;

== Limitations ==
Despite the potential of PAT to influence psychological mechanisms implicated in EDs, several limitations constrain current understanding of these processes and their therapeutic relevance. Research examining emotion dysregulation in EDs illustrates broader challenges in establishing the mechanisms underlying these conditions. Although non-acceptance of emotions has been identified as a transdiagnostic risk factor across psychiatric conditions (Paulus et al., 2021), Zhou et al.’s meta-analysis (2025) highlights that the causal pathways linking emotional dysregulation and EDs remain unclear, largely because of a lack of experimental and longitudinal studies. Further limitations include restricted availability of measurement scales, insufficient cultural specificity, heterogeneity across samples, gender imbalance, and limited developmental analysis. Together, these factors constrain understanding of how specific emotional processes relate to different ED presentations across the lifespan and stages of recovery.

These limitations are also relevant when considering the proposed mechanisms of PAT. Although existing theoretical frameworks offer ways to conceptualise how psychedelic experiences may influence psychological processes responsible for EDs, the emerging nature of psychedelic therapy limits the extent to which proposed mechanisms have been tested. However, with the number of clinical trials increasing as of recently, it will be interesting to see how the theorised therapeutic mechanisms across different ED presentations and stages of recovery emerges during further warranted investigation.

Nevertheless, current limitations in the evidence highlight the need for research that clarifies the relationships between psychological processes that underscore ED behaviours, and treatment outcomes. There are several important psychological components of ED maintenance that represent meaningful targets for treatment, but they should not be considered in isolation from eachother or the neurobiological processes that influence them. A more comprehensive understanding of how these mechanisms interact may help clarify the therapeutic potential of PAT and inform the development of more targeted treatment approaches.

== Conclusion ==
PAT offers a potential framework for addressing several interconnected psychological mechanisms implicated in EDs. Through its proposed effects on emotional processing, reward valuation, cognitive flexibility, and interoceptive awareness, PAT may create opportunities to disrupt established patterns of avoidance, rigid thinking, and maladaptive behavioural reinforcement. The gut–brain interaction may represent an additional biological pathway relevant to these processes.

These mechanisms should not be understood as independent processes. Changes in emotion regulation may influence the ability to tolerate bodily sensations, while shifts in reward valuation and cognitive flexibility may create opportunities to respond differently to distress and challenge entrenched beliefs. However, the extent to which PAT produces these changes, and whether they translate into sustained improvements in ED outcomes, requires further investigation, although preliminary evidence is promising. 

The therapeutic potential of PAT lies not only in the acute psychedelic experience but also in the structured integration process that follows. Integration sessions provide an opportunity to translate emotional breakthroughs, changes in cognitive flexibility, interoceptive shifts, and reward processing into sustained behavioural change. Effective integration involves helping individuals articulate insights, connect them to ED-related patterns, and develop concrete strategies for change. These may include strengthening adaptive coping, challenging rigid beliefs, practising interoceptive awareness, reinforcing positive reward experiences, and supporting nutritional rehabilitation.

By grounding the understanding of PAT in affect regulation theory and the predictive coding framework, therapists may be better positioned to help individuals explore how psychedelic experiences could disrupt maladaptive emotional and cognitive patterns and create opportunities for new learning. Polyvagal-informed approaches may further support the development of mind–body awareness and emotional regulation through mindfulness strategies. Together, these approaches offer a multifaceted framework for translating psychedelic experiences into therapeutic change and addressing the interconnected mechanisms that maintain EDs and associated suffering. 

==See Also==
* [https://w.wiki/TsdG Ayahuasca and the brain] (Wikiversity)
* [https://w.wiki/TscF Emotional effects of psychedelics] (Wikiversity)
* [https://w.wiki/Tsdb Psilocybin and emotion] (Wikiversity)
* [https://w.wiki/TsdS Psilocibyn assisted psychotherapy] (Wikiversity)
* [https://w.wiki/Tsce Psychedelics, altered consciousness, and personal growth] (Wikiversity)
* [[Eating Disorders|Eating disorders]] (Wikiversity)

==References==
{{Hanging indent|1=

{{ic|Try &quot;Edit source&quot; and then wrapping any text to be italicised in two apostrophes e.g., ''this is italics''}}

Anton-Păduraru, D. T., Trofin, F., Nastase, E. V., Miftode, R. S., Miftode, I. L., Trandafirescu, M. F., Cojocaru, E., Țarcă, E., Mindru, D. E., &amp; Dorneanu, O. S. (2023). The Role of the Gut Microbiota in Anorexia Nervosa in Children and Adults-Systematic Review. &quot;International journal of molecular sciences, 25&quot;(1), 41. https://doi.org/10.3390/ijms25010041

Brown, T. A., Vanzhula, I. A., Reilly, E. E., Levinson, C. A., Berner, L. A., Krueger, A., Lavender, J. M., Kaye, W. H., &amp; Wierenga, C. E. (2020). Body mistrust bridges interoceptive awareness and eating disorder symptoms. &quot;Journal of abnormal psychology, 129&quot;(5), 445–456. https://doi.org/10.1037/abn0000516 

Calder, A., Mock, S., Friedli, N., Pasi, P., &amp; Hasler, G. (2023). Psychedelics in the treatment of eating disorders: Rationale and potential mechanisms. &quot;European Neuropsychopharmacology, 75&quot;, 1–14. https://doi.org/10.1016/j.euroneuro.2023.05.008 

Caspani, G., Ruffell, S. G. D., Tsang, W., Netzband, N., Rohani-Shukla, C., Swann, J. R., &amp; Jefferies, W. A. (2024). Mind over matter: the microbial mindscapes of psychedelics and the gut-brain axis. &quot;Pharmacological research, 207&quot;, 107338. https://doi.org/10.1016/j.phrs.2024.107338  

Fitzsimmons, E. E., &amp; Bardone-Cone, A. M. (2010). Differences in coping across stages of recovery from an eating disorder. &quot;The International journal of eating disorders, 43&quot;(8), 689–693. https://doi.org/10.1002/eat.20781 

Hatzipantelis, C. J., &amp; Olson, D. E. (2024). The Effects of Psychedelics on Neuronal Physiology. &quot;Annual review of physiology, 86&quot;, 27–47. https://doi.org/10.1146/annurev-physiol-042022-020923

Hay, P., Aouad, P., Le, A., Marks, P., Maloney, D., National Eating Disorder Research Consortium, Touyz, S., &amp; Maguire, S. (2023). Epidemiology of eating disorders: population, prevalence, disease burden and quality of life informing public policy in Australia-a rapid review. &quot;Journal of eating disorders, 11&quot;(1), 23. https://doi.org/10.1186/s40337-023-00738-7

Li, H., Wang, H., &amp; Wang, X. (2025). Psychedelics and the Autonomic Nervous System: A Perspective on Their Interplay and Therapeutic Potential. &quot;ACS pharmacology &amp; translational science, 8&quot;(3), 899–902. https://doi.org/10.1021/acsptsci.5c00005 

Leppanen, J., Brown, D., McLinden, H., Williams, S., &amp; Tchanturia, K. (2022). The Role of Emotion Regulation in Eating Disorders: A Network Meta-Analysis Approach. &quot;Frontiers in psychiatry, 13&quot;, 793094. https://doi.org/10.3389/fpsyt.2022.793094 

Mograbi, D. C., Rodrigues, R., Bienemann, B., &amp; Huntley, J. (2024). Brain Networks, Neurotransmitters and Psychedelics: Towards a Neurochemistry of Self-Awareness. &quot;Current neurology and neuroscience reports, 24&quot;(8), 323–340. https://doi.org/10.1007/s11910-024-01353-y

Paulus F. W., Ohmann S., Möhler E., Plener P. &amp; Popow C. (2021). Emotional Dysregulation in Children and Adolescents With Psychiatric Disorders. A Narrative Review. &quot;Frontiers in Psychiatry 12&quot;:628252. doi: 10.3389/fpsyt.2021.628252

Peled-Avron L., Aday J. Ss, Kalafateli A. L., Hamilton H. K., Woolley J. D. (2024). Editorial: Down the rabbit hole – the psychological and neural mechanisms of psychedelic compounds and their use in treating mental health and medical conditions. &quot;Frontiers in Psychiatry 15&quot;:1431389. doi: 10.3389/fpsyt.2024.1431389

Porges S. W. (2025). Polyvagal Theory: Current Status, Clinical Applications, and Future Directions. &quot;Clinical neuropsychiatry, 22&quot;(3), 169–184. https://doi.org/10.36131/cnfioritieditore20250301

Schaefer, L. M., Smith, K. E., Anderson, L. M., Cao, L., Crosby, R. D., Engel, S. G., Crow, S. J., Peterson, C. B., &amp; Wonderlich, S. A. (2020). The role of affect in the maintenance of binge-eating disorder: Evidence from an ecological momentary assessment study. &quot;Journal of abnormal psychology, 129&quot;(4), 387–396. https://doi.org/10.1037/abn0000517 

Shank, L. M., Tanofsky-Kraff, M., Kelly, N. R., Jaramillo, M., Rubin, S. G., Altman, D. R., Byrne, M. E., LeMay-Russell, S., Schvey, N. A., Broadney, M. M., Brady, S. M., Yang, S. B., Courville, A. B., Ramirez, S., Crist, A. C., Yanovski, S. Z., &amp; Yanovski, J. A. (2019). The association between alexithymia and eating behavior in children and adolescents. &quot;Appetite, 142&quot;, 104381. https://doi.org/10.1016/j.appet.2019.104381

Wonderlich, J., &amp; Attia, E. (2024). Eating disorders in the DSM-5. In P. Robinson, T. Wade, B. Herpertz-Dahlmann, F. Fernandez-Aranda, J. Treasure, &amp; S. Wonderlich (Eds.), Eating disorders: An international comprehensive view (pp. 7–18). &quot;Springer Nature Switzerland AG&quot;. https://doi.org/10.1007/978-3-031-46096-8_9

Wolfgang, A. S., &amp; Hoge, C. W. (2023). Psychedelic-Assisted Therapy in Military and Veterans Healthcare Systems: Clinical, Legal, and Implementation Considerations. &quot;Current psychiatry reports, 25&quot;(10), 513–532. https://doi.org/10.1007/s11920-023-01446-4 

Zanella, E., &amp; Lee, E. (2022). Integrative review on psychological and social risk and prevention factors of eating disorders including anorexia nervosa and bulimia nervosa: seven major theories. &quot;Heliyon, 8&quot;(11), e11422. https://doi.org/10.1016/j.heliyon.2022.e11422 

Zhou, R., Zhang, L., Liu, Z., &amp; Cao, B. (2025). Emotion regulation difficulties and disordered eating in adolescents and young adults: a meta-analysis. &quot;Journal of eating disorders, 13&quot;(1), 25. https://doi.org/10.1186/s40337-025-01197-y

}}

==External links==
* [https://www.abct.org/fact-sheets/psychedelic-assisted-therapy/ Psychedelic-Assisted Therapy | Fact Sheet] (ABCT - Association for Behavioral and Cognitive Therapies)
* [https://podcasts.apple.com/au/podcast/can-magic-mushrooms-help-treat-anorexia/id189330872?i=1000784809236 Can magic mushrooms help treat anorexia?] (Apple Podcasts)
* [https://www.apa.org/news/podcasts/speaking-of-psychology/eating-disorder The ‘silent epidemic’ of eating disorders] (American Psychological Association)
* [https://www.apa.org/monitor/2023/04/sensations-eating-disorders-suicidal-behavior What is interoception, and how does it affect mental health]? 5 questions for April Smith (American Psychological Association)
* [https://www.cbte.co/what-is-cbte/transdiagnostic-view-eating-disorders/ Transdiagnostic view of eating disorders] (cbte.co)
* [https://psychedelic.support/resources/polyvagal-theory-mind-body-dr-erica-zelfand/ Polyvagal Theory with Dr. Erica Zelfand: Mind-Body Connection] ·(Psychedelic Support)
* [https://www.wholeselfnutrition.org/post/nervous-system-regulation-a-missing-piece-in-eating-disorder-recovery Nervous System Regulation: A Missing Piece in Eating Disorder Recovery]  (wholeselfnutrition.org)
* [https://youtu.be/RwS-CHJcCiY?si=157viTWiOGAQ-7LP Best Neural Entropy - Explainer] (Youtube)

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      <text bytes="37666" sha1="d99m2kuanhgx4nvywe33pzdr1ojvnud" xml:space="preserve">{{title|Psychedelic treatment of eating disorders:&lt;br&gt;How might psychedelic-assisted therapy influence psychological mechanisms involved in eating disorders?}}
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== Overview ==
{{RoundBoxTop|theme=7}}[[File:Neural network - Midjourney and Grok.png|thumb|'''Figure 1.''' Psychedelics are thought to temporarily disrupt rigid neural communication pathways by promoting more flexible patterns of connectivity across networks involved in mood regulation, fear processing, reward learning, and cognitive adaptability. These changes may support therapeutic shifts in behaviour and emotional processing (Hatzipantelis &amp; Olson, 2025).]]Emma, a 27‑year‑old from Canberra, has lived with an eating disorder for nearly two decades. She describes her problem eating behaviours to have started at school, after being bullied about her appearance and experiencing an unsteady home life. Ever since, they have remained in her life as “a way for me to feel in control”. Although she is aware of the harm caused by restrictive eating and compulsive exercise, she feels trapped in her thought patterns characterised by a preoccupation about food and weight concerns, as they've become entrenched in her daily life. 

After reading an article describing emerging research suggesting that psychedelics may alter patterns of neural connectivity that shape behaviour (see Figure 1), she expressed interest in pursuing psychedelic‑assisted therapy through a provider accessible to her.

After participating in her first supervised psilocybin‑assisted therapy session, Emma reported experiencing an emotional journey that allowed her to feel “connected to my body for the first time in years”. After 3 months, she has noticed a shift in how she relates to her body, and is finding it easier to actively call into question how she responds to distress with the support of her psychotherapist. 


Her experience raises a central question: What psychological mechanisms could explain these changes?{{RoundBoxBottom|theme=3}}  

This chapter explores how psychedelic‑assisted therapy (PAT) may influence the emotional, cognitive, and neurobiological processes that underpin eating disorders (EDs).   

{{RoundBoxTop|theme=11}}'''Focus questions'''
{{ic|}}Two central questions will be addressed:
* What psychological processes underpin eating disorders, and how do they guide ED behaviour?
* How might psychedelic‑assisted therapy influence these processes and support recovery?
{{ic|}}{{ic|}}{{RoundBoxBottom}}

== Introduction ==
'''Eating disorders'''  

[[wikipedia:Eating_disorder|Eating disorders]] (EDs) are psychiatric conditions characterised by abnormal eating behaviours that negatively affect physical and mental health. In Australia, the prevalence of EDs is rising particularly among young people. The economic burden is estimated to cost the nation $84 billion, with approximately 10.46% of the population having experienced an ED at some point in their lives (Hay et al., 2023). Although other forms of disordered eating exist, this chapter will focus on only three of them (see table 1), as [[wikipedia:Anorexia|Anorexia Nervosa]] (AN) has the highest mortality rate of any psychiatric disorder, while [[wikipedia:Bulimia|Bulimia Nervosa]] (BN) and [[wikipedia:Binge_eating_disorder|Binge‑Eating Disorder]] (BED) are also highly prevalent. The EDs mentioned are most associated with chronic illness, disability, reduced quality of life, increased suicide risk, and are highly comorbid with [[wikipedia:Mood_disorder|mood disorders]], [[wikipedia:Post-traumatic_stress_disorder|post-traumatic stress disorder]] (PTSD), [[wikipedia:Obsessive–compulsive_disorder|obsessive-compulsive disorder]] (OCD), and [[wikipedia:Substance_use_disorder|substance use disorders]] (Calder et al., 2023).  Despite decades of research, the pathogenesis of EDs remains incompletely understood. Current evidence suggests a complex interplay between genetic predisposition, temperament, hormonal dysregulation, cognitive abnormalities, sociocultural pressures, and traumatic experiences (Calder et al., 2023).  
{| class=&quot;wikitable&quot;
|+Table 1. Eating disorders and associated symptoms
!Eating disorder
!Primary symptoms
|-
|Anorexia Nervosa
|Severe caloric restriction, fear of gaining weight, distorted body image, preoccupation with weight loss, compulsive exercise.
|-
|Bullimia Nervosa
|Intense windows of food intake (binge eating) followed by inappropriate compensatory behaviours also known as 'purging' (eg. vomiting, laxative use), feelings of guilt and loss of control.
|-
|Binge-Eating Disorder
|Recurrent episodes of binge eating not followed by inappropriate compensatory behaviours, feelings of distress and loss of control.
(Wanderlich &amp; Attia., 2024)
|}


Although cognitive‑behavioural therapy (CBT‑E) combined with pharmacological treatment has demonstrated beneficial outcomes, efficacy remains limited and varies across ED types (Calder et al., 2023). Recovery is often long and difficult, with only two‑thirds of individuals with AN and BN eventually recovering, while others can remain ill for many years. This highlights the need for treatment approaches that can accelerate recovery and provide benefit for individuals who do not respond to conventional therapies.


'''Psychedelic-assisted therapy'''

In 2023, Australia legalised the prescription of MDMA and psilocybin under professional supervision, marking a significant shift in mental‑health treatment options. Psychedelic compounds, including [[wikipedia:LSD|LSD]], [[wikipedia:Psilocybin|psilocybin]], [[wikipedia:Dimethyltryptamine|DMT]], [[wikipedia:Ketamine|ketamine]], and [[wikipedia:MDMA|MDMA]], have demonstrated promising therapeutic effects across a wide range of psychiatric conditions. Researchers propose that psychedelics act through psychological and neural mechanisms that increase [[wikipedia:Neuroplasticity|neuroplasticity]], facilitate insight, and foster emotional acceptance (Peled‑Avron et al., 2024). At a neurobiological level, psychedelics influence processes that inform perception, emotion, and behaviour, offering a potential avenue for addressing entrenched ED mechanisms.

PAT differs from pharmacological treatment alone because the drug is administered within a structured therapeutic context designed to maximise safety and clinical benefit (Calder et al., 2023). Treatment typically involves three types of sessions, undertaken numerous times, across several months. Preparatory sessions feature participants undergoing psychoeducation, where a psychotherapist establishes rapport and clear safety protocols. Followed by supervised medication sessions, where the participant undergoes the inward experience with the reassurance of clinicians present in the same space. Lastly, integrative sessions led by the psychotherapist provide an opportunity for individuals to process and explore insights from the previous session, in aims to facilitate behavioural change (Wolfgang &amp; Hoge, 2023). This combination of pharmacological and psychological intervention is theorised to effectively target underlying psychological mechanisms common across various mental health disorders, illustrating PAT’s potential as a valuable transdiagnostic treatment option. 

PAT has become a subject of increasing popularity in ED research because many of the psychological mechanisms it is proposed to influence are the same ones implicated in ED maintenance and comorbidities (Calder et al., 2023; Peled-Avron et al., 2024). Early research, including case study reports, small clinical studies, meta-analyses and reviews indicate that PAT produces improvements in affect, reductions in ED symptom severity, enhanced body image, weight restoration, and reductions in comorbid symptoms. Although preliminary, these findings indicate that PAT may disrupt and promote shifts away from maladaptive coping patterns that become entrenched in treatment resistant ED populations.

== Psychological mechanisms in eating disorders ==


'''Emotion dysregulation'''

Emotion dysregulation is considered to be a significant risk factor for the onset and maintenance of EDs. It refers to difficulties recognising, assessing, and modifying emotional responses to meet situational demands (Zhou et al., 2025). 

Research consistently shows that individuals with EDs experience significant challenges in regulating emotions, increasing their vulnerability to comorbid symptoms, which contribute to the emergence of disordered eating patterns (Leppanen et al., 2022). This idea is supported by affect regulation theory which posits that eating disorders develop and are maintained as maladaptive strategies to manage, tolerate and escape from negative emotions and psychological distress (Schaefer et al., 2020; Zanella &amp; Lee, 2022). This is further exemplified in Fitzsimmons &amp; Bardone-Cone’s article examining differences in coping within eating disorder patients (2010). The authors explain that avoidance and emotion-oriented coping styles often function as maladaptive attempts to manage (di)stress. They explain that behaviours such as binge eating, purging, starvation, and/or compulsive exercise provide temporary relief by shifting attention away from uncomfortable emotions. 

Furthermore, alexithymia, characterised by difficulty identifying and describing one’s own emotions, is strongly associated with ED pathology (Shank et al., 2019). Individuals with high alexithymia often struggle to differentiate emotional states from bodily sensations, contributing to behaviours such as emotional eating, eating in the absence of hunger, or rigid restriction. In BED, alexithymia is linked to binge episodes triggered by poorly understood emotional cues, while in AN and BN, alexithymia may contribute to emotional avoidance and reliance on ED behaviours for affect regulation. 

The effects of trauma are contributing factors to emotion dysregulation, and considered a risk factor for ED development. Individuals who experience sexual, physical, or emotional abuse, neglect, and bullying are likely to experience heightened emotional reactivity, threat perception, and avoidance behaviours (Calder et al., 2023). Researchers explain that trauma often results in lowered distress tolerance and increased reliance on maladaptive coping behaviours, including disordered eating. Furthermore, PTSD comorbidity is common, hence trauma‑related symptoms are hypothesised to frequently interact with ED behaviours in complex ways.  


'''Reward processing dysfunction'''
[[File:Striatum.gif|thumb|'''Figure 2.''' Striatum]]
[[File:Anterior cingulate gyrus animation.gif|thumb|'''Figure 3'''. Anterior Cingulate Cortex ]]
Abnormal reward valuation is understood to be a central psychological mechanism that maintains ED behaviours. Research consistently shows that individuals with eating disorders display altered neural activity response to various stimuli, as well as disruptions in reinforcement learning (Calder et al., 2023). Brain regions involved in reward processing, habit formation, and learning, such as the striatum and anterior cingulate cortex (see figures 2 &amp; 3), exhibit atypical activation patterns and differences in dopamine receptor binding across ED types. The insula (see figure 4), which integrates bodily sensations with conscious thought, emotion, and behaviour, also shows altered responses. Together, these regions have been shown to react differently to food images, taste, and social feedback compared to healthy controls, indicating that reward dysfunction extends beyond eating‑related stimuli for ED populations.
[[File:Insular cortex.gif|thumb|'''Figure 4.''' Insula. ]]
In the context of BN and BED, research shows that food is valued more highly than other types of rewards, thus shaping behaviour through its heightened influence on reward outcomes (Calder et al., 2023). Compulsive behaviours specific to each condition (e.g. bingeing, purging) are therefore more likely to occur when food is overvalued and alternative rewards are discounted or ignored. In addition to the neural changes already described, BN and BED are associated with reduced structural and functional connectivity between frontal control regions and the striatum. This combination of highly salient food rewards, and weakened fronto‑striatal pathways, reduces an individual’s ability to inhibit or modulate reward‑seeking impulses. Weak connectivity in these circuits is thought to predict compulsive reward‑seeking behaviour. As a result, even when individuals experience negative consequences from binge episodes, they may struggle to learn from these outcomes or adjust their behaviour accordingly.


Anhedonia, a global reduction in reward responsiveness, is frequently reported by people who experience AN, resulting in food and eating becoming undervalued or aversive to them (Calder et al., 2023). Researchers propose that reward contamination further contributes to this pattern, where the brain learns to associate normally punishing stimuli (e.g., starvation, excessive exercise) with reward, while normally rewarding stimuli (e.g., high‑calorie foods) become experienced as punishment. Structural reductions in the striatum and somatosensory cortex have also been observed, which accounts for distorted bodily sensations and contributes to anhedonia. These changes support maladaptive conditioning in which starvation and weight loss embody a sense of safety, achievement, and emotional relief. Restrictive and preoccupied behaviours centred on food, body shape, and exercise are therefore reinforced over time.

Consistent with affect‑regulation models, eating‑disorder behaviours also become negatively reinforced because they reduce emotional discomfort. This relief increases the likelihood that the behaviours will be repeated, further embedding them within the individual’s coping pattern.


'''Cognitive rigidity'''

Cognitive rigidity refers to inflexible thinking and behavioural patterns, including difficulty adapting to new information and modifying behaviour. Researchers believe that individuals with EDs often exhibit rigid beliefs about food and weight which interact with a need to exert control over negative emotions. This interaction is the proposed process in which compulsive behaviours and obsessive thoughts develop (Calder et al., 2023). In AN, rigidity manifests as strict dietary rules and fear of losing control, while in BN and BED, binge episodes may feel compulsive and uncontrollable.


'''Interoceptive awareness'''

Interoceptive awareness (IA) refers to the ability to recognise and process internal bodily states such as hunger, satiety, pain, and arousal. IA is impaired across EDs, and contributes to body mistrust, distorted hunger cues, and inappropriate responses to internal sensations (Brown et al., 2020). Individuals may ignore physical discomfort, misinterpret bodily signals, or avoid sensations altogether, reinforcing maladaptive coping.      

 &lt;blockquote&gt;'''''QUIZ: Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{What coping style do people who experience EDs tend to show?
|type=&quot;()&quot;}
+ Avoidance-oriented
- Problem-oriented

{Compulsive behaviours are more likely to occur when food is ... and alternative rewards are ...
|type=&quot;()&quot;}
- undervalued; overvalued
+ overvalued; undervalued
&lt;/quiz&gt;&lt;/blockquote&gt;

== PAT's influence on psychological mechanisms ==

PAT is proposed to influence several psychological mechanisms implicated in EDs, particularly those discussed in the previous section. The next part of this chapter aims to examine the theorised therapeutic mechanisms PAT possesses and practical implications for ED treatment.  


'''Emotion regulation''' 

Emotion dysregulation is a core mechanism implicated in EDs. Affect regulation theory proposes that ED behaviours emerge as maladaptive strategies to escape, reduce, or blunt overwhelming emotional experiences (Schaefer et al., 2020). Restriction, bingeing, purging, and compulsive exercise may temporarily alleviate distress while reinforcing avoidance-oriented coping and limiting opportunities to learn more adaptive ways of responding to difficult emotions. 

Psychedelics often evoke intense emotional experiences that may disrupt habitual avoidance patterns. Researchers propose that, during psychedelic sessions, attempts to suppress or avoid difficult emotions can intensify these experiences, creating conditions in which emotional acceptance becomes a preferred response (Calder et al., 2023). Although this shift does not occur in every individual, experiencing difficult emotions without resorting to ED behaviours may weaken the association between emotional distress and maladaptive coping, particularly when emotional acceptance becomes associated with a more positive or tolerable experience.

The therapeutic value of this process lies in its potential to reshape affective responses. When individuals experience strong emotions without engaging in maladaptive behaviours, they may begin to develop a new approach towards emotional tolerance. Integration sessions can consolidate this learning by helping individuals articulate, differentiate, and reflect on the emotions experienced during dosing. This process may support the development of more adaptive coping strategies, including task-oriented, problem-focused, and socially supported approaches, which are associated with improved ED outcomes (Fitzsimmons &amp; Bardone-Cone, 2010). In this way, PAT may strengthen emotion regulation and reduce reliance on ED behaviours as strategies for managing affect. 


'''Reward processing''' 

Reward dysfunction may contribute to the maintenance of EDs by reinforcing maladaptive behaviours while diminishing the perceived value of adaptive rewards. Predictive coding provides a useful framework for understanding how PAT might influence these processes. Individuals with EDs may hold rigid beliefs, conceptualised as high-level priors, about themselves in relation to food, body weight, and rewarding behaviours (Calder et al., 2023; Mograbi et al., 2024). These beliefs can influence how experiences are perceived and valued, potentially reinforcing existing behavioural patterns. Psychedelics are proposed to weaken high-level priors, allowing bottom-up sensory information to exert greater influence on perception and the valuation of experiences. 

During psychedelic experiences, individuals frequently report a heightened appreciation of sensory, social, and bodily experiences. This shift may counteract anhedonia and support the revaluation of previously feared or avoided stimuli. The therapeutic opportunity lies in translating these temporary changes in perception and reward into meaningful behavioural change. Integration sessions can explore positive and negative moments experienced during dosing and connect them to concrete goals. An example of this, inspired from Calder et al.’s (2023) article, could be to clarify specific plans to nourish the body due to the participant having experienced themselves as a decaying skeleton followed by the realisation of the body being a gift. If the period following dosing provides an opportunity for increased neuroplasticity, it may also be particularly conducive to reinforcing adaptive reward learning through behavioural activation with the help of a therapist. 


'''Cognitive flexibility''' 

Cognitive rigidity is a hallmark of EDs and is characterised by inflexible beliefs about food, weight, body shape, and control. Predictive coding provides a framework for understanding this rigidity, as EDs may involve entrenched priors that resist updating even when confronted with contradictory sensory evidence (Zanella &amp; Lee, 2022). Psychedelics are proposed to disrupt these entrenched priors by increasing neural entropy and reducing the dominance of top-down processing (Calder et al., 2023). This temporary loosening of cognitive constraints may allow individuals to consider alternative perspectives and question long-held beliefs. 

Experiences of ego dissolution may further contribute to cognitive flexibility by reducing attachment to rigid self-concepts (Peled-Avron, 2024; Mograbi et al., 2024). When the boundaries of the self become less defined, individuals may find it easier to question identity-related beliefs that sustain ED pathology. Integration sessions can harness this potential flexibility by supporting cognitive reframing, encouraging behavioural experiments, and strengthening metacognitive awareness. Through these processes, individuals may be better able to translate insights gained during psychedelic experiences into sustained changes in thinking and behaviour.


'''Reconnecting with bodily signals'''

Interoceptive deficits are central to ED pathology, contributing to body mistrust, distorted perceptions of hunger cues, and difficulties responding appropriately to internal sensations (Brown et al., 2020). Psychedelics may enhance interoceptive awareness by altering sensory processing and increasing sensitivity to bodily signals. This proposed mechanism is closely related to autonomic regulation, for which polyvagal theory provides a framework for understanding the relationship between bodily signals, emotional regulation, and perceived safety.

Polyvagal theory emphasises the role of the vagus nerve in interoception, emotional regulation, and the perception of safety (Porges, 2022). Vagal afferents transmit information from the body to the insula, where interoceptive signals are integrated with emotional and cognitive processes. Individuals with EDs may exhibit chronic sympathetic arousal and reduced vagal tone, potentially impairing interoceptive accuracy and contributing to emotional rigidity. Psychedelics may initially increase sympathetic activity, as reflected in physiological responses such as increased heart rate, followed by a parasympathetic shift associated with greater relaxation and an increased capacity for rest (Li et al., 2025). Within a polyvagal framework, these changes may have implications for vagal regulation, interoceptive awareness, and emotional regulation.

The therapeutic value of this proposed mechanism lies in its potential to restore trust in bodily signals. Integration sessions may support this process by helping individuals explore bodily sensations experienced during dosing, connect interoceptive cues with emotional states, and practise interoceptive exposure to hunger, fullness, and anxiety-related sensations. Incorporating mindfulness techniques may further support autonomic regulation and help individuals develop a more adaptive relationship with their bodily experiences.

 A brief note concerning the gut-brain axis
Although gut microbiome disruption is not a direct psychological mechanism in EDs, it is a relevant biological factor to consider when examining the potential effects of PAT. Restrictive or chaotic eating patterns can contribute to gut dysbiosis, which may weaken gut-barrier integrity and contribute to inflammation affecting the brain (Anton-Paduraru et al., 2024). These changes have been shown to influence mood, stress responsivity, cognitive rigidity, and interoceptive awareness through [[wikipedia:Hypothalamic–pituitary–adrenal_axis|HPA-axis activation]], altered neurotransmitter synthesis, and disrupted hunger–satiety signalling. 

Emerging research suggests that psychedelics may also interact with the [[wikipedia:Gut–brain_axis|gut–brain axis]]. Certain microbes can metabolise psychedelic compounds, and microbial activity has been associated with modulatory effects on behavioural outcomes. Additionally, psychedelic use may alter microbial composition towards anti-inflammatory profiles, with potential implications for neuroplasticity, neurotransmitter synthesis and signalling improvements (Caspani et al., 2024). These microbiome-related effects may therefore contribute to changes in mood, cognitive flexibility, and appetite regulation.

Although the therapeutic potential of psychedelics in EDs is considered primarily in relation to psychological mechanisms, including changes in perception, emotional processing, and reduced avoidance, microbiome-related effects may represent an additional pathway through which biological processes influence psychological outcomes. However, the extent to which these interactions contribute to therapeutic outcomes in EDs remains to be established.


&lt;blockquote&gt;'''QUIZ: ''Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{ In predictive coding terms, what are “high‑level priors” in eating disorders? 
|type=&quot;()&quot;}
+ Rigid, entrenched beliefs about food, weight, and the self that shape perception and behaviour
- Flexible beliefs that easily update with new sensory information
- Momentary emotional reactions triggered by external cues

{What is the proposed mechanism by which psychedelics support emotion regulation in PAT for EDs? 
|type=&quot;()&quot;}
- By suppressing emotional intensity to prevent distress
+ By evoking strong emotions that disrupt avoidance patterns and promote emotional acceptance
- By eliminating negative emotions through serotonin release

{What is interoceptive awareness?
|type=&quot;()&quot;}
- The ability to evaluate reward value and anticipate pleasurable outcomes
+ The capacity to sense, interpret, and respond to internal bodily signals such as hunger, fullness, and emotional arousal
- The process of weakening cognitive rigidity through ego dissolution
&lt;/quiz&gt;&lt;/blockquote&gt;

== Limitations ==
Despite the potential of PAT to influence psychological mechanisms implicated in EDs, several limitations constrain current understanding of these processes and their therapeutic relevance. Research examining emotion dysregulation in EDs illustrates broader challenges in establishing the mechanisms underlying these conditions. Although non-acceptance of emotions has been identified as a transdiagnostic risk factor across psychiatric conditions (Paulus et al., 2021), Zhou et al.’s meta-analysis (2025) highlights that the causal pathways linking emotional dysregulation and EDs remain unclear, largely because of a lack of experimental and longitudinal studies. Further limitations include restricted availability of measurement scales, insufficient cultural specificity, heterogeneity across samples, gender imbalance, and limited developmental analysis. Together, these factors constrain understanding of how specific emotional processes relate to different ED presentations across the lifespan and stages of recovery.

These limitations are also relevant when considering the proposed mechanisms of PAT. Although existing theoretical frameworks offer ways to conceptualise how psychedelic experiences may influence psychological processes responsible for EDs, the emerging nature of psychedelic therapy limits the extent to which proposed mechanisms have been tested. However, with the number of clinical trials increasing as of recently, it will be interesting to see how the theorised therapeutic mechanisms across different ED presentations and stages of recovery emerges during further warranted investigation.

Nevertheless, current limitations in the evidence highlight the need for research that clarifies the relationships between psychological processes that underscore ED behaviours, and treatment outcomes. There are several important psychological components of ED maintenance that represent meaningful targets for treatment, but they should not be considered in isolation from eachother or the neurobiological processes that influence them. A more comprehensive understanding of how these mechanisms interact may help clarify the therapeutic potential of PAT and inform the development of more targeted treatment approaches.

== Conclusion ==
PAT offers a potential framework for addressing several interconnected psychological mechanisms implicated in EDs. Through its proposed effects on emotional processing, reward valuation, cognitive flexibility, and interoceptive awareness, PAT may create opportunities to disrupt established patterns of avoidance, rigid thinking, and maladaptive behavioural reinforcement. The gut–brain interaction may represent an additional biological pathway relevant to these processes.

These mechanisms should not be understood as independent processes. Changes in emotion regulation may influence the ability to tolerate bodily sensations, while shifts in reward valuation and cognitive flexibility may create opportunities to respond differently to distress and challenge entrenched beliefs. However, the extent to which PAT produces these changes, and whether they translate into sustained improvements in ED outcomes, requires further investigation, although preliminary evidence is promising. 

The therapeutic potential of PAT lies not only in the acute psychedelic experience but also in the structured integration process that follows. Integration sessions provide an opportunity to translate emotional breakthroughs, changes in cognitive flexibility, interoceptive shifts, and reward processing into sustained behavioural change. Effective integration involves helping individuals articulate insights, connect them to ED-related patterns, and develop concrete strategies for change. These may include strengthening adaptive coping, challenging rigid beliefs, practising interoceptive awareness, reinforcing positive reward experiences, and supporting nutritional rehabilitation.

By grounding the understanding of PAT in affect regulation theory and the predictive coding framework, therapists may be better positioned to help individuals explore how psychedelic experiences could disrupt maladaptive emotional and cognitive patterns and create opportunities for new learning. Polyvagal-informed approaches may further support the development of mind–body awareness and emotional regulation through mindfulness strategies. Together, these approaches offer a multifaceted framework for translating psychedelic experiences into therapeutic change and addressing the interconnected mechanisms that maintain EDs and associated suffering. 

==See Also==
* [https://w.wiki/TsdG Ayahuasca and the brain] (Wikiversity)
* [https://w.wiki/TscF Emotional effects of psychedelics] (Wikiversity)
* [https://w.wiki/Tsdb Psilocybin and emotion] (Wikiversity)
* [https://w.wiki/TsdS Psilocibyn assisted psychotherapy] (Wikiversity)
* [https://w.wiki/Tsce Psychedelics, altered consciousness, and personal growth] (Wikiversity)
* [[Eating Disorders|Eating disorders]] (Wikiversity)

==References==
{{Hanging indent|1=

{{ic|Try &quot;Edit source&quot; and then wrapping any text to be italicised in two apostrophes e.g., ''this is italics''}}

Anton-Păduraru, D. T., Trofin, F., Nastase, E. V., Miftode, R. S., Miftode, I. L., Trandafirescu, M. F., Cojocaru, E., Țarcă, E., Mindru, D. E., &amp; Dorneanu, O. S. (2023). The Role of the Gut Microbiota in Anorexia Nervosa in Children and Adults-Systematic Review. &quot;International journal of molecular sciences, 25&quot;(1), 41. https://doi.org/10.3390/ijms25010041

Brown, T. A., Vanzhula, I. A., Reilly, E. E., Levinson, C. A., Berner, L. A., Krueger, A., Lavender, J. M., Kaye, W. H., &amp; Wierenga, C. E. (2020). Body mistrust bridges interoceptive awareness and eating disorder symptoms. &quot;Journal of abnormal psychology, 129&quot;(5), 445–456. https://doi.org/10.1037/abn0000516 

Calder, A., Mock, S., Friedli, N., Pasi, P., &amp; Hasler, G. (2023). Psychedelics in the treatment of eating disorders: Rationale and potential mechanisms. &quot;European Neuropsychopharmacology, 75&quot;, 1–14. https://doi.org/10.1016/j.euroneuro.2023.05.008 

Caspani, G., Ruffell, S. G. D., Tsang, W., Netzband, N., Rohani-Shukla, C., Swann, J. R., &amp; Jefferies, W. A. (2024). Mind over matter: the microbial mindscapes of psychedelics and the gut-brain axis. &quot;Pharmacological research, 207&quot;, 107338. https://doi.org/10.1016/j.phrs.2024.107338  

Fitzsimmons, E. E., &amp; Bardone-Cone, A. M. (2010). Differences in coping across stages of recovery from an eating disorder. &quot;The International journal of eating disorders, 43&quot;(8), 689–693. https://doi.org/10.1002/eat.20781 

Hatzipantelis, C. J., &amp; Olson, D. E. (2024). The Effects of Psychedelics on Neuronal Physiology. &quot;Annual review of physiology, 86&quot;, 27–47. https://doi.org/10.1146/annurev-physiol-042022-020923

Hay, P., Aouad, P., Le, A., Marks, P., Maloney, D., National Eating Disorder Research Consortium, Touyz, S., &amp; Maguire, S. (2023). Epidemiology of eating disorders: population, prevalence, disease burden and quality of life informing public policy in Australia-a rapid review. &quot;Journal of eating disorders, 11&quot;(1), 23. https://doi.org/10.1186/s40337-023-00738-7

Li, H., Wang, H., &amp; Wang, X. (2025). Psychedelics and the Autonomic Nervous System: A Perspective on Their Interplay and Therapeutic Potential. &quot;ACS pharmacology &amp; translational science, 8&quot;(3), 899–902. https://doi.org/10.1021/acsptsci.5c00005 

Leppanen, J., Brown, D., McLinden, H., Williams, S., &amp; Tchanturia, K. (2022). The Role of Emotion Regulation in Eating Disorders: A Network Meta-Analysis Approach. &quot;Frontiers in psychiatry, 13&quot;, 793094. https://doi.org/10.3389/fpsyt.2022.793094 

Mograbi, D. C., Rodrigues, R., Bienemann, B., &amp; Huntley, J. (2024). Brain Networks, Neurotransmitters and Psychedelics: Towards a Neurochemistry of Self-Awareness. &quot;Current neurology and neuroscience reports, 24&quot;(8), 323–340. https://doi.org/10.1007/s11910-024-01353-y

Paulus F. W., Ohmann S., Möhler E., Plener P. &amp; Popow C. (2021). Emotional Dysregulation in Children and Adolescents With Psychiatric Disorders. A Narrative Review. &quot;Frontiers in Psychiatry 12&quot;:628252. doi: 10.3389/fpsyt.2021.628252

Peled-Avron L., Aday J. Ss, Kalafateli A. L., Hamilton H. K., Woolley J. D. (2024). Editorial: Down the rabbit hole – the psychological and neural mechanisms of psychedelic compounds and their use in treating mental health and medical conditions. &quot;Frontiers in Psychiatry 15&quot;:1431389. doi: 10.3389/fpsyt.2024.1431389

Porges S. W. (2025). Polyvagal Theory: Current Status, Clinical Applications, and Future Directions. &quot;Clinical neuropsychiatry, 22&quot;(3), 169–184. https://doi.org/10.36131/cnfioritieditore20250301

Schaefer, L. M., Smith, K. E., Anderson, L. M., Cao, L., Crosby, R. D., Engel, S. G., Crow, S. J., Peterson, C. B., &amp; Wonderlich, S. A. (2020). The role of affect in the maintenance of binge-eating disorder: Evidence from an ecological momentary assessment study. &quot;Journal of abnormal psychology, 129&quot;(4), 387–396. https://doi.org/10.1037/abn0000517 

Shank, L. M., Tanofsky-Kraff, M., Kelly, N. R., Jaramillo, M., Rubin, S. G., Altman, D. R., Byrne, M. E., LeMay-Russell, S., Schvey, N. A., Broadney, M. M., Brady, S. M., Yang, S. B., Courville, A. B., Ramirez, S., Crist, A. C., Yanovski, S. Z., &amp; Yanovski, J. A. (2019). The association between alexithymia and eating behavior in children and adolescents. &quot;Appetite, 142&quot;, 104381. https://doi.org/10.1016/j.appet.2019.104381

Wonderlich, J., &amp; Attia, E. (2024). Eating disorders in the DSM-5. In P. Robinson, T. Wade, B. Herpertz-Dahlmann, F. Fernandez-Aranda, J. Treasure, &amp; S. Wonderlich (Eds.), Eating disorders: An international comprehensive view (pp. 7–18). &quot;Springer Nature Switzerland AG&quot;. https://doi.org/10.1007/978-3-031-46096-8_9

Wolfgang, A. S., &amp; Hoge, C. W. (2023). Psychedelic-Assisted Therapy in Military and Veterans Healthcare Systems: Clinical, Legal, and Implementation Considerations. &quot;Current psychiatry reports, 25&quot;(10), 513–532. https://doi.org/10.1007/s11920-023-01446-4 

Zanella, E., &amp; Lee, E. (2022). Integrative review on psychological and social risk and prevention factors of eating disorders including anorexia nervosa and bulimia nervosa: seven major theories. &quot;Heliyon, 8&quot;(11), e11422. https://doi.org/10.1016/j.heliyon.2022.e11422 

Zhou, R., Zhang, L., Liu, Z., &amp; Cao, B. (2025). Emotion regulation difficulties and disordered eating in adolescents and young adults: a meta-analysis. &quot;Journal of eating disorders, 13&quot;(1), 25. https://doi.org/10.1186/s40337-025-01197-y

}}

==External links==
* [https://www.abct.org/fact-sheets/psychedelic-assisted-therapy/ Psychedelic-Assisted Therapy | Fact Sheet] (ABCT - Association for Behavioral and Cognitive Therapies)
* [https://podcasts.apple.com/au/podcast/can-magic-mushrooms-help-treat-anorexia/id189330872?i=1000784809236 Can magic mushrooms help treat anorexia?] (Apple Podcasts)
* [https://www.apa.org/news/podcasts/speaking-of-psychology/eating-disorder The ‘silent epidemic’ of eating disorders] (American Psychological Association)
* [https://www.apa.org/monitor/2023/04/sensations-eating-disorders-suicidal-behavior What is interoception, and how does it affect mental health]? 5 questions for April Smith (American Psychological Association)
* [https://www.cbte.co/what-is-cbte/transdiagnostic-view-eating-disorders/ Transdiagnostic view of eating disorders] (cbte.co)
* [https://psychedelic.support/resources/polyvagal-theory-mind-body-dr-erica-zelfand/ Polyvagal Theory with Dr. Erica Zelfand: Mind-Body Connection] ·(Psychedelic Support)
* [https://www.wholeselfnutrition.org/post/nervous-system-regulation-a-missing-piece-in-eating-disorder-recovery Nervous System Regulation: A Missing Piece in Eating Disorder Recovery]  (wholeselfnutrition.org)
* [https://youtu.be/RwS-CHJcCiY?si=157viTWiOGAQ-7LP Best Neural Entropy - Explainer] (Youtube)

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      <text bytes="37671" sha1="2c1k1r70nvbq43x2gd39k5a539pje0y" xml:space="preserve">{{title|Psychedelic treatment of eating disorders:&lt;br&gt;How might psychedelic-assisted therapy influence psychological mechanisms involved in eating disorders?}}
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== Overview ==
{{RoundBoxTop|theme=7}}[[File:Neural network - Midjourney and Grok.png|thumb|'''Figure 1.''' Psychedelics are thought to temporarily disrupt rigid neural communication pathways by promoting more flexible patterns of connectivity across networks involved in mood regulation, fear processing, reward learning, and cognitive adaptability. These changes may support therapeutic shifts in behaviour and emotional processing (Hatzipantelis &amp; Olson, 2025).]]Emma, a 27‑year‑old from Canberra, has lived with an eating disorder for nearly two decades. She describes her problem eating behaviours to have started at school, after being bullied about her appearance and experiencing an unsteady home life. Ever since, they have remained in her life as “a way for me to feel in control”. Although she is aware of the harm caused by restrictive eating and compulsive exercise, she feels trapped in her thought patterns characterised by a preoccupation about food and weight concerns, as they've become entrenched in her daily life. 

After reading an article describing emerging research suggesting that psychedelics may alter patterns of neural connectivity that shape behaviour (see Figure 1), she expressed interest in pursuing psychedelic‑assisted therapy through a provider accessible to her.

After participating in her first supervised psilocybin‑assisted therapy session, Emma reported experiencing an emotional journey that allowed her to feel “connected to my body for the first time in years”. After 3 months, she has noticed a shift in how she relates to her body, and is finding it easier to actively call into question how she responds to distress with the support of her psychotherapist. 


Her experience raises a central question: What psychological mechanisms could explain these changes?{{RoundBoxBottom|theme=3}}  

This chapter explores how psychedelic‑assisted therapy (PAT) may influence the emotional, cognitive, and neurobiological processes that underpin eating disorders (EDs).   

{{RoundBoxTop|theme=11}}'''Focus questions'''
{{ic|}}Two central questions will be addressed:
* What psychological processes underpin eating disorders, and how do they guide ED behaviour?
* How might psychedelic‑assisted therapy influence these processes and support recovery?
{{ic|}}{{ic|}}{{RoundBoxBottom}}

== Introduction ==
'''Eating disorders'''  

[[wikipedia:Eating_disorder|Eating disorders]] (EDs) are psychiatric conditions characterised by abnormal eating behaviours that negatively affect physical and mental health. In Australia, the prevalence of EDs is rising particularly among young people. The economic burden is estimated to cost the nation $84 billion, with approximately 10.46% of the population having experienced an ED at some point in their lives (Hay et al., 2023). Although other forms of disordered eating exist, this chapter will focus on only three of them (see table 1), as [[wikipedia:Anorexia|Anorexia Nervosa]] (AN) has the highest mortality rate of any psychiatric disorder, while [[wikipedia:Bulimia|Bulimia Nervosa]] (BN) and [[wikipedia:Binge_eating_disorder|Binge‑Eating Disorder]] (BED) are also highly prevalent. The EDs mentioned are most associated with chronic illness, disability, reduced quality of life, increased suicide risk, and are highly comorbid with [[wikipedia:Mood_disorder|mood disorders]], [[wikipedia:Post-traumatic_stress_disorder|post-traumatic stress disorder]] (PTSD), [[wikipedia:Obsessive–compulsive_disorder|obsessive-compulsive disorder]] (OCD), and [[wikipedia:Substance_use_disorder|substance use disorders]] (Calder et al., 2023).  Despite decades of research, the pathogenesis of EDs remains incompletely understood. Current evidence suggests a complex interplay between genetic predisposition, temperament, hormonal dysregulation, cognitive abnormalities, sociocultural pressures, and traumatic experiences (Calder et al., 2023).  
{| class=&quot;wikitable&quot;
|+Table 1. Eating disorders and associated symptoms
!Eating disorder
!Primary symptoms
|-
|Anorexia Nervosa
|Severe caloric restriction, fear of gaining weight, distorted body image, preoccupation with weight loss, compulsive exercise.
|-
|Bullimia Nervosa
|Intense windows of food intake (binge eating) followed by inappropriate compensatory behaviours also known as 'purging' (eg. vomiting, laxative use), feelings of guilt and loss of control.
|-
|Binge-Eating Disorder
|Recurrent episodes of binge eating not followed by inappropriate compensatory behaviours, feelings of distress and loss of control.
(Wanderlich &amp; Attia., 2024)
|}


Although cognitive‑behavioural therapy (CBT‑E) combined with pharmacological treatment has demonstrated beneficial outcomes, efficacy remains limited and varies across ED types (Calder et al., 2023). Recovery is often long and difficult, with only two‑thirds of individuals with AN and BN eventually recovering, while others can remain ill for many years. This highlights the need for treatment approaches that can accelerate recovery and provide benefit for individuals who do not respond to conventional therapies.


'''Psychedelic-assisted therapy'''

In 2023, Australia legalised the prescription of MDMA and psilocybin under professional supervision, marking a significant shift in mental‑health treatment options. Psychedelic compounds, including [[wikipedia:LSD|LSD]], [[wikipedia:Psilocybin|psilocybin]], [[wikipedia:Dimethyltryptamine|DMT]], [[wikipedia:Ketamine|ketamine]], and [[wikipedia:MDMA|MDMA]], have demonstrated promising therapeutic effects across a wide range of psychiatric conditions. Researchers propose that psychedelics act through psychological and neural mechanisms that increase [[wikipedia:Neuroplasticity|neuroplasticity]], facilitate insight, and foster emotional acceptance (Peled‑Avron et al., 2024). At a neurobiological level, psychedelics influence processes that inform perception, emotion, and behaviour, offering a potential avenue for addressing entrenched ED mechanisms.

PAT differs from pharmacological treatment alone because the drug is administered within a structured therapeutic context designed to maximise safety and clinical benefit (Calder et al., 2023). Treatment typically involves three types of sessions, undertaken numerous times, across several months. Preparatory sessions feature participants undergoing psychoeducation, where a psychotherapist establishes rapport and clear safety protocols. Followed by supervised medication sessions, where the participant undergoes the inward experience with the reassurance of clinicians present in the same space. Lastly, integrative sessions led by the psychotherapist provide an opportunity for individuals to process and explore insights from the previous session, in aims to facilitate behavioural change (Wolfgang &amp; Hoge, 2023). This combination of pharmacological and psychological intervention is theorised to effectively target underlying psychological mechanisms common across various mental health disorders, illustrating PAT’s potential as a valuable transdiagnostic treatment option. 

PAT has become a subject of increasing popularity in ED research because many of the psychological mechanisms it is proposed to influence are the same ones implicated in ED maintenance and comorbidities (Calder et al., 2023; Peled-Avron et al., 2024). Early research, including case study reports, small clinical studies, meta-analyses and reviews indicate that PAT produces improvements in affect, reductions in ED symptom severity, enhanced body image, weight restoration, and reductions in comorbid symptoms. Although preliminary, these findings indicate that PAT may disrupt and promote shifts away from maladaptive coping patterns that become entrenched in treatment resistant ED populations.

== Psychological mechanisms in eating disorders ==


'''Emotion dysregulation'''

Emotion dysregulation is considered to be a significant risk factor for the onset and maintenance of EDs. It refers to difficulties recognising, assessing, and modifying emotional responses to meet situational demands (Zhou et al., 2025). 

Research consistently shows that individuals with EDs experience significant challenges in regulating emotions, increasing their vulnerability to comorbid symptoms, which contribute to the emergence of disordered eating patterns (Leppanen et al., 2022). This idea is supported by affect regulation theory which posits that eating disorders develop and are maintained as maladaptive strategies to manage, tolerate and escape from negative emotions and psychological distress (Schaefer et al., 2020; Zanella &amp; Lee, 2022). This is further exemplified in Fitzsimmons &amp; Bardone-Cone’s article examining differences in coping within eating disorder patients (2010). The authors explain that avoidance and emotion-oriented coping styles often function as maladaptive attempts to manage (di)stress. They explain that behaviours such as binge eating, purging, starvation, and/or compulsive exercise provide temporary relief by shifting attention away from uncomfortable emotions. 

Furthermore, alexithymia, characterised by difficulty identifying and describing one’s own emotions, is strongly associated with ED pathology (Shank et al., 2019). Individuals with high alexithymia often struggle to differentiate emotional states from bodily sensations, contributing to behaviours such as emotional eating, eating in the absence of hunger, or rigid restriction. In BED, alexithymia is linked to binge episodes triggered by poorly understood emotional cues, while in AN and BN, alexithymia may contribute to emotional avoidance and reliance on ED behaviours for affect regulation. 

The effects of trauma are contributing factors to emotion dysregulation, and considered a risk factor for ED development. Individuals who experience sexual, physical, or emotional abuse, neglect, and bullying are likely to experience heightened emotional reactivity, threat perception, and avoidance behaviours (Calder et al., 2023). Researchers explain that trauma often results in lowered distress tolerance and increased reliance on maladaptive coping behaviours, including disordered eating. Furthermore, PTSD comorbidity is common, hence trauma‑related symptoms are hypothesised to frequently interact with ED behaviours in complex ways.  


'''Reward processing dysfunction'''
[[File:Striatum.gif|thumb|'''Figure 2.''' Striatum]]
[[File:Anterior cingulate gyrus animation.gif|thumb|'''Figure 3'''. Anterior Cingulate Cortex ]]
Abnormal reward valuation is understood to be a central psychological mechanism that maintains ED behaviours. Research consistently shows that individuals with eating disorders display altered neural activity response to various stimuli, as well as disruptions in reinforcement learning (Calder et al., 2023). Brain regions involved in reward processing, habit formation, and learning, such as the striatum and anterior cingulate cortex (see figures 2 &amp; 3), exhibit atypical activation patterns and differences in dopamine receptor binding across ED types. The insula (see figure 4), which integrates bodily sensations with conscious thought, emotion, and behaviour, also shows altered responses. Together, these regions have been shown to react differently to food images, taste, and social feedback compared to healthy controls, indicating that reward dysfunction extends beyond eating‑related stimuli for ED populations.
[[File:Insular cortex.gif|thumb|'''Figure 4.''' Insula. ]]
In the context of BN and BED, research shows that food is valued more highly than other types of rewards, thus shaping behaviour through its heightened influence on reward outcomes (Calder et al., 2023). Compulsive behaviours specific to each condition (e.g. bingeing, purging) are therefore more likely to occur when food is overvalued and alternative rewards are discounted or ignored. In addition to the neural changes already described, BN and BED are associated with reduced structural and functional connectivity between frontal control regions and the striatum. This combination of highly salient food rewards, and weakened fronto‑striatal pathways, reduces an individual’s ability to inhibit or modulate reward‑seeking impulses. Weak connectivity in these circuits is thought to predict compulsive reward‑seeking behaviour. As a result, even when individuals experience negative consequences from binge episodes, they may struggle to learn from these outcomes or adjust their behaviour accordingly.


Anhedonia, a global reduction in reward responsiveness, is frequently reported by people who experience AN, resulting in food and eating becoming undervalued or aversive to them (Calder et al., 2023). Researchers propose that reward contamination further contributes to this pattern, where the brain learns to associate normally punishing stimuli (e.g., starvation, excessive exercise) with reward, while normally rewarding stimuli (e.g., high‑calorie foods) become experienced as punishment. Structural reductions in the striatum and somatosensory cortex have also been observed, which accounts for distorted bodily sensations and contributes to anhedonia. These changes support maladaptive conditioning in which starvation and weight loss embody a sense of safety, achievement, and emotional relief. Restrictive and preoccupied behaviours centred on food, body shape, and exercise are therefore reinforced over time.

Consistent with affect‑regulation models, eating‑disorder behaviours also become negatively reinforced because they reduce emotional discomfort. This relief increases the likelihood that the behaviours will be repeated, further embedding them within the individual’s coping pattern.


'''Cognitive rigidity'''

Cognitive rigidity refers to inflexible thinking and behavioural patterns, including difficulty adapting to new information and modifying behaviour. Researchers believe that individuals with EDs often exhibit rigid beliefs about food and weight which interact with a need to exert control over negative emotions. This interaction is the proposed process in which compulsive behaviours and obsessive thoughts develop (Calder et al., 2023). In AN, rigidity manifests as strict dietary rules and fear of losing control, while in BN and BED, binge episodes may feel compulsive and uncontrollable.


'''Interoceptive awareness'''

Interoceptive awareness (IA) refers to the ability to recognise and process internal bodily states such as hunger, satiety, pain, and arousal. IA is impaired across EDs, and contributes to body mistrust, distorted hunger cues, and inappropriate responses to internal sensations (Brown et al., 2020). Individuals may ignore physical discomfort, misinterpret bodily signals, or avoid sensations altogether, reinforcing maladaptive coping.      

 &lt;blockquote&gt;'''''QUIZ: Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{What coping style do people who experience EDs tend to show?
|type=&quot;()&quot;}
+ Avoidance-oriented
- Problem-oriented

{Compulsive behaviours are more likely to occur when food is ... and alternative rewards are ...
|type=&quot;()&quot;}
- undervalued; overvalued
+ overvalued; undervalued
&lt;/quiz&gt;&lt;/blockquote&gt;

== PAT's influence on psychological mechanisms ==

PAT is proposed to influence several psychological mechanisms implicated in EDs, particularly those discussed in the previous section. The next part of this chapter aims to examine the theorised therapeutic mechanisms PAT possesses and practical implications for ED treatment.  


'''Emotion regulation''' 

Emotion dysregulation is a core mechanism implicated in EDs. Affect regulation theory proposes that ED behaviours emerge as maladaptive strategies to escape, reduce, or blunt overwhelming emotional experiences (Schaefer et al., 2020). Restriction, bingeing, purging, and compulsive exercise may temporarily alleviate distress while reinforcing avoidance-oriented coping and limiting opportunities to learn more adaptive ways of responding to difficult emotions. 

Psychedelics often evoke intense emotional experiences that may disrupt habitual avoidance patterns. Researchers propose that, during psychedelic sessions, attempts to suppress or avoid difficult emotions can intensify these experiences, creating conditions in which emotional acceptance becomes a preferred response (Calder et al., 2023). Although this shift does not occur in every individual, experiencing difficult emotions without resorting to ED behaviours may weaken the association between emotional distress and maladaptive coping, particularly when emotional acceptance becomes associated with a more positive or tolerable experience.

The therapeutic value of this process lies in its potential to reshape affective responses. When individuals experience strong emotions without engaging in maladaptive behaviours, they may begin to develop a new approach towards emotional tolerance. Integration sessions can consolidate this learning by helping individuals articulate, differentiate, and reflect on the emotions experienced during dosing. This process may support the development of more adaptive coping strategies, including task-oriented, problem-focused, and socially supported approaches, which are associated with improved ED outcomes (Fitzsimmons &amp; Bardone-Cone, 2010). In this way, PAT may strengthen emotion regulation and reduce reliance on ED behaviours as strategies for managing affect. 


'''Reward processing''' 

Reward dysfunction may contribute to the maintenance of EDs by reinforcing maladaptive behaviours while diminishing the perceived value of adaptive rewards. Predictive coding provides a useful framework for understanding how PAT might influence these processes. Individuals with EDs may hold rigid beliefs, conceptualised as high-level priors, about themselves in relation to food, body weight, and rewarding behaviours (Calder et al., 2023; Mograbi et al., 2024). These beliefs can influence how experiences are perceived and valued, potentially reinforcing existing behavioural patterns. Psychedelics are proposed to weaken high-level priors, allowing bottom-up sensory information to exert greater influence on perception and the valuation of experiences. 

During psychedelic experiences, individuals frequently report a heightened appreciation of sensory, social, and bodily experiences. This shift may counteract anhedonia and support the revaluation of previously feared or avoided stimuli. The therapeutic opportunity lies in translating these temporary changes in perception and reward into meaningful behavioural change. Integration sessions can explore positive and negative moments experienced during dosing and connect them to concrete goals. An example of this, inspired from Calder et al.’s (2023) article, could be to clarify specific plans to nourish the body due to the participant having experienced themselves as a decaying skeleton followed by the realisation of the body being a gift. If the period following dosing provides an opportunity for increased neuroplasticity, it may also be particularly conducive to reinforcing adaptive reward learning through behavioural activation with the help of a therapist. 


'''Cognitive flexibility''' 

Cognitive rigidity is a hallmark of EDs and is characterised by inflexible beliefs about food, weight, body shape, and control. Predictive coding provides a framework for understanding this rigidity, as EDs may involve entrenched priors that resist updating even when confronted with contradictory sensory evidence (Zanella &amp; Lee, 2022). Psychedelics are proposed to disrupt these entrenched priors by increasing neural entropy and reducing the dominance of top-down processing (Calder et al., 2023). This temporary loosening of cognitive constraints may allow individuals to consider alternative perspectives and question long-held beliefs. 

Experiences of ego dissolution may further contribute to cognitive flexibility by reducing attachment to rigid self-concepts (Peled-Avron, 2024; Mograbi et al., 2024). When the boundaries of the self become less defined, individuals may find it easier to question identity-related beliefs that sustain ED pathology. Integration sessions can harness this potential flexibility by supporting cognitive reframing, encouraging behavioural experiments, and strengthening metacognitive awareness. Through these processes, individuals may be better able to translate insights gained during psychedelic experiences into sustained changes in thinking and behaviour.


'''Reconnecting with bodily signals'''

Interoceptive deficits are central to ED pathology, contributing to body mistrust, distorted perceptions of hunger cues, and difficulties responding appropriately to internal sensations (Brown et al., 2020). Psychedelics may enhance interoceptive awareness by altering sensory processing and increasing sensitivity to bodily signals. This proposed mechanism is closely related to autonomic regulation, for which polyvagal theory provides a framework for understanding the relationship between bodily signals, emotional regulation, and perceived safety.

Polyvagal theory emphasises the role of the vagus nerve in interoception, emotional regulation, and the perception of safety (Porges, 2022). Vagal afferents transmit information from the body to the insula, where interoceptive signals are integrated with emotional and cognitive processes. Individuals with EDs may exhibit chronic sympathetic arousal and reduced vagal tone, potentially impairing interoceptive accuracy and contributing to emotional rigidity. Psychedelics may initially increase sympathetic activity, as reflected in physiological responses such as increased heart rate, followed by a parasympathetic shift associated with greater relaxation and an increased capacity for rest (Li et al., 2025). Within a polyvagal framework, these changes may have implications for vagal regulation, interoceptive awareness, and emotional regulation.

The therapeutic value of this proposed mechanism lies in its potential to restore trust in bodily signals. Integration sessions may support this process by helping individuals explore bodily sensations experienced during dosing, connect interoceptive cues with emotional states, and practise interoceptive exposure to hunger, fullness, and anxiety-related sensations. Incorporating mindfulness techniques may further support autonomic regulation and help individuals develop a more adaptive relationship with their bodily experiences.

 A brief note concerning the gut-brain axis
Although gut microbiome disruption is not a direct psychological mechanism in EDs, it is a relevant biological factor to consider when examining the potential effects of PAT. Restrictive or chaotic eating patterns can contribute to gut dysbiosis, which may weaken gut-barrier integrity and contribute to inflammation affecting the brain (Anton-Paduraru et al., 2024). These changes have been shown to influence mood, stress responsivity, cognitive rigidity, and interoceptive awareness through [[wikipedia:Hypothalamic–pituitary–adrenal_axis|HPA-axis activation]], altered neurotransmitter synthesis, and disrupted hunger–satiety signalling. 

Emerging research suggests that psychedelics may also interact with the [[wikipedia:Gut–brain_axis|gut–brain axis]]. Certain microbes can metabolise psychedelic compounds, and microbial activity has been associated with modulatory effects on behavioural outcomes. Additionally, psychedelic use may alter microbial composition towards anti-inflammatory profiles, which has potential implications for neuroplasticity, neurotransmitter synthesis and signalling improvements (Caspani et al., 2024). These microbiome-related effects may therefore contribute to changes in mood, cognitive flexibility, and appetite regulation.

Although the therapeutic potential of psychedelics in EDs is considered primarily in relation to psychological mechanisms, including changes in perception, emotional processing, and reduced avoidance, microbiome-related effects may represent an additional pathway through which biological processes influence psychological outcomes. However, the extent to which these interactions contribute to therapeutic outcomes in EDs remains to be established.


&lt;blockquote&gt;'''QUIZ: ''Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{ In predictive coding terms, what are “high‑level priors” in eating disorders? 
|type=&quot;()&quot;}
+ Rigid, entrenched beliefs about food, weight, and the self that shape perception and behaviour
- Flexible beliefs that easily update with new sensory information
- Momentary emotional reactions triggered by external cues

{What is the proposed mechanism by which psychedelics support emotion regulation in PAT for EDs? 
|type=&quot;()&quot;}
- By suppressing emotional intensity to prevent distress
+ By evoking strong emotions that disrupt avoidance patterns and promote emotional acceptance
- By eliminating negative emotions through serotonin release

{What is interoceptive awareness?
|type=&quot;()&quot;}
- The ability to evaluate reward value and anticipate pleasurable outcomes
+ The capacity to sense, interpret, and respond to internal bodily signals such as hunger, fullness, and emotional arousal
- The process of weakening cognitive rigidity through ego dissolution
&lt;/quiz&gt;&lt;/blockquote&gt;

== Limitations ==
Despite the potential of PAT to influence psychological mechanisms implicated in EDs, several limitations constrain current understanding of these processes and their therapeutic relevance. Research examining emotion dysregulation in EDs illustrates broader challenges in establishing the mechanisms underlying these conditions. Although non-acceptance of emotions has been identified as a transdiagnostic risk factor across psychiatric conditions (Paulus et al., 2021), Zhou et al.’s meta-analysis (2025) highlights that the causal pathways linking emotional dysregulation and EDs remain unclear, largely because of a lack of experimental and longitudinal studies. Further limitations include restricted availability of measurement scales, insufficient cultural specificity, heterogeneity across samples, gender imbalance, and limited developmental analysis. Together, these factors constrain understanding of how specific emotional processes relate to different ED presentations across the lifespan and stages of recovery.

These limitations are also relevant when considering the proposed mechanisms of PAT. Although existing theoretical frameworks offer ways to conceptualise how psychedelic experiences may influence psychological processes responsible for EDs, the emerging nature of psychedelic therapy limits the extent to which proposed mechanisms have been tested. However, with the number of clinical trials increasing as of recently, it will be interesting to see how the theorised therapeutic mechanisms across different ED presentations and stages of recovery emerges during further warranted investigation.

Nevertheless, current limitations in the evidence highlight the need for research that clarifies the relationships between psychological processes that underscore ED behaviours, and treatment outcomes. There are several important psychological components of ED maintenance that represent meaningful targets for treatment, but they should not be considered in isolation from eachother or the neurobiological processes that influence them. A more comprehensive understanding of how these mechanisms interact may help clarify the therapeutic potential of PAT and inform the development of more targeted treatment approaches.

== Conclusion ==
PAT offers a potential framework for addressing several interconnected psychological mechanisms implicated in EDs. Through its proposed effects on emotional processing, reward valuation, cognitive flexibility, and interoceptive awareness, PAT may create opportunities to disrupt established patterns of avoidance, rigid thinking, and maladaptive behavioural reinforcement. The gut–brain interaction may represent an additional biological pathway relevant to these processes.

These mechanisms should not be understood as independent processes. Changes in emotion regulation may influence the ability to tolerate bodily sensations, while shifts in reward valuation and cognitive flexibility may create opportunities to respond differently to distress and challenge entrenched beliefs. However, the extent to which PAT produces these changes, and whether they translate into sustained improvements in ED outcomes, requires further investigation, although preliminary evidence is promising. 

The therapeutic potential of PAT lies not only in the acute psychedelic experience but also in the structured integration process that follows. Integration sessions provide an opportunity to translate emotional breakthroughs, changes in cognitive flexibility, interoceptive shifts, and reward processing into sustained behavioural change. Effective integration involves helping individuals articulate insights, connect them to ED-related patterns, and develop concrete strategies for change. These may include strengthening adaptive coping, challenging rigid beliefs, practising interoceptive awareness, reinforcing positive reward experiences, and supporting nutritional rehabilitation.

By grounding the understanding of PAT in affect regulation theory and the predictive coding framework, therapists may be better positioned to help individuals explore how psychedelic experiences could disrupt maladaptive emotional and cognitive patterns and create opportunities for new learning. Polyvagal-informed approaches may further support the development of mind–body awareness and emotional regulation through mindfulness strategies. Together, these approaches offer a multifaceted framework for translating psychedelic experiences into therapeutic change and addressing the interconnected mechanisms that maintain EDs and associated suffering. 

==See Also==
* [https://w.wiki/TsdG Ayahuasca and the brain] (Wikiversity)
* [https://w.wiki/TscF Emotional effects of psychedelics] (Wikiversity)
* [https://w.wiki/Tsdb Psilocybin and emotion] (Wikiversity)
* [https://w.wiki/TsdS Psilocibyn assisted psychotherapy] (Wikiversity)
* [https://w.wiki/Tsce Psychedelics, altered consciousness, and personal growth] (Wikiversity)
* [[Eating Disorders|Eating disorders]] (Wikiversity)

==References==
{{Hanging indent|1=

{{ic|Try &quot;Edit source&quot; and then wrapping any text to be italicised in two apostrophes e.g., ''this is italics''}}

Anton-Păduraru, D. T., Trofin, F., Nastase, E. V., Miftode, R. S., Miftode, I. L., Trandafirescu, M. F., Cojocaru, E., Țarcă, E., Mindru, D. E., &amp; Dorneanu, O. S. (2023). The Role of the Gut Microbiota in Anorexia Nervosa in Children and Adults-Systematic Review. &quot;International journal of molecular sciences, 25&quot;(1), 41. https://doi.org/10.3390/ijms25010041

Brown, T. A., Vanzhula, I. A., Reilly, E. E., Levinson, C. A., Berner, L. A., Krueger, A., Lavender, J. M., Kaye, W. H., &amp; Wierenga, C. E. (2020). Body mistrust bridges interoceptive awareness and eating disorder symptoms. &quot;Journal of abnormal psychology, 129&quot;(5), 445–456. https://doi.org/10.1037/abn0000516 

Calder, A., Mock, S., Friedli, N., Pasi, P., &amp; Hasler, G. (2023). Psychedelics in the treatment of eating disorders: Rationale and potential mechanisms. &quot;European Neuropsychopharmacology, 75&quot;, 1–14. https://doi.org/10.1016/j.euroneuro.2023.05.008 

Caspani, G., Ruffell, S. G. D., Tsang, W., Netzband, N., Rohani-Shukla, C., Swann, J. R., &amp; Jefferies, W. A. (2024). Mind over matter: the microbial mindscapes of psychedelics and the gut-brain axis. &quot;Pharmacological research, 207&quot;, 107338. https://doi.org/10.1016/j.phrs.2024.107338  

Fitzsimmons, E. E., &amp; Bardone-Cone, A. M. (2010). Differences in coping across stages of recovery from an eating disorder. &quot;The International journal of eating disorders, 43&quot;(8), 689–693. https://doi.org/10.1002/eat.20781 

Hatzipantelis, C. J., &amp; Olson, D. E. (2024). The Effects of Psychedelics on Neuronal Physiology. &quot;Annual review of physiology, 86&quot;, 27–47. https://doi.org/10.1146/annurev-physiol-042022-020923

Hay, P., Aouad, P., Le, A., Marks, P., Maloney, D., National Eating Disorder Research Consortium, Touyz, S., &amp; Maguire, S. (2023). Epidemiology of eating disorders: population, prevalence, disease burden and quality of life informing public policy in Australia-a rapid review. &quot;Journal of eating disorders, 11&quot;(1), 23. https://doi.org/10.1186/s40337-023-00738-7

Li, H., Wang, H., &amp; Wang, X. (2025). Psychedelics and the Autonomic Nervous System: A Perspective on Their Interplay and Therapeutic Potential. &quot;ACS pharmacology &amp; translational science, 8&quot;(3), 899–902. https://doi.org/10.1021/acsptsci.5c00005 

Leppanen, J., Brown, D., McLinden, H., Williams, S., &amp; Tchanturia, K. (2022). The Role of Emotion Regulation in Eating Disorders: A Network Meta-Analysis Approach. &quot;Frontiers in psychiatry, 13&quot;, 793094. https://doi.org/10.3389/fpsyt.2022.793094 

Mograbi, D. C., Rodrigues, R., Bienemann, B., &amp; Huntley, J. (2024). Brain Networks, Neurotransmitters and Psychedelics: Towards a Neurochemistry of Self-Awareness. &quot;Current neurology and neuroscience reports, 24&quot;(8), 323–340. https://doi.org/10.1007/s11910-024-01353-y

Paulus F. W., Ohmann S., Möhler E., Plener P. &amp; Popow C. (2021). Emotional Dysregulation in Children and Adolescents With Psychiatric Disorders. A Narrative Review. &quot;Frontiers in Psychiatry 12&quot;:628252. doi: 10.3389/fpsyt.2021.628252

Peled-Avron L., Aday J. Ss, Kalafateli A. L., Hamilton H. K., Woolley J. D. (2024). Editorial: Down the rabbit hole – the psychological and neural mechanisms of psychedelic compounds and their use in treating mental health and medical conditions. &quot;Frontiers in Psychiatry 15&quot;:1431389. doi: 10.3389/fpsyt.2024.1431389

Porges S. W. (2025). Polyvagal Theory: Current Status, Clinical Applications, and Future Directions. &quot;Clinical neuropsychiatry, 22&quot;(3), 169–184. https://doi.org/10.36131/cnfioritieditore20250301

Schaefer, L. M., Smith, K. E., Anderson, L. M., Cao, L., Crosby, R. D., Engel, S. G., Crow, S. J., Peterson, C. B., &amp; Wonderlich, S. A. (2020). The role of affect in the maintenance of binge-eating disorder: Evidence from an ecological momentary assessment study. &quot;Journal of abnormal psychology, 129&quot;(4), 387–396. https://doi.org/10.1037/abn0000517 

Shank, L. M., Tanofsky-Kraff, M., Kelly, N. R., Jaramillo, M., Rubin, S. G., Altman, D. R., Byrne, M. E., LeMay-Russell, S., Schvey, N. A., Broadney, M. M., Brady, S. M., Yang, S. B., Courville, A. B., Ramirez, S., Crist, A. C., Yanovski, S. Z., &amp; Yanovski, J. A. (2019). The association between alexithymia and eating behavior in children and adolescents. &quot;Appetite, 142&quot;, 104381. https://doi.org/10.1016/j.appet.2019.104381

Wonderlich, J., &amp; Attia, E. (2024). Eating disorders in the DSM-5. In P. Robinson, T. Wade, B. Herpertz-Dahlmann, F. Fernandez-Aranda, J. Treasure, &amp; S. Wonderlich (Eds.), Eating disorders: An international comprehensive view (pp. 7–18). &quot;Springer Nature Switzerland AG&quot;. https://doi.org/10.1007/978-3-031-46096-8_9

Wolfgang, A. S., &amp; Hoge, C. W. (2023). Psychedelic-Assisted Therapy in Military and Veterans Healthcare Systems: Clinical, Legal, and Implementation Considerations. &quot;Current psychiatry reports, 25&quot;(10), 513–532. https://doi.org/10.1007/s11920-023-01446-4 

Zanella, E., &amp; Lee, E. (2022). Integrative review on psychological and social risk and prevention factors of eating disorders including anorexia nervosa and bulimia nervosa: seven major theories. &quot;Heliyon, 8&quot;(11), e11422. https://doi.org/10.1016/j.heliyon.2022.e11422 

Zhou, R., Zhang, L., Liu, Z., &amp; Cao, B. (2025). Emotion regulation difficulties and disordered eating in adolescents and young adults: a meta-analysis. &quot;Journal of eating disorders, 13&quot;(1), 25. https://doi.org/10.1186/s40337-025-01197-y

}}

==External links==
* [https://www.abct.org/fact-sheets/psychedelic-assisted-therapy/ Psychedelic-Assisted Therapy | Fact Sheet] (ABCT - Association for Behavioral and Cognitive Therapies)
* [https://podcasts.apple.com/au/podcast/can-magic-mushrooms-help-treat-anorexia/id189330872?i=1000784809236 Can magic mushrooms help treat anorexia?] (Apple Podcasts)
* [https://www.apa.org/news/podcasts/speaking-of-psychology/eating-disorder The ‘silent epidemic’ of eating disorders] (American Psychological Association)
* [https://www.apa.org/monitor/2023/04/sensations-eating-disorders-suicidal-behavior What is interoception, and how does it affect mental health]? 5 questions for April Smith (American Psychological Association)
* [https://www.cbte.co/what-is-cbte/transdiagnostic-view-eating-disorders/ Transdiagnostic view of eating disorders] (cbte.co)
* [https://psychedelic.support/resources/polyvagal-theory-mind-body-dr-erica-zelfand/ Polyvagal Theory with Dr. Erica Zelfand: Mind-Body Connection] ·(Psychedelic Support)
* [https://www.wholeselfnutrition.org/post/nervous-system-regulation-a-missing-piece-in-eating-disorder-recovery Nervous System Regulation: A Missing Piece in Eating Disorder Recovery]  (wholeselfnutrition.org)
* [https://youtu.be/RwS-CHJcCiY?si=157viTWiOGAQ-7LP Best Neural Entropy - Explainer] (Youtube)

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== Overview ==
{{RoundBoxTop|theme=7}}[[File:Neural network - Midjourney and Grok.png|thumb|'''Figure 1.''' Psychedelics are thought to temporarily disrupt rigid neural communication pathways by promoting more flexible patterns of connectivity across networks involved in mood regulation, fear processing, reward learning, and cognitive adaptability. These changes may support therapeutic shifts in behaviour and emotional processing (Hatzipantelis &amp; Olson, 2025).]]Emma, a 27‑year‑old from Canberra, has lived with an eating disorder for nearly two decades. She describes her problem eating behaviours to have started at school, after being bullied about her appearance and experiencing an unsteady home life. Ever since, they have remained in her life as “a way for me to feel in control”. Although she is aware of the harm caused by restrictive eating and compulsive exercise, she feels trapped in her thought patterns characterised by a preoccupation about food and weight concerns, as they've become entrenched in her daily life. 

After reading an article describing emerging research suggesting that psychedelics may alter patterns of neural connectivity that shape behaviour (see Figure 1), she expressed interest in pursuing psychedelic‑assisted therapy through a provider accessible to her.

After participating in her first supervised psilocybin‑assisted therapy session, Emma reported experiencing an emotional journey that allowed her to feel “connected to my body for the first time in years”. After 3 months, she has noticed a shift in how she relates to her body, and is finding it easier to actively call into question how she responds to distress with the support of her psychotherapist. 


Her experience raises a central question: What psychological mechanisms could explain these changes?{{RoundBoxBottom|theme=3}}  

This chapter explores how psychedelic‑assisted therapy (PAT) may influence the emotional, cognitive, and neurobiological processes that underpin eating disorders (EDs).   

{{RoundBoxTop|theme=11}}'''Focus questions'''
{{ic|}}Two central questions will be addressed:
* What psychological processes underpin eating disorders, and how do they guide ED behaviour?
* How might psychedelic‑assisted therapy influence these processes and support recovery?
{{ic|}}{{ic|}}{{RoundBoxBottom}}

== Introduction ==
'''Eating disorders'''  

[[wikipedia:Eating_disorder|Eating disorders]] (EDs) are psychiatric conditions characterised by abnormal eating behaviours that negatively affect physical and mental health. In Australia, the prevalence of EDs is rising particularly among young people. The economic burden is estimated to cost the nation $84 billion, with approximately 10.46% of the population having experienced an ED at some point in their lives (Hay et al., 2023). Although other forms of disordered eating exist, this chapter will focus on only three of them (see table 1), as [[wikipedia:Anorexia|Anorexia Nervosa]] (AN) has the highest mortality rate of any psychiatric disorder, while [[wikipedia:Bulimia|Bulimia Nervosa]] (BN) and [[wikipedia:Binge_eating_disorder|Binge‑Eating Disorder]] (BED) are also highly prevalent. The EDs mentioned are most associated with chronic illness, disability, reduced quality of life, increased suicide risk, and are highly comorbid with [[wikipedia:Mood_disorder|mood disorders]], [[wikipedia:Post-traumatic_stress_disorder|post-traumatic stress disorder]] (PTSD), [[wikipedia:Obsessive–compulsive_disorder|obsessive-compulsive disorder]] (OCD), and [[wikipedia:Substance_use_disorder|substance use disorders]] (Calder et al., 2023).  Despite decades of research, the pathogenesis of EDs remains incompletely understood. Current evidence suggests a complex interplay between genetic predisposition, temperament, hormonal dysregulation, cognitive abnormalities, sociocultural pressures, and traumatic experiences (Calder et al., 2023).  
{| class=&quot;wikitable&quot;
|+Table 1. Eating disorders and associated symptoms
!Eating disorder
!Primary symptoms
|-
|Anorexia Nervosa
|Severe caloric restriction, fear of gaining weight, distorted body image, preoccupation with weight loss, compulsive exercise.
|-
|Bullimia Nervosa
|Intense windows of food intake (binge eating) followed by inappropriate compensatory behaviours also known as 'purging' (eg. vomiting, laxative use), feelings of guilt and loss of control.
|-
|Binge-Eating Disorder
|Recurrent episodes of binge eating not followed by inappropriate compensatory behaviours, feelings of distress and loss of control.
(Wanderlich &amp; Attia., 2024)
|}


Although cognitive‑behavioural therapy (CBT‑E) combined with pharmacological treatment has demonstrated beneficial outcomes, efficacy remains limited and varies across ED types (Calder et al., 2023). Recovery is often long and difficult, with only two‑thirds of individuals with AN and BN eventually recovering, while others can remain ill for many years. This highlights the need for treatment approaches that can accelerate recovery and provide benefit for individuals who do not respond to conventional therapies.


'''Psychedelic-assisted therapy'''

In 2023, Australia legalised the prescription of MDMA and psilocybin under professional supervision, marking a significant shift in mental‑health treatment options. Psychedelic compounds, including [[wikipedia:LSD|LSD]], [[wikipedia:Psilocybin|psilocybin]], [[wikipedia:Dimethyltryptamine|DMT]], [[wikipedia:Ketamine|ketamine]], and [[wikipedia:MDMA|MDMA]], have demonstrated promising therapeutic effects across a wide range of psychiatric conditions. Researchers propose that psychedelics act through psychological and neural mechanisms that increase [[wikipedia:Neuroplasticity|neuroplasticity]], facilitate insight, and foster emotional acceptance (Peled‑Avron et al., 2024). At a neurobiological level, psychedelics influence processes that inform perception, emotion, and behaviour, offering a potential avenue for addressing entrenched ED mechanisms.

PAT differs from pharmacological treatment alone because the drug is administered within a structured therapeutic context designed to maximise safety and clinical benefit (Calder et al., 2023). Treatment typically involves three types of sessions, undertaken numerous times, across several months. Preparatory sessions feature participants undergoing psychoeducation, where a psychotherapist establishes rapport and clear safety protocols. Followed by supervised medication sessions, where the participant undergoes the inward experience with the reassurance of clinicians present in the same space. Lastly, integrative sessions led by the psychotherapist provide an opportunity for individuals to process and explore insights from the previous session, in aims to facilitate behavioural change (Wolfgang &amp; Hoge, 2023). This combination of pharmacological and psychological intervention is theorised to effectively target underlying psychological mechanisms common across various mental health disorders, illustrating PAT’s potential as a valuable transdiagnostic treatment option. 

PAT has become a subject of increasing popularity in ED research because many of the psychological mechanisms it is proposed to influence are the same ones implicated in ED maintenance and comorbidities (Calder et al., 2023; Peled-Avron et al., 2024). Early research, including case study reports, small clinical studies, meta-analyses and reviews indicate that PAT produces improvements in affect, reductions in ED symptom severity, enhanced body image, weight restoration, and reductions in comorbid symptoms. Although preliminary, these findings indicate that PAT may disrupt and promote shifts away from maladaptive coping patterns that become entrenched in treatment resistant ED populations.

== Psychological mechanisms in eating disorders ==


'''Emotion dysregulation'''

Emotion dysregulation is considered to be a significant risk factor for the onset and maintenance of EDs. It refers to difficulties recognising, assessing, and modifying emotional responses to meet situational demands (Zhou et al., 2025). 

Research consistently shows that individuals with EDs experience significant challenges in regulating emotions, increasing their vulnerability to comorbid symptoms, which contribute to the emergence of disordered eating patterns (Leppanen et al., 2022). This idea is supported by affect regulation theory which posits that eating disorders develop and are maintained as maladaptive strategies to manage, tolerate and escape from negative emotions and psychological distress (Schaefer et al., 2020; Zanella &amp; Lee, 2022). This is further exemplified in Fitzsimmons &amp; Bardone-Cone’s article examining differences in coping within eating disorder patients (2010). The authors explain that avoidance and emotion-oriented coping styles often function as maladaptive attempts to manage (di)stress. They explain that behaviours such as binge eating, purging, starvation, and/or compulsive exercise provide temporary relief by shifting attention away from uncomfortable emotions. 

Furthermore, alexithymia, characterised by difficulty identifying and describing one’s own emotions, is strongly associated with ED pathology (Shank et al., 2019). Individuals with high alexithymia often struggle to differentiate emotional states from bodily sensations, contributing to behaviours such as emotional eating, eating in the absence of hunger, or rigid restriction. In BED, alexithymia is linked to binge episodes triggered by poorly understood emotional cues, while in AN and BN, alexithymia may contribute to emotional avoidance and reliance on ED behaviours for affect regulation. 

The effects of trauma are contributing factors to emotion dysregulation, and considered a risk factor for ED development. Individuals who experience sexual, physical, or emotional abuse, neglect, and bullying are likely to experience heightened emotional reactivity, threat perception, and avoidance behaviours (Calder et al., 2023). Researchers explain that trauma often results in lowered distress tolerance and increased reliance on maladaptive coping behaviours, including disordered eating. Furthermore, PTSD comorbidity is common, hence trauma‑related symptoms are hypothesised to frequently interact with ED behaviours in complex ways.  


'''Reward processing dysfunction'''
[[File:Striatum.gif|thumb|'''Figure 2.''' Striatum]]
[[File:Anterior cingulate gyrus animation.gif|thumb|'''Figure 3'''. Anterior Cingulate Cortex ]]
Abnormal reward valuation is understood to be a central psychological mechanism that maintains ED behaviours. Research consistently shows that individuals with eating disorders display altered neural activity response to various stimuli, as well as disruptions in reinforcement learning (Calder et al., 2023). Brain regions involved in reward processing, habit formation, and learning, such as the striatum and anterior cingulate cortex (see figures 2 &amp; 3), exhibit atypical activation patterns and differences in dopamine receptor binding across ED types. The insula (see figure 4), which integrates bodily sensations with conscious thought, emotion, and behaviour, also shows altered responses. Together, these regions have been shown to react differently to food images, taste, and social feedback compared to healthy controls, indicating that reward dysfunction extends beyond eating‑related stimuli for ED populations.
[[File:Insular cortex.gif|thumb|'''Figure 4.''' Insula. ]]
In the context of BN and BED, research shows that food is valued more highly than other types of rewards, thus shaping behaviour through its heightened influence on reward outcomes (Calder et al., 2023). Compulsive behaviours specific to each condition (e.g. bingeing, purging) are therefore more likely to occur when food is overvalued and alternative rewards are discounted or ignored. In addition to the neural changes already described, BN and BED are associated with reduced structural and functional connectivity between frontal control regions and the striatum. This combination of highly salient food rewards, and weakened fronto‑striatal pathways, reduces an individual’s ability to inhibit or modulate reward‑seeking impulses. Weak connectivity in these circuits is thought to predict compulsive reward‑seeking behaviour. As a result, even when individuals experience negative consequences from binge episodes, they may struggle to learn from these outcomes or adjust their behaviour accordingly.


Anhedonia, a global reduction in reward responsiveness, is frequently reported by people who experience AN, resulting in food and eating becoming undervalued or aversive to them (Calder et al., 2023). Researchers propose that reward contamination further contributes to this pattern, where the brain learns to associate normally punishing stimuli (e.g., starvation, excessive exercise) with reward, while normally rewarding stimuli (e.g., high‑calorie foods) become experienced as punishment. Structural reductions in the striatum and somatosensory cortex have also been observed, which accounts for distorted bodily sensations and contributes to anhedonia. These changes support maladaptive conditioning in which starvation and weight loss embody a sense of safety, achievement, and emotional relief. Restrictive and preoccupied behaviours centred on food, body shape, and exercise are therefore reinforced over time.

Consistent with affect‑regulation models, eating‑disorder behaviours also become negatively reinforced because they reduce emotional discomfort. This relief increases the likelihood that the behaviours will be repeated, further embedding them within the individual’s coping pattern.


'''Cognitive rigidity'''

Cognitive rigidity refers to inflexible thinking and behavioural patterns, including difficulty adapting to new information and modifying behaviour. Researchers believe that individuals with EDs often exhibit rigid beliefs about food and weight which interact with a need to exert control over negative emotions. This interaction is the proposed process in which compulsive behaviours and obsessive thoughts develop (Calder et al., 2023). In AN, rigidity manifests as strict dietary rules and fear of losing control, while in BN and BED, binge episodes may feel compulsive and uncontrollable.


'''Interoceptive awareness'''

Interoceptive awareness (IA) refers to the ability to recognise and process internal bodily states such as hunger, satiety, pain, and arousal. IA is impaired across EDs, and contributes to body mistrust, distorted hunger cues, and inappropriate responses to internal sensations (Brown et al., 2020). Individuals may ignore physical discomfort, misinterpret bodily signals, or avoid sensations altogether, reinforcing maladaptive coping.      

 &lt;blockquote&gt;'''''QUIZ: Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{What coping style do people who experience EDs tend to show?
|type=&quot;()&quot;}
+ Avoidance-oriented
- Problem-oriented

{Compulsive behaviours are more likely to occur when food is ... and alternative rewards are ...
|type=&quot;()&quot;}
- undervalued; overvalued
+ overvalued; undervalued
&lt;/quiz&gt;&lt;/blockquote&gt;

== PAT's influence on psychological mechanisms ==

PAT is proposed to influence several psychological mechanisms implicated in EDs, particularly those discussed in the previous section. The next part of this chapter aims to examine the theorised therapeutic mechanisms PAT possesses and practical implications for ED treatment.  


'''Emotion regulation''' 

Emotion dysregulation is a core mechanism implicated in EDs. Affect regulation theory proposes that ED behaviours emerge as maladaptive strategies to escape, reduce, or blunt overwhelming emotional experiences (Schaefer et al., 2020). Restriction, bingeing, purging, and compulsive exercise may temporarily alleviate distress while reinforcing avoidance-oriented coping and limiting opportunities to learn more adaptive ways of responding to difficult emotions. 

Psychedelics often evoke intense emotional experiences that may disrupt habitual avoidance patterns. Researchers propose that, during psychedelic sessions, attempts to suppress or avoid difficult emotions can intensify these experiences, creating conditions in which emotional acceptance becomes a preferred response (Calder et al., 2023). Although this shift does not occur in every individual, experiencing difficult emotions without resorting to ED behaviours may weaken the association between emotional distress and maladaptive coping, particularly when emotional acceptance becomes associated with a more positive or tolerable experience.

The therapeutic value of this process lies in its potential to reshape affective responses. When individuals experience strong emotions without engaging in maladaptive behaviours, they may begin to develop a new approach towards emotional tolerance. Integration sessions can consolidate this learning by helping individuals articulate, differentiate, and reflect on the emotions experienced during dosing. This process may support the development of more adaptive coping strategies, including task-oriented, problem-focused, and socially supported approaches, which are associated with improved ED outcomes (Fitzsimmons &amp; Bardone-Cone, 2010). In this way, PAT may strengthen emotion regulation and reduce reliance on ED behaviours as strategies for managing affect. 


'''Reward processing''' 

Reward dysfunction may contribute to the maintenance of EDs by reinforcing maladaptive behaviours while diminishing the perceived value of adaptive rewards. Predictive coding provides a useful framework for understanding how PAT might influence these processes. Individuals with EDs may hold rigid beliefs, conceptualised as high-level priors, about themselves in relation to food, body weight, and rewarding behaviours (Calder et al., 2023; Mograbi et al., 2024). These beliefs can influence how experiences are perceived and valued, potentially reinforcing existing behavioural patterns. Psychedelics are proposed to weaken high-level priors, allowing bottom-up sensory information to exert greater influence on perception and the valuation of experiences. 

During psychedelic experiences, individuals frequently report a heightened appreciation of sensory, social, and bodily experiences. This shift may counteract anhedonia and support the revaluation of previously feared or avoided stimuli. The therapeutic opportunity lies in translating these temporary changes in perception and reward into meaningful behavioural change. Integration sessions can explore positive and negative moments experienced during dosing and connect them to concrete goals. An example of this, inspired from Calder et al.’s (2023) article, could be to clarify specific plans to nourish the body due to the participant having experienced themselves as a decaying skeleton followed by the realisation of the body being a gift. If the period following dosing provides an opportunity for increased neuroplasticity, it may also be particularly conducive to reinforcing adaptive reward learning through behavioural activation with the help of a therapist. 


'''Cognitive flexibility''' 

Cognitive rigidity is a hallmark of EDs and is characterised by inflexible beliefs about food, weight, body shape, and control. Predictive coding provides a framework for understanding this rigidity, as EDs may involve entrenched priors that resist updating even when confronted with contradictory sensory evidence (Zanella &amp; Lee, 2022). Psychedelics are proposed to disrupt these entrenched priors by increasing neural entropy and reducing the dominance of top-down processing (Calder et al., 2023). This temporary loosening of cognitive constraints may allow individuals to consider alternative perspectives and question long-held beliefs. 

Experiences of ego dissolution may further contribute to cognitive flexibility by reducing attachment to rigid self-concepts (Peled-Avron, 2024; Mograbi et al., 2024). When the boundaries of the self become less defined, individuals may find it easier to question identity-related beliefs that sustain ED pathology. Integration sessions can harness this potential flexibility by supporting cognitive reframing, encouraging behavioural experiments, and strengthening metacognitive awareness. Through these processes, individuals may be better able to translate insights gained during psychedelic experiences into sustained changes in thinking and behaviour.


'''Reconnecting with bodily signals'''

Interoceptive deficits are central to ED pathology, contributing to body mistrust, distorted perceptions of hunger cues, and difficulties responding appropriately to internal sensations (Brown et al., 2020). Psychedelics may enhance interoceptive awareness by altering sensory processing and increasing sensitivity to bodily signals. This proposed mechanism is closely related to autonomic regulation, for which polyvagal theory provides a framework for understanding the relationship between bodily signals, emotional regulation, and perceived safety.

Polyvagal theory emphasises the role of the vagus nerve in interoception, emotional regulation, and the perception of safety (Porges, 2022). Vagal afferents transmit information from the body to the insula, where interoceptive signals are integrated with emotional and cognitive processes. Individuals with EDs may exhibit chronic sympathetic arousal and reduced vagal tone, potentially impairing interoceptive accuracy and contributing to emotional rigidity. Psychedelics may initially increase sympathetic activity, as reflected in physiological responses such as increased heart rate, followed by a parasympathetic shift associated with greater relaxation and an increased capacity for rest (Li et al., 2025). Within a polyvagal framework, these changes may have implications for vagal regulation, interoceptive awareness, and emotional regulation.

The therapeutic value of this proposed mechanism lies in its potential to restore trust in bodily signals. Integration sessions may support this process by helping individuals explore bodily sensations experienced during dosing, connect interoceptive cues with emotional states, and practise interoceptive exposure to hunger, fullness, and anxiety-related sensations. Incorporating mindfulness techniques may further support autonomic regulation and help individuals develop a more adaptive relationship with their bodily experiences.

 A brief note concerning the gut-brain axis
Although [[wikipedia:Gut_microbiota|gut microbiome]] disruption is not a direct psychological mechanism in EDs, it is a relevant biological factor to consider when examining the potential effects of PAT. Restrictive or chaotic eating patterns can contribute to gut dysbiosis, which may weaken gut-barrier integrity and contribute to inflammation affecting the brain (Anton-Paduraru et al., 2024). These changes have been shown to influence mood, stress responsivity, cognitive rigidity, and interoceptive awareness through [[wikipedia:Hypothalamic–pituitary–adrenal_axis|HPA-axis activation]], altered neurotransmitter synthesis, and disrupted hunger–satiety signalling. 

Emerging research suggests that psychedelics may also interact with the [[wikipedia:Gut–brain_axis|gut–brain axis]]. Certain microbes can metabolise psychedelic compounds, and microbial activity has been associated with modulatory effects on behavioural outcomes. Additionally, psychedelic use may alter microbial composition towards anti-inflammatory profiles, which has potential implications for neuroplasticity, neurotransmitter synthesis and signalling improvements (Caspani et al., 2024). These microbiome-related effects may therefore contribute to changes in mood, cognitive flexibility, and appetite regulation.

Although the therapeutic potential of psychedelics in EDs is considered primarily in relation to psychological mechanisms, including changes in perception, emotional processing, and reduced avoidance, microbiome-related effects may represent an additional pathway through which biological processes influence psychological outcomes. However, the extent to which these interactions contribute to therapeutic outcomes in EDs remains to be established.


&lt;blockquote&gt;'''QUIZ: ''Choose your answers and click &quot;Submit&quot;:''''' &lt;quiz display=&quot;simple&quot;&gt;
{ In predictive coding terms, what are “high‑level priors” in eating disorders? 
|type=&quot;()&quot;}
+ Rigid, entrenched beliefs about food, weight, and the self that shape perception and behaviour
- Flexible beliefs that easily update with new sensory information
- Momentary emotional reactions triggered by external cues

{What is the proposed mechanism by which psychedelics support emotion regulation in PAT for EDs? 
|type=&quot;()&quot;}
- By suppressing emotional intensity to prevent distress
+ By evoking strong emotions that disrupt avoidance patterns and promote emotional acceptance
- By eliminating negative emotions through serotonin release

{What is interoceptive awareness?
|type=&quot;()&quot;}
- The ability to evaluate reward value and anticipate pleasurable outcomes
+ The capacity to sense, interpret, and respond to internal bodily signals such as hunger, fullness, and emotional arousal
- The process of weakening cognitive rigidity through ego dissolution
&lt;/quiz&gt;&lt;/blockquote&gt;

== Limitations ==
Despite the potential of PAT to influence psychological mechanisms implicated in EDs, several limitations constrain current understanding of these processes and their therapeutic relevance. Research examining emotion dysregulation in EDs illustrates broader challenges in establishing the mechanisms underlying these conditions. Although non-acceptance of emotions has been identified as a transdiagnostic risk factor across psychiatric conditions (Paulus et al., 2021), Zhou et al.’s meta-analysis (2025) highlights that the causal pathways linking emotional dysregulation and EDs remain unclear, largely because of a lack of experimental and longitudinal studies. Further limitations include restricted availability of measurement scales, insufficient cultural specificity, heterogeneity across samples, gender imbalance, and limited developmental analysis. Together, these factors constrain understanding of how specific emotional processes relate to different ED presentations across the lifespan and stages of recovery.

These limitations are also relevant when considering the proposed mechanisms of PAT. Although existing theoretical frameworks offer ways to conceptualise how psychedelic experiences may influence psychological processes responsible for EDs, the emerging nature of psychedelic therapy limits the extent to which proposed mechanisms have been tested. However, with the number of clinical trials increasing as of recently, it will be interesting to see how the theorised therapeutic mechanisms across different ED presentations and stages of recovery emerges during further warranted investigation.

Nevertheless, current limitations in the evidence highlight the need for research that clarifies the relationships between psychological processes that underscore ED behaviours, and treatment outcomes. There are several important psychological components of ED maintenance that represent meaningful targets for treatment, but they should not be considered in isolation from eachother or the neurobiological processes that influence them. A more comprehensive understanding of how these mechanisms interact may help clarify the therapeutic potential of PAT and inform the development of more targeted treatment approaches.

== Conclusion ==
PAT offers a potential framework for addressing several interconnected psychological mechanisms implicated in EDs. Through its proposed effects on emotional processing, reward valuation, cognitive flexibility, and interoceptive awareness, PAT may create opportunities to disrupt established patterns of avoidance, rigid thinking, and maladaptive behavioural reinforcement. The gut–brain interaction may represent an additional biological pathway relevant to these processes.

These mechanisms should not be understood as independent processes. Changes in emotion regulation may influence the ability to tolerate bodily sensations, while shifts in reward valuation and cognitive flexibility may create opportunities to respond differently to distress and challenge entrenched beliefs. However, the extent to which PAT produces these changes, and whether they translate into sustained improvements in ED outcomes, requires further investigation, although preliminary evidence is promising. 

The therapeutic potential of PAT lies not only in the acute psychedelic experience but also in the structured integration process that follows. Integration sessions provide an opportunity to translate emotional breakthroughs, changes in cognitive flexibility, interoceptive shifts, and reward processing into sustained behavioural change. Effective integration involves helping individuals articulate insights, connect them to ED-related patterns, and develop concrete strategies for change. These may include strengthening adaptive coping, challenging rigid beliefs, practising interoceptive awareness, reinforcing positive reward experiences, and supporting nutritional rehabilitation.

By grounding the understanding of PAT in affect regulation theory and the predictive coding framework, therapists may be better positioned to help individuals explore how psychedelic experiences could disrupt maladaptive emotional and cognitive patterns and create opportunities for new learning. Polyvagal-informed approaches may further support the development of mind–body awareness and emotional regulation through mindfulness strategies. Together, these approaches offer a multifaceted framework for translating psychedelic experiences into therapeutic change and addressing the interconnected mechanisms that maintain EDs and associated suffering. 

==See Also==
* [https://w.wiki/TsdG Ayahuasca and the brain] (Wikiversity)
* [https://w.wiki/TscF Emotional effects of psychedelics] (Wikiversity)
* [https://w.wiki/Tsdb Psilocybin and emotion] (Wikiversity)
* [https://w.wiki/TsdS Psilocibyn assisted psychotherapy] (Wikiversity)
* [https://w.wiki/Tsce Psychedelics, altered consciousness, and personal growth] (Wikiversity)
* [[Eating Disorders|Eating disorders]] (Wikiversity)

==References==
{{Hanging indent|1=

{{ic|Try &quot;Edit source&quot; and then wrapping any text to be italicised in two apostrophes e.g., ''this is italics''}}

Anton-Păduraru, D. T., Trofin, F., Nastase, E. V., Miftode, R. S., Miftode, I. L., Trandafirescu, M. F., Cojocaru, E., Țarcă, E., Mindru, D. E., &amp; Dorneanu, O. S. (2023). The Role of the Gut Microbiota in Anorexia Nervosa in Children and Adults-Systematic Review. &quot;International journal of molecular sciences, 25&quot;(1), 41. https://doi.org/10.3390/ijms25010041

Brown, T. A., Vanzhula, I. A., Reilly, E. E., Levinson, C. A., Berner, L. A., Krueger, A., Lavender, J. M., Kaye, W. H., &amp; Wierenga, C. E. (2020). Body mistrust bridges interoceptive awareness and eating disorder symptoms. &quot;Journal of abnormal psychology, 129&quot;(5), 445–456. https://doi.org/10.1037/abn0000516 

Calder, A., Mock, S., Friedli, N., Pasi, P., &amp; Hasler, G. (2023). Psychedelics in the treatment of eating disorders: Rationale and potential mechanisms. &quot;European Neuropsychopharmacology, 75&quot;, 1–14. https://doi.org/10.1016/j.euroneuro.2023.05.008 

Caspani, G., Ruffell, S. G. D., Tsang, W., Netzband, N., Rohani-Shukla, C., Swann, J. R., &amp; Jefferies, W. A. (2024). Mind over matter: the microbial mindscapes of psychedelics and the gut-brain axis. &quot;Pharmacological research, 207&quot;, 107338. https://doi.org/10.1016/j.phrs.2024.107338  

Fitzsimmons, E. E., &amp; Bardone-Cone, A. M. (2010). Differences in coping across stages of recovery from an eating disorder. &quot;The International journal of eating disorders, 43&quot;(8), 689–693. https://doi.org/10.1002/eat.20781 

Hatzipantelis, C. J., &amp; Olson, D. E. (2024). The Effects of Psychedelics on Neuronal Physiology. &quot;Annual review of physiology, 86&quot;, 27–47. https://doi.org/10.1146/annurev-physiol-042022-020923

Hay, P., Aouad, P., Le, A., Marks, P., Maloney, D., National Eating Disorder Research Consortium, Touyz, S., &amp; Maguire, S. (2023). Epidemiology of eating disorders: population, prevalence, disease burden and quality of life informing public policy in Australia-a rapid review. &quot;Journal of eating disorders, 11&quot;(1), 23. https://doi.org/10.1186/s40337-023-00738-7

Li, H., Wang, H., &amp; Wang, X. (2025). Psychedelics and the Autonomic Nervous System: A Perspective on Their Interplay and Therapeutic Potential. &quot;ACS pharmacology &amp; translational science, 8&quot;(3), 899–902. https://doi.org/10.1021/acsptsci.5c00005 

Leppanen, J., Brown, D., McLinden, H., Williams, S., &amp; Tchanturia, K. (2022). The Role of Emotion Regulation in Eating Disorders: A Network Meta-Analysis Approach. &quot;Frontiers in psychiatry, 13&quot;, 793094. https://doi.org/10.3389/fpsyt.2022.793094 

Mograbi, D. C., Rodrigues, R., Bienemann, B., &amp; Huntley, J. (2024). Brain Networks, Neurotransmitters and Psychedelics: Towards a Neurochemistry of Self-Awareness. &quot;Current neurology and neuroscience reports, 24&quot;(8), 323–340. https://doi.org/10.1007/s11910-024-01353-y

Paulus F. W., Ohmann S., Möhler E., Plener P. &amp; Popow C. (2021). Emotional Dysregulation in Children and Adolescents With Psychiatric Disorders. A Narrative Review. &quot;Frontiers in Psychiatry 12&quot;:628252. doi: 10.3389/fpsyt.2021.628252

Peled-Avron L., Aday J. Ss, Kalafateli A. L., Hamilton H. K., Woolley J. D. (2024). Editorial: Down the rabbit hole – the psychological and neural mechanisms of psychedelic compounds and their use in treating mental health and medical conditions. &quot;Frontiers in Psychiatry 15&quot;:1431389. doi: 10.3389/fpsyt.2024.1431389

Porges S. W. (2025). Polyvagal Theory: Current Status, Clinical Applications, and Future Directions. &quot;Clinical neuropsychiatry, 22&quot;(3), 169–184. https://doi.org/10.36131/cnfioritieditore20250301

Schaefer, L. M., Smith, K. E., Anderson, L. M., Cao, L., Crosby, R. D., Engel, S. G., Crow, S. J., Peterson, C. B., &amp; Wonderlich, S. A. (2020). The role of affect in the maintenance of binge-eating disorder: Evidence from an ecological momentary assessment study. &quot;Journal of abnormal psychology, 129&quot;(4), 387–396. https://doi.org/10.1037/abn0000517 

Shank, L. M., Tanofsky-Kraff, M., Kelly, N. R., Jaramillo, M., Rubin, S. G., Altman, D. R., Byrne, M. E., LeMay-Russell, S., Schvey, N. A., Broadney, M. M., Brady, S. M., Yang, S. B., Courville, A. B., Ramirez, S., Crist, A. C., Yanovski, S. Z., &amp; Yanovski, J. A. (2019). The association between alexithymia and eating behavior in children and adolescents. &quot;Appetite, 142&quot;, 104381. https://doi.org/10.1016/j.appet.2019.104381

Wonderlich, J., &amp; Attia, E. (2024). Eating disorders in the DSM-5. In P. Robinson, T. Wade, B. Herpertz-Dahlmann, F. Fernandez-Aranda, J. Treasure, &amp; S. Wonderlich (Eds.), Eating disorders: An international comprehensive view (pp. 7–18). &quot;Springer Nature Switzerland AG&quot;. https://doi.org/10.1007/978-3-031-46096-8_9

Wolfgang, A. S., &amp; Hoge, C. W. (2023). Psychedelic-Assisted Therapy in Military and Veterans Healthcare Systems: Clinical, Legal, and Implementation Considerations. &quot;Current psychiatry reports, 25&quot;(10), 513–532. https://doi.org/10.1007/s11920-023-01446-4 

Zanella, E., &amp; Lee, E. (2022). Integrative review on psychological and social risk and prevention factors of eating disorders including anorexia nervosa and bulimia nervosa: seven major theories. &quot;Heliyon, 8&quot;(11), e11422. https://doi.org/10.1016/j.heliyon.2022.e11422 

Zhou, R., Zhang, L., Liu, Z., &amp; Cao, B. (2025). Emotion regulation difficulties and disordered eating in adolescents and young adults: a meta-analysis. &quot;Journal of eating disorders, 13&quot;(1), 25. https://doi.org/10.1186/s40337-025-01197-y

}}

==External links==
* [https://www.abct.org/fact-sheets/psychedelic-assisted-therapy/ Psychedelic-Assisted Therapy | Fact Sheet] (ABCT - Association for Behavioral and Cognitive Therapies)
* [https://podcasts.apple.com/au/podcast/can-magic-mushrooms-help-treat-anorexia/id189330872?i=1000784809236 Can magic mushrooms help treat anorexia?] (Apple Podcasts)
* [https://www.apa.org/news/podcasts/speaking-of-psychology/eating-disorder The ‘silent epidemic’ of eating disorders] (American Psychological Association)
* [https://www.apa.org/monitor/2023/04/sensations-eating-disorders-suicidal-behavior What is interoception, and how does it affect mental health]? 5 questions for April Smith (American Psychological Association)
* [https://www.cbte.co/what-is-cbte/transdiagnostic-view-eating-disorders/ Transdiagnostic view of eating disorders] (cbte.co)
* [https://psychedelic.support/resources/polyvagal-theory-mind-body-dr-erica-zelfand/ Polyvagal Theory with Dr. Erica Zelfand: Mind-Body Connection] ·(Psychedelic Support)
* [https://www.wholeselfnutrition.org/post/nervous-system-regulation-a-missing-piece-in-eating-disorder-recovery Nervous System Regulation: A Missing Piece in Eating Disorder Recovery]  (wholeselfnutrition.org)
* [https://youtu.be/RwS-CHJcCiY?si=157viTWiOGAQ-7LP Best Neural Entropy - Explainer] (Youtube)

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[[Category:Motivation and emotion/Book/Eating disorder]]
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      <text bytes="2105" sha1="pnemko372e16fbubyes4aw47im9jueg" xml:space="preserve">== Information about the author ==
Hello!

My name is April'''.''' I am currently studying a Bachelor of Politics and International Relations/ Bachelor of Science in Psychology at the University of Canberra. I have always been interested in international relations, and my degree has deepened that interest. I enjoy connecting my degrees and dissecting human behaviour, particularly how emotions, cognitive biases, and leaders' personalities shape the political climate.

I am interested not only in how politicians interact with their citizens, but also in how they interact with one another and how these relationships can influence international events. I find the chain reaction that can emerge from political decisions interesting, as well as the attention to detail at the intersection of psychology and IR. 
[[File:The_Lotus_Eaters-Charles_Joseph_Staniland.jpg|thumb|'''Figure 1.''' A depiction of girls relaxing]]
Some of my personal interests I use to escape studies and the media are art, video editing, travel, reading, and hanging with my mates, as shown in Figure 1.

== Book chapter I am working on ==
Because of my double degree, I am very interested in learning more about [[Motivation and emotion/Book/2026/Power motivation in leadership|Power motivation in leadership]] and investigating how power motivation influences leadership styles and effectiveness. Then sharing my findings with others who may find it as interesting as I do.  

== Social contributions ==

# [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FAlcohol%2C_dopamine%2C_motivation%2C_and_emotion&amp;diff=2826547&amp;oldid=2826540 Changed wording and edited punctuation for clarity] 
# [https://en.wikiversity.org/w/index.php?diff=2826569 Rewording to improve past chapter] 
# [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/456558?entry_id=809513 Provided a suggestion on discussion form about what to investigate]
# [[Talk:Motivation and emotion/Book/2024/Stockholm syndrome motivation#c-PsychstudentUniversity!-20260826131100-Comment|Made a comment on previous chapter]]</text>
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    <title>Talk:Motivation and emotion/Book/2026/Possible selves and goal pursuit</title>
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      <text bytes="8531" sha1="ku267w289a67vq0d2hysf6kp4nnvf7y" xml:space="preserve">==Generative AI statement==

Generative AI (ChatGBT) was used as a supplementary tool during the development of this book chapter. Its main uses were to help generate ideas for structuring the chapter, improve the readability and flow of my writing, and assist with formatting elements such as interactive features, images, and text boxes.

Generative AI was not used as a substitute for scholarly research, critical thinning, or independent analysis. All substantive information and claims in the chapter were drawn from scholarly literature and interpreted through my own analysis. I did not directly reproduce AI-generated content as academic evidence, and the final wording and argumentation were developed in my own words. Because generative AI can produce inaccurate or misleading information, any suggestions it provided were critically evaluated and cross-checked against reliable sources before use.

I take full responsibility for the accuracy, interpretation, and the final presentation of the work submitted. 

Link to AI conversation: https://chatgpt.com/g/g-p-6a7dc8d61f0c8191ae45bf5b2fd4dee9-motivation-and-emotion/c/6a7dcc90-14d4-83ec-9083-c3a2bdf3b7ce 

- Jack4234

== Identity-based motivation as a companion to possible selves ==
Hi Jack4234, our chapters overlap - I'm writing [[Motivation and emotion/Book/2026/Indigenous Australian role models and motivation|Indigenous Australian role models and motivation]], and possible selves is one of the mechanisms I use to explain how role models influence goal pursuit.

Two sources you might find useful, if you have not already got them:

* Oyserman and Destin (2010) is a strong companion to Markus and Nurius (1986). Their contribution is explaining ''why'' possible selves sometimes fail to drive action: when a goal feels identity-incongruent, experienced difficulty gets interpreted as &quot;this is pointless and not for people like me&quot; rather than as a signal that the goal matters. That gives you a mechanism for the gap between holding a possible self and actually pursuing it.
*: Oyserman, D., &amp; Destin, M. (2010). Identity-based motivation: Implications for intervention. ''The Counseling Psychologist, 38''(7), 1001–1043. https://doi.org/10.1177/0011000010374775
* Morgenroth et al. (2015) may also be worth a look for their &quot;representation of the possible&quot; function - it connects possible selves back to where they come from.
*: Morgenroth, T., Ryan, M. K., &amp; Peters, K. (2015). The motivational theory of role modeling: How role models influence role aspirants' goals. ''Review of General Psychology, 19''(4), 465–483. https://doi.org/10.1037/gpr0000059

Happy to add a &quot;See also&quot; link from my chapter to yours if you would like to do the same - the two topics connect closely. [[User:Jshottt|Jshottt]] ([[User talk:Jshottt|discuss]] • [[Special:Contributions/Jshottt|contribs]]) 14:18, 27 August 2026 (UTC)

:Hi there
:I am writing the book chapter [[Motivation and emotion/Book/2026/Self-concept and motivation|Self-concept and motivation]], a topic which closely aligns to your focus on possible selves. Building on Jshottt's message here, I have been reading another interesting study by Oyserman about how identities drive goal pursuit. I think this could fit nicely in your 'When possible selves facilitate goal pursuit' sub heading. Nurra and Oyserman (2018) found that children who were primed to think of their adult selves as not being far away were more motivated. Their possible selves felt more achievable and thus were more motivating, than those who were primed to think of their adult selves as far away.
:I discuss the findings in my chapter and I've included the resources below, if you'd like to check it out. 
:Nurra, C., &amp; Oyserman, D. (2018). From future self to current action: An identity-based motivation perspective. ''Self and Identity, 17''(3), 343-364. https://doi.org/10.1080/15298868.2017.1375003 
:Oyserman, D. (2024), Identity-based motivation and the motivational consequences of difficulty. ''Social and Personality Psychology Compass, 18'', e70028. https://doi.org/10.1111/spc3.70028 [[User:U3253363|U3253363]] ([[User talk:U3253363|discuss]] • [[Special:Contributions/U3253363|contribs]]) 03:29, 9 September 2026 (UTC)

== Feedback on possible selves and goal pursuit ==

I found the distinction between hoped-for and feared possible selves really interesting, particularly how these future self-representations can influence goal pursuit. It could be useful to further emphasise how self-efficacy may determine whether imagining a possible self actually translates into motivated behaviour. This could help explain why having a desired future self does not always result in successful goal pursuit. [[User:U3188047|U3188047]] ([[User talk:U3188047|discuss]] • [[Special:Contributions/U3188047|contribs]]) 20:38, 27 August 2026 (UTC)


&lt;!-- Official topic development feedback --&gt;
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# Excellent alignment between sub-title, focus questions, and heading structure
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# Excellent – Scenario, image, evocative description of the problem/topic, and focus questions
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# Good balance of theory and research

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# Add in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]] (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
&lt;!-- Scenarios/examples/case studies --&gt;
# Consider use of more scenarios/examples/case studies 
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## Use alphabetical order
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|9=
&lt;!-- User page --&gt;
# Used effectively
# Brief description about self – consider expanding
&lt;!-- Links to profile(s) --&gt;
# Consider linking to your [https://portfolio.canberra.edu.au/ eportfolio] page and/or any other professional online profile or resume such as [https://www.linkedin.com/ LinkedIn]. This is not required, but it can be useful to interlink your professional networks.
&lt;!-- Link to book chapter --&gt;
# A link to the book chapter is provided
|10=
&lt;!-- Social contribution --&gt;
# Three different types of contributions with direct link(s) to evidence
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:57, 30 August 2026 (UTC)</text>
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  <page>
    <title>User:Leilab23</title>
    <ns>2</ns>
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      <timestamp>2026-10-19T03:36:31Z</timestamp>
      <contributor>
        <username>Leilab23</username>
        <id>3106779</id>
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      <comment>/* Social contributions */</comment>
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      <text bytes="2093" sha1="a2zah8domp14j6ov6d5w1eld5fm2a3g" xml:space="preserve">==== About ====
Hi I'm Leila!

I am currently completing a double degree in Psychological Science and Human Movement Health Science, driven by a passion for understanding the complex relationships between the mind, body, movement, wellbeing and health behaviours.

I chose &quot;Psychedelic treatment of eating disorders&quot; as my topic because I am fascinated by the psychological processes underlying maladaptive behaviours and the profound ways in which they can affect the body. I was particularly interested to discover that psychedelic-assisted therapy has recently been proposed to help disrupt the emotional and motivational processes characteristic of eating disorders. Exploring this emerging idea in research provides a novel and engaging opportunity to deepen my understanding of psychology and the potential for innovative approaches to treatment.

===== Social contributions =====

# [[Talk:Motivation and emotion/Book/2026/Competence motivation in self-determination theory#c-~2026-55912-84-20261019032900-Book Chapter Feedback (Social Contribution)|14:30, 19 October 2026: Provided feedback on book chapter &quot;Competence motivation in self-determination theory&quot;]]
# [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/455261?entry_id=805825 15:21, 19 August 2026: Posted about motivation or emotion or the assessment tasks to the UCLearn discussion forum]
# [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2025/Cortical_structures_and_motivational_drive&amp;oldid=2828825 08:50, 28 August 2026: Direct edit to improve a book chapter page (Grammar &amp; Sentence Structure)][Psychologically, motivation involves an individual's thoughts, emotions, and beliefs about their capabilities. However, motivation is also physiological, with research indicating that it is deeply linked to cortical structures within the brain (Rolls, 2023).]
# [[Talk:Motivation and emotion/Book/2026/Athletic identity loss and returning to sport after injury#c-Leilab23-20260827224100-Feedback|08:40, 28 August 2026: Provided feedback by commenting on a book chapter's talk page]]</text>
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  <page>
    <title>Talk:Motivation and emotion/Book/2026/Competence motivation in self-determination theory</title>
    <ns>1</ns>
    <id>331814</id>
    <revision>
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      <contributor>
        <username>~2026-55912-84</username>
        <id>3112904</id>
      </contributor>
      <comment>/* Book Chapter Feedback (Social Contribution) */ new section</comment>
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      <text bytes="7950" sha1="9ot3cbjfcpa0jzq2k8d4gb547xiw7q6" xml:space="preserve">== External Link Suggestion ==

Hey! 

Here is a possible resource for your external links section! 

https://selfdeterminationtheory.org/the-theory/

- Amira [[User:Amirrorslens|Amirrorslens]] ([[User talk:Amirrorslens|discuss]] • [[Special:Contributions/Amirrorslens|contribs]]) 17:50, 3 September 2026 (UTC)

== Article ! ==

Here's an article for your topic development! This article is competence focused :)

[https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/5ucach4vsn?route=details Motivation reconsidered: The concept of competence] [[User:Amirrorslens|Amirrorslens]] ([[User talk:Amirrorslens|discuss]] • [[Special:Contributions/Amirrorslens|contribs]]) 20:11, 3 September 2026 (UTC)

== Recommendation for 'see also' section ==
Hi there, 

Great job on your topic development, I enjoyed reading your work thus far!

I noticed that you had not yet added the ''See also'' section to your chapter, so I took the liberty of [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FCompetence_motivation_in_self-determination_theory&amp;diff=2832537&amp;oldid=2831095 adding it for you]! It might be worth linking some relevant book chapters or Wikipedia pages in this section (e.g., [[Motivation and emotion/Book/2011/Self-determination theory|self-determination theory]] (Book chapter, 2011)).

Best regards.  [[User:U3285438|U3285438]] ([[User talk:U3285438|discuss]] • [[Special:Contributions/U3285438|contribs]]) 04:19, 10 September 2026 (UTC)

&lt;!-- Official topic development feedback --&gt;
{{METF/2026
|1=
&lt;!-- Title --&gt;
# Title and subtitle are correctly worded and use [[w:Letter case#Sentence casing|sentence casing]]
|2=
&lt;!-- Headings --&gt;
&lt;!-- 2-level --&gt;
# Promising [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]] – could benefit from further development and/or refinement
&lt;!-- Alignment with focus questions --&gt;
# Very good alignment between sub-title, focus questions, and heading structure, but there may be room for improvement
# Remove/change &quot;Add research on ...&quot; heading
|3=
&lt;!-- Overview--&gt;
# Solid development
&lt;!-- Scenario --&gt;
# Promising scenario; could benefit from further development to make it more compelling and illustrative
# Maybe rewrite the scenario in 3rd person perspective instead of 2nd person perspective
# The image could be more relevant to the scenario
&lt;!-- Description --&gt;
# A promising description of the problem/topic is planned or presented
&lt;!-- Focus questions --&gt;
&lt;!-- Alignment and quality --&gt;
# The focus questions are well aligned with the sub-title and top-level headings
|4=
&lt;!-- Key points--&gt;
&lt;!-- Overall --&gt;
# Promising development
# Focus on the core topic - how does competence affect motivated behaviour according to SDT?
# Consider competence frustration and competence satisfaction
# Provide more detailed edit summaries
&lt;!-- Other --&gt;
# Use correct capitalisation ([https://apastyle.apa.org/style-grammar-guidelines/capitalization APA style is a &quot;down&quot; style]) – [https://polishedpaper.com/blog/capitalization-apa-style more info]
# Do these key points include [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, this needs to be acknowledged in the edit summaries, otherwise it violates academic integrity.
&lt;!-- Conclusion --&gt;
# Conclusion is underway
# What are the practical, take-home messages? (address the focus questions)
|5=
&lt;!-- Figure --&gt;
# Relevant figure(s) presented, captioned, and cited
&lt;!-- Caption --&gt;
# Figure caption(s) provide(s) a reasonably clear description that is connected with the main text
&lt;!-- Cite --&gt;
# Figure(s) are cited at least once in the main text
|6=
&lt;!-- Learning feature --&gt;
&lt;!-- Interwiki links ---&gt;
# Two in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]]. Also embed links to [[Motivation and emotion/Book|book chapters]].
&lt;!-- Scenarios/examples/case studies --&gt;
# Consider incorporating additional scenarios, examples, or case studies to illustrate key concepts. These could build on the Overview scenario or introduce new real-world situations in the main body of the chapter to demonstrate how the concepts apply in practice.
&lt;!-- Quiz --&gt;
# Promising use of quiz question(s)
&lt;!-- Tables --&gt;
# Also consider using [[Motivation and emotion/Wikiversity/Tables|table(s)]] to summarise key information
|7=
&lt;!-- References --&gt;
&lt;!-- Overall --&gt;
# Good
&lt;!-- Systematic reviews --&gt;
# At least one relevant systematic review and/or meta-analysis has been identified
&lt;!-- APA style --&gt;
# Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]:
## alphabetical order
## capitalisation
## [[Help:Wikitext quick reference|italicisation]]
|8=
&lt;!-- Resources --&gt;
&lt;!-- See also --&gt;
# See also
## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Link to the most relevant Wikiversity book chapters and Wikipedia resources about this topic
&lt;!-- External links --&gt;
# External links
## One of two required external links provided
## Rename links so that they are more user friendly (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Include source in brackets after link
## Link to the most relevant external resources about this topic
|9=
# Used effectively
&lt;!-- Description about self --&gt;
# Excellent description about self provided
&lt;!-- Links to profile(s) --&gt;
# Consider linking to your professional online profile or resume such as [https://www.linkedin.com/ LinkedIn]. This is not required, but it can be useful to interlink your professional networks.
&lt;!-- Link to book chapter --&gt;
# A link to the book chapter is provided
|10=
&lt;!-- Social contribution --&gt;
# One out of three types of contributions made with direct link(s) to evidence. The other types of contribution are making:
#* direct improvements to other [[Motivation and emotion/Book|chapters (past or current)]]
#* comments on the [[Help:Talk page|talk page]]s of other [[Motivation and emotion/Book|chapters (past or current)]]
# To add direct links to evidence of Wikiversity edits or comments: view the page history, select the version of the page before and after your contributions, click &quot;compare selected revisions&quot;, and paste the comparison URL on your user page. For more info, see [[Motivation and emotion/Assessment/Chapter#Making and summarising social contributions|Making and summarising social contributions]]. This was demonstrated in [[Motivation and emotion/Tutorials/Wiki editing#Social contributions|Tutorial 2]].
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:33, 15 September 2026 (UTC)

== Book Chapter Feedback (Social Contribution) ==
Hey [https://uclearn.canberra.edu.au/courses/20143/users/111267 Nyambugi],

I really appreciate how succinctly you tie your ideas together. Each point feels specific, well‑elaborated, and thoughtfully developed, yet the writing remains concise and easy to follow.

The use of colour throughout the chapter is engaging and adds a dynamic visual element.

I also think you’ve done an excellent job looping back to the case scenarios introduced at the beginning. Using them as evolving examples gives the chapter a strong sense of continuity, and I think it shows that you have a natural ability for structuring a book chapter effectively! 

The only suggestion I’d make is to expand the conclusion slightly. Bringing all the ideas you mentioned together in a more comprehensive way would help reinforce how the concepts connect and flow into one another, strengthening the reader’s overall understanding. But in saying that, I love the take‑home messages, they work so well to provide a clear to-the-point summary of everything discussed.

Kind regards, [[Special:Contributions/~2026-55912-84|~2026-55912-84]] ([[User talk:~2026-55912-84|talk]]) 03:29, 19 October 2026 (UTC)</text>
      <sha1>9ot3cbjfcpa0jzq2k8d4gb547xiw7q6</sha1>
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    <revision>
      <id>2841443</id>
      <parentid>2841442</parentid>
      <timestamp>2026-10-19T03:32:33Z</timestamp>
      <contributor>
        <username>Leilab23</username>
        <id>3106779</id>
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      <text bytes="8107" sha1="c3hxgoyg55q6e1ehllq20d8x2y7pcbx" xml:space="preserve">== External Link Suggestion ==

Hey! 

Here is a possible resource for your external links section! 

https://selfdeterminationtheory.org/the-theory/

- Amira [[User:Amirrorslens|Amirrorslens]] ([[User talk:Amirrorslens|discuss]] • [[Special:Contributions/Amirrorslens|contribs]]) 17:50, 3 September 2026 (UTC)

== Article ! ==

Here's an article for your topic development! This article is competence focused :)

[https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/5ucach4vsn?route=details Motivation reconsidered: The concept of competence] [[User:Amirrorslens|Amirrorslens]] ([[User talk:Amirrorslens|discuss]] • [[Special:Contributions/Amirrorslens|contribs]]) 20:11, 3 September 2026 (UTC)

== Recommendation for 'see also' section ==
Hi there, 

Great job on your topic development, I enjoyed reading your work thus far!

I noticed that you had not yet added the ''See also'' section to your chapter, so I took the liberty of [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FCompetence_motivation_in_self-determination_theory&amp;diff=2832537&amp;oldid=2831095 adding it for you]! It might be worth linking some relevant book chapters or Wikipedia pages in this section (e.g., [[Motivation and emotion/Book/2011/Self-determination theory|self-determination theory]] (Book chapter, 2011)).

Best regards.  [[User:U3285438|U3285438]] ([[User talk:U3285438|discuss]] • [[Special:Contributions/U3285438|contribs]]) 04:19, 10 September 2026 (UTC)

&lt;!-- Official topic development feedback --&gt;
{{METF/2026
|1=
&lt;!-- Title --&gt;
# Title and subtitle are correctly worded and use [[w:Letter case#Sentence casing|sentence casing]]
|2=
&lt;!-- Headings --&gt;
&lt;!-- 2-level --&gt;
# Promising [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]] – could benefit from further development and/or refinement
&lt;!-- Alignment with focus questions --&gt;
# Very good alignment between sub-title, focus questions, and heading structure, but there may be room for improvement
# Remove/change &quot;Add research on ...&quot; heading
|3=
&lt;!-- Overview--&gt;
# Solid development
&lt;!-- Scenario --&gt;
# Promising scenario; could benefit from further development to make it more compelling and illustrative
# Maybe rewrite the scenario in 3rd person perspective instead of 2nd person perspective
# The image could be more relevant to the scenario
&lt;!-- Description --&gt;
# A promising description of the problem/topic is planned or presented
&lt;!-- Focus questions --&gt;
&lt;!-- Alignment and quality --&gt;
# The focus questions are well aligned with the sub-title and top-level headings
|4=
&lt;!-- Key points--&gt;
&lt;!-- Overall --&gt;
# Promising development
# Focus on the core topic - how does competence affect motivated behaviour according to SDT?
# Consider competence frustration and competence satisfaction
# Provide more detailed edit summaries
&lt;!-- Other --&gt;
# Use correct capitalisation ([https://apastyle.apa.org/style-grammar-guidelines/capitalization APA style is a &quot;down&quot; style]) – [https://polishedpaper.com/blog/capitalization-apa-style more info]
# Do these key points include [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, this needs to be acknowledged in the edit summaries, otherwise it violates academic integrity.
&lt;!-- Conclusion --&gt;
# Conclusion is underway
# What are the practical, take-home messages? (address the focus questions)
|5=
&lt;!-- Figure --&gt;
# Relevant figure(s) presented, captioned, and cited
&lt;!-- Caption --&gt;
# Figure caption(s) provide(s) a reasonably clear description that is connected with the main text
&lt;!-- Cite --&gt;
# Figure(s) are cited at least once in the main text
|6=
&lt;!-- Learning feature --&gt;
&lt;!-- Interwiki links ---&gt;
# Two in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]]. Also embed links to [[Motivation and emotion/Book|book chapters]].
&lt;!-- Scenarios/examples/case studies --&gt;
# Consider incorporating additional scenarios, examples, or case studies to illustrate key concepts. These could build on the Overview scenario or introduce new real-world situations in the main body of the chapter to demonstrate how the concepts apply in practice.
&lt;!-- Quiz --&gt;
# Promising use of quiz question(s)
&lt;!-- Tables --&gt;
# Also consider using [[Motivation and emotion/Wikiversity/Tables|table(s)]] to summarise key information
|7=
&lt;!-- References --&gt;
&lt;!-- Overall --&gt;
# Good
&lt;!-- Systematic reviews --&gt;
# At least one relevant systematic review and/or meta-analysis has been identified
&lt;!-- APA style --&gt;
# Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]:
## alphabetical order
## capitalisation
## [[Help:Wikitext quick reference|italicisation]]
|8=
&lt;!-- Resources --&gt;
&lt;!-- See also --&gt;
# See also
## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Link to the most relevant Wikiversity book chapters and Wikipedia resources about this topic
&lt;!-- External links --&gt;
# External links
## One of two required external links provided
## Rename links so that they are more user friendly (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
## Include source in brackets after link
## Link to the most relevant external resources about this topic
|9=
# Used effectively
&lt;!-- Description about self --&gt;
# Excellent description about self provided
&lt;!-- Links to profile(s) --&gt;
# Consider linking to your professional online profile or resume such as [https://www.linkedin.com/ LinkedIn]. This is not required, but it can be useful to interlink your professional networks.
&lt;!-- Link to book chapter --&gt;
# A link to the book chapter is provided
|10=
&lt;!-- Social contribution --&gt;
# One out of three types of contributions made with direct link(s) to evidence. The other types of contribution are making:
#* direct improvements to other [[Motivation and emotion/Book|chapters (past or current)]]
#* comments on the [[Help:Talk page|talk page]]s of other [[Motivation and emotion/Book|chapters (past or current)]]
# To add direct links to evidence of Wikiversity edits or comments: view the page history, select the version of the page before and after your contributions, click &quot;compare selected revisions&quot;, and paste the comparison URL on your user page. For more info, see [[Motivation and emotion/Assessment/Chapter#Making and summarising social contributions|Making and summarising social contributions]]. This was demonstrated in [[Motivation and emotion/Tutorials/Wiki editing#Social contributions|Tutorial 2]].
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:33, 15 September 2026 (UTC)

== Book Chapter Feedback (Social Contribution) ==
Hey [https://uclearn.canberra.edu.au/courses/20143/users/111267 Nyambugi],

I really appreciate how succinctly you tie your ideas together. Each point feels specific, well‑elaborated, and thoughtfully developed, yet the writing remains concise and easy to follow.

The use of colour throughout the chapter is engaging and adds a dynamic visual element.

I also think you’ve done an excellent job looping back to the case scenarios introduced at the beginning. Using them as evolving examples gives the chapter a strong sense of continuity, and I think it shows that you have a natural ability for structuring a book chapter effectively! 

The only suggestion I’d make is to expand the conclusion slightly. Bringing all the ideas you mentioned together in a more comprehensive way would help reinforce how the concepts connect and flow into one another, strengthening the reader’s overall understanding. But in saying that, I love the take‑home messages, they work so well to provide a clear to-the-point summary of everything discussed.

Kind regards, [[Special:Contributions/~2026-55912-84|~2026-55912-84]] ([[User talk:~2026-55912-84|talk]]) 03:29, 19 October 2026 (UTC)

:From Leilab23 ^^^ [[User:Leilab23|U3220827]] ([[User talk:Leilab23|discuss]] • [[Special:Contributions/Leilab23|contribs]]) 03:32, 19 October 2026 (UTC)</text>
      <sha1>c3hxgoyg55q6e1ehllq20d8x2y7pcbx</sha1>
    </revision>
  </page>
  <page>
    <title>Talk:Motivation and emotion/Book/2026/Overconfidence in decision-making</title>
    <ns>1</ns>
    <id>331833</id>
    <revision>
      <id>2841472</id>
      <parentid>2831369</parentid>
      <timestamp>2026-10-19T07:39:04Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <comment>Book chapter feedback</comment>
      <origin>2841472</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="15963" sha1="t5lnezslem5dfu87kpeuf3i312joiog" xml:space="preserve">== Acknowledgements ==
Gen AI was utlizied to help with the coding and organisation of the book chapter.

== Heading casing ==
{| style=&quot;float: center; background:transparent;color:inherit;&quot;
|-
| [[File:Crystal Clear app ktip.svg|48px|left]]
| {{#if:BellaJohnson1|Hi [[User:BellaJohnson1|BellaJohnson1]].|}} FYI, the recommended [[Wikiversity]] heading style uses [[w:Letter case#Sentence_case|sentence casing]]. For example:&lt;br&gt;
&lt;big&gt;&lt;big&gt;Self-determination theory&lt;/big&gt;&lt;/big&gt;
rather than
&lt;big&gt;&lt;big&gt;Self-Determination Theory&lt;/big&gt;&lt;/big&gt;

Here's an example chapter with correct heading casing: [[Motivation and emotion/Book/2019/Growth mindset development|Growth mindset development]]

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:25, 5 September 2026 (UTC)
|}

&lt;!-- Official topic development feedback --&gt;
{{METF/2026
|1=
&lt;!-- Title --&gt;
# Title and subtitle are correctly worded and use [[w:Letter case#Sentence casing|sentence casing]]
|2=
&lt;!-- Headings --&gt;
# See earlier comment about [[#heading casing|heading casing]]
&lt;!-- Heading structure --&gt;
&lt;!-- 2-level --&gt;
# Promising [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]] – could benefit from further development and/or refinement
# Remove headings for table and purpose (fixed)
# Questions for readers should be in a feature box rather than a section heading per se; place each reflection question in the most relevant corresponding section 
&lt;!-- Alignment with focus questions --&gt;
# Excellent alignment between sub-title, focus questions, and heading structure
|3=
&lt;!-- Overview--&gt;
# Excellent – Scenario, image, evocative description of the problem/topic, and focus questions
&lt;!-- GenAI ---&gt;
# Does this section include [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, it needs to be acknowledged as such in the edit summaries, otherwise it violates academic integrity.
&lt;!-- Scenario --&gt;
# A scenario or case study is presented in a feature box at the start of this section
# I moved an image into the feature box to help attract reader interest
&lt;!-- Description --&gt;
# A clear description of the problem/topic is planned or presented
&lt;!-- Focus questions --&gt;
# Focus questions are aligned with sub-title and top-level headings
|4=
&lt;!-- Key points--&gt;
&lt;!-- Overall --&gt;
# Promising development
# Plan at least one paragraph before branching into sub-sections
# Direct quotes need page numbers
# Avoid overusing direct quotes; write about concepts in your own words, with citations
# Highlight the most relevant theories and synthesise the best research on the topic
# Provide more detailed edit summaries
&lt;!-- Theory and research --&gt;
# Strive for an integrated balance of the best psychological theory and research about this topic, with practical examples.
# Select the best theories about this topic
# Select the best research about this topic
&lt;!-- GenAI ---&gt;
# Do these key points include [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, this needs to be acknowledged in the edit summaries, otherwise it violates academic integrity.
&lt;!-- Conclusion --&gt;
# Conclusion is underway
# What are the practical, take-home messages? (address the focus questions)
|5=
&lt;!-- Figure --&gt;
# Relevant figure(s) are presented and captioned
&lt;!-- Cite --&gt;
# Cite each figure at least once in the main text using APA style (e.g., see Figure 1)
|6=
&lt;!-- Learning feature --&gt;
&lt;!-- Interwiki links ---&gt;
# Add in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]] (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
&lt;!-- Scenarios/examples/case studies --&gt;
# Consider use of more scenarios/examples/case studies 
&lt;!-- Quiz --&gt;
# Placeholder use of quiz/reflection question(s)
&lt;!-- Tables --&gt;
# Promising use of table(s)
# Citation(s)? Does this table include [[Motivation and emotion/Assessment/Using generative AI|genAI content]]? If so, this needs to be acknowledged in the edit summaries, otherwise it violates academic integrity.
|7=
&lt;!-- References --&gt;
&lt;!-- Overall --&gt;
# Basic
&lt;!-- Systematic reviews --&gt;
# What are the most relevant systematic reviews/meta-analyses about this topic?
&lt;!-- APA style --&gt;
# Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]:
## check author name (last reference isn't listed properly)
## capitalisation
## [[Help:Wikitext quick reference|italicisation]]
## [https://apastyle.apa.org/instructional-aids/reference-guide.pdf doi formatting]
## make doi hyperlinks active (i.e., clickable)
## use dois where available instead of other links
## include hyperlinked dois
## page numbers should be separated by an en-dash (–)
|8=
&lt;!-- Resources --&gt;
&lt;!-- See also --&gt;
# See also
## To be developed (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]])
&lt;!-- External links --&gt;
# External links
## Move academic sources into the &quot;References&quot; sections and provide in-text citation
## Link to the most relevant non-peer-reviewed external resources about this topic
|9=
&lt;!-- User page --&gt;
# Good
&lt;!-- Description about self --&gt;
# Description about self provided
&lt;!-- Links to profile(s) --&gt;
# Consider linking to your [https://portfolio.canberra.edu.au/ eportfolio] page and/or any other professional online profile or resume such as [https://www.linkedin.com/ LinkedIn]. This is not required, but it can be useful to interlink your professional networks.
&lt;!-- Link to book chapter --&gt;
# A link to the book chapter is provided
|10=
&lt;!-- Social contribution --&gt;
# One out of three types of contributions made with direct link(s) to evidence. The other types of contribution are making:
#* direct improvements to other [[Motivation and emotion/Book|chapters (past or current)]]
#* comments on the [[Help:Talk page|talk page]]s of other [[Motivation and emotion/Book|chapters (past or current)]]
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:25, 5 September 2026 (UTC)

&lt;!-- Official book chapter feedback --&gt;
{{MEBF/2026
|1=
&lt;!-- Overall comments... --&gt;
# This is a basic chapter
# The main strengths include:
#* theory is clearly explained
#* integrating with related pages using embedded links
# The main area(s) for potential improvement:
#* more detailed review of the best psychological research about the topic
#* quality of written expression
#* overuse of unacknowledged [[Motivation and emotion/Assessment/Using generative AI]] (watch out for [[w:AI slop|AI slop]])—express more in your own words
&lt;!-- Overall - Edit summaries --&gt;
#* Use more specific [[w:Help:Edit summary|edit summaries]] to clearly communicate the changes made in each edit
&lt;!-- Overall – Citations --&gt;
# Reasonably good use of academic, peer-reviewed citations to support claims
&lt;!-- Overall – Word count --&gt;
# Under the [[Motivation and emotion/Assessment/Chapter#Wordcount|maximum word count]], so there is room to expand
&lt;!-- Overall – Copyedits --&gt;
# For additional feedback, see the following comments and [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FOverconfidence_in_decision-making&amp;diff=2841471&amp;oldid=2837340 these copyedits]
|2=
&lt;!-- Overview – Comments... --&gt;
# Very good
&lt;!-- Overview – Scenario --&gt;
&lt;!-- Overview – Scenario - Description --&gt;
# Engaging scenario or case study
&lt;!-- Overview – Scenario - Figure --&gt;
# Figure 1 is relevant to the scenario
&lt;!-- Overview – Scenario - Feature box --&gt;
# The scenario uses an appropriate feature box
&lt;!-- Overview – Explains problem --&gt;
# Explains the psychological problem or phenomenon reasonably well
# Quality of written expression needs improvement
&lt;!-- Overview – Focus questions --&gt;
# The focus questions are excellent (clear and relevant)
# The focus questions could be improved by:
## splitting double-barrelled questions into separate questions
|3=
&lt;!-- Theory comments... --&gt;
&lt;!-- Theory – Breadth --&gt;
# Reasonably good—relevant theories are selected, described, and explained, with some room for improvement
&lt;!-- Theory – Builds on --&gt;
# Build more strongly on [[w:|Wikipedia]] articles and/or/but not related [[Motivation and emotion/Book|chapters]] by embedding interwiki links for key terms
&lt;!-- Theory – Depth --&gt;
# Reasonably good depth is provided about key theory(ies)
&lt;!-- Theory – Tables/Figures/Lists --&gt;
# Basic use of tables, figures, and/or lists to clearly convey key theoretical information
&lt;!-- Theory – Citations --&gt;
# In some places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological theory about the topic.
&lt;!-- Theory – Examples --&gt;
# Consider using more examples to illustrate theoretical concepts
|4=
&lt;!-- Research comments... --&gt;
&lt;!-- Research – Key findings --&gt;
# Insufficient review of relevant research
# Greater emphasis on systematic reviews and/or meta-analyses would be ideal
# More detail about key studies would be ideal
# In some places, the chapter could be strengthened by including more academic, peer-reviewed citations (e.g., see the {{f}} tags). This would help to demonstrate a deeper understanding of relevant psychological science about the topic.
&lt;!-- Research – Critical thinking --&gt;
# Insufficient [[w:Critical thinking|critical thinking]] about relevant research is evident
# [[w:Critical thinking|Critical thinking]] about research could be further evidenced by:
## describing the methodology (e.g., sample, measures) in important studies
## considering the strength of relationships
## acknowledging limitations
## pointing out critiques/counterarguments
## suggesting ''specific'' directions for future research
|5=
&lt;!-- Integration comments... --&gt;
# Insufficient integration between the most relevant theory(ies) and the best research
# The chapter places more emphasis on theory than on research; strive for an integrated balance
# Insufficient integration with related [[Motivation and emotion/Book|chapters]]
|6=
&lt;!-- Conclusion comments... --&gt;
# Very good summary and conclusion
# Highlight the importance of the problem or phenomenon of interest
&lt;!-- Conclusion – Key points --&gt;
# Key points are well summarised
&lt;!-- Conclusion – Focus questions --&gt;
# The focus questions are addressed
&lt;!-- Conclusion – Take-home messages --&gt;
# Add practical, take-home message(s)
|7=
&lt;!-- Written expression – Style comments... --&gt;
&lt;!-- Written expression – Written expression --&gt;
# Written expression
## The quality of written expression is OK but there are several aspects which are below professional standard
&lt;!-- Written expression – Sentences --&gt;
## Some sentences could be explained more clearly (e.g., see the {{explain}} and {{rewrite}} tags); consider using [https://www.studiosity.com/students/ Studiosity] for targetted feedback to help improve the quality of written expression

&lt;!-- Written expression – Layout --&gt;
# Layout
## Avoid having sections with 1 sub-heading – use 0 or 2+ sub-headings
## See earlier comment about [[#Heading casing|heading casing]]
## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags)
&lt;!-- Written expression – Grammar --&gt;
# Grammar
## The grammar for many sentences could be improved (e.g., see {{g}} tags); consider using a grammar checking tool, [https://www.studiosity.com/students/ Studiosity], and/or peer feedback
## Improve the clarity and flow of the writing by checking and correct use of commas. See [https://www.grammarly.com/blog/comma/ Grammarly's guide to using commas].
## Check and correct use of [https://www.google.com.au/search?q=affect+vs.+effect+grammar affect vs. effect]
&lt;!-- Written expression – Spelling --&gt;
# Spelling
## Many words are misspelt (e.g., see the {{sp}} tags). Spell-checking tools are available in most internet browsers and word processing software packages.
&lt;!-- Written expression – Proofreading --&gt;
# Proofreading
## More proofreading is needed (e.g., fix punctuation and typographical errors) to bring the quality of written expression closer to a professional standard
&lt;!-- Written expression – APA style - Quotes --&gt;
## Use double (not single) quotation marks &quot;to introduce a word or phrase used ... as slang, or as an invented or coined expression&quot; ([https://apastyle.apa.org/products/publication-manual-7th-edition APA Style 7th ed.], 2020, p. 159)
## Direct quotes need page numbers—even better, communicate about concepts in your own words
&lt;!-- Written expression – Figures --&gt;
## Figures
### Reasonably well captioned
&lt;!-- Written expression – Figures - Citations --&gt;
### Refer to each Figure at least once within the main text (e.g., &quot;(see Figure 1)&quot;)
&lt;!-- Written expression – Tables --&gt;
## Tables
### Very well captioned
&lt;!-- Written expression – Tables - Citations --&gt;
### Refer to each Table at least once within the main text (e.g., see Table 1)
&lt;!-- Written expression – Citations --&gt;
# Citations use basic [https://apastyle.apa.org/products/publication-manual-7th-edition APA Style (7th ed.)]
# In many places, better use could be made of academic, peer-reviewed citations (e.g., see the {{f}} tags)
## A full stop is needed after &quot;et al&quot; (i.e., &quot;et al.&quot;) because it is an abbreviation of [[wikt:et alii|et alii]]
&lt;!-- Written expression – References --&gt;
## References use very good APA style:
### Check and correct use of italicisation
|8=
&lt;!-- Learning features comments... --&gt;
# Reasonably good use of learning features
&lt;!-- Learning features – Wikipedia embedded links --&gt;
# Add embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding interwiki links for the first mention of key words and technical concepts would make the text more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]].
&lt;!-- Learning features – Wikiversity embedded links --&gt;
# Add embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project.
&lt;!-- Learning features – Figures, tables, feature boxes, scenarios --&gt;
# Insufficient use of figure(s)
# Basic use of table(s)
# Basic use of feature box(es)
# Basic use of scenarios, case studies, or examples
&lt;!-- Learning features – Quizzes --&gt;
# Good use of quiz(zes) and/or reflection question(s)
# The quiz questions could be more effective as learning prompts by being embedded as single questions within each corresponding section rather than as a set of questions at the end
&lt;!-- Learning features – See also --&gt;
# Reasonably good use of the [[{{PAGENAME}}#See also|See also]] section
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Add more links
&lt;!-- Learning features – External links --&gt;
# Good use of the [[{{PAGENAME}}#External links|External links]] section
## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing]
## Use alphabetical order
|9=
&lt;!-- Social contribution comments... --&gt;
# ~2 logged, useful, mostly minor/moderate/major contributions with [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]]
# ~1 logged contributions without [[Motivation and emotion/Assessment/Chapter/Summarising social contributions#How to add direct links to contributions|direct links to evidence]], so unable to easily verify and assess. See [[Motivation and emotion/Tutorials|tutorials]] for guidance about how to get direct links to evidence.
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:38, 19 October 2026 (UTC)</text>
      <sha1>t5lnezslem5dfu87kpeuf3i312joiog</sha1>
    </revision>
  </page>
  <page>
    <title>User:The Citer</title>
    <ns>2</ns>
    <id>331894</id>
    <revision>
      <id>2841268</id>
      <parentid>2837981</parentid>
      <timestamp>2026-10-18T12:41:43Z</timestamp>
      <contributor>
        <username>The Citer</username>
        <id>3110681</id>
      </contributor>
      <minor />
      <origin>2841268</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1789" sha1="rnn815kvovalrm1izrp0as83a89uwfp" xml:space="preserve">Hi. I'm not the saddest citer in MediaWiki. I'm now improving animal articles; I like adding phylogenies. I may add content to plant articles once in a while.
==Origin==
Apparently, a mysterious editor was &quot;Citing&quot; articles but without tracing the source/&quot;cite&quot;. But even then, I was dubbed '''''The Citer''''' and I created an account to make an article about Microkingdoms.

I was almost banned from editing articles, so I made a promise that I would only create articles. It turns out, this is actually edited? Yes, I added a link in Oophaga sylvatica, which is considered editing, but even that made complaints about '''''The Citer'''''.
===Criticism===
Ever since I wanted to make an article about microkingdoms, people kept complaining about me. In fact, I was added to the [[Wikipedia:Administrators' noticeboard/Incidents]], which goes to show your reputation can get ruined if you want the wrong thing. And, you know what happened: I got blocked.
==Migration to [https://species.wikimedia.org/wiki/Main_Page Wikispecies]==
After being blocked on Wikipedia, I moved to wikispecies, where I survived much longer. I had a good time up until I made The Other Citer, which marked my downfall.
===Post-Other Citer Blockage===
After my &quot;back-up&quot; account was blocked, I hit a new low: I created Orthokaryote, and when I collabrated with myself, you guessed it: /*&quot;we&quot;*/ got BLOCKED.
==Post second blockage==
After all that, it makes sense of why I'm here. But if you block me, then I will have to move yet again.
==Why don't I just try to request being unblocked?==
You see, it's just easier to move than to waste hours trying to be unblocked.

=Social Circle=
==Friends==
[There is no text right here]
==Enemies==
[There is no text right here]
==Frenemies==
[There is no text right here]</text>
      <sha1>rnn815kvovalrm1izrp0as83a89uwfp</sha1>
    </revision>
  </page>
  <page>
    <title>Talk:Motivation and emotion/Book/2026/Apocalyptic fear</title>
    <ns>1</ns>
    <id>331957</id>
    <revision>
      <id>2841258</id>
      <parentid>2836126</parentid>
      <timestamp>2026-10-18T12:10:29Z</timestamp>
      <contributor>
        <username>Jack4234</username>
        <id>3106762</id>
      </contributor>
      <origin>2841258</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="6422" sha1="iqec0vokpn1lxwhlvmxp8pc80qmwp0s" xml:space="preserve">== Heading casing ==
{| style=&quot;float: center; background:transparent;color:inherit;&quot;
|-
| [[File:Crystal Clear app ktip.svg|48px|left]]
| {{#if:LazPulch|Hi [[User:LazPulch|LazPulch]].|}} FYI, the recommended [[Wikiversity]] heading style uses [[w:Letter case#Sentence_case|sentence casing]]. For example:&lt;br&gt;
&lt;big&gt;&lt;big&gt;Self-determination theory&lt;/big&gt;&lt;/big&gt;
rather than
&lt;big&gt;&lt;big&gt;Self-Determination Theory&lt;/big&gt;&lt;/big&gt;

Here's an example chapter with correct heading casing: [[Motivation and emotion/Book/2019/Growth mindset development|Growth mindset development]]

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 20:58, 9 September 2026 (UTC)
|}

&lt;!-- Official topic development feedback --&gt;
{{METF/2026
|1=
&lt;!-- Title --&gt;
# Title and/or subtitle not correctly worded and/or didn't use [[w:Letter case#Sentence casing|sentence casing]] (fixed)
|2=
&lt;!-- Headings --&gt;
# See earlier comment about [[#heading casing|heading casing]]
&lt;!-- Heading structure --&gt;
&lt;!-- 2-level --&gt;
# Clear [[Motivation and emotion/Assessment/Major project/Structure|2-level heading structure]]
&lt;!-- Alignment with focus questions --&gt;
# Excellent alignment between sub-title, focus questions, and heading structure
|3=
&lt;!-- Overview--&gt;
# Excellent – Scenario, image, evocative description of the problem/topic, and focus questions
&lt;!-- Scenario --&gt;
# A scenario or case study is presented in a feature box with an image at the start of this section
&lt;!-- Description --&gt;
# A clear description of the problem/topic is planned or presented
&lt;!-- Style --&gt;
# Use present, rather than future, tense
&lt;!-- Focus questions --&gt;
# Focus questions are aligned with sub-title and top-level headings
|4=
&lt;!-- Key points--&gt;
&lt;!-- Overall --&gt;
# Excellent – key points are well developed for each section
# Promising balance of theory and research; consider integrating/synthesising theory and research rather than presenting separately
# Perhaps also consider types/categories of AF (e.g., include eco-anxiety/ecological destruction fears (there is growing research about this))
&lt;!-- Theory and research --&gt;
&lt;!-- Citation style --&gt;
# Use [https://apastyle.apa.org/style-grammar-guidelines/citations/basic-principles APA style 7th edition for citations] (e.g., do not include author initials)
# Use correct capitalisation ([https://apastyle.apa.org/style-grammar-guidelines/capitalization APA style is a &quot;down&quot; style]) – [https://polishedpaper.com/blog/capitalization-apa-style more info]
&lt;!-- Other --&gt;
# For sections with sub-sections, provide key points for an overview paragraph prior to branching into the sub-headings
&lt;!-- Conclusion --&gt;
# Conclusion is underway
# What are the practical, take-home messages? (address the focus questions)
|5=
&lt;!-- Figure --&gt;
# Relevant figure(s) are presented and captioned
&lt;!-- Cite --&gt;
# Cite each figure at least once in the main text using APA style (e.g., see Figure 1)
|6=
&lt;!-- Learning feature --&gt;
&lt;!-- Interwiki links ---&gt;
# Excellent in-text [[m:Help:Interwiki linking|interwiki links]] for first mention of key terms to [[w:|Wikipedia]] and/or [[Motivation and emotion/Book|book chapters]]
&lt;!-- Scenarios/examples/case studies --&gt;
# Promising use of scenarios/examples/case studies
&lt;!-- Quiz --&gt;
# Promising use of quiz question(s)
# Place each quiz question in the most relevant section
# Focus the quiz question(s) on the take-home messages
&lt;!-- Tables --&gt;
# Also consider using tables to summarise key information
|7=
&lt;!-- References --&gt;
&lt;!-- Overall --&gt;
# Good
&lt;!-- Systematic reviews --&gt;
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# Only include references which have been accessed and read
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# Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]:
## capitalisation
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## use dois where available instead of other links
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# See also
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## Very good
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&lt;!-- User page --&gt;
# Used effectively
&lt;!-- Description about self --&gt;
# Description about self provided
&lt;!-- Links to profile(s) --&gt;
# Consider linking to your [https://portfolio.canberra.edu.au/ eportfolio] page and/or any other professional online profile or resume such as [https://www.linkedin.com/ LinkedIn]. This is not required, but it can be useful to interlink your professional networks.
&lt;!-- Link to book chapter --&gt;
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&lt;!-- Social contribution --&gt;
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#* comments on the [[Help:Talk page|talk page]]s of other [[Motivation and emotion/Book|chapters (past or current)]]
#* posts about the unit or project on the {{Motivation and emotion/Canvas}} discussion forum
}}

==General Feedback==
Hi!
This is looking like the start of a really interesting chapter. I think that this is something that might be a lot more common than we think. The use of Leave the World Behind is great because I felt that it was a really relatable movie because something like that did not seem impossible to happen to us. 
Potentially the use of some more photos accompanying the case study would be great because I think it might elicit some more emotions and can help both kinds of learners. 
Can't wait to see how this turns out!--[[User:Yellowvines|Yellowvines]] ([[User talk:Yellowvines|discuss]] • [[Special:Contributions/Yellowvines|contribs]]) 02:26, 6 October 2026 (UTC)

==Feedback==

Hi, 

Firstly, great choice of topic and well done. It looks and reads great. 

One small thing I noticed is that there seems to be a few in-text citations that are missing from the reference list, including Ajzen (1991), Turner and Walsmely (2020), and Paul and Alan (2024). It might be worth doing a quick check that all in-text citations have corresponding reference-list entries.

- jack4234</text>
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      <comment>/* Emotion Dysregulation research suggestion */ Reply</comment>
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      <text bytes="7477" sha1="0g30qojodr1dzog8rzu2bkccoklao4f" xml:space="preserve">== Heading casing ==
{| style=&quot;float: center; background:transparent;color:inherit;&quot;
|-
| [[File:Crystal Clear app ktip.svg|48px|left]]
| {{#if:Leilab23|Hi [[User:Leilab23|Leilab23]].|}} FYI, the recommended [[Wikiversity]] heading style uses [[w:Letter case#Sentence_case|sentence casing]]. For example:&lt;br&gt;
&lt;big&gt;&lt;big&gt;Self-determination theory&lt;/big&gt;&lt;/big&gt;
rather than
&lt;big&gt;&lt;big&gt;Self-Determination Theory&lt;/big&gt;&lt;/big&gt;

Here's an example chapter with correct heading casing: [[Motivation and emotion/Book/2019/Growth mindset development|Growth mindset development]]

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 05:50, 12 September 2026 (UTC)
|}
&lt;!-- Official topic development feedback --&gt;
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# The structure may be planning too much background info and too little emphasis on integrating the best theory and research about the topic (psychedelic treatment of EDs)
# Provide a more descriptive heading for the most important section: Trip to...ED Recovery?
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### Also link to relevant [[w:|Wikipedia]] pages
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&lt;!-- Link to book chapter --&gt;
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&lt;!-- Social contribution --&gt;
# Good – two out of three types of contributions made with direct link(s) to evidence. The other type of contribution is making:
#* direct improvements to other [[Motivation and emotion/Book|chapters (past or current)]]
# To add direct links to evidence of Wikiversity edits or comments: view the page history, select the version of the page before and after your contributions, click &quot;compare selected revisions&quot;, and paste the comparison URL on your user page. For more info, see [[Motivation and emotion/Assessment/Chapter#Making and summarising social contributions|Making and summarising social contributions]]. This was demonstrated in [[Motivation and emotion/Tutorials/Wiki editing#Social contributions|Tutorial 2]].
}}
-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 05:50, 12 September 2026 (UTC)

== Emotion Dysregulation research suggestion ==
Hello, this is such an interesting topic and I like how you have set it out. You mention emotion dysregulation and it's influence on eating disorders. I wonder if there is a link between comorbid conditions to eating disorders that impact the emotional regulation (for example PTSD). Best of luck with your page.  [[User:U3228742|U3228742]] ([[User talk:U3228742|discuss]] • [[Special:Contributions/U3228742|contribs]]) 06:41, 17 October 2026 (UTC)

:Hi thanks so much for your comment :) It was a very interesting subject and hard to summarise haha, so I appreciate your kind words. What you've pointed out was definetly a key point of interest in some of the research. I think looking at treatment options for PTSD and ED's in combination, especially in children, would prove to be a very important field of study, considering how much unrest and violence is occuring on a global scale at the moment.  [[User:Leilab23|U3220827]] ([[User talk:Leilab23|discuss]] • [[Special:Contributions/Leilab23|contribs]]) 04:17, 19 October 2026 (UTC)</text>
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{{METF/2026
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&lt;!-- Overview--&gt;
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&lt;!-- Link to book chapter --&gt;
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# Excellent – at least three different types of contributions with direct link(s) to evidence
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-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:16, 15 September 2026 (UTC)

== Suggestion about chapter ==

Hi,

You made really good progress for your book chapter.

I found Wallas’ Four-Stage Model of the Creative Process theory related to creativity, which I thought you can include in your book chapter. 

Please find reference below for the theory:

Sadler-Smith, E. (2015). Wallas’ Four-Stage Model of the Creative Process: More Than Meets the Eye? Creativity Research Journal, 27(4), 342–352. https://doi.org/10.1080/10400419.2015.1087277

All the best.

--[[User:P U3270518|P U3270518]] ([[User talk:P U3270518|discuss]] • [[Special:Contributions/P U3270518|contribs]]) 09:38, 16 September 2026 (UTC)

== Reccomendations: Overview and headings ==
Hello,

I really like this topic and I think you've encapculated the core components of it very well in your book chapter so far. As I am a super creative person, I love this topic. I have two main points of feedback, feel free to take pieces or ignore entirely. I am obviously a student (same as you) and am writing this feedback based on my own understanding of what the assessment requires. Hope this helps. :)

For the overview, you brought up two distinct components of your topic (creativity and then effort) which is good but you may have gone on a little bit too long. I believe if you were to shorten your overview to just the scenario, you could get your point accross more succinctly. See my example of your scenario trimmed:

&quot;''You have been staring at a blank page for hours, trying to come up with an original idea for a creative project. Just when you decide to take a break, an idea suddenly comes to you. You feel excited and inspired, and you immediately start working. At first, everything seems to flow naturally and you feel confident about what you are creating. As you continue, however, the excitement begins to fade. The idea is harder to develop than you expected, and finishing the project requires concentration, persistence, and several changes along the way.'' Where did that initial creative spark go and how and why does one persevere despite it?&quot;

Then I would proceed to add your explanation beneath the scenario. I did a little rewording to help clarify your key points.

&quot;''This experience shows how inspiration can provide a starting point for creativity but also that creativity does not depend on inspiration alone, particularly in its execution. Inspiration can help people recognise new possibilities and motivate them to turn those possibilities into action (Oleynick et al., 2014) while developing the initial idea can require continual effort, revision, problem-solving, and persistence. This raises an interesting question: Does inspiration drive us to put effort into creative work, or can the effort we put into creating also lead to new inspiration?&quot;'' 

I did remove one of your sources as I found it detracted from the actual concepts you were discussing in your scenario. I'm sure it'd be very easy to reuse it in the body of your chapter so don't stress. 

My next major piece of advice actual involves your heading and chapter structure. This is not to say I believe all the work you have done is void, but I believe reorganising and clarifying creative features will really strengthen your chapter (aforementioned, I'm very passionate about this topic lol) 

Here's my suggestion on a potential structure shift. (H = heading, SH = subheading)

H1 Creativity

SH1 Creativity and humanity. Here is where I would outline what creativity actually is. What mechanisms define it? Why do we do it? (socially, culturally, etc) This can be really broad and involve pretty much anything you want but I believe starting with a strong explanation of this key component will really strengthen your chapter overall. Again, it may seem obvious, but the concept itself is very difficult to pin down in one classification.

SH2 Creativity and inspiration. This is where I would discuss what it means to be creatively inspired. I would link this back to your original paragraph in your first heading+ this point you made after your scenario. &quot;'''''Creative inspiration can give people new ideas and motivate them to start creating.''' It can also help people see new possibilities and feel more interested in developing an idea. Inspiration can connect the discovery of an idea with the motivation to pursue it. This is reflected in the distinction between being “inspired by” something and being “inspired to” act on it (Oleynick et al., 2014).''&quot; You may use that piece as this headings finisher perhaps.

H2 Effort

SH1 Effort. What is it and why is it important? Again, rinse and repeat above. What is effort? Why is it hard? Why do we feel inclined to do it more in certain situations than others? I would recoommend linking in motiviational theories (Perhaps something to do with goals?) for effort or tie it into other models discussed in class when your explain it. I would try to focus more on the motivational explanations here rather than direct application to creativity, for fear of sounding repetitive throughout the chapter.

SH2 How effort applies to creativity. Applying the above explanation to creativity. I would definitly tie in some motiviational theories here, particularly to do with success and goals. 

H3 Insipration - the middle ground between creativity and effort (or some such title, you write what you like). You probably don't need subheadings for this (really depends on your word count so far I guess) but this is where I would discuss the interchangeable socioeconomics of inspiration on creativity/effort/persistence (which is a component you've mentioned a few times in your book chapter so far. When I say socioeconomics, I don't mean the impact of one on the other (I would save that for my final heading/conclusion) but rather the manifestation of them. A theoretical case study could be a good way to do this. Say there are three people, one with objectively high amounts of inspiration, one with objectively higher amounts of creativity, and one with objectively higher amounts of effort. Posing questions to your readers such as &quot;in a task of putting together a lego set, which person do you think would complete the task first?&quot; Would give them a chance to apply the knowledge they've learnt recently. You can then give the answers to each question by explaining the practical application of each component and how that would shape their behavior. I.e. &quot;As mentioned in the efforts heading, person #3 would theoritically be more inclined to complete the lego set faster as the process involves less creativity or inspiration and more effort.&quot; Explain, seperate, apply, question, answer. Obviously this is just one option of how you could do this. You may choose to not to and that's also fine. (I would recommend not linking the three components until H4 UNLESS you have enough words/not enough content in H3. Then you may want to make H4 a SH in H3. Again, this is totally up to you, it's just how i would focus on it.)

H4 Creativity, inspiration, effort. Here is where I would tie in the three realms youve discussed and then loop it all back into 1. how people can generate more creativity, 2. how they can increase insipration, 3. how they can practice dicipline to increase effort application. Here I would really focus on the application of these constructs into practical senses. Maybe tie it into your first scenario. I.e. how the person applied motiviational psychology to increase their inclination to putting in effort which in turn improved their capacty to be creative as they did not believe themselves to be as limited in terms of skills as they has originally. 

You have 90% of your information already down pat, I just think it would benefit reorganisation to further clarify the flow of how your model works and tie it in a bit better to real world application.

Good job and good luck 


[[User:Monuc9|Monuc9]] ([[User talk:Monuc9|discuss]] • [[Special:Contributions/Monuc9|contribs]]) 03:07, 9 October 2026 (UTC)


==General feedback==

This looks like an interesting topic and I think the overall structure works well. one area that might be worth developing further is the effort -&gt; inspiration side of the relationship. currently there is quite a lot explaining how inspiration can motivate effort, but less on how persistence and continued creative work could lead to new ideas. part of my research question is about goal persistence which is why this probably jumped out to me. 

A couple of sources that might be useful are:

The dual pathway to creativity model: creative ideation as function of flexibility and persistence: https://doi.org/10.1080/10463281003765323 

chapter five - the creation and curation of all things worthy: inspiration as vital force in persons and cultures: 10.1016/bs.adms.2020.01.002 

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__TOC__

== Overview ==
&lt;div style=&quot;border:1px solid #668cff; border-radius:6px; padding:10px; margin:8px 4px 25px 4px;&quot;&gt;[[File:The family in Ghana.jpg|thumb|176x176px|'''Figure 1'''. Family posing for photo, smiling {{ic|explain how this relates to homeschooling}}]]

;Case study

When Sarah decided to withdraw her 12-year-old son, Liam, from mainstream secondary school, she was met with well-meaning caution from family and friends. Liam had experienced escalating anxiety linked to peer dynamics and a rigid classroom environment, which left him disengaged from learning. Initially, Sarah struggled with the daily transition, worrying about lesson planning, social isolation, and whether she possessed the teaching skills required. However, after establishing a flexible routine tailored to Liam's specific learning style and incorporating community homeschool groups, his confidence rebounded. This chapter explores the underlying psychological factors driving decisions like Sarah's, examining the interplay between parental motivations, psychological theories, and educational outcomes.
&lt;/div&gt;

The decision to educate children at home represents a significant departure from conventional schooling models. While often stereotyped as an ideological rejection of public education systems, contemporary empirical literature reveals a complex, highly motivated population driven by diverse pedagogical, relational, and philosophical goals. Understanding these decisions requires examining psychological frameworks of parental involvement and motivation.

;Focus questions
* What are the primary push and pull factors influencing parental decisions to homeschool?
* How do psychological frameworks such as the parental involvement model and expectancy-value theory explain these motivations?
* In what ways do family circumstances, child-specific needs, and educational values interact with the decision to homeschool?
* How do parental motivations evolve over time, and how do they align with empirical outcomes research?

== Push and pull motivations ==
Decisions to transition to home-based education are frequently characterised by researchers as a combination of &quot;push&quot; factors (dissatisfaction with conventional school environments) and &quot;pull&quot; factors (positive aspirations for home-based learning environments) {{f}}. 

=== Push motivations ===
[[File:Bully - The Noun Project.svg|thumb|150px|'''Figure 2'''. Bully putting down another person]]

Push factors typically stem from negative experiences within conventional school systems {{f}}. Research indicates that concerns regarding school environments, negative peer socialisation, [[w:Bullying|bullying]], and institutional inflexibility heavily influence initial withdrawals {{f}}. For some families, inflexible curricula or an inability of traditional schools to accommodate specific learning needs serve as primary catalysts {{f}}. 

=== Pull motivations ===
Conversely, pull factors reflect proactive desires to curate a specific educational and social environment {{f}}. These include a desire for individualized instruction, alignment with family religious or philosophical values, and the promotion of autonomous learning styles {{f}}. Studies across diverse international contexts demonstrate that pedagogical and relational goals frequently outweigh anti-institutional sentiments {{f}}.

== How do psychological theories explain parental motivation? ==
{{expand}}

=== Parental involvement model ===
The most theoretically grounded frame for this topic is the parental involvement model {{explain}} established by Hoover-Dempsey and Sandler {{f}}. Green and Hoover-Dempsey (2007) conducted a systematic examination revealing that [[w:Homeschooling|homeschooling]] parents are motivated primarily by active role construction, a strong sense of efficacy for helping their child learn, and positive perceptions of their life context {{expand}}. This framework suggests that parental motivation is deeply rooted in a psychological sense of responsibility and capability regarding their child's educational trajectory.

{{example}}

=== Expectancy-value theory and self-determination theory ===
[[File:Self-Determination-Theory.png|thumb|'''Figure 3'''. Self-Determination Theory Model]]

Expectancy-value reasoning complements this model, wherein parents weigh the perceived expectancy of success in home education against the subjective value of achieving specific developmental and academic goals {{f}}. Furthermore, [[w:Self-determination theory|Self-Determination Theory]] (SDT) helps explain why autonomy-supportive home environments appeal to parents seeking to foster intrinsic motivation, competence, and relatedness in their children {{f}}. 

== What influences the decision to homeschool? ==
{{expand}}

=== Parental values and educational goals ===
Parental values significantly shape the architecture of home education {{f}}. Whether driven by ideological frameworks, religious convictions, or a commitment to [[w:Progressive|progressive]] [[w:Pedagogy |pedagogical]] philosophies, parents establish learning environments designed to reflect their core belief systems {{f}}.

=== Family circumstances and practical barriers ===
Practical feasibility acts as a crucial moderating influenc {{f}}. Resource constraints, flexible work arrangements, financial considerations, and the availability of local homeschooling cooperatives or support networks often determine whether families can successfully transition from initial motivation to sustained implementation {{f}}.

'''Reflection question: Balancing motivation and practical needs'''

Imagine parents who want to homeschool their child because of difficulties at school but are concerned about balancing teaching responsibilities with work and family commitments. What factors should they consider before making a decision? Reflect on how parental motivation, confidence, financial resources, and the child's educational and social needs may influence their choice.

{{ic|Include answers}}

{| class=&quot;wikitable&quot; style=&quot;width:100%; margin:auto;&quot;
|+ Table 1: Summary of Key Empirical Studies on Homeschooling Motivations
! Study
! Context / Sample
! Primary Motivational Themes Identified
|-
| Green &amp; Hoover-Dempsey (2007)
| United States (Systematic examination)
| Active role construction, parental self-efficacy, positive life context perception.
|-
| Collom (2005)
| United States (Survey)
| Academic/pedagogical concerns rated highest; religious base subsiding.
|-
| Tan (2019)
| Singapore (Qualitative, 10 families)
| Individualised instruction, dissatisfaction with exam-oriented schooling.
|-
| Brabant et al. (2003)
| Quebec, Canada (203 families)
| Seven motivational factors; absence of single religious/anti-state dominance.
|-
| Kostelecká et al. (2023)
| Czech Republic (Survey/Interviews)
| Distinction between system dissatisfaction, family values, and lifestyle factors.
|}

== How do motivations change and what does research reveal? ==
{{expand}}

=== Changing motivations over time ===
[[File:MontreGousset001.jpg|thumb|'''Figure 4'''. Vintage Handwatch showing the Time] {{ic|explain how this relates to the topic}}]

Research indicates that the reasons parents initially start homeschooling often differ from the reasons they continue {{f}}. Initial reactive motivations (such as resolving an immediate bullying incident or school conflict) frequently evolve into proactive, long-term pedagogical commitments as parents build confidence and adapt to their children's changing developmental needs {{f}}.

=== Critical evaluation of the evidence ===
To critically evaluate whether parental confidence {{ic|about what?}} is justified, outcomes literature provides an essential counterweight {{f}}. Ray (2017) reports mostly positive academic and socialisation outcomes in systematic reviews, though selection-bias limitations must be acknowledged. Conversely, Martin-Chang et al. (2011) found that structured homeschoolers outperformed public school peers while unstructured homeschoolers scored lowest. This tension between highly motivated, efficacious parents and mixed outcome empirical evidence forms the critical core of the homeschool debate.

{| style=&quot;width:50%; background:#F4CECE; color:black; border-radius:12px; border:0; padding:2px;&quot;
|-
! style=&quot;background:#E07F87; color:black; border-radius:12px 12px 0 0; border:0; padding:2px;&quot; | 
&lt;big&gt;Quiz: Why do parents choose homeschooling?&lt;/big&gt;
|-
| style=&quot;border-radius:0 0 12px 12px; padding:2px; border:0;&quot; |

&lt;div style=&quot;margin-top:-15px;&quot;&gt;
&lt;quiz display=simple&gt;

{Which example best represents a push (avoidance) motivation for homeschooling?
|type=&quot;()&quot;}
- A parent wants greater flexibility in their child's learning schedule.
+ A parent withdraws their child because of persistent bullying at school.
- A parent wants to incorporate family values into education.
- A parent enjoys designing individualised learning activities.

{According to Self-Determination Theory, which three psychological needs may help explain parental motivations for homeschooling?
|type=&quot;()&quot;}
- Achievement, security, and independence
- Confidence, motivation, and responsibility
+ Autonomy, competence, and relatedness
- Control, intelligence, and emotional stability

{A parent believes homeschooling would benefit their child but doubts their ability to teach effectively. Which psychological concept best explains this concern?
|type=&quot;()&quot;}
- Intrinsic motivation
+ Parental self-efficacy
- Relatedness
- Avoidance motivation

{Which example best illustrates a pull (approach) motivation for homeschooling?
|type=&quot;()&quot;}
- A parent removes their child following repeated school-related anxiety.
- A parent withdraws their child because of unresolved bullying.
+ A parent chooses homeschooling to provide individualised, interest-based learning.
- A parent removes their child because of dissatisfaction with school discipline.

{How might parental motivations for homeschooling change over time?
|type=&quot;()&quot;}
- Parents' motivations always remain unchanged after beginning homeschooling.
+ Initial concerns about school experiences may develop into positive educational goals.
- Parents eventually become motivated only by academic achievement.
- Negative school experiences always remain the primary motivation.

{A parent values homeschooling and feels confident teaching but cannot reduce their working hours. What does this example demonstrate?
|type=&quot;()&quot;}
- Strong motivation guarantees that homeschooling is achievable.
- Parental confidence is unrelated to educational decisions.
- Homeschooling decisions depend entirely on personal values.
+ Practical circumstances can limit parents' ability to act on their motivations.

&lt;/quiz&gt;
&lt;/div&gt;

|}

== Conclusion ==
Parental motivation to homeschool is a dynamic psychological process influenced by both push (avoidance) and pull (approach) factors (Collom, 2005; Green &amp; Hoover-Dempsey, 2007). While negative school experiences, such as bullying and unmet learning needs, may initially motivate parents to consider homeschooling, positive goals involving individualised education, family values, and flexibility can also shape their decisions.

Psychological theories help explain these motivations. Self-Determination Theory (Deci &amp; Ryan, 2000) highlights the importance of autonomy, competence, and relatedness, while Bandura's (1997) self-efficacy theory explains how parents' confidence in their teaching abilities may influence their decision to homeschool. These motivations may also evolve as families gain experience and their children's educational needs change (Neuman &amp; Guterman, 2017).

The key takeaway is that homeschooling decisions involve more than dissatisfaction with conventional schooling. Parents should consider their educational values, children's needs, teaching confidence, and available resources before making this decision. For educators and policymakers, understanding these motivations can help identify unmet educational needs and improve support for families. Ultimately, recognising the interaction between psychological and practical factors provides a more balanced understanding of why parents choose homeschooling.

== See also ==
* [[w:Homeschooling|Homeschooling]] {Wikipedia)
* [[wikipedia:Homeschooling|Homeschooling]] (Wikipedia)

== References ==
Brabant, C., Bourdon, S., &amp; Jutras, F. (2003). Home Education in Quebec: Family First. ''Evaluation &amp; Research in Education'', 17(2-3), 112–131. https://doi.org/10.1080/09500790308668296

Collom, E. (2005). The Ins and Outs of Homeschooling. ''Education and Urban Society'', 37(3), 307–335. https://doi.org/10.1177/0013124504274190

Green, C. L., &amp; Hoover-Dempsey, K. V. (2007). Why Do Parents Homeschool? A Systematic Examination of Parental Involvement. ''Education and Urban Society'', 39(2), 264–285. https://doi.org/10.1177/0013124506294862

Kostelecká, Y. et al. (2023). Motivace rodičů k domácímu vzdělávání v českém kontextu. ''Sociológia - Slovak Sociological Review'', 55(5), 496–521. https://doi.org/10.31577/sociologia.2023.55.5.18

Martin-Chang, S., Gould, O. N., &amp; Meuse, R. E. (2011). The impact of schooling on academic achievement: Evidence from homeschooled and traditionally schooled students. ''Canadian Journal of Behavioural Science / Revue canadienne des sciences du comportement'', 43(3), 195–202. https://doi.org/10.1037/a0022697

Ray, B. D. (2017). A systematic review of the empirical research on selected aspects of homeschooling as a school choice. ''Journal of School Choice'', 11(4), 604–621. https://doi.org/10.1080/15582159.2017.1395638

Tan, M. H. (2019). Homeschooling in Singaporean Chinese families: beyond pedagogues and ideologues. ''Educational Studies'', 46(2), 135–153. https://doi.org/10.1080/03055698.2019.1584850

== External links ==
* [https://www.home-school.edu/ Resource Guide on Home Education and Parental Involvement]
* [https://eric.ed.gov/ Educational Resources Information Center (ERIC) Database on Homeschooling]
* [https://www.tandfonline.com/loi/rjsc20 Journal of School Choice Research Archives]
* [http://learnmate.com.au/homeschool-vs-school/ Homeschooling vs school: what’s better?] (Learnmate)
* [https://theconversation.com/the-lasting-appeal-of-homeschooling-what-motivated-families-to-continue-after-schools-reopened-post-pandemic-280118 The lasting appeal of homeschooling: what motivated families to continue after schools reopened post‑pandemic] (The Conversation) 
* [https://theconversation.com/why-parents-of-twice-exceptional-children-choose-homeschooling-over-public-school-244385 Why parents of ‘twice‑exceptional’ children choose homeschooling over public school] (The Conversation)</text>
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Meetings at the Pelican Club about the Smith-Slavin match

==Overview==
Multiple meetings of members of the London Pelican Club, some of whom were associated with boxing, to hear about the [[Social Victorians/Boxing/Smith-Slavin 1889-12-23|Smith-Slavin match]] in Bruges, Belgium, on 23 December 1890.

Many newspapers published stories about this series of events, some of which are present here; the big stories on the first page, above the fold, have been given prominence.

==Logistics==
A number of meetings took place — of the members of the Pelican Club as well as of at least 2 committees established to investigate the Smith-Slavin fight, plus at least 1 subcommittee.
* Tuesday afternoon, 7 January 1890, when people were questioned
* Wednesday, 8 January 1890
==Related Events==
* The [[Social Victorians/Boxing/Smith-Slavin 1889-12-23|Smith-Slavin Fight]], 23 December 1889 
* The Pelican Club Meetings
* The [[Social Victorians/Boxing/Fracas at the Trocadero|Fracas at the Trocadero]] 
==Who Was Present==

=== Tuesday Afternoon ===
# The Marquis of Queensberry
# Sir John D. Astley, president
# Captain Archibald Drummond
# Kim Montagu, Viscount Mandeville
# Mr. G. A. Baird (&quot;Mr. Abington&quot;), Smith's backer
# Mr. Fleming, Smith's manager
# Frank Slavin
===Wednesday===
# Sir John D. Astley, president
# Marquis of Queensberry
# Captain Archibald Drummond
# Sir W. Gordon-Cumming
# Mr. Robert Martin
# Mr. John Corlett
# Mr. Walter Dickson
# Mr. Cecil Raleigh (Hon. Sec.)
# Mr. Charles Hawtrey
==Entertainment==

==Anthology==
Newspaper articles are in chronological order by date of publication in the newspaper cited. So many newspapers printed reports, and so many of those reports are word-for-word the same, or nearly, in all or in part (see copy-paste editing), the following is a selection hoping to be representative rather than comprehensive or complete.

The Thursday, 9 January 1890 ''Evening News and Post'', first-page, above-the-fold story. The two editorial interpolations in square brackets are sic.&lt;blockquote&gt;Last night a meeting of the members of the Pelican Club was held to receive and consider the report of the committee which had been appointed to inquire into the circumstances of the disgraceful scenes at Bruges on the occaaion of the fight between Jem Smith, Champion of England, and Frank P. Slavin. Champion of Australia. There was a crowded attendance. Sir J. D. Astley presided, and amongst those present were the Marquis of Queensberry, Viscount Mandeville, Lord Chursten, Capt. Archibald Drummond, Col. Brabazon, Major Winter, Capt. de Wyndt [?], Hon. T. Willoughby, Messrs. John Corlett, Walter Dickson, Hugh Drummond, Walter Pallant, George Edwardes, Charles Harris, David James, Robert Martin, Arthur Roberts, [J.?] L. Shine, C. Bertram, C. Coborn, C. Collette, W. Cosier, A. Crocker, C. Danby, A. de Vere-Smith, C. Disraeli, C. H. Hawtrey, F. B. Hesseltine, C. B. B. Johnson, W. J. A. Knowles, J. F. M'Adams, T. Lumley, Cecil Raleigh (hon. secretary), W. E. Shine, J. M. Small, S. Smith, E. Solomon, E. Ellis, A. E. Welts (proprietor of the club), and W. C. K. Wick.

The Chairman, in opening the proceedings, said that the reason of the general meeting being summoned was in the interests of the noble art, and to endeavour to find out who brought the roughs to the ringside, and who provided the funds for the purpose. Three or four committee meetings had been held, and the result would be laid before them. Many might say they ought to have done more, but he could assure them that the committee had done their best to find out and thoroughly sift matters to the bottom. Those who would pay a sufficient sum for the purpose in view would undoubtedly keep the thing as dark as possible. There was not use slightest question that money flowed freely, and that roughs were forthcoming. Much testimony had been brought before the committee, but he regretted to say that he did not think all had spoken truly. The public were only too anxious to imagine wrong upon the smallest circumstantial evidence, but he was certain that they could not be trusted in judging matters of wrong-doing, and they were not always correct. This was often the case in racing as well as in other sports, which, he need hardly tell them, he could personally vouch for. What was to be done was to put the world at large in full knowledge of the disgraceful proceedings which occurred at Bruges in the course of the late fight. In the first place, a sub-committee had been formed, who had submitted to the full committee a resolution which had been drawn up.

The Committee's Report.

The committee's report was then read as follows:

Gentlemen — You have been called together in order that the committee may inform you of the action taken with regard to the recent prize fight between Frank Slavin and Jem Smith. It is hardly necessary to remind you that the Pelican Club, as the Pelican Club, has nothing whatever to do with prize fighting. Individual members of this or of any other club are, of course, perfectly free to patronise prize fights if they desire to do so. But the Pelican Club, in its corporate capacity, does not concern itself with them in any way, and does not desire, as it has obviously no right, to interfere with them or whatever may pertain to them. Unfortunately, however, it appeared that in connection with the fight between Slavin and Smith certain things occurred of which it became the duty of the Pelican Club to take notice. And, to begin with, Mr. John Fleming, an official of the club, was present in the capacity of Smith's manager. The report of the fight reached London, as you are aware, early on Monday, December 23. No sooner was attention called to the fact that Slavin had treated with brutality, which every member  of this club and every honest Englishman cannot too strongly reprehend, than a special meeting of the committee was convened by telegraph. The honorary secretary in the meantime wrote a letter to the papers repudiating any connection of the Pelican Club with the fight, and at the meeting of the committee Mr. Fleming was called to appear in person. He was at once informed that he was suspended from the performance of his usual duties here, and he was requested to state to writing the nature of his association with the fight in question, and what he knew regarding it. Since that day the committee have sat many times and for many hours. They are in receipt of a large mass of correspondence — some very emphatic, but, unfortunately anonymous. They have examined on several occasions a number of eye-witnesses of the fight, and they are, they believe, in full possession of every fact of importance in connection with the fight. With regard to Mr. Fleming, his statement practically amounts to this: The preliminaries of the fight between Slavin and Smith were concluded on September 16, 1889, that is, long anterior to the glove contest between Smith and Jackson, and although Mr. Fleming determined to sever his connection with Smith after the glove fight, he felt himself in duty bound to carry the fight with Slavin through to a conclusion, as his last action in the capacity of Smith's manager, and in this the committee did not consider him to blame. Smith went into training at Newmarket, where Mr. Fleming saw Smith occasionally, and meantime Mr. Fleming went to Belgium, and, in connection with Mr. Dunning of the ''Sportsman'' newspaper, they made arrangements that the fight should be fought on the private ground of a gentleman near Bruges, and with that gentleman they made the following agreement. [This is to the effect that they undertake no rough element should be present, no noise should be made, and if anything untoward should occur they should indemnify the gentleman in question against all damages and pay any expenses which might be paid by him.] It is of course impossible to say what is passing is the mind of any man, but it seems fair and reasonable to assume that neither Mr. Fleming nor Mr. Dunning contemplated the presence of roughs when they signed the agreement. Subsequently, however, a rumour did reach Mr. Fleming that both sides had organized what is known as a &quot;corner,&quot; and he went straight to his partner in the agreement, Mr. Dunning, and told him what he had heard. Mr. Dunning informed him that he also had heard similar reports, but he had been able to assure himself that Slavin at least had no intention of employing roughs and, as we all know, Mr. Dunning's information has been justified by facts. Mr. Flemming then sought Smith, and Smith said that as long as Slavin did not have a &quot;corner&quot; he (Smith) did not want one. Mr. Fleming, however, continued to feel some anxiety on the subject, and took every possible precaution to keep the place a secret. Whether his effects were intentionally thwarted cannot be said, but on the morning of the fight there were present in Bruges a number of roughs who obviously had not come all that way for their own diversion, and who could not have paid their own way thither had they so desired. Mr. Fleming had kept himself steadily aloof from Smith's seconds up to this point. He crossed to Belgium with several members of thus club; with them he remained, and with them he returned. When, however, he found the rough element that he had feared was actually in Brugues, he apprised the owner of the ground where the fight was to take place of this fact. He said plainly, &quot;The roughs are here; it is entirely for you to say whether you will allow the fight to proceed or not.&quot; The gentleman in question replied that he would let the fight go on, but if there was any row he would send for the police instantly. Now this is not the simple unsubstantial explanation of Mr. Fleming. These facts have been verified most completely by independent witnesses of honour and character, whose words it is impossible to doubt. These witnesses have spoken, moreover, very fully of Mr. Fleming's conduct in this matter, as also of the personal abuse he received; of his absenting himself from Smith's party at the ring side, and completely disassociating himself from Smith's party altogether. The committee have subjected Mr. Fleming's statement, and indeed his whole actions so far as they can inform themselves of them, apart from his statement, to the most searching inquiry, and as a result, at the committee meeting held on January 1, when scarcely a single member was absent, it was proposed by Mr. Burton and seconded by Mr. Beckett, &quot;That this committee, after hearing Mr. Fleming's statement, and the evidence of gentlemen of undoubted character who were present at the ring side, are of opinion that Mr. Fleming is in no way responsible for the ruffianism that took place at the Smith and Slavin fight.&quot; This resolution was carried unanimously. It is with very great regret that the committee find it their duty to inform you that in the course of their investigation the name of a member of this club, Mr. G. Baird, has frequently been mentioned. The committee have most anxiously considered whether the conduct of Mr. Baird ought properly to come within the scope of their inquiry, but in the face of Rule 17, they have felt it necessary to proceed.  [This rule is the ordinary club rule, which provides that if the conduct of a member outside the club is unbecoming a gentleman, the committee have power to call upon him to resign.] The com- [Col. 3c–4a] mittee would feel great satisfaction if they could state explicitly that any given man had actually paid the men who behaved so disgracefully in Smith's corner, but such a transaction is very difficult of absolute proof. The committee do not impute to Mr. Baird that he paid the ruffians: he may not have known they were going to the fight at all. But it does appear that he did make use to Slavin of language unbecoming a gentleman and member of this club. The varied and entirely independent evidence before the committee on this point is absolutely conclusive.

At this point the report ceased, and Sir John Astley informed the meeting that, in view of the evidence they had taken, the following resolution had been unanimously carried by the committee:

&quot;That the committee, while regretting Mr. Baird's individual conduct at the fight, do not find any evidence has been brought before them to justify them in finding that Mr. Baird was in any way responsible for the appearance of the roughs at the ring side in Belgium who prevented the fight from being fought to a conclusion.&quot;

Mr. Charles Hawtrey at this stage asked a number of questions, which were answered by the chairman.

Lord Queensberry, somewhat to the surprise of his brother committeemen, then said that it was with a certain amount of hesitation and pain that he proposed:

&quot;That the inquiry into Mr. Baird's conduct be continued from the point where the committee have left off.&quot;

Mr. John Corlett protested against the action of Lord Queensberry, who, he remarked, was a member of the committee which had adopted the report and previous resolution. He (Mr. Corlett) did not think any further action was justified, seeing what evidence they had had before them and the difficulty of obtaining evidence, in view of the fact that they were not a legal body, and could not take evidence on oath.

Major Noah proposed, and asked Lord Queensberry to accept, as an amendment, the following:

Resolved that the conduct of Mr. Baird be referred back to the committee for further consideration, and they be instructed to report to the general meeting to be convened one month from this date.

The committee, with the exception of Lord Queensberry, regarded this as a distinct vote of want of confidence.

Captain Drummond and Mr. Hugh Drummond having spoken, a show of hands was taken, from which it was obvious that the majority of the members accepted the amendment of Major Noah.

Sir John Astley then announced that the committee would resign, and that day fortnight another general meeting would be held, when the members of the club would be asked to appoint another committee. A good deal of discussion took place, and many gentlemen protested against the vote being regarded as one of want of confidence in the committee. — In reply, the committee and secretary pointed out the difficulty of obtaining anything like definite evidence in such a case as the present. — The matter, therefore, now stands over a fortnight.&lt;ref&gt;&quot;The Smith-Slavin Fight. Who Paid the Roughs? — Resignation of the Pelican Club Committee.&quot; ''Evening News''(London) 9 January 1890, Thursday: 1 [of 4], Col. 2a–3a [of 7]. ''British Newspaper Archive''https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0003283%2F18900109&amp;page=1&amp;article=007&amp;stringtohighlight=mandeville+viscount. Print title: ''Evening News and Post'', n.p.&lt;/ref&gt;&lt;/blockquote&gt;The ''Sportsman'' put this very substantial report on the last page, but it did give it the better part of 3 full columns.&lt;blockquote&gt;&quot;The Late Fight. Meeting of the Pelican Club. Stormy Proceedings. The Committee Resigns.&quot; ''The Sportsman'' 9 January 1890, Thursday: 4 [of 4], Col. 1a–3c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001055%2F18900109&amp;page=4&amp;article=049&amp;stringtohighlight=mandeville+viscount. Same print title and p.

Last night a meeting of the members of the Pelican Club was held to receive and consider the report of the committee which had been appointed to inquire into the circumstances of the disgraceful scenes at Bruges on the occasion of the fight between Jem Smith., Champion of England, and Frank P. Slavin, Champion of Australia. There was a crowded attendance. Sir J. D. Astley presided, and amongst those present were the Marquis of Queensberry, Viscount Mandeville, Lord Churston, Capt. Archibald Drummond, Col. Brabazon, Major Winter, Capt. de Wyndt, Major Noah, Hon. T. Willoughby, Messrs. John Corlett, Walter Dickson, Hugh Drummond, Walter Pallant, George Edwardes, Charles Harris, David James, Robert Martin, Arthur Roberts, J. L. Shine, C. Bertram, C. Coborn, C. Collette, W. Cosier, A. Crocker, C. Danby, A. de Vere-Smith, C. Disraeli, C. H. Hawtrey, F. B. Hesseltine, C. B. B. Johnson, W. J. A. Knowles, J. F. M‘Adam, T. Lumley, Cecil Raleigh (hon. secretary), W. E. Shine, J. M. Small, S. Smith, E. Solomon, E. Ellis, A. E. Wells (proprietor of the club), and W. C. K. Wick.

The meeting, unquestionably the most important that has ever taken place in the history of the club, was intensely animated from start to finish. The rapid arrival of members in cabs and private vehicles long before the hour fixed for the meeting — 4.30 — proved how great was the interest felt in the proceedings, and Denman-street was several times blocked by the traffic. Prior to the important gathering a meeting of the committee was held, this being constituted as follows:— Sir John D. Astley (chairman), Marquis of Queensberry, Lord Esmé Gordon, Capt. Archibald Drummond, Mr Hugh Drummond, Mr. John Corlett, Mr Walter Pallant, Mr Robert Martin, Mr. Arthur Ernest Wells, and Mr Cecil Raleigh (hon. secretary). What took place at this meeting did not transpire, but no doubt the members were engaged in mapping out the evening programme. Their labours were concluded in time to ensure a punctual start of the special general meeting. This was held in the large club room, which barely sufficed to accommodate the deeply-interested assemblage eager to hear the outcome of the committee’s lengthy deliberations. Probably few were prepared for the remarkable scene witnessed before the proceedings were brought to a close. Acting upon one of the most widely-drawn Pelican Club rules, which lays it down that so far as smoking is concerned every room shall be a &quot;Liberty Hall,&quot; almost every member calmed his nerves with a Havanna [sic] of the choicest brand. Nevertheless the spirit which pervaded the meeting was of a distinctly business-like character, and great indeed was the astonishment of the committee to find that their &quot;whitewashing&quot; proposals were not swallowed so readily as they evidently anticipated they would be. The chairman, in his usual bluff and hearty manner, introduced the subject-matter without any needless waste of words, and called upon Mr Cecil Raleigh to read the report of the committee. This will be found set forth below. The impression generally created was that the committee had discovered very little of what took place at the fight in view of the number of gentlemen called as witnesses and the length of time spent in their deliberations. The chairman, however, pointed out that some of the testimony adduced was not in the opinion of the committee truthful, and this may in some measure account for the singularly negative result arrived at.

Briefly put the verdicts seemed to be &quot;not guilty&quot; in the case of Mr Fleming, and &quot;not proven&quot; against Mr Baird. It will be remembered that immediately after the fight the Pelican Club declared its intention of &quot;sifting the matter to the bottom.&quot; The majority of the members yesterday were of opinion that the matter could hardly be called &quot;sifted to the bottom&quot; ''if the persons responsible for the presence of the roughs at the ring-side were not indicated''. This, it need scarcely be pointed out, was not done. &quot;Not one word,&quot; said Mr Corlett, &quot;had been brought out in the course of the inquiry to incriminate Mr Baird.&quot; This was said in reply to the Marquis of Queensberry, who, though a member of the Committee of Inquiry, dissented from its report on the ground that since Tuesday evening he had discovered new evidence of an important nature, for which reason he desired the conduct of Mr Baird to be still further investigated. Mr Hawtrey made a very pertinent remark concerning the appointment of the referee, but quietly subsided when Sir John came out with, &quot;Excuse me, Mr Hawtrey, but I think you know as much about prize-fighting as a duck knows about an umbrella.&quot; Major Noah capped Lord Queensberry's amendment with another, referring the report back to the committee. The Marquis promptly seconded it, and at the same time withdrew his amendment in favour of the later one. The members of the &quot;inner circle&quot; began to look astonished at the strength of the opposition. It was no less unexpected than inconvenient, though it may be mentioned that there was a singular lack of official formula in the meeting throughout. When at last the chairman put the amendment it was found impossible to tell the result from the hands raised for and against. &quot;Call 'Aye' and 'No,'&quot; said Sir John, and immediately there came a roar of &quot;Ayes,&quot; followed by a treble pipe of &quot;Noes.&quot; &quot;I cannot decide,&quot; said Sir John, &quot;you must split into two parties, 'Ayes' to the right, 'Noes' to the left.&quot; No sooner was the room divided than the result of the voting was seen at once, the amendment being carried by an overwhelming majority. Confusion reigned supreme for a time; the committee conferred together and resigned in a body, excepting, of course, Lord Queensberry and Lord Esmé Gordon, the latter not being present. Sir John announced that another meeting would be held in a fortnight, when the members would be enabled to select &quot;a better lot.&quot; And then, to cap the climax, the meeting dissolved without a vote of thanks to the chairman.

The Chairman in opening the proceedings said that the reason of the general meeting being summoned was in the interests of the noble art, and to endeavour to find out who brought the roughs to the ringside, and who provided the funds for the purpose. Three or four committee meetings had been held, and the result would be laid before them. Many might say they ought to have done more, but he could assure them that the committee had done their best to find out and thoroughly sift matters to the bottom. Those who would pay a sufficient sum for the purpose in view would undoubtedly keep the thing as dark as possible. There was not the slightest question that money flowed freely, and that roughs were forthcoming. Much testimony had been brought before the committee, but he regretted to say that he did not think all had spoken truly. The public were only too anxious to imagine wrong upon the smallest circumstantial evidence, but he was certain that they could not be trusted in judging matters of wrong-doing, and they were not always correct. This was often the case in racing as well as in other sports, which, he need hardly tell them, he could personally vouch for. What was to be done was to put the world at large in full knowledge of the disgraceful proceedings which occurred at Bruges in the course of the late fight. In the first place, a sub-committee had been formed, who had submitted to the full committee a resolution which had been drawn up.

The Committee's Report

Sir John then called on Mr Cecil Raleigh (the hon. secretary) to read the following report:

Report of the Committee of the Pelican Club to the general meeting of members on Wednesday, January 8:

Gentlemen — You have been called together to-day in order that the committee may inform you of the action they have taken with regard to the recent prize fight between Frank Slavin and Jem Smith.

It is hardly necessary to remind you that the Pelican Club, as the Pelican Club, has nothing whatever to do with prize fighting. Individual members of this, as of any other club, are of course perfectly free to patronise or promote prize fights if they desire to do so. But the Pelican Club in its corporate capacity does not concern itself with them in any way, and it has no desire, as it obviously has no right, to interfere with them or whatever may pertain to them.

Unfortunately, however, it appeared that in connection with this fight between Slavin and Smith, certain things occurred of which it became the duty of the Pelican Club to take notice.

And, to begin with, Mr. John Fleming, an official of the club, was present in the capacity of Smith's manager. The report of the fight reached London, as you are aware, early on Monday, December 23, and no sooner was it known that Slavin had been treated with a brutal cowardice which every member of this club and every honest Englishman cannot too strongly reprehend, than a special meeting of the committee was convened by telegraph on Tuesday.

Your hon. secretary in the meantime wrote a letter to the papers repudiating any connection of the Pelican Club with the fight, and at the meeting of the committee Mr. Fleming was called to appear in person. He was at once informed that he was suspended from the performance of his usual duties here, [Col. 1c–2a] and he was requested to state to writing the nature of his association with the fight in question, and what he knew regarding it.

Since that day, gentlemen, the committee have sat many times and for many hours. They are in receipt of a large mass of correspondence — some very emphatic, but, unfortunately anonymous; they have examined on several occasions a number of eye-witnesses of the fight, and they are, they believe, in full possession of every fact of importance in connection with the fight. With regard to Mr. Fleming, his statement practically amounts to this: The preliminaries of the fight between Slavin and Smith were concluded on September 16, 1889, that is, long anterior to the glove contest between Smith and Jackson, and although Mr. Fleming determined to sever his connection with Smith after the glove fight, he felt himself in duty bound to carry the fight with Slavin through to a conclusion, as his last action in the capacity of Smith's manager, and in this the committee did not consider him to blame. Smith went into training at Newmarket, where Mr. Fleming saw Smith occasionally, and meantime Mr. Fleming went to Belgium, and, in connection with Mr. Dunning of the ''Sportsman'' newspaper, they made arrangements that the fight should be fought on the private ground of a gentleman near Bruges, and with that gentleman they made the following agreement. 

Re Smith v. Slavin

# You undertake not to allow any rough element to be present, and no noise to be made by cheering, &amp;c., at ring side or elsewhere on my grounds, situated at St. Michael, Bruges, Belgium, and should any damage be caused by anyone to said grounds, my residence, or live or dead stock, you guarantee to be responsible in every way.
# You undertake to guarantee that the place, names of any gentlemen residing in or near Bruges (within five miles) be not mentioned in any newspaper or print before, during, or after fight.
# You undertake the number of spectators on ''both your sides'' do not exceed from forty to fifty ''altogether'', and to be guaranted by representatives of both sides in every way.
# You undertake that, should anything untoward occur, to indemnify me, and all expenses that I may be put to in any way before or after the fight you agree to pay.

(Signed) John Fleming

(Signed) G. T. Dunning

It is, of course, impossible, gentlemen, to say what is passing in the mind of any man, but it seems fair and reasonable to assume that neither Mr Fleming nor Mr Dunning contemplated the presence of roughs when they signed that agreement.

Subsequently, however, a rumour did reach Mr Fleming to the effect that both sides had organised what is known as a corner,&quot; and he went straight to his partner in the agreement, Mr Dunning, and told him what he had heard.

Mr Dunning informed him that he also had heard similar reports, but he had been able to assure himself that Slavin, at least, had no intention of employing roughs, and, as we all know, Mr Dunning's information has been justified by facts.

Mr Fleming then sought Smith, and Smith said that as long as Slavin did not have a &quot;corner,&quot; he (Smith) did not want one. Mr Fleming, however, continued to feel some anxiety on the subject and he took every possible precaution to keep the place selected for the fight a secret. Whether his efforts were intentionally thwarted cannot be said, but on the morning of the fight there were present at Bruges a number of roughs who obviously had not come all that way for their own diversion, and who could not have paid their own way thither even had they so desired. Mr Fleming had kept himself studiously aloof from even Smith's seconds up to this point. He had crossed to Belgium with several members of this club, with them he remained and with them he returned. When, however, he found the rough element that he feared, was actually present in Bruges, he apprised the owner of the ground where the fight was to take place of the fact. He said plainly, &quot;The roughs ''are'' here, and it is entirely for you to say whether you will allow the fight to proceed or not.&quot;

The gentleman in question replied that he would let the fight go on, but if there was any row he should instantly send for the police.

Now, this is not the simple unsubstantiated explanation of Mr Fleming. This fact has been verified most completely by independent witnesses of honour and character whose word it is impossible to doubt. The witnesses have spoken, moreover, very fully of Mr Fleming's conduct in the matter as a whole, of the abuse he received, of absenting himself from Smith’s part of the ring, of his completely disassociating himself from Smith's party.

The committee have subjected Mr Fleming's statement, and indeed his actions, so far as they can inform themselves of them apart from his statement, to the most searching inquiry, and as a result, at a committee meeting held on Wednesday, January 1, when scarcely a single member was absent, it was proposed by Mr Burton, and seconded by Mr Beckett,

&quot;That this committee, after hearing Mr Fleming's statement, and the evidence of gentlemen of undoubted character who were present at the ring-side, are of opinion that Mr Fleming was in no way responsible for the ruffianism that took place at the Slavin and Smith fight.&quot;

This resolution was carried ''unanimously''.

Gentlemen, it is with very great regret that the committee find it their duty to inform you that in the course of their investigations the name of a member of this club, Mr. G. A. Baird, has frequently been mentioned. The committee have most anxiously considered whether the conduct of Mr Baird ought properly to come within the scope of their inquiry, but in face of Rule 17 they have felt it necessary to proceed.

The Rule in question says:— &quot;Any member whose conduct, in or out of the club, shall be unbecoming a gentleman, in the opinion of the committee, or with respect to whom any matter may have transpired which might be calculated to render his continued membership of the club injurious to its character or interests, shall, if the committee on inquiry find the same substantiated, be requested to resign; and in case of non-compliance he shall be subject to expulsion. Any member so resigning or expelled shall cease to have any claim upon the club whatsoever, and not be eligible for re-election in the ordinary manner, but he may be re-instated by the vote of a special general meeting, such vote to be a majority of not less than three-fourths of the members present.&quot;

The committee would feel great satisfaction if they could state explicitly that any given man did actually pay the men who behaved so disgracefully in Smith's corner, but such a transaction is very difficult of absolute proof. The committee do not impute it to Mr. G. Baird that he paid the ruffians in question. He may not have known they were coming to the fight at all, but it does appear that he did make use to Slavin of language unbecoming a gentleman and a member of this club. The varied and entirely independent evidence before the committee on this point is absolutely conclusive.

At the finish of the hon. secretary's statement of the committee's doings, Mr Raleigh read the resolution arrived at on Tuesday night, as follows:

&quot;That the committee, while regretting Mr. Baird's individual conduct at the fight, do not find any evidence has been brought before them to justify them in finding that Mr. Baird was in any way responsible for the appearance of the roughs at the ring-side in Belgium who prevented the fight from being fought to a conclusion. Carried unanimously.&quot;

The hon. sec. went on to say that he hoped the general meeting would ratify the foregoing document, and come to the unanimous conclusion that their committee had done right.

Mr C. H. Hawtrey asked for an explanation with respect to a statement in T&lt;small&gt;HE&lt;/small&gt; S&lt;small&gt;PORTSMAN&lt;/small&gt; to the effect that Smith objected to all the referees suggested by Slavin. It appeared to him that Mr Fleming, as Smith's manager, would be the objecting party.

The Chairman said that the referee was appointed by the stakeholder, and that the Smith party had nothing whatever to do with it.

Mr Hawtrey said he simply asked the question for information.

A member who witnessed the fight said he was fully under the impression that Fleming was not to be blamed in the matter, but he could not absolve Mr Baird. It appeared to him that Mr Baird was undoubtedly the leader of the rough division, and if this was true he was not fit to be a member of the Pelican Club.

The Marquis of Queensberry said that although he did not wish to find fault with the action of the committee he must say that fresh evidence had reached them on the previous day, and he was of opinion that sufficient time had not been given to the matter so far as it concerned Mr Baird, and therefore he begged to move the following amendment:

&quot;That the examination into Mr Baird's conduct should be reopened and continued by the committee from the point it left off.&quot;

Because a man had thousands of pounds to throw about that was no reason he should be allowed to do as he liked, and he must say he had very grave suspicions with with respect to that gentleman's proceedings. (Hear, hear.)

Mr Hawtrey seconded the amendment.

Mr John Corlett said that they appeared to meet under most novel conditions, and he must strongly object to the Marquis of Queensberry springing a surprise upon them by the amendment just read. The marquis formed one of the committee himself, and on the previous night had fully coincided with the decision arrived at, and now he apparently sought to sever himself from his fellow-committeemen. To expel a member was a very serious matter, and in his opinion Mr Baird’s conduct had nothing whatever to do with the result of the fight. He trusted that the meeting would not be led away by other reports. Mr Baird, it was acknowledged, had promised to Smith, in the event of his success, the stakes, amounting to 1000''l.'', and there was not the slightest doubt that his seconds, who were not of very high class, had determined to cut up the sum stated at all costs. There was not one word brought out in the course of the investigation to incriminate Mr Baird, and while the mere fact of bad language in the club would be most severely dealt with by the committee, outside they had really no jurisdiction. He had heard that adverse comments had been passed with respect to the inquiry held by the committee. Amongst others, why had not Mr E. Bailey been called? On this point he could only say that he interviewed the gentleman mentioned, and that his evidence would have agreed precisely with that of others who were before them. The committee had done their honest duty in [Col. 2c–3a] the matter and be regretted the one of their own body should now appear to be in opposition to them.

The Marquis of Queensberry was sorry to think that Mr Corlett had misunderstood his remarks. What he stated was that he was perfectly satisfied with the result of the committee's inquiries, but that sufficient time had not been given to thoroughly sift the fresh evidence that had been offered regarding Mr Baird, whose evidence, he might state, flatly contradicted that of Mr Fleming.

Mr Corlett moved the following in reply to Lord Queensberry's resolution:— &quot;That the report of the committee be adopted.&quot;

Mr Hugh Drummond seconded the amendment.

Major Noah proposed a second amendment, as follows:— &quot;That the conduct of Mr Baird be referred back to the committee for further consideration, and that they be instructed to report to a general meeting to be convened one month from this date.&quot;

Lord Queensberry seconded.

A desultory discussion ensued, in which Mr R. Martin and Mr H. Drummond took a prominent part, and eventually, amidst great excitement and confusion, the chairman put Major Noah's amendment, Lord Queensberry having withdrawn his in its favour.


 those present were   Mandeville, be.   count   Drummond, Col.  de Wyndt, Major   John Corlett,     Walter    i, David James,     J. L. Bhine, C.  + w Cesier, A.    sith, C. Disracii,   C. B. B. Johnson,   T. Lamley, Cecil   4. c  ine, J. M. Small,  A. B.          nd private vehicles is passing in the mind of ma  10 meeting—4.30—   est felt in the pro- t  ereral times blocked       4  Astley      «mé Gordon, Capt  , Mr John l  Robert Martin, Mr   cet t Me ( Harris,    Cecil Raleigh (hoo   his meeting did pot   “rs were engaged in   me Their labours ‘     start of the  s Leld in the larg   accommodat the   to hear tt   gthy deliberations :  the remarkable   dings were brought   f the most wisely   a lays it down .  concerned] every   i almost every     a Havanna of the however,   spirit which per   distinctly basi-   indeed was the fact. € rou    to find tha their   not swallowed +0 to or not.”  ted they would be.   2nd beariy manner,   thout any needless   Mr Cecil Raleigh to   This will be fuand   generally created     discovered very have  the fight Flem:       me spent in their   wever, pointed out   ced was not io the     al, and this may in airy,and as ¢  singularly negative      to be guilty   not proven against this committee, after |  1 that immediately   jub declared its :    matter to the   he yes  aiter could     f the re   rewghs at the ring- Bnd © thet y te ke  need searcely be course of their in  Not one word,  Stake deh Band     out im the .” This   Queensberry, who,   ee of Inquiry, dis-  nd that since Tues-   ew evidence of an   son be desired the   li further investi-   tat cadens  or with ‘which  referee, bat membership of the    out with,  aru    on as   nows about an um-   ord   the report back   seconded it.   wb in the or but be  ibers of the * inner vote of a  the strength of the  lee tha  «  pected than incon- present.”  ed that there was     eam tho ahem ates hohe) a  read the report of the committ  set forth bel w The  mas that the committee ha  little of what took place  view of the namber of €  witnesses and the length of  dcliberations. The chairman, |  that some of the testimony ack  cyinion of the committee trutl  some measure account for the  result arrived at.  Briefly put the verdicts seeme  im the case of Mr Fleming, and ‘  Mr Baird It will be rememter  after the fight the Pelican  intention of “ sifting the  bo! town, The majority of  terday were of opinion that the  te called to the bottom  sponsible for the presence of th  side wee not iadiewted, This,  pomted out, was not done.  said Mr Corlett, been |  of the inquiry to incrimin  was said in reply to the Marquis  

ses the result from corner, but such a transaction  ia  ast “Call ‘Ave absolute The committee  immechately there Mr G. Baird that be paid the  ry a pipe of He may not have known  ir John, ‘* you must t at all, but it does appea  Noes’ to the vin of lan  gen member of  The werk  seen at pendent evideoce before the co  an  overwbelming  ject is absolutely conclusive.  teme for a time; At the finish of the hon, seer  and in a the committox's Mr Ra  ton arrived at on Tuesday nigh  “That the committee, while r  not  indivichsal conduct at the  members would be evidence has been  And then, to cap was in  withoat a vote of  in finding that Mr  for the appearance of the  Belgiam who prevented  to a Carried  —_  roceedings said that The hon. see. went on to say  age para 4  and to endeavour — ems vend  and come to the unanimous cone  dpe mittee had done quite  nen beld, amd the Mrec. H. Hawtrey  SES toe  respect to a staternent in Te:  Many might say effect that Smith objected to all t  it be could assure  their te  by Slavin !t appeared to him |  aie  owes Ee Ev  the bottom. Those ‘The Chairman said that the re  the purpose in view the stakebolder, and that |  ns dark as not whatever to do with it  n that money flowed  rtheoming. Much wtrey said be simply ash  re the committee, A member who witnessed the |  1 pot think all had  oly too anxious to under the impression that Fk  circumstantial evi- blamed im the matter, but he ¢  ould not be trusted dombtediy  Baird It appeared vo bim tbat  the healer of the  cence, ow =  im judging matters of  always correct. This was often  well as in otber sports, whict  them, he could personally vouc!  be done was to put the world at  ledge of the  Bruges in the  lat  place, a sub-committee bad be  eubmitted to the full committe  bad been drawn up.  THE  Sir Jomx then called on M  ) to read the follov  Keport of the Committee of  the general meeting of mem  January &amp;  have been |  in order that the committee ms  action they bave taken with re  prize fight between Frank Slavin  It is badly necessary to  Pelican Club, as the Pelican Clu  1  ever to do with prize fighting,  this, as of any other club, are of  to patronise or promote prize fig  cho 80. Bat the Pelican (lub in  docs not concern itself with then  has no desire, as it obviously has  with them or whatever may pert.  Vnfortunat , it ap  nection with is fight betwee  occurred of whieh  the Pelican Club to take notice.  Xo begin with, Mr Jobn Flemir  club, was present in the capacity  ‘The report of the fight reached Lon  cease in  ia. rachag ea   be need hardly veil    rge im tull know-   occurred at them on the day, and b  ight. In the first   formed, who had   a resolution which   REPORT.   Cecil Raleigh (the   g report   Le — —__—    rs on Wednesday,   lled together to-day   inform you of the   arl to the recent   nd Jem Smith.   ind you that the   has pothing what-   lividual members of uis   ourse free   ts if y desire to   s corporabe capacity   in amy way, and it   &gt; right, to interfere   n to them,   eared that im con-   Slavin and Smith,   became the duty of to in the event of hi:     ¥  . an official of the  eee) pee manager. |  |  eee aot ame enrd  Al  TH  —_  4  ——  writing the nature the matter, and b% th.  in question, and should por, to be in «  Marans Queensberry  committee bave sat that Mr had misundersto  They are in receipt be stated was that he was perfec  ce—some very «m- of the committee’s inc  ous, they have ex- | time bad not been ven to  ber of eye-witpesses that had offered  elieve, in full whose evidence, be might state  co commected that of Mr  . bis statement —“Th  and «Smith were  be  1889, that is   st between Jackson  A ser  ning determined to follows —‘ That the conduct of |  after the glove-con- back to the committee for furth  eatisfactory conduct that they be instructed to rep:  bound to carry the to be convened one month fre  aclusion as his last  a? ord Queensberry |  nena&quot;  ager Abd 1D Ae  to bleme and Mr H took a  market, where Mr :  )  And roeantiDe  Major  in connection with  with«r  x newspaper, made The meeting divided, and t  Kl be fougbt in the carried by an overwbelming ma  iding near Bruges,  Walter Pallant rose and said that  On the result being declared  ade the following  a want of im the com  IN to, they hed no option bat to rs  any rongh element Major N oah stated  ewer a  most em  wa  mm, a should supported Major )  o sald grounds, he could assure them that t  ou guarantee to sider it their daty to resign, a  yf. wy  that the place, The chairmas briefly stated th  1 of near resolved to resign in @ body,  meeting would be called in a fort  im any  ter fight. a * better lot.” (Laughter. )  spectators on beth The meeting then broke up  to fifty alto ether, | witboat the customary vote of  arr” —  nytbing untoward  FRACAS  AT THE T  r that | may CHARLEY MITCHELL  tthe fight you MANDEVILI  JouN FLEMWINo. Asan addendum to the impe  G. T, Pelican Club committee on Tues.  emen, to say what of at Me 8am  but it seems fair the Trocadero, Piccadilly C  either Mr Fleming deville and Mr Abington,  presence of roaghs in attendance at Denman-s  ur did reach Mr by * Pony” Moore, his son-in-le  des had organised Jem Carney (the Bi  1 be went straight Baldock, Bob Habbi.  jam, Car  Mr Dunning, and party, who seats in the  cussed things pugilistic, the  be also bad heard devoted to the recent imterna  to assure himself Frank P. Slavin and Jem Smit  the matter  ation of employing thon of Mh  tebell, # nd ho  Junning’s inforwa- between the pair. Su  mith and jumped up and ‘ went  did not strike him. Lord Ma  did not have a in and asked Mitebell t«  went one. Mr the  feel some anxiety  anna in oo. estroack him ehern!ly on the  tter directed his attention  “Fony boore, at once  felt re  intentionally  af morning of the proceed ngs not lasting  longe which  s t way for their own paper coneerning the  m paid their own way than the customary pinch of  salt Mr Fleming had hit, be did net ** square ap”  to rom even Smith's take off his coat and  it He bad crossed soon became noised abroad  thi of this club, with thing up,” and a crowd  thered o returned. Whea, bat the police saw Mitchell  a nt that be fe rod, safely across the  road. a ed the  owner 0 take place of the JOHN  L.  SULLIVAN s are bere, and it  is willaitow the fight PAIR  PLé d that be would let Joux L Bu has been  s any row he should the Smitb-Slavin fight to  som see bow an English fighter ca  | stantiated ex ** This man Smith is litthe  better » been + mo&lt;t 1 be wen’t the  doubt sow oe. brad to Smith ow you  ¢ as a whole, of  the very fully of Mr on meeting bim im this  ¢ fair play is unknown. The  r absenting himself namber of ‘heelers’  alwe his completely dis- from defeat. Slavin or  Jacks bility, look for a match with  m s  state  anm this country, and | am  pefle we  ear statement, to the and I am  re result, at a  com- want a  big January 1, when fight so long as it is im a  chub-b breaking for  me,  —— at, it was  proposed  Beckett, Mr  Fleming's THE SLAVIN  TES wer 40%. and it having been  de  oo:  eer | oe the bem oe  ~~  Tee at regret that  the rm you that in  the a member Amount already  acknowledg Mr B. Tabernacle. a  oe H.8.  cee s  frequently © most  anxiously ( Mr Baird t  acknow of their ld be  from  — e felt it necessary DETERMINED  FIGHT LD  whose be R. PERRIN  (“CURLBY”) f the committee, PHIPPIN  (Shore matter may have Earty yesterday a  ¢ sted to render bis old style, for a substantial  pur sb injurious to  its near Tunbridge Wells  be &gt; committee om in- well-known East-end  boxers, , be requested  to ance be be See  dite er so resigning  or im upon the  club e for re-election in  toe Me  trace’ e  reinstated aol, tm everything was carried out im a  «  pes  -_ ths of the members scen  i Bymonds’s, and * it  wil satisfaction if they ” Killam,  of man did actuslly at Astley’s  Amphitbeatre acefully in Smith's Blavin-Goode encounter,  victory s very difficult of Pbippin's last  a:  in © not impute it to Theatre, where, in a six-roand  cc to the before Bolton, of Bt.  George's. be did use to Yesterday both men  ¢ and  a  condition, sale  “Cu mittee on this  sub- and entirely inde- Both men s-aled about  Tst 66  7 After the third  round Gee Ghee  he  attenth ows fourth round eut “  Curle; ; Mr  Baird’s nd that any In the niath  round ened eee, Bee  ox~nd y way responsible end of the  eleventh the ri claimed a fou! for a  blow from being The referee, however,  disallow aly.” refused to leave his seat, and  the bat ho hoped the alternative but to award  the Curley,” the battle having  last pon that their  com- n explanation with  BOXIN to  the referees Mr  TED party Teo Parrrcnarp, the  celeb roe owas who possesses an unbeaten  recor Smith party from Germany yesterday  © pany with Mr EB. W.  Bayly, be  bev nt sail he was fully qi estun,  Pritebard ing was not to be life, and being fully restored to  b kd not ab-olve Mr stood ready to accept any  or Mr Beied was un- issued during his absence from  tt th division, and if offer appears from bim under  a pamember of the will cover any  mo news  of 1 that although be crowd to Fleet-street, and  when action of the com- Prank  Slavin, ence bad reached were followed  | ras of  that  together  cheered o the matter so  far Champions to  tl be beg sed to SIX-ROUND  CONTEST TreRE a com pany  &amp; conduct  | Sloagh, on y evening,  many present. The of  tres by  the Wall, who ts traiming  from to“ ToT” having left for Loudon  | i to throw of his tne visit, so tar  ae 1 allowed to do conorrned, wae a  ure. ad very grave  sus- amongst the company,  t some amusement, however, Mr  | as lad, and Bo ome  furwerd Iment eal i bis soo Marry havea  tu st strongly | watch ot, 5 i  tu  eee aa ees,  oe ment  just reat. Tbe Bix-nou xD Cowtrerr.— EL  Bull, Attlee —On taking the centre of the  ring himself, and The lacs went for each  other roncided with the displayed the was  an sought to a shate the '''best''' of  | ommitteemen  To ti  name cur a they qu &lt;/blockquote&gt;The Thursday, 9 January 1890 ''Evening Star'':&lt;blockquote&gt;The proceedings at the special general meeting of the Pelican Club yesterday evening in connection with the late Championship Fight at Bruges were of a very  lively nature, and it looks as if some of the members were rather startled when the conduct of Mr. (Abington) Baird at the fight was called in question.

The Committee presented a report exonerating both Mr. G. A. Baird (Smith’s backer) and Mr. John Fleming (Smith’s manager), but the meeting seemed to think that due inquiry had not been made into the conduct of Mr. Baird, and after a heated discussion referred back that part of the report relating to him.

The fat was then in the fire, and the committee thereupon resigned in a body, and a general meeting will be held on the 22nd inst. to elect a new committee. The proceedings from the first were of an exciting nature, and great confusion prevailed at the finish, the meeting dissolving without the usual vote of thanks to the chairman.

Mr. John Corlett could not see that anything had transpired to incriminate the &quot;Squire,&quot; but even the endeavours of the proprietor of ''Pink 'Un'' to &quot;make things pleasant&quot; were of no avail, and the Marquis of Queensbury and his friends carried the day.

These pugilists and their “noble&quot; patrons seem to be going from bad to worse. After the Pelican meeting it appears that there was a fracas in the Trocadero Music Hall, in which Lord Mandeville, Mr. Abington, Charley Mitchell, &quot;Pony&quot; Moore, Jack Baldock (such names mingled !), and two or three other professional boxers were engaged [sic]

It appears that &quot;The Squire's&quot; opinions on the late ﬁght  happened not to coincide with those of Mitchell, and high words were exchanged between the pair. Suddenly the Birmingham boxer jumped up and &quot;went for&quot; Mr. Abington, but did not strike him. Lord Mandeville immediately interposed and asked Mitchell to be quiet, whereupon the latter directed his attention to his lordship, and struck him sharply on the forehead.

The ''Sportsman'' adds that Carney and Bates then sprang to the assistance of his lordship, and Mitchell and Moore left the building, but it is thought this will not be the end of the affair.&lt;ref&gt;&quot;Sporting Twinkles.&quot; ''Evening Star'' 9 January 1890, Thursday: 3 [of 4], Col. 3c [of 5]. ''British Newspaper Archive''https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0001707%2F18900109&amp;page=3&amp;article=033&amp;stringtohighlight=mandeville+viscount. Print title: ''Star of the East'', p. 3.&lt;/ref&gt;&lt;/blockquote&gt;

The Saturday, 11 January 1890, ''Liverpool Weekly Courier'':&lt;blockquote&gt;The committee of the Pelican Club (Sir John Astley in the chair) was occupied for many hours in investigating the circumstances of the recent disgraceful prize-fight near Bruges. Among the witnesess examined were Mr. Vezey (the referee), Mr. G. Abington Baird, Lord Mandeville, and Slavin. The evidence of the latter was so favourable to Mr. Baird that this gentleman was exonerated from the charge of having aided, abetted, or paid the Birmingham roughs who assisted the contest with knuckle-dusters and blows. It would seem that their services had been requisitioned by others for the especial benefit of an obnoxious pugilist, who did not, however, put in an appearance.&lt;p&gt;

On Wednesday a special general meeting of the members of the Pelican Cub was held at the clubhouse, Denman-street, Piccadilly, for the purpose of considering the report of the committee of proceedings in connection with the recent prize-fight between Smith and Slavin. The meeting was private, but the following account of the proceedings was officially furnished:— John Astley, Bart., presided. The report of the committee stated that the Pelican Club, as a club, had nothing whatever to do with the prize-fight. Unfortunately, however, it appeared that in connection with the fight certain things occurred of which it became the duty of the club to take notice. To begin with, Mr. John Fleming, an official of the club, was present in the capacity of Smith's manager. The report of the fight reached London early on Monday, December 23d. No sooner was attention called to the fact that Slavin had been treated with brutality, which every member of the club and every honest Englishman could not too strongly condemn, than a special meeting of the committee was convened. The hon. secretary in the meantime wrote a letter to the papers repudiating any connection of the Pelican Club with the fight, and at a meeting of the committee Mr. Fleming was called to appear in person. He was at once informed that he was suspended from the performance of his usual duties at the club, and was requested to state in writing the nature of his association with the fight and what he knew of it. Since that day the committee had sat many times. They had been in receipt of a mass of correspondence, some very emphatic, but unfortunately anonymous. They had examined on several occasions a number of eyewitnesses of the fight, and were, they believed, in full possession of every fact of importance with regard to Mr. Fleming. His statement practically amounted to this, the preliminaries of the fight between Slavin and Smith were concluded on September 16th last, long anterior to the glove contest between Smith and Jackson, and although Mr. Fleming determined to sever his connection with Smith after the glove fight, he felt himself in duty bound to carry the fight with Slavin through to a conclusion. In this the committee did not consider him to blame. It seemed, furthermore, only fair and reasonable to assume that Mr. Fleming never contemplated the presence of the roughs when the agreement was signed. Subsequently, however, a rumour did reach Mr. Fleming that both sides had organised what is known as a &quot;corner,&quot; and he took every possible precaution to keep the place selected a secret. Whether his efforts were intentionally thwarted could not be said, but on the morning of the fight there were present in Bruges a number of roughs, who obviously had not come all that way for their own diversion, and who could not have paid their own way thither, had they so desired. Mr. Fleming, on discovering this, informed the owner of the ground of the fact. That gentleman said he would let the fight go on, but if there was any row he would send for the police instantly. The committee had consequently arrived at the conclusion that Mr. Fleming was in no way responsible for the ruffianism that took place. The committee, however, regretted to state that in the course of their investigations the name of a member of the club, Mr. G. W. Baird, was frequently mentioned. The committee had most anxiously considered whether the conduct of Mr. Baird ought properly to come within the scope of their inquiry, but in face of the club rules they felt it necessary to proceed. The committee would feel great satisfaction if they could state explicitly that any given man had actually paid the men who behaved so disgracefully in Smith's &quot;corner,&quot;  but such a transaction was very difficult of absolute proof. The committee did not impute to Mr. Baird that he paid the ruffians in question. He  may not have known they were going to the fight at all. But it did appear that he made use to Slavin of language unbecoming a gentleman and a member of that club. The evidence before the committee on this point was absolutely conclusive. Sir John Ashley informed the meeting that in view of the evidence they had taken the committee had unanimously resolved that while regretting Mr. Baird's conduct at the fight, they did not find [Col. c–a] that any evidence had been brought before them to justify them in finding Mr. Baird was in any way responsible for the appearance of the roughs at the ring ride who prevented the fight from being fought to a conclusion. The Marquis of Queensberry moved an amendment to the resolution that the inquiry into Mr. Baird's conduct be continued from the point where the committee have left off[.] Mr. J. Corlett protested against the action of Lord Queensberry, who was a member of the committee which had adopted the report and resolution. Mr. Noah proposed that the conduct of Mr. Baird be referred back to the committee for further consideration, and that they be instructed to report to a general meeting to be convened one month from this date. The committee, with the  exception of Lord Queensberry, regarded this as a vote of want of confidence. On a show of hands being taken it was obvious that the majority of the members accepted the amendment of Mr. Noah. Sir John Astley then announzed [sic?] that the commmittee would resign, and the meeting was adjourned for a fortnight.&lt;ref&gt;&quot;The Slavin-Smith Prize Fight. Action of the Pelican Club.&quot; ''Liverpool Weekly Courier'' 11 January 1890, Saturday: 3 [of 8], Col. 4b–5a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0003067%2F18900111&amp;page=3&amp;article=042&amp;stringtohighlight=mandeville+viscount. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;The Sunday, 12 January 1890, ''Reynolds's Newspaper'' has a longish report on the Pelican Club meeting and the fracas at the Trocadero:&lt;blockquote&gt;A special general meeting of the Pelican Club, convened by the committee with reference to the Smith-Slavin fight, near Bruges, drew a very full attendance of members. Sir John Astley (the president) took the chair, and was supported by the Marquis of Queensberry, Captain Archibald Drummond, Sir W. Gordon-Cumming, Mr. Robert Martin, Mr. John Corlett, Mr. Walter Dickson, and others, including Mr. Cecil Raleigh (hon. sec.) A resolution of the committee, stating that while they censured the language used by Mr. Abington Baird at the fight, yet they could not on the evidence before them connect him with the hiring of roughs, was first read; and then the opposition was led by Mr. Charles Hawtrey, who put some most pertinent questions to the Chairman. An unexpected mine was immediately afterwards sprung by Lord Queensberry, who declared that as a member of the committee he agreed with the decision of that body, yet nevertheless as a private individual he thought further investigation desirable.&lt;p&gt;

Some very strong remarks from Mr. John Corlett and a forcible speech by Mr. Hugh Drummond caused great excitement. Finally, Major Noah proposed, and the Marquis of Queensberry seconded, the following amendment: — &quot;That this inquiry into Mr. Baird's conduct be referred back to the committee with instructions to report to a general meeting to be convened one month from date.&quot; Amid intense commotion this was carried by a majority of at least three to one. Some desultory speaking followed, and then Sir John Astley announced that the amendment would be taken by the committee as a vote of censure, and that, consequently, he and his colleagues, would resign there and then. This determination was adhered to, despite the vehement protests of those who had voted with the majority that they had every confidence in the committee, but only wished for further inquiry into Mr. Baird's conduct.&lt;ref&gt;&quot;The Recent Prize Fight.&quot; ''Reynolds's Newspaper'' 12 January 1890, Sunday: 6 [of 8], Col. 4a–b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0000101%2F18900112&amp;page=6&amp;article=053&amp;stringtohighlight=mandeville+viscount. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;This report is from the Sunday, 12 January 1890, ''Lloyd's Weekly Newspaper'':&lt;blockquote&gt;A meeting of the committee of the Pelican club was held on Tuesday afternoon, Sir John D. Astley presiding, to consider the action of certain parties in connection with the brutality displayed by some hired ruffians at the recent championship prize fight between Jem Smith and Frank Slavin at Bruges, and among the members present were the Marquis of Queensberry and Captain Hugh Drummond. Lord Mandeville, Mr. G. A. Baird (&quot;Mr. Abington&quot;), Mr. Fleming, Frank Slavin, and others were examined, and, after a long discussion, it was decided by the committee to exonerate &quot;Mr. Abington&quot; (Smith's backer) and Mr. Fleming (Smith's manager) from all blame.

A special general meeting of the club, convened for Wednesday, drew a very full attendance of members. Sir John Astley (the president) took the chair, and was supported by the Marquis of Queensberry, Captain Archibald Drummond, Sir W. Gordon-Cumming, Mr. Robert Martin, Mr. John Corlett, Mr. Walter Dickson, and others, including Mr. Cecil Raleigh, the honorary secretary. A resolution of the committee, stating that while they censured the language used by Mr. Abington Baird at the fight, yet they could not on the evidence before them connect him with the hiring of roughs, was first read; and then the opposition was led by Mr. Charles Hawtrey, who put some most pertinent questions to the chairman. An unexpected mine was immediately afterwards sprung by Lord Queensberry, who declared that as a member of the committee he agreed with the decision of that body, yet nevertheless as a private individual he thought further investigation desirable.&lt;ref&gt;&quot;The Pelican Club and the Fight.&quot; ''Lloyd's Weekly Newspaper'' 12 January 1890, Sunday: 1 [of 12], Col. 5a [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.com/image-viewer?issue=BL%2F0000079%2F18900112&amp;page=1&amp;article=005&amp;stringtohighlight=mandeville+viscount. Same print title, n.p.&lt;/ref&gt;&lt;/blockquote&gt;

== Notes and Questions ==
# 

==References==
{{reflist}}</text>
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  <page>
    <title>Fungi Phyla</title>
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      <text bytes="3621" sha1="p66yhnkbc8lrg1g48gtz5jbpz43pj18" xml:space="preserve">[[File:Fungi_collage.jpg|thumb|300x300px|Diversity of fungi.]]
Fungi is any member of the group of eukaryotic organisms that includes yeasts, molds, and mushrooms. These organisms are classified in the biological kingdom, '''Fungi'''. &lt;br&gt; The fungi kingdom has 65480+ species and 8 phyla.
This list tries to give the following information on each Division:

*Division Name
*A link to a subpage discussing that Phylum in more detail (if it yet exists)
*Name Meaning (in English)
*An English Common Name, where one is in regular use
*Distinguishing characteristics of fungi within the Division/phylum
*An approximate number of species described within that Division.&lt;br &gt;
Since mycology does not stand still, this number can change.
You can also see [[Introduction to Taxonomy]] for more on that topic.
==Ascomycota==
[[File:Scarlet_elf_cap_cadnant_dingle.jpg|thumb|100px|right]]
[[/Ascomycota/]]

Name Meaning: Bladder fungus

English Common Name: Ascomycetes, sac fungi

Major distinguishing characteristics: Tend to have fruiting bodies (ascocarp). Filamentous, producing hyphae separated by septa. Can reproduce asexually.

Approximate number of species described: 30,000
==Basidiomycota==
[[File:Haeckel_Basimycetes.jpg|thumb|100px|right]]
[[/Basidiomycota/]]

Name Meaning: Small base fungus

English Common Name: Basidiomycetes, club fungi

Major distinguishing characteristics: Bracket fungi, toadstools, smuts and rust. Sexual reproduction.

Approximate number of species described: 31,515
==Blastocladiomycota==
[[File:WJD103_6-16-11.jpg|thumb|100px|right]]
[[/Blastocladiomycota/]]

Name Meaning: Offshoot branch fungus

English Common Name: Blastoclads

Major distinguishing characteristics:

Approximate number of species described: &lt;200
==Chytridiomycota==
[[File:Spizellomycete.jpg|thumb|100px|right]]
[[/Chytridiomycota/]]

Name Meaning: Little cooking pot fungus

English Common Name: Chytrids

Major distinguishing characteristics: Predominantly Aquatic saprotrophic or parasitic. Have a posterior flagellum. Tend to be single celled but can also be multicellular.

Approximate number of species described: 1000+
==Glomeromycota==
[[File:Gigaspora_margarita.JPG|thumb|100px|right]]
[[/Glomeromycota/]]

Name Meaning: Ball of yarn fungus

English Common Name: Glomeromycetes, AM fungi

Major distinguishing characteristics: Mainly arbuscular mycorrhizae present, terrestrial with a small presence on wetlands. Reproduction is asexual but requires plant roots.

Approximate number of species described: 284
==Microsporidia==
[[File:Fibrillanosema_spore.jpg|thumb|100px|right]]
[[/Microsporidia/]]

Name Meaning: Small seeds

English Common Name: Microsporans

Major distinguishing characteristics:

Approximate number of species described: 1400
==Neocallimastigomycota==
[[File:Liebetanzomyces polymorphus (10.3897-mycokeys.40.28337) Figure 2.jpg|thumb|100px|right]]
[[/Neocallimastigomycota/]]

Name Meaning: New beautiful whip fungus

English Common Name: Neocallimastigomycetes

Major distinguishing characteristics: Predominantly located in digestive tract of herbivorous animals. Anaerobic, terrestrial and aquatic.

Approximate number of species described: approx. 20
==Zygomycota==
[[File:Phycomyces.JPG|thumb|100px|right]]
[[/Zygomycota/]]

Name Meaning: Pair fungus

English Common Name: Zygomycetes

Major distinguishing characteristics: Most are saprobes and reproduce sexually and asexually.
Approximate number of species described: approx. 1060
==References==
[[Wikipedia:Phylum]]&lt;br&gt;
[[Wikipedia:Fungus]]
[[Category:Fungi]]
[[Category:Mycology]]
[[Category:Fungus phyla]]
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= '''How do parental aspirations shape children’s academic motivation and performance?''' =


== Overview ==
The focus on this chapter is on understanding what are the factors affecting a parent's attitude of aspiration or expectation towards their child. The current research suggests that parental aspirations may be more complex than the layman may believe, as it involves an complex interplay between socioeconomic factors, cultural, and parenting habits. 

'''Learning outcomes'''

After finishing this chapter, the reader shall come to understand 3 outcomes:

# What exactly are expectations or aspirations that a parent may have towards their child 
#

== What are 'expectations' or 'aspirations'? that parent might hold? ==
Expectations or aspirations that a parent may hold for their child is not necessarily concrete. It may include more short-term aspirations such as grades for the oncoming exam, or expectations for longer periods such as educational attainment, which may be receiving their high school diploma or a certain number of years of schooling (Pinquart &amp; Ebeling, 2020). 

An important aspect of parental aspirations is socioeconomic status (SES) or other factors. Parents who are from higher socioeconomic backgrounds tend to have higher aspirations for their child. And, due to their resources of being from a higher socioeconomic background, they have the resources to support their child and increase their chances of succeeding and meeting these aspirations.  

Not only is aspirations dependent on on SES, it is also based on the child's actual age as well. Parents base all of their expectations and aspirations on their child's previous achievements. Due to the development of the child's autonomy, parents often aspirations and expectations begin to decline as they get older (Pinquart &amp; Ebeling, 2020). Researchers have found that children who are from Hispanic or African American backgrounds have far less resources than those of non-minority groups (Spera et al., 2009). So, in turn, these parents view education as a 'vehicle for upward mobility'. As a result, this can impact parental attitudes of those from lower SES backgrounds, erring on the side of the importance of it, and the academic aspirations that they have for their children. 


The differences between cultures is also important to note. People from collectivist cultures have have stronger influence of parental aspirations. Studies on family-school relationships have shown that 

== Why do parents care about how well their child  performs in school? ==

== Socioeconomic factors relating to education ==

== Can the weight of expectations negatively affect a child's future? ==

== Expectancy value model ==
The relationship between a parent a child is a cascading process. First, it starts off with the parental beliefs and values that then influence the parent to change their behaviour to promoting their child's engagement with whatever domain they are interested. This, in turn, promotes that child's own beliefs of self-efficacy (self-concept), and their values of the tasks. This will naturally trigger changes in behaviour of the child and potential achievements they have in that domain. 

== Conclusion ==
While parent's expectations relating to their child's academic success can be seen as a negative, it also helps establish success for that child to do well in their future.


The decades of research on parental aspirations toward their children support that a parent's own background, whether it is cultural, socioeconomic, or academic are all important antecedents in their behaviour. A parent's own (positive or negative) experience with schooling can further influence their aspirations. One who enjoyed their schooling may foster and environment where their children will also be likely to seek higher education and have increased motivation in staying on that path. 


== References ==


Pinquart, M., &amp; Ebeling, M. (2020). Parental educational xxpectations and academic cchievement in Children and Adolescents—A Meta-analysis. ''Educational Psychology Review'', ''32''(2), 463–480. &lt;nowiki&gt;https://doi.org/10.1007/s10648-019-09506-z&lt;/nowiki&gt;

Spera, C., Wentzel, K. R., &amp; Matto, H. C. (2009). Parental aspirations for their children’s educational attainment: Relations to ethnicity, parental education, children’s academic performance, and parental perceptions of school climate. ''Journal of Youth &amp; Adolescence'', ''38''(8), 1140–1152. (43239635). &lt;nowiki&gt;https://doi.org/10.1007/s10964-008-9314-7&lt;/nowiki&gt;</text>
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      <text bytes="4550" sha1="5dhcp2nm0mufjs0di0vt3j87a5s9fkh" xml:space="preserve">= '''How do parental aspirations shape children’s academic motivation and performance?''' =


== Overview ==
The focus on this chapter is on understanding what are the factors affecting a parent's attitude of aspiration or expectation towards their child. The current research suggests that parental aspirations may be more complex than the layman may believe, as it involves an complex interplay between socioeconomic factors, cultural, and parenting habits. 

'''Learning outcomes'''

After finishing this chapter, the reader shall come to understand 3 outcomes:

# What exactly are expectations or aspirations that a parent may have towards their child 
#

== What are 'expectations' or 'aspirations'? that parent might hold? ==
Expectations or aspirations that a parent may hold for their child is not necessarily concrete. It may include more short-term aspirations such as grades for the oncoming exam, or expectations for longer periods such as educational attainment, which may be receiving their high school diploma or a certain number of years of schooling (Pinquart &amp; Ebeling, 2020). 

An important aspect of parental aspirations is socioeconomic status (SES) or other factors. Parents who are from higher socioeconomic backgrounds tend to have higher aspirations for their child. And, due to their resources of being from a higher socioeconomic background, they have the resources to support their child and increase their chances of succeeding and meeting these aspirations.  

Not only is aspirations dependent on on SES, it is also based on the child's actual age as well. Parents base all of their expectations and aspirations on their child's previous achievements. Due to the development of the child's autonomy, parents often aspirations and expectations begin to decline as they get older (Pinquart &amp; Ebeling, 2020). Researchers have found that children who are from Hispanic or African American backgrounds have far less resources than those of non-minority groups (Spera et al., 2009). So, in turn, these parents view education as a 'vehicle for upward mobility'. As a result, this can impact parental attitudes of those from lower SES backgrounds, erring on the side of the importance of it, and the academic aspirations that they have for their children. 


The differences between cultures is also important to note. People from collectivist cultures have have stronger influence of parental aspirations. Studies on family-school relationships have shown that 

== Why do parents care about how well their child  performs in school? ==

== Socioeconomic factors relating to education ==

== Can the weight of expectations negatively affect a child's future? ==

== Expectancy value model ==
The relationship between a parent a child is a cascading process. First, it starts off with the parental beliefs and values that then influence the parent to change their behaviour to promoting their child's engagement with whatever domain they are interested. This, in turn, promotes that child's own beliefs of self-efficacy (self-concept), and their values of the tasks. This will naturally trigger changes in behaviour of the child and potential achievements they have in that domain. 

== Conclusion ==
While parent's expectations relating to their child's academic success can be seen as a negative, it also helps establish success for that child to do well in their future.


The decades of research on parental aspirations toward their children support that a parent's own background, whether it is cultural, socioeconomic, or academic are all important antecedents in their behaviour. A parent's own (positive or negative) experience with schooling can further influence their aspirations. One who enjoyed their schooling may foster and environment where their children will also be likely to seek higher education and have increased motivation in staying on that path. 


== References ==


Pinquart, M., &amp; Ebeling, M. (2020). Parental educational xxpectations and academic cchievement in Children and Adolescents—A Meta-analysis. ''Educational Psychology Review'', ''32''(2), 463–480. &lt;nowiki&gt;https://doi.org/10.1007/s10648-019-09506-z&lt;/nowiki&gt;

Spera, C., Wentzel, K. R., &amp; Matto, H. C. (2009). Parental aspirations for their children’s educational attainment: Relations to ethnicity, parental education, children’s academic performance, and parental perceptions of school climate. ''Journal of Youth &amp; Adolescence'', ''38''(8), 1140–1152. (43239635). &lt;nowiki&gt;https://doi.org/10.1007/s10964-008-9314-7&lt;/nowiki&gt;</text>
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:''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].''
:''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  
::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]''

== Abstract ==

This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. 

== Maddison Historical Statistics == 

[[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).&lt;ref&gt;See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.&lt;/ref&gt;'']]

The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. 

When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2023.&lt;ref&gt;Bolt and van Zanden (2024).&lt;/ref&gt; This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807.&lt;ref&gt;The dramatic drop in the orange line between 1808 and 1809 in Figure 1 could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.&lt;/ref&gt; We focus this analysis on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are those used in the Maddison data, which match [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]].) 

We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of North Sea oil. With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2023; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. 

This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. 

== Nobel economists and others ==

Banerjee and Duflo (2019, p. 207) said, &quot;despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive.&quot; That appeared shortly before they won the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. 

While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, &quot;The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services.&quot; In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. 

Mokyr (2017, p. 255) also said that, &quot;intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished.&quot; That resistance, he suggested, drives &quot;the empirical regularity that no society remains at the cutting edge of technological creativity for very long&quot;.&lt;ref&gt;Mokyr (2017, p. 260).&lt;/ref&gt; This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US and the UK, visible in Figure 1.  

Mokyr (2017, p. 60) also mentioned &quot;entrepreneurs of hate&quot;, who convince others to dislike some group in a way that may benefit those &quot;entrepreneurs&quot; and major media organizations, who promote such &quot;entrepreneurs&quot; to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.&lt;ref&gt;See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and [[Managing the good and the evils of social media]], accessed 2026-10-14.&lt;/ref&gt; When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites.  

Successful entrepreneurs of hate who demonize immigrants are featured in news coverage that portrays immigrants as criminal threats, when the threats are nonexistent&lt;ref&gt;Muchow and Stanishevska (2026); Ajzenman(2023).&lt;/ref&gt; or result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.&lt;ref&gt;Marie and Paolo (2024). See also the Wikipedia article on &quot;[[w:Immigration and crime|Immigration and crime]]&quot;, accessed 2026-10-12.&lt;/ref&gt; Mixed results are reported by research on sanctuary jurisdictions: Some studies show no impact.&lt;ref&gt;Martínez et al. (2017).&lt;/ref&gt; Most others show less crime with stronger economies, lower unemployment, higher median incomes, less poverty, less reliance on public assistance, etc.&lt;ref&gt;Wong (2017). See also the Wikipedia article on &quot;[[w:Sanctuary city|sanctuary city]]&quot;, accessed 2026-10-12.&lt;/ref&gt; In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities were ''more'' prone to crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded &quot;that sanctuary policies have no effect on crime rates, despite narratives to the contrary.&quot;&lt;ref&gt;Roll (2017); Gonzalez O’Brien, et al. (2017).&lt;/ref&gt;

We next discuss competition in media markets before discussing immigrants further. 

=== Diversity of ownership of the major media === 

Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations, and in hierarchical societies the religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate the designated evil others and give increasing shares of what they produce so the secular elites would &quot;protect&quot; them in wars against the designated evil others.

Acemoglu and Robinson (2012, p. 461) said, &quot;Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power ... in the United States [and] ... in the context of British democratization. Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799] ... .&quot; ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) 

But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.&lt;ref&gt;Hendrix (2015, p. 64), quoted from the Wikipedia article on the &quot;[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand&lt;ref&gt;Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; and was much more popular than Tetzel's.&lt;ref&gt;Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; 

Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the Church of England, denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature,&lt;ref&gt;Raymond (2006), cited from the Wikipedia article on &quot;[[w:Pamphlet war|pamphlet war]]&quot;, accessed 2026-10-15.&lt;/ref&gt; theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.&lt;ref&gt;Hibbert et al. (2010, p. 928), cited from the Wikipedia article on &quot;[[w:Henry VIII|Henry VIII]]&quot;, accessed 2026-10-15.&lt;/ref&gt;

A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.&lt;ref&gt;Foxley (2013, p. 207), cited from the Wikipedia article on &quot;[[w:Levellers|Levellers]], accessed 2026-10-15.&lt;/ref&gt; However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that became the US over a century later. 

That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792&lt;ref&gt;Wikipedia &quot;[[w:Postal Service Act|Postal Service Act]]&quot;, accessed 2023-07-11.&lt;/ref&gt; made a major contribution to making the US what it is today.  Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.&lt;ref&gt;Historian, USPS (2010).&lt;/ref&gt; McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.&lt;ref name=McC-N2010&gt;McChesney and Nichols (2010, pp. 310-311, note 88).&lt;/ref&gt; 

During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;John (1995). See also the interview with him at &quot;[[Media concentration per Columbia History Professor Richard John]]&quot; on Wikiversity, accessed 2026-10-12.&lt;/ref&gt; In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.&lt;ref&gt;The &quot;6 percent per year&quot; growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in &quot;[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; on Wikiversity, accessed 2026-10-13.&lt;/ref&gt; 

One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. 

FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, which the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.&lt;ref&gt;This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on &quot;[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; in Wikiversity, accessed 2026-10-13.&lt;/ref&gt;

But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, &quot;the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred.&quot; They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. 

Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.&lt;ref&gt;On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of &quot;influencers&quot; by for-profit social media as essentially unleashed &quot;a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures.&quot; In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.&lt;/ref&gt; 

And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2021, p. 139) noted, &quot;In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%.  The top rate was then cut in half, with the announced objective of boosting growth.  But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.&quot;

=== Immigrants === 

We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. [[w:English Council of State|Lord Protector Cromwell]], who replaced Charles I, refused to authorize as many monopolies as his predecessors, presumably supported by the growing number of independent publishers of pamphlets, books, and newspapers mentioned above. He also encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. 

But Mokyr is not alone in proclaiming the contributions of immigrants to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how &quot;the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology.&quot;

Aghion et al. (2021, p. 292) also discuss (a) &quot;a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita&quot; and (b) the overrepresentation of immigrants in patent applications.&lt;ref&gt;e.g., Aghion et al. (2026, pp. 266-267).&lt;/ref&gt; However, [[w:Dean Baker|Baker]] (2016, pp. 77-78) claimed that &quot;over the last four decades ... stronger patent protection seems to be associated with slower growth,&quot; seemingly the opposite of the claim just quoted from Aghion et al. 

Anther example of how technology winners protect their status against competition is the [[w:Supreme Court of the United States|US Supreme Court]] decision in ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]''. [[w:Lawrence Lessig|Lessig]], who represented the plaintiff in that case, asked how could extending the copyright on existing works &quot;promote the Progress of Science and useful Arts&quot;, as required by the [[w:Copyright Clause|Copyright Clause]] of the US Constitution? Lessig lost that case. His (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to limit rather than &quot;promote the Progress of Science and useful Arts&quot;. This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000, which would bankrupt his parents and which they could not recover even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.&lt;ref&gt;Lessig (2004, p. 42).&lt;/ref&gt; This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP). The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, becauses much of their income is derived from copyright royalties, or (b) SLAPP laws, because anti-SLAPP laws, which exist in some jurisdictions but not others,&lt;ref&gt;[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the &quot;JAWBONE act&quot;, to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on &quot;[[Foundation for Individual Rights and Expression]]&quot;, accessed 2026-10-16.&lt;/ref&gt; limit the power of major corporations, which provide most of the money for the media. 

Similarly Graves (2023) asked, &quot;Do copyrights and paywalls on refereed academic journals violate the US constitution?&quot; No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.&lt;ref&gt;Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on &quot;[[Wikimedia concerns with European copyright rules including AI and scientific research]]&quot;. That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).&lt;/ref&gt;

=== Industrial Revolution ===

There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. 

Mokyr (2017, p.  3) says, &quot;The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society.&quot; He described &quot;three cultural elements&quot; required for &quot;sustainable economic growth propelled by technological progress&quot;: (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. &quot;[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.&lt;ref&gt;Mokyr (2017, pp. 19-20).&lt;/ref&gt; Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, &quot;The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution.&quot; 

Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, &quot;European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?&quot; Aghion et al. (2021, p. 20) describe the &quot;first Industrial Revolution&quot; as having been triggered by &quot;the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866.&quot;&lt;ref&gt;The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.&lt;/ref&gt;

The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not &quot;phases of growth and decline&quot; with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. 

Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, &quot;the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward.&quot; ... However, &quot;the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant to thousand or seven thousand years previously.&quot; (chapter 5) They also claim that, &quot;English national production per capita doubled from 1500 to 1700&quot;, (chapter 5), and &quot;Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root.&quot; (p. 45, chapter 2)

Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. 

Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the &quot;Old Pretender&quot;, a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. 

When Queen Anne died in 1702, she was succeeded by George I. His parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, &quot;and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts&quot;, according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs moved to confiscate &quot;[[w:Commons|commons]]&quot;, land whose use had been traditionally shared by commoners, and give to nobles. The Levellers had been excluded from the government of Lord Protector Cromwell, but the spirit of levelling still stalked the land. Some commoners joined &quot;Blacks&quot;, so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.&lt;ref&gt;Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on &quot;[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.&lt;/ref&gt; 

But not all accused were summarily executed. In 1724 &quot;John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized&quot; with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.&lt;ref&gt;Acemoglu and Robinson (2012, pp. 304-305).&lt;/ref&gt; 

These kinds of actions by the parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded &quot;universal [adult male] suffrage&quot; and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, &quot;The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The Manchester Observer called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... .&quot; And the British government placed enough other limits on its power that enough other commoners were allowed to became successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. 

== In sum ==

The above suggests that the rate of economic growth changes with either change in administration -- a new head of state -- or some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. 

However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).&lt;ref&gt;Graves (2025) includes an analysis of the data in Neff and Pickard (2024).&lt;/ref&gt; 

== Caveat ==

The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  

== Notes ==
{{reflist}}

== Bibliography ==

* &lt;!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)--&gt;{{cite Q|Q85764011}}
* &lt;!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)--&gt;{{cite Q|Q141241291}}
* &lt;!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)--&gt;{{cite Q|Q125292212}}
* &lt;!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)--&gt;{{cite Q|Q7997840}} 
* &lt;!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)--&gt;{{cite Q|Q137641358}}
* &lt;!--Ajzenman, Nicolas (29 January 2023). &quot;Migrants don't cause crime rates to increase — but false perceptions endure anyway&quot;. The Conversation.--&gt;{{cite Q|Q141758664}}
* &lt;!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) &quot;European Immigrants and the United States’ Rise to the Technological Frontier&quot;--&gt;{{cite Q|Q141678287}}
* &lt;!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer--&gt;{{cite Q|Q100216001}}

* &lt;!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) &quot;Maddison style estimates of the evolution of the world economy: A new 2023 update&quot;, Journal of Economic Surveys, 1-41--&gt;{{cite Q|Q126723821}}
* &lt;!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__&gt;{{cite Q|Q57945943}}
* &lt;!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia--&gt;{{cite Q|Q141759196}}
* &lt;!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition--&gt;{{cite Q|Q141156783}}
* &lt;!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies--&gt;{{cite Q|Q141158362}}
* &lt;!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)--&gt;{{cite Q|Q136227988}}
* &lt;!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) &quot;The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration--&gt;{{cite Q|Q55932800}}
* &lt;!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)--&gt;{{cite Q|Q132855526}}
* &lt;!--Graves (2023-03-21)  Do copyrights and paywalls on academic journals violate the US Constitution?--&gt;{{cite Q|Q126116187}}
* &lt;!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.--&gt;{{cite Q|Q137188993}}
* &lt;!-- Historian, USPS (2010) Postage Rates for Periodicals --&gt;{{cite Q|Q112167199}}
* &lt;!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse--&gt;{{cite Q|Q54641943}}
* &lt;!--Volker Leppin and Timothy J. Wengert (2015) &quot;Sources for and against the Posting of the Ninety-Five Theses&quot;--&gt;{{cite Q|Q141737347}}
* &lt;!--Lawrence Lessig (2004) Free Culture--&gt;{{cite Q|Q830526}}
* &lt;!--Olivier Marie and Paolo Pinotti (2024-02-01) &quot;Immigration and Crime: An International Perspective&quot;, Journal of Economic Perspectives. 38 (1): 181–200--&gt;{{cite Q|Q128434874}}
* &lt;!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). &quot;
Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime&quot;
. Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.--&gt;{{cite Q|Q55932802}}
* &lt;!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) --&gt;{{cite Q|Q104888067}}.
* &lt;!-- Robert W. McChesney; John Nichols (2016). People get ready--&gt;{{cite Q|Q87619174}}
* &lt;!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)--&gt;{{cite Q|Q136118590}}
* &lt;!--Ashley N. Muchow &amp; Taisiia Stanishevska (2026) &quot;From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest&quot;, Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)--&gt;{{cite Q|Q141760694}}
* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* &lt;!--John Hely Owen (1938)  War at Sea Under Queen Anne 1702–1708--&gt;{{cite Q|Q141757101}}
* &lt;!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation--&gt;{{cite Q|Q141761223}}
* &lt;!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain--&gt;{{cite Q|Q141761849}}
* &lt;!--Nick Roll (2017-07-16) &quot;Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.--&gt;{{cite Q|Q141735231}}
* &lt;!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)--&gt;{{cite Q|Q137669960}}
* &lt;!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)--&gt;{{cite Q|Q137669987}}
* &lt;!--J. L. van Zanden  and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30--&gt;{{cite Q|Q137670058}} 
* &lt;!--Tom K. Wong (2017-01-26) &quot;The Effects of Sanctuary Policies on Crime and the Economy&quot;--&gt;{{cite Q|Q98775875}}

[[Category:Original research]]
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:''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].''
:''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  
::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]''

== Abstract ==

This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. 

== Maddison Historical Statistics == 

[[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).&lt;ref&gt;See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.&lt;/ref&gt;'']]

The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. 

When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.&lt;ref&gt;Bolt and van Zanden (2024).&lt;/ref&gt; This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807.&lt;ref&gt;The dramatic drop in the orange line between 1808 and 1809 in Figure 1 could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.&lt;/ref&gt; We focus this analysis on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are those used in the Maddison data, which match [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]].) 

We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of North Sea oil. With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. 

This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. 

== Nobel economists and others ==

Banerjee and Duflo (2019, p. 207) said, &quot;despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive.&quot; That appeared shortly before they won the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. 

While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, &quot;The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services.&quot; In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. 

Mokyr (2017, p. 255) also said that, &quot;intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished.&quot; That resistance, he suggested, drives &quot;the empirical regularity that no society remains at the cutting edge of technological creativity for very long&quot;.&lt;ref&gt;Mokyr (2017, p. 260).&lt;/ref&gt; This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US and the UK, visible in Figure 1.  

Mokyr (2017, p. 60) also mentioned &quot;entrepreneurs of hate&quot;, who convince others to dislike some group in a way that may benefit those &quot;entrepreneurs&quot; and major media organizations, who promote such &quot;entrepreneurs&quot; to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.&lt;ref&gt;See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and [[Managing the good and the evils of social media]], accessed 2026-10-14.&lt;/ref&gt; When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites.  

Successful entrepreneurs of hate who demonize immigrants are featured in news coverage that portrays immigrants as criminal threats, when the threats are nonexistent&lt;ref&gt;Muchow and Stanishevska (2026); Ajzenman(2023).&lt;/ref&gt; or result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.&lt;ref&gt;Marie and Paolo (2024). See also the Wikipedia article on &quot;[[w:Immigration and crime|Immigration and crime]]&quot;, accessed 2026-10-12.&lt;/ref&gt; Mixed results are reported by research on sanctuary jurisdictions: Some studies show no impact.&lt;ref&gt;Martínez et al. (2017).&lt;/ref&gt; Most others show less crime with stronger economies, lower unemployment, higher median incomes, less poverty, less reliance on public assistance, etc.&lt;ref&gt;Wong (2017). See also the Wikipedia article on &quot;[[w:Sanctuary city|sanctuary city]]&quot;, accessed 2026-10-12.&lt;/ref&gt; In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities were ''more'' prone to crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded &quot;that sanctuary policies have no effect on crime rates, despite narratives to the contrary.&quot;&lt;ref&gt;Roll (2017); Gonzalez O’Brien, et al. (2017).&lt;/ref&gt;

We next discuss competition in media markets before discussing immigrants further. 

=== Diversity of ownership of the major media === 

Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations, and in hierarchical societies the religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate the designated evil others and give increasing shares of what they produce so the secular elites would &quot;protect&quot; them in wars against the designated evil others.

Acemoglu and Robinson (2012, p. 461) said, &quot;Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power ... in the United States [and] ... in the context of British democratization. Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799] ... .&quot; ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) 

But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.&lt;ref&gt;Hendrix (2015, p. 64), quoted from the Wikipedia article on the &quot;[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand&lt;ref&gt;Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; and was much more popular than Tetzel's.&lt;ref&gt;Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; 

Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the Church of England, denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature,&lt;ref&gt;Raymond (2006), cited from the Wikipedia article on &quot;[[w:Pamphlet war|pamphlet war]]&quot;, accessed 2026-10-15.&lt;/ref&gt; theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.&lt;ref&gt;Hibbert et al. (2010, p. 928), cited from the Wikipedia article on &quot;[[w:Henry VIII|Henry VIII]]&quot;, accessed 2026-10-15.&lt;/ref&gt;

A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.&lt;ref&gt;Foxley (2013, p. 207), cited from the Wikipedia article on &quot;[[w:Levellers|Levellers]], accessed 2026-10-15.&lt;/ref&gt; However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that became the US over a century later. 

That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792&lt;ref&gt;Wikipedia &quot;[[w:Postal Service Act|Postal Service Act]]&quot;, accessed 2023-07-11.&lt;/ref&gt; made a major contribution to making the US what it is today.  Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.&lt;ref&gt;Historian, USPS (2010).&lt;/ref&gt; McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.&lt;ref name=McC-N2010&gt;McChesney and Nichols (2010, pp. 310-311, note 88).&lt;/ref&gt; 

During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;John (1995). See also the interview with him at &quot;[[Media concentration per Columbia History Professor Richard John]]&quot; on Wikiversity, accessed 2026-10-12.&lt;/ref&gt; In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.&lt;ref&gt;The &quot;6 percent per year&quot; growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in &quot;[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; on Wikiversity, accessed 2026-10-13.&lt;/ref&gt; 

One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. 

FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, which the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.&lt;ref&gt;This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on &quot;[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; in Wikiversity, accessed 2026-10-13.&lt;/ref&gt;

But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, &quot;the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred.&quot; They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. 

Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.&lt;ref&gt;On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of &quot;influencers&quot; by for-profit social media as essentially unleashed &quot;a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures.&quot; In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.&lt;/ref&gt; 

And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2021, p. 139) noted, &quot;In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%.  The top rate was then cut in half, with the announced objective of boosting growth.  But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.&quot;

=== Immigrants === 

We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. [[w:English Council of State|Lord Protector Cromwell]], who replaced Charles I, refused to authorize as many monopolies as his predecessors, presumably supported by the growing number of independent publishers of pamphlets, books, and newspapers mentioned above. He also encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. 

But Mokyr is not alone in proclaiming the contributions of immigrants to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how &quot;the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology.&quot;

Aghion et al. (2021, p. 292) also discuss (a) &quot;a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita&quot; and (b) the overrepresentation of immigrants in patent applications.&lt;ref&gt;e.g., Aghion et al. (2026, pp. 266-267).&lt;/ref&gt; However, [[w:Dean Baker|Baker]] (2016, pp. 77-78) claimed that &quot;over the last four decades ... stronger patent protection seems to be associated with slower growth,&quot; seemingly the opposite of the claim just quoted from Aghion et al. 

Anther example of how technology winners protect their status against competition is the [[w:Supreme Court of the United States|US Supreme Court]] decision in ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]''. [[w:Lawrence Lessig|Lessig]], who represented the plaintiff in that case, asked how could extending the copyright on existing works &quot;promote the Progress of Science and useful Arts&quot;, as required by the [[w:Copyright Clause|Copyright Clause]] of the US Constitution? Lessig lost that case. His (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to limit rather than &quot;promote the Progress of Science and useful Arts&quot;. This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000, which would bankrupt his parents and which they could not recover even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.&lt;ref&gt;Lessig (2004, p. 42).&lt;/ref&gt; This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP). The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, becauses much of their income is derived from copyright royalties, or (b) SLAPP laws, because anti-SLAPP laws, which exist in some jurisdictions but not others,&lt;ref&gt;[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the &quot;JAWBONE act&quot;, to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on &quot;[[Foundation for Individual Rights and Expression]]&quot;, accessed 2026-10-16.&lt;/ref&gt; limit the power of major corporations, which provide most of the money for the media. 

Similarly Graves (2023) asked, &quot;Do copyrights and paywalls on refereed academic journals violate the US constitution?&quot; No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.&lt;ref&gt;Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on &quot;[[Wikimedia concerns with European copyright rules including AI and scientific research]]&quot;. That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).&lt;/ref&gt;

=== Industrial Revolution ===

There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. 

Mokyr (2017, p.  3) says, &quot;The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society.&quot; He described &quot;three cultural elements&quot; required for &quot;sustainable economic growth propelled by technological progress&quot;: (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. &quot;[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.&lt;ref&gt;Mokyr (2017, pp. 19-20).&lt;/ref&gt; Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, &quot;The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution.&quot; 

Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, &quot;European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?&quot; Aghion et al. (2021, p. 20) describe the &quot;first Industrial Revolution&quot; as having been triggered by &quot;the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866.&quot;&lt;ref&gt;The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.&lt;/ref&gt;

The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not &quot;phases of growth and decline&quot; with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. 

Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, &quot;the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward.&quot; ... However, &quot;the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant to thousand or seven thousand years previously.&quot; (chapter 5) They also claim that, &quot;English national production per capita doubled from 1500 to 1700&quot;, (chapter 5), and &quot;Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root.&quot; (p. 45, chapter 2)

Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. 

Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the &quot;Old Pretender&quot;, a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. 

When Queen Anne died in 1702, she was succeeded by George I. His parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, &quot;and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts&quot;, according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs moved to confiscate &quot;[[w:Commons|commons]]&quot;, land whose use had been traditionally shared by commoners, and give to nobles. The Levellers had been excluded from the government of Lord Protector Cromwell, but the spirit of levelling still stalked the land. Some commoners joined &quot;Blacks&quot;, so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.&lt;ref&gt;Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on &quot;[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.&lt;/ref&gt; 

But not all accused were summarily executed. In 1724 &quot;John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized&quot; with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.&lt;ref&gt;Acemoglu and Robinson (2012, pp. 304-305).&lt;/ref&gt; 

These kinds of actions by the parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded &quot;universal [adult male] suffrage&quot; and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, &quot;The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The Manchester Observer called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... .&quot; And the British government placed enough other limits on its power that enough other commoners were allowed to became successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. 

== In sum ==

The above suggests that the rate of economic growth changes with either change in administration -- a new head of state -- or some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. 

However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).&lt;ref&gt;Graves (2025) includes an analysis of the data in Neff and Pickard (2024).&lt;/ref&gt; 

== Caveat ==

The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  

== Notes ==
{{reflist}}

== Bibliography ==

* &lt;!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)--&gt;{{cite Q|Q85764011}}
* &lt;!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)--&gt;{{cite Q|Q141241291}}
* &lt;!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)--&gt;{{cite Q|Q125292212}}
* &lt;!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)--&gt;{{cite Q|Q7997840}} 
* &lt;!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)--&gt;{{cite Q|Q137641358}}
* &lt;!--Ajzenman, Nicolas (29 January 2023). &quot;Migrants don't cause crime rates to increase — but false perceptions endure anyway&quot;. The Conversation.--&gt;{{cite Q|Q141758664}}
* &lt;!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) &quot;European Immigrants and the United States’ Rise to the Technological Frontier&quot;--&gt;{{cite Q|Q141678287}}
* &lt;!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer--&gt;{{cite Q|Q100216001}}

* &lt;!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) &quot;Maddison style estimates of the evolution of the world economy: A new 2023 update&quot;, Journal of Economic Surveys, 1-41--&gt;{{cite Q|Q126723821}}
* &lt;!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__&gt;{{cite Q|Q57945943}}
* &lt;!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia--&gt;{{cite Q|Q141759196}}
* &lt;!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition--&gt;{{cite Q|Q141156783}}
* &lt;!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies--&gt;{{cite Q|Q141158362}}
* &lt;!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)--&gt;{{cite Q|Q136227988}}
* &lt;!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) &quot;The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration--&gt;{{cite Q|Q55932800}}
* &lt;!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)--&gt;{{cite Q|Q132855526}}
* &lt;!--Graves (2023-03-21)  Do copyrights and paywalls on academic journals violate the US Constitution?--&gt;{{cite Q|Q126116187}}
* &lt;!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.--&gt;{{cite Q|Q137188993}}
* &lt;!-- Historian, USPS (2010) Postage Rates for Periodicals --&gt;{{cite Q|Q112167199}}
* &lt;!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse--&gt;{{cite Q|Q54641943}}
* &lt;!--Volker Leppin and Timothy J. Wengert (2015) &quot;Sources for and against the Posting of the Ninety-Five Theses&quot;--&gt;{{cite Q|Q141737347}}
* &lt;!--Lawrence Lessig (2004) Free Culture--&gt;{{cite Q|Q830526}}
* &lt;!--Olivier Marie and Paolo Pinotti (2024-02-01) &quot;Immigration and Crime: An International Perspective&quot;, Journal of Economic Perspectives. 38 (1): 181–200--&gt;{{cite Q|Q128434874}}
* &lt;!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). &quot;
Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime&quot;
. Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.--&gt;{{cite Q|Q55932802}}
* &lt;!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) --&gt;{{cite Q|Q104888067}}.
* &lt;!-- Robert W. McChesney; John Nichols (2016). People get ready--&gt;{{cite Q|Q87619174}}
* &lt;!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)--&gt;{{cite Q|Q136118590}}
* &lt;!--Ashley N. Muchow &amp; Taisiia Stanishevska (2026) &quot;From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest&quot;, Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)--&gt;{{cite Q|Q141760694}}
* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* &lt;!--John Hely Owen (1938)  War at Sea Under Queen Anne 1702–1708--&gt;{{cite Q|Q141757101}}
* &lt;!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation--&gt;{{cite Q|Q141761223}}
* &lt;!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain--&gt;{{cite Q|Q141761849}}
* &lt;!--Nick Roll (2017-07-16) &quot;Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.--&gt;{{cite Q|Q141735231}}
* &lt;!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)--&gt;{{cite Q|Q137669960}}
* &lt;!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)--&gt;{{cite Q|Q137669987}}
* &lt;!--J. L. van Zanden  and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30--&gt;{{cite Q|Q137670058}} 
* &lt;!--Tom K. Wong (2017-01-26) &quot;The Effects of Sanctuary Policies on Crime and the Economy&quot;--&gt;{{cite Q|Q98775875}}

[[Category:Original research]]
[[Category:Research]]
[[Category:Economics]]
[[Category:Macroeconomics]]
[[Category:Gross domestic product]]
[[Category:Economic growth]]
[[Category:Modern Monetary Theory]]
[[Category:Political science]]
[[Category:Freedom and abundance]]
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      <comment>better desc of Holland / NLD</comment>
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      <text bytes="45481" sha1="2tfa3e0f4qutuyowajxmw48b8a26yn0" xml:space="preserve">{{Research project}} 
:''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].''
:''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  
::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]''

== Abstract ==

This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. 

== Maddison Historical Statistics == 

[[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).&lt;ref&gt;See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.&lt;/ref&gt;'']]

The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. 

When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.&lt;ref&gt;Bolt and van Zanden (2024).&lt;/ref&gt; This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]], which negatively impacted them, but because the available data prior to 1807 were for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are those used in the Maddison data, which match [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]].) 

We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of North Sea oil. With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. 

This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. 

== Nobel economists and others ==

Banerjee and Duflo (2019, p. 207) said, &quot;despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive.&quot; That appeared shortly before they won the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. 

While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, &quot;The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services.&quot; In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. 

Mokyr (2017, p. 255) also said that, &quot;intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished.&quot; That resistance, he suggested, drives &quot;the empirical regularity that no society remains at the cutting edge of technological creativity for very long&quot;.&lt;ref&gt;Mokyr (2017, p. 260).&lt;/ref&gt; This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US and the UK, visible in Figure 1.  

Mokyr (2017, p. 60) also mentioned &quot;entrepreneurs of hate&quot;, who convince others to dislike some group in a way that may benefit those &quot;entrepreneurs&quot; and major media organizations, who promote such &quot;entrepreneurs&quot; to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.&lt;ref&gt;See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and [[Managing the good and the evils of social media]], accessed 2026-10-14.&lt;/ref&gt; When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites.  

Successful entrepreneurs of hate who demonize immigrants are featured in news coverage that portrays immigrants as criminal threats, when the threats are nonexistent&lt;ref&gt;Muchow and Stanishevska (2026); Ajzenman(2023).&lt;/ref&gt; or result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.&lt;ref&gt;Marie and Paolo (2024). See also the Wikipedia article on &quot;[[w:Immigration and crime|Immigration and crime]]&quot;, accessed 2026-10-12.&lt;/ref&gt; Mixed results are reported by research on sanctuary jurisdictions: Some studies show no impact.&lt;ref&gt;Martínez et al. (2017).&lt;/ref&gt; Most others show less crime with stronger economies, lower unemployment, higher median incomes, less poverty, less reliance on public assistance, etc.&lt;ref&gt;Wong (2017). See also the Wikipedia article on &quot;[[w:Sanctuary city|sanctuary city]]&quot;, accessed 2026-10-12.&lt;/ref&gt; In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities were ''more'' prone to crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded &quot;that sanctuary policies have no effect on crime rates, despite narratives to the contrary.&quot;&lt;ref&gt;Roll (2017); Gonzalez O’Brien, et al. (2017).&lt;/ref&gt;

We next discuss competition in media markets before discussing immigrants further. 

=== Diversity of ownership of the major media === 

Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations, and in hierarchical societies the religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate the designated evil others and give increasing shares of what they produce so the secular elites would &quot;protect&quot; them in wars against the designated evil others.

Acemoglu and Robinson (2012, p. 461) said, &quot;Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power ... in the United States [and] ... in the context of British democratization. Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799] ... .&quot; ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) 

But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.&lt;ref&gt;Hendrix (2015, p. 64), quoted from the Wikipedia article on the &quot;[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand&lt;ref&gt;Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; and was much more popular than Tetzel's.&lt;ref&gt;Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; 

Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the Church of England, denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature,&lt;ref&gt;Raymond (2006), cited from the Wikipedia article on &quot;[[w:Pamphlet war|pamphlet war]]&quot;, accessed 2026-10-15.&lt;/ref&gt; theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.&lt;ref&gt;Hibbert et al. (2010, p. 928), cited from the Wikipedia article on &quot;[[w:Henry VIII|Henry VIII]]&quot;, accessed 2026-10-15.&lt;/ref&gt;

A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.&lt;ref&gt;Foxley (2013, p. 207), cited from the Wikipedia article on &quot;[[w:Levellers|Levellers]], accessed 2026-10-15.&lt;/ref&gt; However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that became the US over a century later. 

That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792&lt;ref&gt;Wikipedia &quot;[[w:Postal Service Act|Postal Service Act]]&quot;, accessed 2023-07-11.&lt;/ref&gt; made a major contribution to making the US what it is today.  Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.&lt;ref&gt;Historian, USPS (2010).&lt;/ref&gt; McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.&lt;ref name=McC-N2010&gt;McChesney and Nichols (2010, pp. 310-311, note 88).&lt;/ref&gt; 

During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;John (1995). See also the interview with him at &quot;[[Media concentration per Columbia History Professor Richard John]]&quot; on Wikiversity, accessed 2026-10-12.&lt;/ref&gt; In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.&lt;ref&gt;The &quot;6 percent per year&quot; growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in &quot;[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; on Wikiversity, accessed 2026-10-13.&lt;/ref&gt; 

One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. 

FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, which the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.&lt;ref&gt;This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on &quot;[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; in Wikiversity, accessed 2026-10-13.&lt;/ref&gt;

But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, &quot;the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred.&quot; They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. 

Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.&lt;ref&gt;On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of &quot;influencers&quot; by for-profit social media as essentially unleashed &quot;a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures.&quot; In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.&lt;/ref&gt; 

And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2021, p. 139) noted, &quot;In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%.  The top rate was then cut in half, with the announced objective of boosting growth.  But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.&quot;

=== Immigrants === 

We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. [[w:English Council of State|Lord Protector Cromwell]], who replaced Charles I, refused to authorize as many monopolies as his predecessors, presumably supported by the growing number of independent publishers of pamphlets, books, and newspapers mentioned above. He also encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. 

But Mokyr is not alone in proclaiming the contributions of immigrants to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how &quot;the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology.&quot;

Aghion et al. (2021, p. 292) also discuss (a) &quot;a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita&quot; and (b) the overrepresentation of immigrants in patent applications.&lt;ref&gt;e.g., Aghion et al. (2026, pp. 266-267).&lt;/ref&gt; However, [[w:Dean Baker|Baker]] (2016, pp. 77-78) claimed that &quot;over the last four decades ... stronger patent protection seems to be associated with slower growth,&quot; seemingly the opposite of the claim just quoted from Aghion et al. 

Anther example of how technology winners protect their status against competition is the [[w:Supreme Court of the United States|US Supreme Court]] decision in ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]''. [[w:Lawrence Lessig|Lessig]], who represented the plaintiff in that case, asked how could extending the copyright on existing works &quot;promote the Progress of Science and useful Arts&quot;, as required by the [[w:Copyright Clause|Copyright Clause]] of the US Constitution? Lessig lost that case. His (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to limit rather than &quot;promote the Progress of Science and useful Arts&quot;. This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000, which would bankrupt his parents and which they could not recover even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.&lt;ref&gt;Lessig (2004, p. 42).&lt;/ref&gt; This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP). The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, becauses much of their income is derived from copyright royalties, or (b) SLAPP laws, because anti-SLAPP laws, which exist in some jurisdictions but not others,&lt;ref&gt;[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the &quot;JAWBONE act&quot;, to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on &quot;[[Foundation for Individual Rights and Expression]]&quot;, accessed 2026-10-16.&lt;/ref&gt; limit the power of major corporations, which provide most of the money for the media. 

Similarly Graves (2023) asked, &quot;Do copyrights and paywalls on refereed academic journals violate the US constitution?&quot; No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.&lt;ref&gt;Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on &quot;[[Wikimedia concerns with European copyright rules including AI and scientific research]]&quot;. That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).&lt;/ref&gt;

=== Industrial Revolution ===

There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. 

Mokyr (2017, p.  3) says, &quot;The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society.&quot; He described &quot;three cultural elements&quot; required for &quot;sustainable economic growth propelled by technological progress&quot;: (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. &quot;[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.&lt;ref&gt;Mokyr (2017, pp. 19-20).&lt;/ref&gt; Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, &quot;The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution.&quot; 

Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, &quot;European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?&quot; Aghion et al. (2021, p. 20) describe the &quot;first Industrial Revolution&quot; as having been triggered by &quot;the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866.&quot;&lt;ref&gt;The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.&lt;/ref&gt;

The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not &quot;phases of growth and decline&quot; with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. 

Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, &quot;the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward.&quot; ... However, &quot;the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant to thousand or seven thousand years previously.&quot; (chapter 5) They also claim that, &quot;English national production per capita doubled from 1500 to 1700&quot;, (chapter 5), and &quot;Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root.&quot; (p. 45, chapter 2)

Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. 

Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the &quot;Old Pretender&quot;, a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. 

When Queen Anne died in 1702, she was succeeded by George I. His parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, &quot;and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts&quot;, according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs moved to confiscate &quot;[[w:Commons|commons]]&quot;, land whose use had been traditionally shared by commoners, and give to nobles. The Levellers had been excluded from the government of Lord Protector Cromwell, but the spirit of levelling still stalked the land. Some commoners joined &quot;Blacks&quot;, so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.&lt;ref&gt;Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on &quot;[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.&lt;/ref&gt; 

But not all accused were summarily executed. In 1724 &quot;John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized&quot; with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.&lt;ref&gt;Acemoglu and Robinson (2012, pp. 304-305).&lt;/ref&gt; 

These kinds of actions by the parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded &quot;universal [adult male] suffrage&quot; and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, &quot;The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The Manchester Observer called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... .&quot; And the British government placed enough other limits on its power that enough other commoners were allowed to became successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. 

== In sum ==

The above suggests that the rate of economic growth changes with either change in administration -- a new head of state -- or some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. 

However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).&lt;ref&gt;Graves (2025) includes an analysis of the data in Neff and Pickard (2024).&lt;/ref&gt; 

== Caveat ==

The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  

== Notes ==
{{reflist}}

== Bibliography ==

* &lt;!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)--&gt;{{cite Q|Q85764011}}
* &lt;!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)--&gt;{{cite Q|Q141241291}}
* &lt;!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)--&gt;{{cite Q|Q125292212}}
* &lt;!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)--&gt;{{cite Q|Q7997840}} 
* &lt;!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)--&gt;{{cite Q|Q137641358}}
* &lt;!--Ajzenman, Nicolas (29 January 2023). &quot;Migrants don't cause crime rates to increase — but false perceptions endure anyway&quot;. The Conversation.--&gt;{{cite Q|Q141758664}}
* &lt;!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) &quot;European Immigrants and the United States’ Rise to the Technological Frontier&quot;--&gt;{{cite Q|Q141678287}}
* &lt;!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer--&gt;{{cite Q|Q100216001}}

* &lt;!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) &quot;Maddison style estimates of the evolution of the world economy: A new 2023 update&quot;, Journal of Economic Surveys, 1-41--&gt;{{cite Q|Q126723821}}
* &lt;!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__&gt;{{cite Q|Q57945943}}
* &lt;!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia--&gt;{{cite Q|Q141759196}}
* &lt;!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition--&gt;{{cite Q|Q141156783}}
* &lt;!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies--&gt;{{cite Q|Q141158362}}
* &lt;!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)--&gt;{{cite Q|Q136227988}}
* &lt;!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) &quot;The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration--&gt;{{cite Q|Q55932800}}
* &lt;!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)--&gt;{{cite Q|Q132855526}}
* &lt;!--Graves (2023-03-21)  Do copyrights and paywalls on academic journals violate the US Constitution?--&gt;{{cite Q|Q126116187}}
* &lt;!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.--&gt;{{cite Q|Q137188993}}
* &lt;!-- Historian, USPS (2010) Postage Rates for Periodicals --&gt;{{cite Q|Q112167199}}
* &lt;!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse--&gt;{{cite Q|Q54641943}}
* &lt;!--Volker Leppin and Timothy J. Wengert (2015) &quot;Sources for and against the Posting of the Ninety-Five Theses&quot;--&gt;{{cite Q|Q141737347}}
* &lt;!--Lawrence Lessig (2004) Free Culture--&gt;{{cite Q|Q830526}}
* &lt;!--Olivier Marie and Paolo Pinotti (2024-02-01) &quot;Immigration and Crime: An International Perspective&quot;, Journal of Economic Perspectives. 38 (1): 181–200--&gt;{{cite Q|Q128434874}}
* &lt;!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). &quot;
Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime&quot;
. Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.--&gt;{{cite Q|Q55932802}}
* &lt;!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) --&gt;{{cite Q|Q104888067}}.
* &lt;!-- Robert W. McChesney; John Nichols (2016). People get ready--&gt;{{cite Q|Q87619174}}
* &lt;!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)--&gt;{{cite Q|Q136118590}}
* &lt;!--Ashley N. Muchow &amp; Taisiia Stanishevska (2026) &quot;From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest&quot;, Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)--&gt;{{cite Q|Q141760694}}
* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* &lt;!--John Hely Owen (1938)  War at Sea Under Queen Anne 1702–1708--&gt;{{cite Q|Q141757101}}
* &lt;!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation--&gt;{{cite Q|Q141761223}}
* &lt;!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain--&gt;{{cite Q|Q141761849}}
* &lt;!--Nick Roll (2017-07-16) &quot;Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.--&gt;{{cite Q|Q141735231}}
* &lt;!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)--&gt;{{cite Q|Q137669960}}
* &lt;!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)--&gt;{{cite Q|Q137669987}}
* &lt;!--J. L. van Zanden  and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30--&gt;{{cite Q|Q137670058}} 
* &lt;!--Tom K. Wong (2017-01-26) &quot;The Effects of Sanctuary Policies on Crime and the Economy&quot;--&gt;{{cite Q|Q98775875}}

[[Category:Original research]]
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:''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].''
:''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  
::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]''

== Abstract ==

This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. 

== Maddison Historical Statistics == 

[[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).&lt;ref&gt;See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.&lt;/ref&gt;'']]

The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. 

When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.&lt;ref&gt;Bolt and van Zanden (2024).&lt;/ref&gt; This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]], which negatively impacted them, but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are those used in the Maddison data, which match [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]].) 

We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of North Sea oil. With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. 

This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. 

== Nobel economists and others ==

Banerjee and Duflo (2019, p. 207) said, &quot;despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive.&quot; That appeared shortly before they won the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. 

While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, &quot;The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services.&quot; In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. 

Mokyr (2017, p. 255) also said that, &quot;intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished.&quot; That resistance, he suggested, drives &quot;the empirical regularity that no society remains at the cutting edge of technological creativity for very long&quot;.&lt;ref&gt;Mokyr (2017, p. 260).&lt;/ref&gt; This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US and the UK, visible in Figure 1.  

Mokyr (2017, p. 60) also mentioned &quot;entrepreneurs of hate&quot;, who convince others to dislike some group in a way that may benefit those &quot;entrepreneurs&quot; and major media organizations, who promote such &quot;entrepreneurs&quot; to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.&lt;ref&gt;See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and [[Managing the good and the evils of social media]], accessed 2026-10-14.&lt;/ref&gt; When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites.  

Successful entrepreneurs of hate who demonize immigrants are featured in news coverage that portrays immigrants as criminal threats, when the threats are nonexistent&lt;ref&gt;Muchow and Stanishevska (2026); Ajzenman(2023).&lt;/ref&gt; or result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.&lt;ref&gt;Marie and Paolo (2024). See also the Wikipedia article on &quot;[[w:Immigration and crime|Immigration and crime]]&quot;, accessed 2026-10-12.&lt;/ref&gt; Mixed results are reported by research on sanctuary jurisdictions: Some studies show no impact.&lt;ref&gt;Martínez et al. (2017).&lt;/ref&gt; Most others show less crime with stronger economies, lower unemployment, higher median incomes, less poverty, less reliance on public assistance, etc.&lt;ref&gt;Wong (2017). See also the Wikipedia article on &quot;[[w:Sanctuary city|sanctuary city]]&quot;, accessed 2026-10-12.&lt;/ref&gt; In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities were ''more'' prone to crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded &quot;that sanctuary policies have no effect on crime rates, despite narratives to the contrary.&quot;&lt;ref&gt;Roll (2017); Gonzalez O’Brien, et al. (2017).&lt;/ref&gt;

We next discuss competition in media markets before discussing immigrants further. 

=== Diversity of ownership of the major media === 

Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations, and in hierarchical societies the religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate the designated evil others and give increasing shares of what they produce so the secular elites would &quot;protect&quot; them in wars against the designated evil others.

Acemoglu and Robinson (2012, p. 461) said, &quot;Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power ... in the United States [and] ... in the context of British democratization. Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799] ... .&quot; ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) 

But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.&lt;ref&gt;Hendrix (2015, p. 64), quoted from the Wikipedia article on the &quot;[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand&lt;ref&gt;Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; and was much more popular than Tetzel's.&lt;ref&gt;Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; 

Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the Church of England, denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature,&lt;ref&gt;Raymond (2006), cited from the Wikipedia article on &quot;[[w:Pamphlet war|pamphlet war]]&quot;, accessed 2026-10-15.&lt;/ref&gt; theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.&lt;ref&gt;Hibbert et al. (2010, p. 928), cited from the Wikipedia article on &quot;[[w:Henry VIII|Henry VIII]]&quot;, accessed 2026-10-15.&lt;/ref&gt;

A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.&lt;ref&gt;Foxley (2013, p. 207), cited from the Wikipedia article on &quot;[[w:Levellers|Levellers]], accessed 2026-10-15.&lt;/ref&gt; However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that became the US over a century later. 

That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792&lt;ref&gt;Wikipedia &quot;[[w:Postal Service Act|Postal Service Act]]&quot;, accessed 2023-07-11.&lt;/ref&gt; made a major contribution to making the US what it is today.  Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.&lt;ref&gt;Historian, USPS (2010).&lt;/ref&gt; McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.&lt;ref name=McC-N2010&gt;McChesney and Nichols (2010, pp. 310-311, note 88).&lt;/ref&gt; 

During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;John (1995). See also the interview with him at &quot;[[Media concentration per Columbia History Professor Richard John]]&quot; on Wikiversity, accessed 2026-10-12.&lt;/ref&gt; In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.&lt;ref&gt;The &quot;6 percent per year&quot; growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in &quot;[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; on Wikiversity, accessed 2026-10-13.&lt;/ref&gt; 

One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. 

FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, which the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.&lt;ref&gt;This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on &quot;[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; in Wikiversity, accessed 2026-10-13.&lt;/ref&gt;

But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, &quot;the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred.&quot; They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. 

Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.&lt;ref&gt;On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of &quot;influencers&quot; by for-profit social media as essentially unleashed &quot;a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures.&quot; In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.&lt;/ref&gt; 

And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2021, p. 139) noted, &quot;In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%.  The top rate was then cut in half, with the announced objective of boosting growth.  But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.&quot;

=== Immigrants === 

We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. [[w:English Council of State|Lord Protector Cromwell]], who replaced Charles I, refused to authorize as many monopolies as his predecessors, presumably supported by the growing number of independent publishers of pamphlets, books, and newspapers mentioned above. He also encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. 

But Mokyr is not alone in proclaiming the contributions of immigrants to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how &quot;the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology.&quot;

Aghion et al. (2021, p. 292) also discuss (a) &quot;a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita&quot; and (b) the overrepresentation of immigrants in patent applications.&lt;ref&gt;e.g., Aghion et al. (2026, pp. 266-267).&lt;/ref&gt; However, [[w:Dean Baker|Baker]] (2016, pp. 77-78) claimed that &quot;over the last four decades ... stronger patent protection seems to be associated with slower growth,&quot; seemingly the opposite of the claim just quoted from Aghion et al. 

Anther example of how technology winners protect their status against competition is the [[w:Supreme Court of the United States|US Supreme Court]] decision in ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]''. [[w:Lawrence Lessig|Lessig]], who represented the plaintiff in that case, asked how could extending the copyright on existing works &quot;promote the Progress of Science and useful Arts&quot;, as required by the [[w:Copyright Clause|Copyright Clause]] of the US Constitution? Lessig lost that case. His (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to limit rather than &quot;promote the Progress of Science and useful Arts&quot;. This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000, which would bankrupt his parents and which they could not recover even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.&lt;ref&gt;Lessig (2004, p. 42).&lt;/ref&gt; This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP). The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, becauses much of their income is derived from copyright royalties, or (b) SLAPP laws, because anti-SLAPP laws, which exist in some jurisdictions but not others,&lt;ref&gt;[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the &quot;JAWBONE act&quot;, to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on &quot;[[Foundation for Individual Rights and Expression]]&quot;, accessed 2026-10-16.&lt;/ref&gt; limit the power of major corporations, which provide most of the money for the media. 

Similarly Graves (2023) asked, &quot;Do copyrights and paywalls on refereed academic journals violate the US constitution?&quot; No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.&lt;ref&gt;Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on &quot;[[Wikimedia concerns with European copyright rules including AI and scientific research]]&quot;. That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).&lt;/ref&gt;

=== Industrial Revolution ===

There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. 

Mokyr (2017, p.  3) says, &quot;The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society.&quot; He described &quot;three cultural elements&quot; required for &quot;sustainable economic growth propelled by technological progress&quot;: (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. &quot;[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.&lt;ref&gt;Mokyr (2017, pp. 19-20).&lt;/ref&gt; Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, &quot;The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution.&quot; 

Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, &quot;European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?&quot; Aghion et al. (2021, p. 20) describe the &quot;first Industrial Revolution&quot; as having been triggered by &quot;the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866.&quot;&lt;ref&gt;The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.&lt;/ref&gt;

The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not &quot;phases of growth and decline&quot; with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. 

Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, &quot;the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward.&quot; ... However, &quot;the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant to thousand or seven thousand years previously.&quot; (chapter 5) They also claim that, &quot;English national production per capita doubled from 1500 to 1700&quot;, (chapter 5), and &quot;Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root.&quot; (p. 45, chapter 2)

Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. 

Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the &quot;Old Pretender&quot;, a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. 

When Queen Anne died in 1702, she was succeeded by George I. His parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, &quot;and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts&quot;, according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs moved to confiscate &quot;[[w:Commons|commons]]&quot;, land whose use had been traditionally shared by commoners, and give to nobles. The Levellers had been excluded from the government of Lord Protector Cromwell, but the spirit of levelling still stalked the land. Some commoners joined &quot;Blacks&quot;, so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.&lt;ref&gt;Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on &quot;[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.&lt;/ref&gt; 

But not all accused were summarily executed. In 1724 &quot;John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized&quot; with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.&lt;ref&gt;Acemoglu and Robinson (2012, pp. 304-305).&lt;/ref&gt; 

These kinds of actions by the parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded &quot;universal [adult male] suffrage&quot; and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, &quot;The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The Manchester Observer called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... .&quot; And the British government placed enough other limits on its power that enough other commoners were allowed to became successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. 

== In sum ==

The above suggests that the rate of economic growth changes with either change in administration -- a new head of state -- or some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. 

However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).&lt;ref&gt;Graves (2025) includes an analysis of the data in Neff and Pickard (2024).&lt;/ref&gt; 

== Caveat ==

The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  

== Notes ==
{{reflist}}

== Bibliography ==

* &lt;!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)--&gt;{{cite Q|Q85764011}}
* &lt;!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)--&gt;{{cite Q|Q141241291}}
* &lt;!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)--&gt;{{cite Q|Q125292212}}
* &lt;!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)--&gt;{{cite Q|Q7997840}} 
* &lt;!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)--&gt;{{cite Q|Q137641358}}
* &lt;!--Ajzenman, Nicolas (29 January 2023). &quot;Migrants don't cause crime rates to increase — but false perceptions endure anyway&quot;. The Conversation.--&gt;{{cite Q|Q141758664}}
* &lt;!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) &quot;European Immigrants and the United States’ Rise to the Technological Frontier&quot;--&gt;{{cite Q|Q141678287}}
* &lt;!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer--&gt;{{cite Q|Q100216001}}

* &lt;!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) &quot;Maddison style estimates of the evolution of the world economy: A new 2023 update&quot;, Journal of Economic Surveys, 1-41--&gt;{{cite Q|Q126723821}}
* &lt;!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__&gt;{{cite Q|Q57945943}}
* &lt;!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia--&gt;{{cite Q|Q141759196}}
* &lt;!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition--&gt;{{cite Q|Q141156783}}
* &lt;!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies--&gt;{{cite Q|Q141158362}}
* &lt;!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)--&gt;{{cite Q|Q136227988}}
* &lt;!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) &quot;The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration--&gt;{{cite Q|Q55932800}}
* &lt;!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)--&gt;{{cite Q|Q132855526}}
* &lt;!--Graves (2023-03-21)  Do copyrights and paywalls on academic journals violate the US Constitution?--&gt;{{cite Q|Q126116187}}
* &lt;!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.--&gt;{{cite Q|Q137188993}}
* &lt;!-- Historian, USPS (2010) Postage Rates for Periodicals --&gt;{{cite Q|Q112167199}}
* &lt;!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse--&gt;{{cite Q|Q54641943}}
* &lt;!--Volker Leppin and Timothy J. Wengert (2015) &quot;Sources for and against the Posting of the Ninety-Five Theses&quot;--&gt;{{cite Q|Q141737347}}
* &lt;!--Lawrence Lessig (2004) Free Culture--&gt;{{cite Q|Q830526}}
* &lt;!--Olivier Marie and Paolo Pinotti (2024-02-01) &quot;Immigration and Crime: An International Perspective&quot;, Journal of Economic Perspectives. 38 (1): 181–200--&gt;{{cite Q|Q128434874}}
* &lt;!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). &quot;
Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime&quot;
. Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.--&gt;{{cite Q|Q55932802}}
* &lt;!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) --&gt;{{cite Q|Q104888067}}.
* &lt;!-- Robert W. McChesney; John Nichols (2016). People get ready--&gt;{{cite Q|Q87619174}}
* &lt;!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)--&gt;{{cite Q|Q136118590}}
* &lt;!--Ashley N. Muchow &amp; Taisiia Stanishevska (2026) &quot;From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest&quot;, Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)--&gt;{{cite Q|Q141760694}}
* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* &lt;!--John Hely Owen (1938)  War at Sea Under Queen Anne 1702–1708--&gt;{{cite Q|Q141757101}}
* &lt;!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation--&gt;{{cite Q|Q141761223}}
* &lt;!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain--&gt;{{cite Q|Q141761849}}
* &lt;!--Nick Roll (2017-07-16) &quot;Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.--&gt;{{cite Q|Q141735231}}
* &lt;!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)--&gt;{{cite Q|Q137669960}}
* &lt;!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)--&gt;{{cite Q|Q137669987}}
* &lt;!--J. L. van Zanden  and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30--&gt;{{cite Q|Q137670058}} 
* &lt;!--Tom K. Wong (2017-01-26) &quot;The Effects of Sanctuary Policies on Crime and the Economy&quot;--&gt;{{cite Q|Q98775875}}

[[Category:Original research]]
[[Category:Research]]
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:''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].''
:''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  
::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]''

== Abstract ==

This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. 

== Maddison Historical Statistics == 

[[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).&lt;ref&gt;See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.&lt;/ref&gt;'']]

The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. 

When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.&lt;ref&gt;Bolt and van Zanden (2024).&lt;/ref&gt; This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them), but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are those used in the Maddison data, which match [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]].) 

We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of North Sea oil. With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. 

This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. 

== Nobel economists and others ==

Banerjee and Duflo (2019, p. 207) said, &quot;despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive.&quot; That appeared shortly before they won the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. 

While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, &quot;The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services.&quot; In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. 

Mokyr (2017, p. 255) also said that, &quot;intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished.&quot; That resistance, he suggested, drives &quot;the empirical regularity that no society remains at the cutting edge of technological creativity for very long&quot;.&lt;ref&gt;Mokyr (2017, p. 260).&lt;/ref&gt; This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US and the UK, visible in Figure 1.  

Mokyr (2017, p. 60) also mentioned &quot;entrepreneurs of hate&quot;, who convince others to dislike some group in a way that may benefit those &quot;entrepreneurs&quot; and major media organizations, who promote such &quot;entrepreneurs&quot; to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.&lt;ref&gt;See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and [[Managing the good and the evils of social media]], accessed 2026-10-14.&lt;/ref&gt; When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites.  

Successful entrepreneurs of hate who demonize immigrants are featured in news coverage that portrays immigrants as criminal threats, when the threats are nonexistent&lt;ref&gt;Muchow and Stanishevska (2026); Ajzenman(2023).&lt;/ref&gt; or result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.&lt;ref&gt;Marie and Paolo (2024). See also the Wikipedia article on &quot;[[w:Immigration and crime|Immigration and crime]]&quot;, accessed 2026-10-12.&lt;/ref&gt; Mixed results are reported by research on sanctuary jurisdictions: Some studies show no impact.&lt;ref&gt;Martínez et al. (2017).&lt;/ref&gt; Most others show less crime with stronger economies, lower unemployment, higher median incomes, less poverty, less reliance on public assistance, etc.&lt;ref&gt;Wong (2017). See also the Wikipedia article on &quot;[[w:Sanctuary city|sanctuary city]]&quot;, accessed 2026-10-12.&lt;/ref&gt; In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities were ''more'' prone to crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded &quot;that sanctuary policies have no effect on crime rates, despite narratives to the contrary.&quot;&lt;ref&gt;Roll (2017); Gonzalez O’Brien, et al. (2017).&lt;/ref&gt;

We next discuss competition in media markets before discussing immigrants further. 

=== Diversity of ownership of the major media === 

Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations, and in hierarchical societies the religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate the designated evil others and give increasing shares of what they produce so the secular elites would &quot;protect&quot; them in wars against the designated evil others.

Acemoglu and Robinson (2012, p. 461) said, &quot;Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power ... in the United States [and] ... in the context of British democratization. Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799] ... .&quot; ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) 

But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.&lt;ref&gt;Hendrix (2015, p. 64), quoted from the Wikipedia article on the &quot;[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand&lt;ref&gt;Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; and was much more popular than Tetzel's.&lt;ref&gt;Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; 

Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the Church of England, denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature,&lt;ref&gt;Raymond (2006), cited from the Wikipedia article on &quot;[[w:Pamphlet war|pamphlet war]]&quot;, accessed 2026-10-15.&lt;/ref&gt; theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.&lt;ref&gt;Hibbert et al. (2010, p. 928), cited from the Wikipedia article on &quot;[[w:Henry VIII|Henry VIII]]&quot;, accessed 2026-10-15.&lt;/ref&gt;

A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.&lt;ref&gt;Foxley (2013, p. 207), cited from the Wikipedia article on &quot;[[w:Levellers|Levellers]], accessed 2026-10-15.&lt;/ref&gt; However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that became the US over a century later. 

That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792&lt;ref&gt;Wikipedia &quot;[[w:Postal Service Act|Postal Service Act]]&quot;, accessed 2023-07-11.&lt;/ref&gt; made a major contribution to making the US what it is today.  Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.&lt;ref&gt;Historian, USPS (2010).&lt;/ref&gt; McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.&lt;ref name=McC-N2010&gt;McChesney and Nichols (2010, pp. 310-311, note 88).&lt;/ref&gt; 

During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;John (1995). See also the interview with him at &quot;[[Media concentration per Columbia History Professor Richard John]]&quot; on Wikiversity, accessed 2026-10-12.&lt;/ref&gt; In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.&lt;ref&gt;The &quot;6 percent per year&quot; growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in &quot;[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; on Wikiversity, accessed 2026-10-13.&lt;/ref&gt; 

One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. 

FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, which the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.&lt;ref&gt;This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on &quot;[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; in Wikiversity, accessed 2026-10-13.&lt;/ref&gt;

But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, &quot;the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred.&quot; They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. 

Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.&lt;ref&gt;On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of &quot;influencers&quot; by for-profit social media as essentially unleashed &quot;a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures.&quot; In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.&lt;/ref&gt; 

And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2021, p. 139) noted, &quot;In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%.  The top rate was then cut in half, with the announced objective of boosting growth.  But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.&quot;

=== Immigrants === 

We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. [[w:English Council of State|Lord Protector Cromwell]], who replaced Charles I, refused to authorize as many monopolies as his predecessors, presumably supported by the growing number of independent publishers of pamphlets, books, and newspapers mentioned above. He also encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. 

But Mokyr is not alone in proclaiming the contributions of immigrants to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how &quot;the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology.&quot;

Aghion et al. (2021, p. 292) also discuss (a) &quot;a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita&quot; and (b) the overrepresentation of immigrants in patent applications.&lt;ref&gt;e.g., Aghion et al. (2026, pp. 266-267).&lt;/ref&gt; However, [[w:Dean Baker|Baker]] (2016, pp. 77-78) claimed that &quot;over the last four decades ... stronger patent protection seems to be associated with slower growth,&quot; seemingly the opposite of the claim just quoted from Aghion et al. 

Anther example of how technology winners protect their status against competition is the [[w:Supreme Court of the United States|US Supreme Court]] decision in ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]''. [[w:Lawrence Lessig|Lessig]], who represented the plaintiff in that case, asked how could extending the copyright on existing works &quot;promote the Progress of Science and useful Arts&quot;, as required by the [[w:Copyright Clause|Copyright Clause]] of the US Constitution? Lessig lost that case. His (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to limit rather than &quot;promote the Progress of Science and useful Arts&quot;. This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000, which would bankrupt his parents and which they could not recover even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.&lt;ref&gt;Lessig (2004, p. 42).&lt;/ref&gt; This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP). The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, becauses much of their income is derived from copyright royalties, or (b) SLAPP laws, because anti-SLAPP laws, which exist in some jurisdictions but not others,&lt;ref&gt;[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the &quot;JAWBONE act&quot;, to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on &quot;[[Foundation for Individual Rights and Expression]]&quot;, accessed 2026-10-16.&lt;/ref&gt; limit the power of major corporations, which provide most of the money for the media. 

Similarly Graves (2023) asked, &quot;Do copyrights and paywalls on refereed academic journals violate the US constitution?&quot; No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.&lt;ref&gt;Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on &quot;[[Wikimedia concerns with European copyright rules including AI and scientific research]]&quot;. That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).&lt;/ref&gt;

=== Industrial Revolution ===

There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. 

Mokyr (2017, p.  3) says, &quot;The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society.&quot; He described &quot;three cultural elements&quot; required for &quot;sustainable economic growth propelled by technological progress&quot;: (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. &quot;[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.&lt;ref&gt;Mokyr (2017, pp. 19-20).&lt;/ref&gt; Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, &quot;The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution.&quot; 

Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, &quot;European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?&quot; Aghion et al. (2021, p. 20) describe the &quot;first Industrial Revolution&quot; as having been triggered by &quot;the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866.&quot;&lt;ref&gt;The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.&lt;/ref&gt;

The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not &quot;phases of growth and decline&quot; with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. 

Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, &quot;the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward.&quot; ... However, &quot;the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant to thousand or seven thousand years previously.&quot; (chapter 5) They also claim that, &quot;English national production per capita doubled from 1500 to 1700&quot;, (chapter 5), and &quot;Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root.&quot; (p. 45, chapter 2)

Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. 

Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the &quot;Old Pretender&quot;, a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. 

When Queen Anne died in 1702, she was succeeded by George I. His parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, &quot;and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts&quot;, according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs moved to confiscate &quot;[[w:Commons|commons]]&quot;, land whose use had been traditionally shared by commoners, and give to nobles. The Levellers had been excluded from the government of Lord Protector Cromwell, but the spirit of levelling still stalked the land. Some commoners joined &quot;Blacks&quot;, so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.&lt;ref&gt;Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on &quot;[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.&lt;/ref&gt; 

But not all accused were summarily executed. In 1724 &quot;John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized&quot; with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.&lt;ref&gt;Acemoglu and Robinson (2012, pp. 304-305).&lt;/ref&gt; 

These kinds of actions by the parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded &quot;universal [adult male] suffrage&quot; and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, &quot;The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The Manchester Observer called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... .&quot; And the British government placed enough other limits on its power that enough other commoners were allowed to became successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. 

== In sum ==

The above suggests that the rate of economic growth changes with either change in administration -- a new head of state -- or some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. 

However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).&lt;ref&gt;Graves (2025) includes an analysis of the data in Neff and Pickard (2024).&lt;/ref&gt; 

== Caveat ==

The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  

== Notes ==
{{reflist}}

== Bibliography ==

* &lt;!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)--&gt;{{cite Q|Q85764011}}
* &lt;!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)--&gt;{{cite Q|Q141241291}}
* &lt;!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)--&gt;{{cite Q|Q125292212}}
* &lt;!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)--&gt;{{cite Q|Q7997840}} 
* &lt;!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)--&gt;{{cite Q|Q137641358}}
* &lt;!--Ajzenman, Nicolas (29 January 2023). &quot;Migrants don't cause crime rates to increase — but false perceptions endure anyway&quot;. The Conversation.--&gt;{{cite Q|Q141758664}}
* &lt;!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) &quot;European Immigrants and the United States’ Rise to the Technological Frontier&quot;--&gt;{{cite Q|Q141678287}}
* &lt;!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer--&gt;{{cite Q|Q100216001}}

* &lt;!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) &quot;Maddison style estimates of the evolution of the world economy: A new 2023 update&quot;, Journal of Economic Surveys, 1-41--&gt;{{cite Q|Q126723821}}
* &lt;!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__&gt;{{cite Q|Q57945943}}
* &lt;!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia--&gt;{{cite Q|Q141759196}}
* &lt;!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition--&gt;{{cite Q|Q141156783}}
* &lt;!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies--&gt;{{cite Q|Q141158362}}
* &lt;!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)--&gt;{{cite Q|Q136227988}}
* &lt;!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) &quot;The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration--&gt;{{cite Q|Q55932800}}
* &lt;!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)--&gt;{{cite Q|Q132855526}}
* &lt;!--Graves (2023-03-21)  Do copyrights and paywalls on academic journals violate the US Constitution?--&gt;{{cite Q|Q126116187}}
* &lt;!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.--&gt;{{cite Q|Q137188993}}
* &lt;!-- Historian, USPS (2010) Postage Rates for Periodicals --&gt;{{cite Q|Q112167199}}
* &lt;!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse--&gt;{{cite Q|Q54641943}}
* &lt;!--Volker Leppin and Timothy J. Wengert (2015) &quot;Sources for and against the Posting of the Ninety-Five Theses&quot;--&gt;{{cite Q|Q141737347}}
* &lt;!--Lawrence Lessig (2004) Free Culture--&gt;{{cite Q|Q830526}}
* &lt;!--Olivier Marie and Paolo Pinotti (2024-02-01) &quot;Immigration and Crime: An International Perspective&quot;, Journal of Economic Perspectives. 38 (1): 181–200--&gt;{{cite Q|Q128434874}}
* &lt;!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). &quot;
Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime&quot;
. Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.--&gt;{{cite Q|Q55932802}}
* &lt;!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) --&gt;{{cite Q|Q104888067}}.
* &lt;!-- Robert W. McChesney; John Nichols (2016). People get ready--&gt;{{cite Q|Q87619174}}
* &lt;!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)--&gt;{{cite Q|Q136118590}}
* &lt;!--Ashley N. Muchow &amp; Taisiia Stanishevska (2026) &quot;From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest&quot;, Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)--&gt;{{cite Q|Q141760694}}
* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* &lt;!--John Hely Owen (1938)  War at Sea Under Queen Anne 1702–1708--&gt;{{cite Q|Q141757101}}
* &lt;!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation--&gt;{{cite Q|Q141761223}}
* &lt;!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain--&gt;{{cite Q|Q141761849}}
* &lt;!--Nick Roll (2017-07-16) &quot;Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.--&gt;{{cite Q|Q141735231}}
* &lt;!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)--&gt;{{cite Q|Q137669960}}
* &lt;!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)--&gt;{{cite Q|Q137669987}}
* &lt;!--J. L. van Zanden  and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30--&gt;{{cite Q|Q137670058}} 
* &lt;!--Tom K. Wong (2017-01-26) &quot;The Effects of Sanctuary Policies on Crime and the Economy&quot;--&gt;{{cite Q|Q98775875}}

[[Category:Original research]]
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:''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].''
:''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  
::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]''

== Abstract ==

This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. 

== Maddison Historical Statistics == 

[[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).&lt;ref&gt;See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.&lt;/ref&gt;'']]

The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. 

When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.&lt;ref&gt;Bolt and van Zanden (2024).&lt;/ref&gt; This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are those used in the Maddison data, which match [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]].) 

We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of North Sea oil. With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. 

This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. 

== Nobel economists and others ==

Banerjee and Duflo (2019, p. 207) said, &quot;despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive.&quot; That appeared shortly before they won the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. 

While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, &quot;The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services.&quot; In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. 

Mokyr (2017, p. 255) also said that, &quot;intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished.&quot; That resistance, he suggested, drives &quot;the empirical regularity that no society remains at the cutting edge of technological creativity for very long&quot;.&lt;ref&gt;Mokyr (2017, p. 260).&lt;/ref&gt; This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US and the UK, visible in Figure 1.  

Mokyr (2017, p. 60) also mentioned &quot;entrepreneurs of hate&quot;, who convince others to dislike some group in a way that may benefit those &quot;entrepreneurs&quot; and major media organizations, who promote such &quot;entrepreneurs&quot; to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.&lt;ref&gt;See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and [[Managing the good and the evils of social media]], accessed 2026-10-14.&lt;/ref&gt; When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites.  

Successful entrepreneurs of hate who demonize immigrants are featured in news coverage that portrays immigrants as criminal threats, when the threats are nonexistent&lt;ref&gt;Muchow and Stanishevska (2026); Ajzenman(2023).&lt;/ref&gt; or result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.&lt;ref&gt;Marie and Paolo (2024). See also the Wikipedia article on &quot;[[w:Immigration and crime|Immigration and crime]]&quot;, accessed 2026-10-12.&lt;/ref&gt; Mixed results are reported by research on sanctuary jurisdictions: Some studies show no impact.&lt;ref&gt;Martínez et al. (2017).&lt;/ref&gt; Most others show less crime with stronger economies, lower unemployment, higher median incomes, less poverty, less reliance on public assistance, etc.&lt;ref&gt;Wong (2017). See also the Wikipedia article on &quot;[[w:Sanctuary city|sanctuary city]]&quot;, accessed 2026-10-12.&lt;/ref&gt; In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities were ''more'' prone to crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded &quot;that sanctuary policies have no effect on crime rates, despite narratives to the contrary.&quot;&lt;ref&gt;Roll (2017); Gonzalez O’Brien, et al. (2017).&lt;/ref&gt;

We next discuss competition in media markets before discussing immigrants further. 

=== Diversity of ownership of the major media === 

Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations, and in hierarchical societies the religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate the designated evil others and give increasing shares of what they produce so the secular elites would &quot;protect&quot; them in wars against the designated evil others.

Acemoglu and Robinson (2012, p. 461) said, &quot;Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power ... in the United States [and] ... in the context of British democratization. Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799] ... .&quot; ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) 

But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.&lt;ref&gt;Hendrix (2015, p. 64), quoted from the Wikipedia article on the &quot;[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand&lt;ref&gt;Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; and was much more popular than Tetzel's.&lt;ref&gt;Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; 

Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the Church of England, denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature,&lt;ref&gt;Raymond (2006), cited from the Wikipedia article on &quot;[[w:Pamphlet war|pamphlet war]]&quot;, accessed 2026-10-15.&lt;/ref&gt; theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.&lt;ref&gt;Hibbert et al. (2010, p. 928), cited from the Wikipedia article on &quot;[[w:Henry VIII|Henry VIII]]&quot;, accessed 2026-10-15.&lt;/ref&gt;

A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.&lt;ref&gt;Foxley (2013, p. 207), cited from the Wikipedia article on &quot;[[w:Levellers|Levellers]], accessed 2026-10-15.&lt;/ref&gt; However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that became the US over a century later. 

That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792&lt;ref&gt;Wikipedia &quot;[[w:Postal Service Act|Postal Service Act]]&quot;, accessed 2023-07-11.&lt;/ref&gt; made a major contribution to making the US what it is today.  Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.&lt;ref&gt;Historian, USPS (2010).&lt;/ref&gt; McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.&lt;ref name=McC-N2010&gt;McChesney and Nichols (2010, pp. 310-311, note 88).&lt;/ref&gt; 

During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;John (1995). See also the interview with him at &quot;[[Media concentration per Columbia History Professor Richard John]]&quot; on Wikiversity, accessed 2026-10-12.&lt;/ref&gt; In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.&lt;ref&gt;The &quot;6 percent per year&quot; growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in &quot;[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; on Wikiversity, accessed 2026-10-13.&lt;/ref&gt; 

One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. 

FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, which the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.&lt;ref&gt;This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on &quot;[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; in Wikiversity, accessed 2026-10-13.&lt;/ref&gt;

But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, &quot;the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred.&quot; They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. 

Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.&lt;ref&gt;On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of &quot;influencers&quot; by for-profit social media as essentially unleashed &quot;a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures.&quot; In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.&lt;/ref&gt; 

And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2021, p. 139) noted, &quot;In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%.  The top rate was then cut in half, with the announced objective of boosting growth.  But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.&quot;

=== Immigrants === 

We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. [[w:English Council of State|Lord Protector Cromwell]], who replaced Charles I, refused to authorize as many monopolies as his predecessors, presumably supported by the growing number of independent publishers of pamphlets, books, and newspapers mentioned above. He also encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. 

But Mokyr is not alone in proclaiming the contributions of immigrants to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how &quot;the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology.&quot;

Aghion et al. (2021, p. 292) also discuss (a) &quot;a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita&quot; and (b) the overrepresentation of immigrants in patent applications.&lt;ref&gt;e.g., Aghion et al. (2026, pp. 266-267).&lt;/ref&gt; However, [[w:Dean Baker|Baker]] (2016, pp. 77-78) claimed that &quot;over the last four decades ... stronger patent protection seems to be associated with slower growth,&quot; seemingly the opposite of the claim just quoted from Aghion et al. 

Anther example of how technology winners protect their status against competition is the [[w:Supreme Court of the United States|US Supreme Court]] decision in ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]''. [[w:Lawrence Lessig|Lessig]], who represented the plaintiff in that case, asked how could extending the copyright on existing works &quot;promote the Progress of Science and useful Arts&quot;, as required by the [[w:Copyright Clause|Copyright Clause]] of the US Constitution? Lessig lost that case. His (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to limit rather than &quot;promote the Progress of Science and useful Arts&quot;. This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000, which would bankrupt his parents and which they could not recover even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.&lt;ref&gt;Lessig (2004, p. 42).&lt;/ref&gt; This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP). The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, becauses much of their income is derived from copyright royalties, or (b) SLAPP laws, because anti-SLAPP laws, which exist in some jurisdictions but not others,&lt;ref&gt;[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the &quot;JAWBONE act&quot;, to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on &quot;[[Foundation for Individual Rights and Expression]]&quot;, accessed 2026-10-16.&lt;/ref&gt; limit the power of major corporations, which provide most of the money for the media. 

Similarly Graves (2023) asked, &quot;Do copyrights and paywalls on refereed academic journals violate the US constitution?&quot; No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.&lt;ref&gt;Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on &quot;[[Wikimedia concerns with European copyright rules including AI and scientific research]]&quot;. That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).&lt;/ref&gt;

=== Industrial Revolution ===

There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. 

Mokyr (2017, p.  3) says, &quot;The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society.&quot; He described &quot;three cultural elements&quot; required for &quot;sustainable economic growth propelled by technological progress&quot;: (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. &quot;[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.&lt;ref&gt;Mokyr (2017, pp. 19-20).&lt;/ref&gt; Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, &quot;The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution.&quot; 

Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, &quot;European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?&quot; Aghion et al. (2021, p. 20) describe the &quot;first Industrial Revolution&quot; as having been triggered by &quot;the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866.&quot;&lt;ref&gt;The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.&lt;/ref&gt;

The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not &quot;phases of growth and decline&quot; with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. 

Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, &quot;the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward.&quot; ... However, &quot;the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant to thousand or seven thousand years previously.&quot; (chapter 5) They also claim that, &quot;English national production per capita doubled from 1500 to 1700&quot;, (chapter 5), and &quot;Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root.&quot; (p. 45, chapter 2)

Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. 

Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the &quot;Old Pretender&quot;, a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. 

When Queen Anne died in 1702, she was succeeded by George I. His parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, &quot;and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts&quot;, according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs moved to confiscate &quot;[[w:Commons|commons]]&quot;, land whose use had been traditionally shared by commoners, and give to nobles. The Levellers had been excluded from the government of Lord Protector Cromwell, but the spirit of levelling still stalked the land. Some commoners joined &quot;Blacks&quot;, so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.&lt;ref&gt;Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on &quot;[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.&lt;/ref&gt; 

But not all accused were summarily executed. In 1724 &quot;John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized&quot; with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.&lt;ref&gt;Acemoglu and Robinson (2012, pp. 304-305).&lt;/ref&gt; 

These kinds of actions by the parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded &quot;universal [adult male] suffrage&quot; and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, &quot;The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The Manchester Observer called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... .&quot; And the British government placed enough other limits on its power that enough other commoners were allowed to became successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. 

== In sum ==

The above suggests that the rate of economic growth changes with either change in administration -- a new head of state -- or some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. 

However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).&lt;ref&gt;Graves (2025) includes an analysis of the data in Neff and Pickard (2024).&lt;/ref&gt; 

== Caveat ==

The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  

== Notes ==
{{reflist}}

== Bibliography ==

* &lt;!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)--&gt;{{cite Q|Q85764011}}
* &lt;!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)--&gt;{{cite Q|Q141241291}}
* &lt;!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)--&gt;{{cite Q|Q125292212}}
* &lt;!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)--&gt;{{cite Q|Q7997840}} 
* &lt;!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)--&gt;{{cite Q|Q137641358}}
* &lt;!--Ajzenman, Nicolas (29 January 2023). &quot;Migrants don't cause crime rates to increase — but false perceptions endure anyway&quot;. The Conversation.--&gt;{{cite Q|Q141758664}}
* &lt;!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) &quot;European Immigrants and the United States’ Rise to the Technological Frontier&quot;--&gt;{{cite Q|Q141678287}}
* &lt;!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer--&gt;{{cite Q|Q100216001}}

* &lt;!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) &quot;Maddison style estimates of the evolution of the world economy: A new 2023 update&quot;, Journal of Economic Surveys, 1-41--&gt;{{cite Q|Q126723821}}
* &lt;!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__&gt;{{cite Q|Q57945943}}
* &lt;!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia--&gt;{{cite Q|Q141759196}}
* &lt;!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition--&gt;{{cite Q|Q141156783}}
* &lt;!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies--&gt;{{cite Q|Q141158362}}
* &lt;!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)--&gt;{{cite Q|Q136227988}}
* &lt;!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) &quot;The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration--&gt;{{cite Q|Q55932800}}
* &lt;!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)--&gt;{{cite Q|Q132855526}}
* &lt;!--Graves (2023-03-21)  Do copyrights and paywalls on academic journals violate the US Constitution?--&gt;{{cite Q|Q126116187}}
* &lt;!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.--&gt;{{cite Q|Q137188993}}
* &lt;!-- Historian, USPS (2010) Postage Rates for Periodicals --&gt;{{cite Q|Q112167199}}
* &lt;!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse--&gt;{{cite Q|Q54641943}}
* &lt;!--Volker Leppin and Timothy J. Wengert (2015) &quot;Sources for and against the Posting of the Ninety-Five Theses&quot;--&gt;{{cite Q|Q141737347}}
* &lt;!--Lawrence Lessig (2004) Free Culture--&gt;{{cite Q|Q830526}}
* &lt;!--Olivier Marie and Paolo Pinotti (2024-02-01) &quot;Immigration and Crime: An International Perspective&quot;, Journal of Economic Perspectives. 38 (1): 181–200--&gt;{{cite Q|Q128434874}}
* &lt;!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). &quot;
Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime&quot;
. Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.--&gt;{{cite Q|Q55932802}}
* &lt;!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) --&gt;{{cite Q|Q104888067}}.
* &lt;!-- Robert W. McChesney; John Nichols (2016). People get ready--&gt;{{cite Q|Q87619174}}
* &lt;!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)--&gt;{{cite Q|Q136118590}}
* &lt;!--Ashley N. Muchow &amp; Taisiia Stanishevska (2026) &quot;From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest&quot;, Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)--&gt;{{cite Q|Q141760694}}
* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* &lt;!--John Hely Owen (1938)  War at Sea Under Queen Anne 1702–1708--&gt;{{cite Q|Q141757101}}
* &lt;!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation--&gt;{{cite Q|Q141761223}}
* &lt;!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain--&gt;{{cite Q|Q141761849}}
* &lt;!--Nick Roll (2017-07-16) &quot;Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.--&gt;{{cite Q|Q141735231}}
* &lt;!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)--&gt;{{cite Q|Q137669960}}
* &lt;!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)--&gt;{{cite Q|Q137669987}}
* &lt;!--J. L. van Zanden  and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30--&gt;{{cite Q|Q137670058}} 
* &lt;!--Tom K. Wong (2017-01-26) &quot;The Effects of Sanctuary Policies on Crime and the Economy&quot;--&gt;{{cite Q|Q98775875}}

[[Category:Original research]]
[[Category:Research]]
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[[Category:Political science]]
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      <text bytes="45483" sha1="rcko0mwbr9ftn6j1c7w03b6fea9k2lb" xml:space="preserve">{{Research project}} 
:''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].''
:''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  
::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]''

== Abstract ==

This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. 

== Maddison Historical Statistics == 

[[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).&lt;ref&gt;See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.&lt;/ref&gt;'']]

The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. 

When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.&lt;ref&gt;Bolt and van Zanden (2024).&lt;/ref&gt; This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are those used in the Maddison data, which match [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]].) 

We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of North Sea oil. With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. 

This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. 

== Nobel economists and others ==

Banerjee and Duflo (2019, p. 207) said, &quot;despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive.&quot; That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. 

While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, &quot;The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services.&quot; In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. 

Mokyr (2017, p. 255) also said that, &quot;intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished.&quot; That resistance, he suggested, drives &quot;the empirical regularity that no society remains at the cutting edge of technological creativity for very long&quot;.&lt;ref&gt;Mokyr (2017, p. 260).&lt;/ref&gt; This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US and the UK, visible in Figure 1.  

Mokyr (2017, p. 60) also mentioned &quot;entrepreneurs of hate&quot;, who convince others to dislike some group in a way that may benefit those &quot;entrepreneurs&quot; and major media organizations, who promote such &quot;entrepreneurs&quot; to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.&lt;ref&gt;See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and [[Managing the good and the evils of social media]], accessed 2026-10-14.&lt;/ref&gt; When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites.  

Successful entrepreneurs of hate who demonize immigrants are featured in news coverage that portrays immigrants as criminal threats, when the threats are nonexistent&lt;ref&gt;Muchow and Stanishevska (2026); Ajzenman(2023).&lt;/ref&gt; or result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.&lt;ref&gt;Marie and Paolo (2024). See also the Wikipedia article on &quot;[[w:Immigration and crime|Immigration and crime]]&quot;, accessed 2026-10-12.&lt;/ref&gt; Mixed results are reported by research on sanctuary jurisdictions: Some studies show no impact.&lt;ref&gt;Martínez et al. (2017).&lt;/ref&gt; Most others show less crime with stronger economies, lower unemployment, higher median incomes, less poverty, less reliance on public assistance, etc.&lt;ref&gt;Wong (2017). See also the Wikipedia article on &quot;[[w:Sanctuary city|sanctuary city]]&quot;, accessed 2026-10-12.&lt;/ref&gt; In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities were ''more'' prone to crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded &quot;that sanctuary policies have no effect on crime rates, despite narratives to the contrary.&quot;&lt;ref&gt;Roll (2017); Gonzalez O’Brien, et al. (2017).&lt;/ref&gt;

We next discuss competition in media markets before discussing immigrants further. 

=== Diversity of ownership of the major media === 

Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations, and in hierarchical societies the religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate the designated evil others and give increasing shares of what they produce so the secular elites would &quot;protect&quot; them in wars against the designated evil others.

Acemoglu and Robinson (2012, p. 461) said, &quot;Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power ... in the United States [and] ... in the context of British democratization. Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799] ... .&quot; ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) 

But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.&lt;ref&gt;Hendrix (2015, p. 64), quoted from the Wikipedia article on the &quot;[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand&lt;ref&gt;Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; and was much more popular than Tetzel's.&lt;ref&gt;Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; 

Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the Church of England, denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature,&lt;ref&gt;Raymond (2006), cited from the Wikipedia article on &quot;[[w:Pamphlet war|pamphlet war]]&quot;, accessed 2026-10-15.&lt;/ref&gt; theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.&lt;ref&gt;Hibbert et al. (2010, p. 928), cited from the Wikipedia article on &quot;[[w:Henry VIII|Henry VIII]]&quot;, accessed 2026-10-15.&lt;/ref&gt;

A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.&lt;ref&gt;Foxley (2013, p. 207), cited from the Wikipedia article on &quot;[[w:Levellers|Levellers]], accessed 2026-10-15.&lt;/ref&gt; However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that became the US over a century later. 

That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792&lt;ref&gt;Wikipedia &quot;[[w:Postal Service Act|Postal Service Act]]&quot;, accessed 2023-07-11.&lt;/ref&gt; made a major contribution to making the US what it is today.  Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.&lt;ref&gt;Historian, USPS (2010).&lt;/ref&gt; McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.&lt;ref name=McC-N2010&gt;McChesney and Nichols (2010, pp. 310-311, note 88).&lt;/ref&gt; 

During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;John (1995). See also the interview with him at &quot;[[Media concentration per Columbia History Professor Richard John]]&quot; on Wikiversity, accessed 2026-10-12.&lt;/ref&gt; In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.&lt;ref&gt;The &quot;6 percent per year&quot; growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in &quot;[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; on Wikiversity, accessed 2026-10-13.&lt;/ref&gt; 

One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. 

FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, which the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.&lt;ref&gt;This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on &quot;[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; in Wikiversity, accessed 2026-10-13.&lt;/ref&gt;

But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, &quot;the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred.&quot; They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. 

Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.&lt;ref&gt;On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of &quot;influencers&quot; by for-profit social media as essentially unleashed &quot;a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures.&quot; In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.&lt;/ref&gt; 

And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2021, p. 139) noted, &quot;In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%.  The top rate was then cut in half, with the announced objective of boosting growth.  But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.&quot;

=== Immigrants === 

We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. [[w:English Council of State|Lord Protector Cromwell]], who replaced Charles I, refused to authorize as many monopolies as his predecessors, presumably supported by the growing number of independent publishers of pamphlets, books, and newspapers mentioned above. He also encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. 

But Mokyr is not alone in proclaiming the contributions of immigrants to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how &quot;the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology.&quot;

Aghion et al. (2021, p. 292) also discuss (a) &quot;a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita&quot; and (b) the overrepresentation of immigrants in patent applications.&lt;ref&gt;e.g., Aghion et al. (2026, pp. 266-267).&lt;/ref&gt; However, [[w:Dean Baker|Baker]] (2016, pp. 77-78) claimed that &quot;over the last four decades ... stronger patent protection seems to be associated with slower growth,&quot; seemingly the opposite of the claim just quoted from Aghion et al. 

Anther example of how technology winners protect their status against competition is the [[w:Supreme Court of the United States|US Supreme Court]] decision in ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]''. [[w:Lawrence Lessig|Lessig]], who represented the plaintiff in that case, asked how could extending the copyright on existing works &quot;promote the Progress of Science and useful Arts&quot;, as required by the [[w:Copyright Clause|Copyright Clause]] of the US Constitution? Lessig lost that case. His (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to limit rather than &quot;promote the Progress of Science and useful Arts&quot;. This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000, which would bankrupt his parents and which they could not recover even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.&lt;ref&gt;Lessig (2004, p. 42).&lt;/ref&gt; This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP). The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, becauses much of their income is derived from copyright royalties, or (b) SLAPP laws, because anti-SLAPP laws, which exist in some jurisdictions but not others,&lt;ref&gt;[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the &quot;JAWBONE act&quot;, to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on &quot;[[Foundation for Individual Rights and Expression]]&quot;, accessed 2026-10-16.&lt;/ref&gt; limit the power of major corporations, which provide most of the money for the media. 

Similarly Graves (2023) asked, &quot;Do copyrights and paywalls on refereed academic journals violate the US constitution?&quot; No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.&lt;ref&gt;Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on &quot;[[Wikimedia concerns with European copyright rules including AI and scientific research]]&quot;. That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).&lt;/ref&gt;

=== Industrial Revolution ===

There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. 

Mokyr (2017, p.  3) says, &quot;The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society.&quot; He described &quot;three cultural elements&quot; required for &quot;sustainable economic growth propelled by technological progress&quot;: (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. &quot;[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.&lt;ref&gt;Mokyr (2017, pp. 19-20).&lt;/ref&gt; Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, &quot;The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution.&quot; 

Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, &quot;European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?&quot; Aghion et al. (2021, p. 20) describe the &quot;first Industrial Revolution&quot; as having been triggered by &quot;the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866.&quot;&lt;ref&gt;The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.&lt;/ref&gt;

The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not &quot;phases of growth and decline&quot; with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. 

Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, &quot;the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward.&quot; ... However, &quot;the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant to thousand or seven thousand years previously.&quot; (chapter 5) They also claim that, &quot;English national production per capita doubled from 1500 to 1700&quot;, (chapter 5), and &quot;Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root.&quot; (p. 45, chapter 2)

Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. 

Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the &quot;Old Pretender&quot;, a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. 

When Queen Anne died in 1702, she was succeeded by George I. His parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, &quot;and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts&quot;, according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs moved to confiscate &quot;[[w:Commons|commons]]&quot;, land whose use had been traditionally shared by commoners, and give to nobles. The Levellers had been excluded from the government of Lord Protector Cromwell, but the spirit of levelling still stalked the land. Some commoners joined &quot;Blacks&quot;, so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.&lt;ref&gt;Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on &quot;[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.&lt;/ref&gt; 

But not all accused were summarily executed. In 1724 &quot;John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized&quot; with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.&lt;ref&gt;Acemoglu and Robinson (2012, pp. 304-305).&lt;/ref&gt; 

These kinds of actions by the parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded &quot;universal [adult male] suffrage&quot; and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, &quot;The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The Manchester Observer called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... .&quot; And the British government placed enough other limits on its power that enough other commoners were allowed to became successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. 

== In sum ==

The above suggests that the rate of economic growth changes with either change in administration -- a new head of state -- or some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. 

However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).&lt;ref&gt;Graves (2025) includes an analysis of the data in Neff and Pickard (2024).&lt;/ref&gt; 

== Caveat ==

The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  

== Notes ==
{{reflist}}

== Bibliography ==

* &lt;!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)--&gt;{{cite Q|Q85764011}}
* &lt;!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)--&gt;{{cite Q|Q141241291}}
* &lt;!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)--&gt;{{cite Q|Q125292212}}
* &lt;!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)--&gt;{{cite Q|Q7997840}} 
* &lt;!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)--&gt;{{cite Q|Q137641358}}
* &lt;!--Ajzenman, Nicolas (29 January 2023). &quot;Migrants don't cause crime rates to increase — but false perceptions endure anyway&quot;. The Conversation.--&gt;{{cite Q|Q141758664}}
* &lt;!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) &quot;European Immigrants and the United States’ Rise to the Technological Frontier&quot;--&gt;{{cite Q|Q141678287}}
* &lt;!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer--&gt;{{cite Q|Q100216001}}

* &lt;!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) &quot;Maddison style estimates of the evolution of the world economy: A new 2023 update&quot;, Journal of Economic Surveys, 1-41--&gt;{{cite Q|Q126723821}}
* &lt;!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__&gt;{{cite Q|Q57945943}}
* &lt;!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia--&gt;{{cite Q|Q141759196}}
* &lt;!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition--&gt;{{cite Q|Q141156783}}
* &lt;!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies--&gt;{{cite Q|Q141158362}}
* &lt;!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)--&gt;{{cite Q|Q136227988}}
* &lt;!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) &quot;The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration--&gt;{{cite Q|Q55932800}}
* &lt;!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)--&gt;{{cite Q|Q132855526}}
* &lt;!--Graves (2023-03-21)  Do copyrights and paywalls on academic journals violate the US Constitution?--&gt;{{cite Q|Q126116187}}
* &lt;!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.--&gt;{{cite Q|Q137188993}}
* &lt;!-- Historian, USPS (2010) Postage Rates for Periodicals --&gt;{{cite Q|Q112167199}}
* &lt;!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse--&gt;{{cite Q|Q54641943}}
* &lt;!--Volker Leppin and Timothy J. Wengert (2015) &quot;Sources for and against the Posting of the Ninety-Five Theses&quot;--&gt;{{cite Q|Q141737347}}
* &lt;!--Lawrence Lessig (2004) Free Culture--&gt;{{cite Q|Q830526}}
* &lt;!--Olivier Marie and Paolo Pinotti (2024-02-01) &quot;Immigration and Crime: An International Perspective&quot;, Journal of Economic Perspectives. 38 (1): 181–200--&gt;{{cite Q|Q128434874}}
* &lt;!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). &quot;
Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime&quot;
. Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.--&gt;{{cite Q|Q55932802}}
* &lt;!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) --&gt;{{cite Q|Q104888067}}.
* &lt;!-- Robert W. McChesney; John Nichols (2016). People get ready--&gt;{{cite Q|Q87619174}}
* &lt;!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)--&gt;{{cite Q|Q136118590}}
* &lt;!--Ashley N. Muchow &amp; Taisiia Stanishevska (2026) &quot;From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest&quot;, Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)--&gt;{{cite Q|Q141760694}}
* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* &lt;!--John Hely Owen (1938)  War at Sea Under Queen Anne 1702–1708--&gt;{{cite Q|Q141757101}}
* &lt;!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation--&gt;{{cite Q|Q141761223}}
* &lt;!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain--&gt;{{cite Q|Q141761849}}
* &lt;!--Nick Roll (2017-07-16) &quot;Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.--&gt;{{cite Q|Q141735231}}
* &lt;!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)--&gt;{{cite Q|Q137669960}}
* &lt;!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)--&gt;{{cite Q|Q137669987}}
* &lt;!--J. L. van Zanden  and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30--&gt;{{cite Q|Q137670058}} 
* &lt;!--Tom K. Wong (2017-01-26) &quot;The Effects of Sanctuary Policies on Crime and the Economy&quot;--&gt;{{cite Q|Q98775875}}

[[Category:Original research]]
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:''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].''
:''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  
::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]''

== Abstract ==

This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. 

== Maddison Historical Statistics == 

[[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).&lt;ref&gt;See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.&lt;/ref&gt;'']]

The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. 

When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.&lt;ref&gt;Bolt and van Zanden (2024).&lt;/ref&gt; This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are those used in the Maddison data, which match [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]].) 

We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of North Sea oil. With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. 

This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. 

== Nobel economists and others ==

Banerjee and Duflo (2019, p. 207) said, &quot;despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive.&quot; That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. 

While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, &quot;The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services.&quot; In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. 

Mokyr (2017, p. 255) also said that, &quot;intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished.&quot; That resistance, he suggested, drives &quot;the empirical regularity that no society remains at the cutting edge of technological creativity for very long&quot;.&lt;ref&gt;Mokyr (2017, p. 260).&lt;/ref&gt; This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1.  

Mokyr (2017, p. 60) also mentioned &quot;entrepreneurs of hate&quot;, who convince others to dislike some group in a way that may benefit those &quot;entrepreneurs&quot; and major media organizations, who promote such &quot;entrepreneurs&quot; to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.&lt;ref&gt;See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and [[Managing the good and the evils of social media]], accessed 2026-10-14.&lt;/ref&gt; When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites.  

Successful entrepreneurs of hate who demonize immigrants are featured in news coverage that portrays immigrants as criminal threats, when the threats are nonexistent&lt;ref&gt;Muchow and Stanishevska (2026); Ajzenman(2023).&lt;/ref&gt; or result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.&lt;ref&gt;Marie and Paolo (2024). See also the Wikipedia article on &quot;[[w:Immigration and crime|Immigration and crime]]&quot;, accessed 2026-10-12.&lt;/ref&gt; Mixed results are reported by research on sanctuary jurisdictions: Some studies show no impact.&lt;ref&gt;Martínez et al. (2017).&lt;/ref&gt; Most others show less crime with stronger economies, lower unemployment, higher median incomes, less poverty, less reliance on public assistance, etc.&lt;ref&gt;Wong (2017). See also the Wikipedia article on &quot;[[w:Sanctuary city|sanctuary city]]&quot;, accessed 2026-10-12.&lt;/ref&gt; In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities were ''more'' prone to crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded &quot;that sanctuary policies have no effect on crime rates, despite narratives to the contrary.&quot;&lt;ref&gt;Roll (2017); Gonzalez O’Brien, et al. (2017).&lt;/ref&gt;

We next discuss competition in media markets before discussing immigrants further. 

=== Diversity of ownership of the major media === 

Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations, and in hierarchical societies the religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate the designated evil others and give increasing shares of what they produce so the secular elites would &quot;protect&quot; them in wars against the designated evil others.

Acemoglu and Robinson (2012, p. 461) said, &quot;Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power ... in the United States [and] ... in the context of British democratization. Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799] ... .&quot; ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) 

But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.&lt;ref&gt;Hendrix (2015, p. 64), quoted from the Wikipedia article on the &quot;[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand&lt;ref&gt;Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; and was much more popular than Tetzel's.&lt;ref&gt;Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; 

Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the Church of England, denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature,&lt;ref&gt;Raymond (2006), cited from the Wikipedia article on &quot;[[w:Pamphlet war|pamphlet war]]&quot;, accessed 2026-10-15.&lt;/ref&gt; theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.&lt;ref&gt;Hibbert et al. (2010, p. 928), cited from the Wikipedia article on &quot;[[w:Henry VIII|Henry VIII]]&quot;, accessed 2026-10-15.&lt;/ref&gt;

A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.&lt;ref&gt;Foxley (2013, p. 207), cited from the Wikipedia article on &quot;[[w:Levellers|Levellers]], accessed 2026-10-15.&lt;/ref&gt; However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that became the US over a century later. 

That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792&lt;ref&gt;Wikipedia &quot;[[w:Postal Service Act|Postal Service Act]]&quot;, accessed 2023-07-11.&lt;/ref&gt; made a major contribution to making the US what it is today.  Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.&lt;ref&gt;Historian, USPS (2010).&lt;/ref&gt; McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.&lt;ref name=McC-N2010&gt;McChesney and Nichols (2010, pp. 310-311, note 88).&lt;/ref&gt; 

During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;John (1995). See also the interview with him at &quot;[[Media concentration per Columbia History Professor Richard John]]&quot; on Wikiversity, accessed 2026-10-12.&lt;/ref&gt; In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.&lt;ref&gt;The &quot;6 percent per year&quot; growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in &quot;[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; on Wikiversity, accessed 2026-10-13.&lt;/ref&gt; 

One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. 

FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, which the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.&lt;ref&gt;This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on &quot;[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; in Wikiversity, accessed 2026-10-13.&lt;/ref&gt;

But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, &quot;the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred.&quot; They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. 

Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.&lt;ref&gt;On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of &quot;influencers&quot; by for-profit social media as essentially unleashed &quot;a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures.&quot; In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.&lt;/ref&gt; 

And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2021, p. 139) noted, &quot;In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%.  The top rate was then cut in half, with the announced objective of boosting growth.  But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.&quot;

=== Immigrants === 

We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. [[w:English Council of State|Lord Protector Cromwell]], who replaced Charles I, refused to authorize as many monopolies as his predecessors, presumably supported by the growing number of independent publishers of pamphlets, books, and newspapers mentioned above. He also encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. 

But Mokyr is not alone in proclaiming the contributions of immigrants to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how &quot;the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology.&quot;

Aghion et al. (2021, p. 292) also discuss (a) &quot;a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita&quot; and (b) the overrepresentation of immigrants in patent applications.&lt;ref&gt;e.g., Aghion et al. (2026, pp. 266-267).&lt;/ref&gt; However, [[w:Dean Baker|Baker]] (2016, pp. 77-78) claimed that &quot;over the last four decades ... stronger patent protection seems to be associated with slower growth,&quot; seemingly the opposite of the claim just quoted from Aghion et al. 

Anther example of how technology winners protect their status against competition is the [[w:Supreme Court of the United States|US Supreme Court]] decision in ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]''. [[w:Lawrence Lessig|Lessig]], who represented the plaintiff in that case, asked how could extending the copyright on existing works &quot;promote the Progress of Science and useful Arts&quot;, as required by the [[w:Copyright Clause|Copyright Clause]] of the US Constitution? Lessig lost that case. His (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to limit rather than &quot;promote the Progress of Science and useful Arts&quot;. This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000, which would bankrupt his parents and which they could not recover even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.&lt;ref&gt;Lessig (2004, p. 42).&lt;/ref&gt; This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP). The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, becauses much of their income is derived from copyright royalties, or (b) SLAPP laws, because anti-SLAPP laws, which exist in some jurisdictions but not others,&lt;ref&gt;[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the &quot;JAWBONE act&quot;, to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on &quot;[[Foundation for Individual Rights and Expression]]&quot;, accessed 2026-10-16.&lt;/ref&gt; limit the power of major corporations, which provide most of the money for the media. 

Similarly Graves (2023) asked, &quot;Do copyrights and paywalls on refereed academic journals violate the US constitution?&quot; No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.&lt;ref&gt;Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on &quot;[[Wikimedia concerns with European copyright rules including AI and scientific research]]&quot;. That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).&lt;/ref&gt;

=== Industrial Revolution ===

There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. 

Mokyr (2017, p.  3) says, &quot;The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society.&quot; He described &quot;three cultural elements&quot; required for &quot;sustainable economic growth propelled by technological progress&quot;: (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. &quot;[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.&lt;ref&gt;Mokyr (2017, pp. 19-20).&lt;/ref&gt; Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, &quot;The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution.&quot; 

Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, &quot;European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?&quot; Aghion et al. (2021, p. 20) describe the &quot;first Industrial Revolution&quot; as having been triggered by &quot;the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866.&quot;&lt;ref&gt;The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.&lt;/ref&gt;

The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not &quot;phases of growth and decline&quot; with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. 

Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, &quot;the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward.&quot; ... However, &quot;the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant to thousand or seven thousand years previously.&quot; (chapter 5) They also claim that, &quot;English national production per capita doubled from 1500 to 1700&quot;, (chapter 5), and &quot;Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root.&quot; (p. 45, chapter 2)

Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. 

Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the &quot;Old Pretender&quot;, a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. 

When Queen Anne died in 1702, she was succeeded by George I. His parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, &quot;and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts&quot;, according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs moved to confiscate &quot;[[w:Commons|commons]]&quot;, land whose use had been traditionally shared by commoners, and give to nobles. The Levellers had been excluded from the government of Lord Protector Cromwell, but the spirit of levelling still stalked the land. Some commoners joined &quot;Blacks&quot;, so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.&lt;ref&gt;Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on &quot;[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.&lt;/ref&gt; 

But not all accused were summarily executed. In 1724 &quot;John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized&quot; with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.&lt;ref&gt;Acemoglu and Robinson (2012, pp. 304-305).&lt;/ref&gt; 

These kinds of actions by the parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded &quot;universal [adult male] suffrage&quot; and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, &quot;The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The Manchester Observer called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... .&quot; And the British government placed enough other limits on its power that enough other commoners were allowed to became successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. 

== In sum ==

The above suggests that the rate of economic growth changes with either change in administration -- a new head of state -- or some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. 

However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).&lt;ref&gt;Graves (2025) includes an analysis of the data in Neff and Pickard (2024).&lt;/ref&gt; 

== Caveat ==

The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  

== Notes ==
{{reflist}}

== Bibliography ==

* &lt;!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)--&gt;{{cite Q|Q85764011}}
* &lt;!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)--&gt;{{cite Q|Q141241291}}
* &lt;!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)--&gt;{{cite Q|Q125292212}}
* &lt;!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)--&gt;{{cite Q|Q7997840}} 
* &lt;!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)--&gt;{{cite Q|Q137641358}}
* &lt;!--Ajzenman, Nicolas (29 January 2023). &quot;Migrants don't cause crime rates to increase — but false perceptions endure anyway&quot;. The Conversation.--&gt;{{cite Q|Q141758664}}
* &lt;!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) &quot;European Immigrants and the United States’ Rise to the Technological Frontier&quot;--&gt;{{cite Q|Q141678287}}
* &lt;!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer--&gt;{{cite Q|Q100216001}}

* &lt;!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) &quot;Maddison style estimates of the evolution of the world economy: A new 2023 update&quot;, Journal of Economic Surveys, 1-41--&gt;{{cite Q|Q126723821}}
* &lt;!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__&gt;{{cite Q|Q57945943}}
* &lt;!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia--&gt;{{cite Q|Q141759196}}
* &lt;!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition--&gt;{{cite Q|Q141156783}}
* &lt;!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies--&gt;{{cite Q|Q141158362}}
* &lt;!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)--&gt;{{cite Q|Q136227988}}
* &lt;!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) &quot;The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration--&gt;{{cite Q|Q55932800}}
* &lt;!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)--&gt;{{cite Q|Q132855526}}
* &lt;!--Graves (2023-03-21)  Do copyrights and paywalls on academic journals violate the US Constitution?--&gt;{{cite Q|Q126116187}}
* &lt;!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.--&gt;{{cite Q|Q137188993}}
* &lt;!-- Historian, USPS (2010) Postage Rates for Periodicals --&gt;{{cite Q|Q112167199}}
* &lt;!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse--&gt;{{cite Q|Q54641943}}
* &lt;!--Volker Leppin and Timothy J. Wengert (2015) &quot;Sources for and against the Posting of the Ninety-Five Theses&quot;--&gt;{{cite Q|Q141737347}}
* &lt;!--Lawrence Lessig (2004) Free Culture--&gt;{{cite Q|Q830526}}
* &lt;!--Olivier Marie and Paolo Pinotti (2024-02-01) &quot;Immigration and Crime: An International Perspective&quot;, Journal of Economic Perspectives. 38 (1): 181–200--&gt;{{cite Q|Q128434874}}
* &lt;!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). &quot;
Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime&quot;
. Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.--&gt;{{cite Q|Q55932802}}
* &lt;!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) --&gt;{{cite Q|Q104888067}}.
* &lt;!-- Robert W. McChesney; John Nichols (2016). People get ready--&gt;{{cite Q|Q87619174}}
* &lt;!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)--&gt;{{cite Q|Q136118590}}
* &lt;!--Ashley N. Muchow &amp; Taisiia Stanishevska (2026) &quot;From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest&quot;, Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)--&gt;{{cite Q|Q141760694}}
* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* &lt;!--John Hely Owen (1938)  War at Sea Under Queen Anne 1702–1708--&gt;{{cite Q|Q141757101}}
* &lt;!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation--&gt;{{cite Q|Q141761223}}
* &lt;!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain--&gt;{{cite Q|Q141761849}}
* &lt;!--Nick Roll (2017-07-16) &quot;Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.--&gt;{{cite Q|Q141735231}}
* &lt;!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)--&gt;{{cite Q|Q137669960}}
* &lt;!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)--&gt;{{cite Q|Q137669987}}
* &lt;!--J. L. van Zanden  and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30--&gt;{{cite Q|Q137670058}} 
* &lt;!--Tom K. Wong (2017-01-26) &quot;The Effects of Sanctuary Policies on Crime and the Economy&quot;--&gt;{{cite Q|Q98775875}}

[[Category:Original research]]
[[Category:Research]]
[[Category:Economics]]
[[Category:Macroeconomics]]
[[Category:Gross domestic product]]
[[Category:Economic growth]]
[[Category:Modern Monetary Theory]]
[[Category:Political science]]
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:''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].''
:''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  
::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]''

== Abstract ==

This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. 

== Maddison Historical Statistics == 

[[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).&lt;ref&gt;See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.&lt;/ref&gt;'']]

The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. 

When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.&lt;ref&gt;Bolt and van Zanden (2024).&lt;/ref&gt; This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are those used in the Maddison data, which match [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]].) 

We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of North Sea oil. With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. 

This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. 

== Nobel economists and others ==

Banerjee and Duflo (2019, p. 207) said, &quot;despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive.&quot; That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. 

While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, &quot;The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services.&quot; In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. 

Mokyr (2017, p. 255) also said that, &quot;intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished.&quot; That resistance, he suggested, drives &quot;the empirical regularity that no society remains at the cutting edge of technological creativity for very long&quot;.&lt;ref&gt;Mokyr (2017, p. 260).&lt;/ref&gt; This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1.  

Mokyr (2017, p. 60) also mentioned &quot;entrepreneurs of hate&quot;, who convince others to dislike some group in a way that may benefit those &quot;entrepreneurs&quot; and major media organizations, who promote such &quot;entrepreneurs&quot; to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.&lt;ref&gt;See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and the Wikiversity article on &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-14.&lt;/ref&gt; When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites.  

Successful entrepreneurs of hate who demonize immigrants are featured in news coverage that portrays immigrants as criminal threats, when the threats are nonexistent&lt;ref&gt;Muchow and Stanishevska (2026); Ajzenman(2023).&lt;/ref&gt; or result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.&lt;ref&gt;Marie and Paolo (2024). See also the Wikipedia article on &quot;[[w:Immigration and crime|Immigration and crime]]&quot;, accessed 2026-10-12.&lt;/ref&gt; Mixed results are reported by research on sanctuary jurisdictions: Some studies show no impact.&lt;ref&gt;Martínez et al. (2017).&lt;/ref&gt; Most others show less crime with stronger economies, lower unemployment, higher median incomes, less poverty, less reliance on public assistance, etc.&lt;ref&gt;Wong (2017). See also the Wikipedia article on &quot;[[w:Sanctuary city|sanctuary city]]&quot;, accessed 2026-10-12.&lt;/ref&gt; In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities were ''more'' prone to crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded &quot;that sanctuary policies have no effect on crime rates, despite narratives to the contrary.&quot;&lt;ref&gt;Roll (2017); Gonzalez O’Brien, et al. (2017).&lt;/ref&gt;

We next discuss competition in media markets before discussing immigrants further. 

=== Diversity of ownership of the major media === 

Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations, and in hierarchical societies the religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate the designated evil others and give increasing shares of what they produce so the secular elites would &quot;protect&quot; them in wars against the designated evil others.

Acemoglu and Robinson (2012, p. 461) said, &quot;Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power ... in the United States [and] ... in the context of British democratization. Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799] ... .&quot; ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) 

But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.&lt;ref&gt;Hendrix (2015, p. 64), quoted from the Wikipedia article on the &quot;[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand&lt;ref&gt;Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; and was much more popular than Tetzel's.&lt;ref&gt;Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; 

Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the Church of England, denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature,&lt;ref&gt;Raymond (2006), cited from the Wikipedia article on &quot;[[w:Pamphlet war|pamphlet war]]&quot;, accessed 2026-10-15.&lt;/ref&gt; theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.&lt;ref&gt;Hibbert et al. (2010, p. 928), cited from the Wikipedia article on &quot;[[w:Henry VIII|Henry VIII]]&quot;, accessed 2026-10-15.&lt;/ref&gt;

A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.&lt;ref&gt;Foxley (2013, p. 207), cited from the Wikipedia article on &quot;[[w:Levellers|Levellers]], accessed 2026-10-15.&lt;/ref&gt; However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that became the US over a century later. 

That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792&lt;ref&gt;Wikipedia &quot;[[w:Postal Service Act|Postal Service Act]]&quot;, accessed 2023-07-11.&lt;/ref&gt; made a major contribution to making the US what it is today.  Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.&lt;ref&gt;Historian, USPS (2010).&lt;/ref&gt; McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.&lt;ref name=McC-N2010&gt;McChesney and Nichols (2010, pp. 310-311, note 88).&lt;/ref&gt; 

During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;John (1995). See also the interview with him at &quot;[[Media concentration per Columbia History Professor Richard John]]&quot; on Wikiversity, accessed 2026-10-12.&lt;/ref&gt; In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.&lt;ref&gt;The &quot;6 percent per year&quot; growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in &quot;[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; on Wikiversity, accessed 2026-10-13.&lt;/ref&gt; 

One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. 

FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, which the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.&lt;ref&gt;This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on &quot;[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; in Wikiversity, accessed 2026-10-13.&lt;/ref&gt;

But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, &quot;the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred.&quot; They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. 

Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.&lt;ref&gt;On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of &quot;influencers&quot; by for-profit social media as essentially unleashed &quot;a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures.&quot; In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.&lt;/ref&gt; 

And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2021, p. 139) noted, &quot;In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%.  The top rate was then cut in half, with the announced objective of boosting growth.  But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.&quot;

=== Immigrants === 

We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. [[w:English Council of State|Lord Protector Cromwell]], who replaced Charles I, refused to authorize as many monopolies as his predecessors, presumably supported by the growing number of independent publishers of pamphlets, books, and newspapers mentioned above. He also encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. 

But Mokyr is not alone in proclaiming the contributions of immigrants to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how &quot;the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology.&quot;

Aghion et al. (2021, p. 292) also discuss (a) &quot;a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita&quot; and (b) the overrepresentation of immigrants in patent applications.&lt;ref&gt;e.g., Aghion et al. (2026, pp. 266-267).&lt;/ref&gt; However, [[w:Dean Baker|Baker]] (2016, pp. 77-78) claimed that &quot;over the last four decades ... stronger patent protection seems to be associated with slower growth,&quot; seemingly the opposite of the claim just quoted from Aghion et al. 

Anther example of how technology winners protect their status against competition is the [[w:Supreme Court of the United States|US Supreme Court]] decision in ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]''. [[w:Lawrence Lessig|Lessig]], who represented the plaintiff in that case, asked how could extending the copyright on existing works &quot;promote the Progress of Science and useful Arts&quot;, as required by the [[w:Copyright Clause|Copyright Clause]] of the US Constitution? Lessig lost that case. His (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to limit rather than &quot;promote the Progress of Science and useful Arts&quot;. This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000, which would bankrupt his parents and which they could not recover even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.&lt;ref&gt;Lessig (2004, p. 42).&lt;/ref&gt; This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP). The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, becauses much of their income is derived from copyright royalties, or (b) SLAPP laws, because anti-SLAPP laws, which exist in some jurisdictions but not others,&lt;ref&gt;[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the &quot;JAWBONE act&quot;, to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on &quot;[[Foundation for Individual Rights and Expression]]&quot;, accessed 2026-10-16.&lt;/ref&gt; limit the power of major corporations, which provide most of the money for the media. 

Similarly Graves (2023) asked, &quot;Do copyrights and paywalls on refereed academic journals violate the US constitution?&quot; No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.&lt;ref&gt;Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on &quot;[[Wikimedia concerns with European copyright rules including AI and scientific research]]&quot;. That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).&lt;/ref&gt;

=== Industrial Revolution ===

There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. 

Mokyr (2017, p.  3) says, &quot;The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society.&quot; He described &quot;three cultural elements&quot; required for &quot;sustainable economic growth propelled by technological progress&quot;: (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. &quot;[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.&lt;ref&gt;Mokyr (2017, pp. 19-20).&lt;/ref&gt; Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, &quot;The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution.&quot; 

Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, &quot;European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?&quot; Aghion et al. (2021, p. 20) describe the &quot;first Industrial Revolution&quot; as having been triggered by &quot;the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866.&quot;&lt;ref&gt;The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.&lt;/ref&gt;

The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not &quot;phases of growth and decline&quot; with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. 

Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, &quot;the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward.&quot; ... However, &quot;the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant to thousand or seven thousand years previously.&quot; (chapter 5) They also claim that, &quot;English national production per capita doubled from 1500 to 1700&quot;, (chapter 5), and &quot;Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root.&quot; (p. 45, chapter 2)

Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. 

Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the &quot;Old Pretender&quot;, a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. 

When Queen Anne died in 1702, she was succeeded by George I. His parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, &quot;and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts&quot;, according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs moved to confiscate &quot;[[w:Commons|commons]]&quot;, land whose use had been traditionally shared by commoners, and give to nobles. The Levellers had been excluded from the government of Lord Protector Cromwell, but the spirit of levelling still stalked the land. Some commoners joined &quot;Blacks&quot;, so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.&lt;ref&gt;Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on &quot;[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.&lt;/ref&gt; 

But not all accused were summarily executed. In 1724 &quot;John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized&quot; with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.&lt;ref&gt;Acemoglu and Robinson (2012, pp. 304-305).&lt;/ref&gt; 

These kinds of actions by the parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded &quot;universal [adult male] suffrage&quot; and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, &quot;The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The Manchester Observer called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... .&quot; And the British government placed enough other limits on its power that enough other commoners were allowed to became successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. 

== In sum ==

The above suggests that the rate of economic growth changes with either change in administration -- a new head of state -- or some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. 

However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).&lt;ref&gt;Graves (2025) includes an analysis of the data in Neff and Pickard (2024).&lt;/ref&gt; 

== Caveat ==

The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  

== Notes ==
{{reflist}}

== Bibliography ==

* &lt;!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)--&gt;{{cite Q|Q85764011}}
* &lt;!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)--&gt;{{cite Q|Q141241291}}
* &lt;!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)--&gt;{{cite Q|Q125292212}}
* &lt;!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)--&gt;{{cite Q|Q7997840}} 
* &lt;!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)--&gt;{{cite Q|Q137641358}}
* &lt;!--Ajzenman, Nicolas (29 January 2023). &quot;Migrants don't cause crime rates to increase — but false perceptions endure anyway&quot;. The Conversation.--&gt;{{cite Q|Q141758664}}
* &lt;!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) &quot;European Immigrants and the United States’ Rise to the Technological Frontier&quot;--&gt;{{cite Q|Q141678287}}
* &lt;!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer--&gt;{{cite Q|Q100216001}}

* &lt;!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) &quot;Maddison style estimates of the evolution of the world economy: A new 2023 update&quot;, Journal of Economic Surveys, 1-41--&gt;{{cite Q|Q126723821}}
* &lt;!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__&gt;{{cite Q|Q57945943}}
* &lt;!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia--&gt;{{cite Q|Q141759196}}
* &lt;!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition--&gt;{{cite Q|Q141156783}}
* &lt;!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies--&gt;{{cite Q|Q141158362}}
* &lt;!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)--&gt;{{cite Q|Q136227988}}
* &lt;!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) &quot;The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration--&gt;{{cite Q|Q55932800}}
* &lt;!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)--&gt;{{cite Q|Q132855526}}
* &lt;!--Graves (2023-03-21)  Do copyrights and paywalls on academic journals violate the US Constitution?--&gt;{{cite Q|Q126116187}}
* &lt;!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.--&gt;{{cite Q|Q137188993}}
* &lt;!-- Historian, USPS (2010) Postage Rates for Periodicals --&gt;{{cite Q|Q112167199}}
* &lt;!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse--&gt;{{cite Q|Q54641943}}
* &lt;!--Volker Leppin and Timothy J. Wengert (2015) &quot;Sources for and against the Posting of the Ninety-Five Theses&quot;--&gt;{{cite Q|Q141737347}}
* &lt;!--Lawrence Lessig (2004) Free Culture--&gt;{{cite Q|Q830526}}
* &lt;!--Olivier Marie and Paolo Pinotti (2024-02-01) &quot;Immigration and Crime: An International Perspective&quot;, Journal of Economic Perspectives. 38 (1): 181–200--&gt;{{cite Q|Q128434874}}
* &lt;!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). &quot;
Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime&quot;
. Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.--&gt;{{cite Q|Q55932802}}
* &lt;!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) --&gt;{{cite Q|Q104888067}}.
* &lt;!-- Robert W. McChesney; John Nichols (2016). People get ready--&gt;{{cite Q|Q87619174}}
* &lt;!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)--&gt;{{cite Q|Q136118590}}
* &lt;!--Ashley N. Muchow &amp; Taisiia Stanishevska (2026) &quot;From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest&quot;, Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)--&gt;{{cite Q|Q141760694}}
* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* &lt;!--John Hely Owen (1938)  War at Sea Under Queen Anne 1702–1708--&gt;{{cite Q|Q141757101}}
* &lt;!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation--&gt;{{cite Q|Q141761223}}
* &lt;!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain--&gt;{{cite Q|Q141761849}}
* &lt;!--Nick Roll (2017-07-16) &quot;Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.--&gt;{{cite Q|Q141735231}}
* &lt;!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)--&gt;{{cite Q|Q137669960}}
* &lt;!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)--&gt;{{cite Q|Q137669987}}
* &lt;!--J. L. van Zanden  and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30--&gt;{{cite Q|Q137670058}} 
* &lt;!--Tom K. Wong (2017-01-26) &quot;The Effects of Sanctuary Policies on Crime and the Economy&quot;--&gt;{{cite Q|Q98775875}}

[[Category:Original research]]
[[Category:Research]]
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:''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].''
:''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  
::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]''

== Abstract ==

This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. 

== Maddison Historical Statistics == 

[[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).&lt;ref&gt;See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.&lt;/ref&gt;'']]

The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. 

When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.&lt;ref&gt;Bolt and van Zanden (2024).&lt;/ref&gt; This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]], used in the Maddison data.) 

We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of North Sea oil. With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. 

This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. 

== Nobel economists and others ==

Banerjee and Duflo (2019, p. 207) said, &quot;despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive.&quot; That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. 

While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, &quot;The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services.&quot; In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. 

Mokyr (2017, p. 255) also said that, &quot;intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished.&quot; That resistance, he suggested, drives &quot;the empirical regularity that no society remains at the cutting edge of technological creativity for very long&quot;.&lt;ref&gt;Mokyr (2017, p. 260).&lt;/ref&gt; This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1.  

Mokyr (2017, p. 60) also mentioned &quot;entrepreneurs of hate&quot;, who convince others to dislike some group in a way that may benefit those &quot;entrepreneurs&quot; and major media organizations, who promote such &quot;entrepreneurs&quot; to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.&lt;ref&gt;See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and the Wikiversity article on &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-14.&lt;/ref&gt; When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites.  

Successful entrepreneurs of hate who demonize immigrants are featured in news coverage that portrays immigrants as criminal threats, when the threats are nonexistent&lt;ref&gt;Muchow and Stanishevska (2026); Ajzenman(2023).&lt;/ref&gt; or result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.&lt;ref&gt;Marie and Paolo (2024). See also the Wikipedia article on &quot;[[w:Immigration and crime|Immigration and crime]]&quot;, accessed 2026-10-12.&lt;/ref&gt; Mixed results are reported by research on sanctuary jurisdictions: Some studies show no impact.&lt;ref&gt;Martínez et al. (2017).&lt;/ref&gt; Most others show less crime with stronger economies, lower unemployment, higher median incomes, less poverty, less reliance on public assistance, etc.&lt;ref&gt;Wong (2017). See also the Wikipedia article on &quot;[[w:Sanctuary city|sanctuary city]]&quot;, accessed 2026-10-12.&lt;/ref&gt; In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities were ''more'' prone to crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded &quot;that sanctuary policies have no effect on crime rates, despite narratives to the contrary.&quot;&lt;ref&gt;Roll (2017); Gonzalez O’Brien, et al. (2017).&lt;/ref&gt;

We next discuss competition in media markets before discussing immigrants further. 

=== Diversity of ownership of the major media === 

Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations, and in hierarchical societies the religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate the designated evil others and give increasing shares of what they produce so the secular elites would &quot;protect&quot; them in wars against the designated evil others.

Acemoglu and Robinson (2012, p. 461) said, &quot;Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power ... in the United States [and] ... in the context of British democratization. Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799] ... .&quot; ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) 

But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.&lt;ref&gt;Hendrix (2015, p. 64), quoted from the Wikipedia article on the &quot;[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand&lt;ref&gt;Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; and was much more popular than Tetzel's.&lt;ref&gt;Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; 

Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the Church of England, denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature,&lt;ref&gt;Raymond (2006), cited from the Wikipedia article on &quot;[[w:Pamphlet war|pamphlet war]]&quot;, accessed 2026-10-15.&lt;/ref&gt; theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.&lt;ref&gt;Hibbert et al. (2010, p. 928), cited from the Wikipedia article on &quot;[[w:Henry VIII|Henry VIII]]&quot;, accessed 2026-10-15.&lt;/ref&gt;

A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.&lt;ref&gt;Foxley (2013, p. 207), cited from the Wikipedia article on &quot;[[w:Levellers|Levellers]], accessed 2026-10-15.&lt;/ref&gt; However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that became the US over a century later. 

That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792&lt;ref&gt;Wikipedia &quot;[[w:Postal Service Act|Postal Service Act]]&quot;, accessed 2023-07-11.&lt;/ref&gt; made a major contribution to making the US what it is today.  Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.&lt;ref&gt;Historian, USPS (2010).&lt;/ref&gt; McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.&lt;ref name=McC-N2010&gt;McChesney and Nichols (2010, pp. 310-311, note 88).&lt;/ref&gt; 

During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;John (1995). See also the interview with him at &quot;[[Media concentration per Columbia History Professor Richard John]]&quot; on Wikiversity, accessed 2026-10-12.&lt;/ref&gt; In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.&lt;ref&gt;The &quot;6 percent per year&quot; growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in &quot;[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; on Wikiversity, accessed 2026-10-13.&lt;/ref&gt; 

One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. 

FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, which the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.&lt;ref&gt;This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on &quot;[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; in Wikiversity, accessed 2026-10-13.&lt;/ref&gt;

But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, &quot;the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred.&quot; They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. 

Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.&lt;ref&gt;On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of &quot;influencers&quot; by for-profit social media as essentially unleashed &quot;a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures.&quot; In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.&lt;/ref&gt; 

And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2021, p. 139) noted, &quot;In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%.  The top rate was then cut in half, with the announced objective of boosting growth.  But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.&quot;

=== Immigrants === 

We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. [[w:English Council of State|Lord Protector Cromwell]], who replaced Charles I, refused to authorize as many monopolies as his predecessors, presumably supported by the growing number of independent publishers of pamphlets, books, and newspapers mentioned above. He also encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. 

But Mokyr is not alone in proclaiming the contributions of immigrants to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how &quot;the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology.&quot;

Aghion et al. (2021, p. 292) also discuss (a) &quot;a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita&quot; and (b) the overrepresentation of immigrants in patent applications.&lt;ref&gt;e.g., Aghion et al. (2026, pp. 266-267).&lt;/ref&gt; However, [[w:Dean Baker|Baker]] (2016, pp. 77-78) claimed that &quot;over the last four decades ... stronger patent protection seems to be associated with slower growth,&quot; seemingly the opposite of the claim just quoted from Aghion et al. 

Anther example of how technology winners protect their status against competition is the [[w:Supreme Court of the United States|US Supreme Court]] decision in ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]''. [[w:Lawrence Lessig|Lessig]], who represented the plaintiff in that case, asked how could extending the copyright on existing works &quot;promote the Progress of Science and useful Arts&quot;, as required by the [[w:Copyright Clause|Copyright Clause]] of the US Constitution? Lessig lost that case. His (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to limit rather than &quot;promote the Progress of Science and useful Arts&quot;. This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000, which would bankrupt his parents and which they could not recover even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.&lt;ref&gt;Lessig (2004, p. 42).&lt;/ref&gt; This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP). The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, becauses much of their income is derived from copyright royalties, or (b) SLAPP laws, because anti-SLAPP laws, which exist in some jurisdictions but not others,&lt;ref&gt;[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the &quot;JAWBONE act&quot;, to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on &quot;[[Foundation for Individual Rights and Expression]]&quot;, accessed 2026-10-16.&lt;/ref&gt; limit the power of major corporations, which provide most of the money for the media. 

Similarly Graves (2023) asked, &quot;Do copyrights and paywalls on refereed academic journals violate the US constitution?&quot; No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.&lt;ref&gt;Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on &quot;[[Wikimedia concerns with European copyright rules including AI and scientific research]]&quot;. That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).&lt;/ref&gt;

=== Industrial Revolution ===

There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. 

Mokyr (2017, p.  3) says, &quot;The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society.&quot; He described &quot;three cultural elements&quot; required for &quot;sustainable economic growth propelled by technological progress&quot;: (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. &quot;[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.&lt;ref&gt;Mokyr (2017, pp. 19-20).&lt;/ref&gt; Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, &quot;The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution.&quot; 

Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, &quot;European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?&quot; Aghion et al. (2021, p. 20) describe the &quot;first Industrial Revolution&quot; as having been triggered by &quot;the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866.&quot;&lt;ref&gt;The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.&lt;/ref&gt;

The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not &quot;phases of growth and decline&quot; with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. 

Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, &quot;the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward.&quot; ... However, &quot;the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant to thousand or seven thousand years previously.&quot; (chapter 5) They also claim that, &quot;English national production per capita doubled from 1500 to 1700&quot;, (chapter 5), and &quot;Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root.&quot; (p. 45, chapter 2)

Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. 

Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the &quot;Old Pretender&quot;, a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. 

When Queen Anne died in 1702, she was succeeded by George I. His parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, &quot;and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts&quot;, according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs moved to confiscate &quot;[[w:Commons|commons]]&quot;, land whose use had been traditionally shared by commoners, and give to nobles. The Levellers had been excluded from the government of Lord Protector Cromwell, but the spirit of levelling still stalked the land. Some commoners joined &quot;Blacks&quot;, so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.&lt;ref&gt;Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on &quot;[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.&lt;/ref&gt; 

But not all accused were summarily executed. In 1724 &quot;John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized&quot; with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.&lt;ref&gt;Acemoglu and Robinson (2012, pp. 304-305).&lt;/ref&gt; 

These kinds of actions by the parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded &quot;universal [adult male] suffrage&quot; and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, &quot;The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The Manchester Observer called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... .&quot; And the British government placed enough other limits on its power that enough other commoners were allowed to became successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. 

== In sum ==

The above suggests that the rate of economic growth changes with either change in administration -- a new head of state -- or some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. 

However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).&lt;ref&gt;Graves (2025) includes an analysis of the data in Neff and Pickard (2024).&lt;/ref&gt; 

== Caveat ==

The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  

== Notes ==
{{reflist}}

== Bibliography ==

* &lt;!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)--&gt;{{cite Q|Q85764011}}
* &lt;!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)--&gt;{{cite Q|Q141241291}}
* &lt;!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)--&gt;{{cite Q|Q125292212}}
* &lt;!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)--&gt;{{cite Q|Q7997840}} 
* &lt;!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)--&gt;{{cite Q|Q137641358}}
* &lt;!--Ajzenman, Nicolas (29 January 2023). &quot;Migrants don't cause crime rates to increase — but false perceptions endure anyway&quot;. The Conversation.--&gt;{{cite Q|Q141758664}}
* &lt;!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) &quot;European Immigrants and the United States’ Rise to the Technological Frontier&quot;--&gt;{{cite Q|Q141678287}}
* &lt;!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer--&gt;{{cite Q|Q100216001}}

* &lt;!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) &quot;Maddison style estimates of the evolution of the world economy: A new 2023 update&quot;, Journal of Economic Surveys, 1-41--&gt;{{cite Q|Q126723821}}
* &lt;!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__&gt;{{cite Q|Q57945943}}
* &lt;!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia--&gt;{{cite Q|Q141759196}}
* &lt;!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition--&gt;{{cite Q|Q141156783}}
* &lt;!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies--&gt;{{cite Q|Q141158362}}
* &lt;!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)--&gt;{{cite Q|Q136227988}}
* &lt;!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) &quot;The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration--&gt;{{cite Q|Q55932800}}
* &lt;!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)--&gt;{{cite Q|Q132855526}}
* &lt;!--Graves (2023-03-21)  Do copyrights and paywalls on academic journals violate the US Constitution?--&gt;{{cite Q|Q126116187}}
* &lt;!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.--&gt;{{cite Q|Q137188993}}
* &lt;!-- Historian, USPS (2010) Postage Rates for Periodicals --&gt;{{cite Q|Q112167199}}
* &lt;!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse--&gt;{{cite Q|Q54641943}}
* &lt;!--Volker Leppin and Timothy J. Wengert (2015) &quot;Sources for and against the Posting of the Ninety-Five Theses&quot;--&gt;{{cite Q|Q141737347}}
* &lt;!--Lawrence Lessig (2004) Free Culture--&gt;{{cite Q|Q830526}}
* &lt;!--Olivier Marie and Paolo Pinotti (2024-02-01) &quot;Immigration and Crime: An International Perspective&quot;, Journal of Economic Perspectives. 38 (1): 181–200--&gt;{{cite Q|Q128434874}}
* &lt;!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). &quot;
Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime&quot;
. Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.--&gt;{{cite Q|Q55932802}}
* &lt;!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) --&gt;{{cite Q|Q104888067}}.
* &lt;!-- Robert W. McChesney; John Nichols (2016). People get ready--&gt;{{cite Q|Q87619174}}
* &lt;!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)--&gt;{{cite Q|Q136118590}}
* &lt;!--Ashley N. Muchow &amp; Taisiia Stanishevska (2026) &quot;From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest&quot;, Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)--&gt;{{cite Q|Q141760694}}
* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* &lt;!--John Hely Owen (1938)  War at Sea Under Queen Anne 1702–1708--&gt;{{cite Q|Q141757101}}
* &lt;!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation--&gt;{{cite Q|Q141761223}}
* &lt;!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain--&gt;{{cite Q|Q141761849}}
* &lt;!--Nick Roll (2017-07-16) &quot;Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.--&gt;{{cite Q|Q141735231}}
* &lt;!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)--&gt;{{cite Q|Q137669960}}
* &lt;!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)--&gt;{{cite Q|Q137669987}}
* &lt;!--J. L. van Zanden  and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30--&gt;{{cite Q|Q137670058}} 
* &lt;!--Tom K. Wong (2017-01-26) &quot;The Effects of Sanctuary Policies on Crime and the Economy&quot;--&gt;{{cite Q|Q98775875}}

[[Category:Original research]]
[[Category:Research]]
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[[Category:Political science]]
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      <text bytes="45704" sha1="rcfaj6hrsd1nb674a2qaycx7vmkhdsr" xml:space="preserve">{{Research project}} 
:''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].''
:''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  
::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]''

== Abstract ==

This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. 

== Maddison Historical Statistics == 

[[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).&lt;ref&gt;See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.&lt;/ref&gt;'']]

The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. 

When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.&lt;ref&gt;Bolt and van Zanden (2024).&lt;/ref&gt; This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]], used in the Maddison data.) 

We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of [[w:North Sea oil|North Sea oil]].&lt;ref&gt;Dośpiał-Borysiak (2017).&lt;/ref&gt; With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. 

This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. 

== Nobel economists and others ==

Banerjee and Duflo (2019, p. 207) said, &quot;despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive.&quot; That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. 

While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, &quot;The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services.&quot; In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. 

Mokyr (2017, p. 255) also said that, &quot;intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished.&quot; That resistance, he suggested, drives &quot;the empirical regularity that no society remains at the cutting edge of technological creativity for very long&quot;.&lt;ref&gt;Mokyr (2017, p. 260).&lt;/ref&gt; This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1.  

Mokyr (2017, p. 60) also mentioned &quot;entrepreneurs of hate&quot;, who convince others to dislike some group in a way that may benefit those &quot;entrepreneurs&quot; and major media organizations, who promote such &quot;entrepreneurs&quot; to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.&lt;ref&gt;See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and the Wikiversity article on &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-14.&lt;/ref&gt; When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites.  

Successful entrepreneurs of hate who demonize immigrants are featured in news coverage that portrays immigrants as criminal threats, when the threats are nonexistent&lt;ref&gt;Muchow and Stanishevska (2026); Ajzenman(2023).&lt;/ref&gt; or result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.&lt;ref&gt;Marie and Paolo (2024). See also the Wikipedia article on &quot;[[w:Immigration and crime|Immigration and crime]]&quot;, accessed 2026-10-12.&lt;/ref&gt; Mixed results are reported by research on sanctuary jurisdictions: Some studies show no impact.&lt;ref&gt;Martínez et al. (2017).&lt;/ref&gt; Most others show less crime with stronger economies, lower unemployment, higher median incomes, less poverty, less reliance on public assistance, etc.&lt;ref&gt;Wong (2017). See also the Wikipedia article on &quot;[[w:Sanctuary city|sanctuary city]]&quot;, accessed 2026-10-12.&lt;/ref&gt; In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities were ''more'' prone to crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded &quot;that sanctuary policies have no effect on crime rates, despite narratives to the contrary.&quot;&lt;ref&gt;Roll (2017); Gonzalez O’Brien, et al. (2017).&lt;/ref&gt;

We next discuss competition in media markets before discussing immigrants further. 

=== Diversity of ownership of the major media === 

Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations, and in hierarchical societies the religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate the designated evil others and give increasing shares of what they produce so the secular elites would &quot;protect&quot; them in wars against the designated evil others.

Acemoglu and Robinson (2012, p. 461) said, &quot;Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power ... in the United States [and] ... in the context of British democratization. Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799] ... .&quot; ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) 

But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.&lt;ref&gt;Hendrix (2015, p. 64), quoted from the Wikipedia article on the &quot;[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand&lt;ref&gt;Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; and was much more popular than Tetzel's.&lt;ref&gt;Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; 

Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the Church of England, denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature,&lt;ref&gt;Raymond (2006), cited from the Wikipedia article on &quot;[[w:Pamphlet war|pamphlet war]]&quot;, accessed 2026-10-15.&lt;/ref&gt; theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.&lt;ref&gt;Hibbert et al. (2010, p. 928), cited from the Wikipedia article on &quot;[[w:Henry VIII|Henry VIII]]&quot;, accessed 2026-10-15.&lt;/ref&gt;

A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.&lt;ref&gt;Foxley (2013, p. 207), cited from the Wikipedia article on &quot;[[w:Levellers|Levellers]], accessed 2026-10-15.&lt;/ref&gt; However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that became the US over a century later. 

That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792&lt;ref&gt;Wikipedia &quot;[[w:Postal Service Act|Postal Service Act]]&quot;, accessed 2023-07-11.&lt;/ref&gt; made a major contribution to making the US what it is today.  Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.&lt;ref&gt;Historian, USPS (2010).&lt;/ref&gt; McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.&lt;ref name=McC-N2010&gt;McChesney and Nichols (2010, pp. 310-311, note 88).&lt;/ref&gt; 

During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;John (1995). See also the interview with him at &quot;[[Media concentration per Columbia History Professor Richard John]]&quot; on Wikiversity, accessed 2026-10-12.&lt;/ref&gt; In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.&lt;ref&gt;The &quot;6 percent per year&quot; growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in &quot;[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; on Wikiversity, accessed 2026-10-13.&lt;/ref&gt; 

One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. 

FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, which the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.&lt;ref&gt;This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on &quot;[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; in Wikiversity, accessed 2026-10-13.&lt;/ref&gt;

But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, &quot;the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred.&quot; They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. 

Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.&lt;ref&gt;On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of &quot;influencers&quot; by for-profit social media as essentially unleashed &quot;a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures.&quot; In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.&lt;/ref&gt; 

And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2021, p. 139) noted, &quot;In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%.  The top rate was then cut in half, with the announced objective of boosting growth.  But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.&quot;

=== Immigrants === 

We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. [[w:English Council of State|Lord Protector Cromwell]], who replaced Charles I, refused to authorize as many monopolies as his predecessors, presumably supported by the growing number of independent publishers of pamphlets, books, and newspapers mentioned above. He also encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. 

But Mokyr is not alone in proclaiming the contributions of immigrants to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how &quot;the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology.&quot;

Aghion et al. (2021, p. 292) also discuss (a) &quot;a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita&quot; and (b) the overrepresentation of immigrants in patent applications.&lt;ref&gt;e.g., Aghion et al. (2026, pp. 266-267).&lt;/ref&gt; However, [[w:Dean Baker|Baker]] (2016, pp. 77-78) claimed that &quot;over the last four decades ... stronger patent protection seems to be associated with slower growth,&quot; seemingly the opposite of the claim just quoted from Aghion et al. 

Anther example of how technology winners protect their status against competition is the [[w:Supreme Court of the United States|US Supreme Court]] decision in ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]''. [[w:Lawrence Lessig|Lessig]], who represented the plaintiff in that case, asked how could extending the copyright on existing works &quot;promote the Progress of Science and useful Arts&quot;, as required by the [[w:Copyright Clause|Copyright Clause]] of the US Constitution? Lessig lost that case. His (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to limit rather than &quot;promote the Progress of Science and useful Arts&quot;. This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000, which would bankrupt his parents and which they could not recover even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.&lt;ref&gt;Lessig (2004, p. 42).&lt;/ref&gt; This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP). The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, becauses much of their income is derived from copyright royalties, or (b) SLAPP laws, because anti-SLAPP laws, which exist in some jurisdictions but not others,&lt;ref&gt;[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the &quot;JAWBONE act&quot;, to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on &quot;[[Foundation for Individual Rights and Expression]]&quot;, accessed 2026-10-16.&lt;/ref&gt; limit the power of major corporations, which provide most of the money for the media. 

Similarly Graves (2023) asked, &quot;Do copyrights and paywalls on refereed academic journals violate the US constitution?&quot; No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.&lt;ref&gt;Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on &quot;[[Wikimedia concerns with European copyright rules including AI and scientific research]]&quot;. That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).&lt;/ref&gt;

=== Industrial Revolution ===

There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. 

Mokyr (2017, p.  3) says, &quot;The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society.&quot; He described &quot;three cultural elements&quot; required for &quot;sustainable economic growth propelled by technological progress&quot;: (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. &quot;[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.&lt;ref&gt;Mokyr (2017, pp. 19-20).&lt;/ref&gt; Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, &quot;The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution.&quot; 

Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, &quot;European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?&quot; Aghion et al. (2021, p. 20) describe the &quot;first Industrial Revolution&quot; as having been triggered by &quot;the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866.&quot;&lt;ref&gt;The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.&lt;/ref&gt;

The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not &quot;phases of growth and decline&quot; with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. 

Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, &quot;the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward.&quot; ... However, &quot;the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant to thousand or seven thousand years previously.&quot; (chapter 5) They also claim that, &quot;English national production per capita doubled from 1500 to 1700&quot;, (chapter 5), and &quot;Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root.&quot; (p. 45, chapter 2)

Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. 

Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the &quot;Old Pretender&quot;, a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. 

When Queen Anne died in 1702, she was succeeded by George I. His parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, &quot;and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts&quot;, according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs moved to confiscate &quot;[[w:Commons|commons]]&quot;, land whose use had been traditionally shared by commoners, and give to nobles. The Levellers had been excluded from the government of Lord Protector Cromwell, but the spirit of levelling still stalked the land. Some commoners joined &quot;Blacks&quot;, so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.&lt;ref&gt;Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on &quot;[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.&lt;/ref&gt; 

But not all accused were summarily executed. In 1724 &quot;John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized&quot; with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.&lt;ref&gt;Acemoglu and Robinson (2012, pp. 304-305).&lt;/ref&gt; 

These kinds of actions by the parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded &quot;universal [adult male] suffrage&quot; and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, &quot;The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The Manchester Observer called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... .&quot; And the British government placed enough other limits on its power that enough other commoners were allowed to became successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. 

== In sum ==

The above suggests that the rate of economic growth changes with either change in administration -- a new head of state -- or some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. 

However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).&lt;ref&gt;Graves (2025) includes an analysis of the data in Neff and Pickard (2024).&lt;/ref&gt; 

== Caveat ==

The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  

== Notes ==
{{reflist}}

== Bibliography ==

* &lt;!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)--&gt;{{cite Q|Q85764011}}
* &lt;!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)--&gt;{{cite Q|Q141241291}}
* &lt;!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)--&gt;{{cite Q|Q125292212}}
* &lt;!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)--&gt;{{cite Q|Q7997840}} 
* &lt;!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)--&gt;{{cite Q|Q137641358}}
* &lt;!--Ajzenman, Nicolas (29 January 2023). &quot;Migrants don't cause crime rates to increase — but false perceptions endure anyway&quot;. The Conversation.--&gt;{{cite Q|Q141758664}}
* &lt;!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) &quot;European Immigrants and the United States’ Rise to the Technological Frontier&quot;--&gt;{{cite Q|Q141678287}}
* &lt;!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer--&gt;{{cite Q|Q100216001}}

* &lt;!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) &quot;Maddison style estimates of the evolution of the world economy: A new 2023 update&quot;, Journal of Economic Surveys, 1-41--&gt;{{cite Q|Q126723821}}
* &lt;!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__&gt;{{cite Q|Q57945943}}


* &lt;!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition--&gt;{{cite Q|Q141156783}}
* &lt;!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies--&gt;{{cite Q|Q141158362}}
* &lt;!--Katarzyna Dośpiał-Borysiak (2017) &quot;Model of state management of petroleum sector -- Case of Norway--&gt;{{cite Q|Q141774179}}
* &lt;!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)--&gt;{{cite Q|Q136227988}}
* &lt;!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) &quot;The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration--&gt;{{cite Q|Q55932800}}
* &lt;!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)--&gt;{{cite Q|Q132855526}}
* &lt;!--Graves (2023-03-21)  Do copyrights and paywalls on academic journals violate the US Constitution?--&gt;{{cite Q|Q126116187}}
* &lt;!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.--&gt;{{cite Q|Q137188993}}
* &lt;!-- Historian, USPS (2010) Postage Rates for Periodicals --&gt;{{cite Q|Q112167199}}
* &lt;!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse--&gt;{{cite Q|Q54641943}}
* &lt;!--Volker Leppin and Timothy J. Wengert (2015) &quot;Sources for and against the Posting of the Ninety-Five Theses&quot;--&gt;{{cite Q|Q141737347}}
* &lt;!--Lawrence Lessig (2004) Free Culture--&gt;{{cite Q|Q830526}}
* &lt;!--Olivier Marie and Paolo Pinotti (2024-02-01) &quot;Immigration and Crime: An International Perspective&quot;, Journal of Economic Perspectives. 38 (1): 181–200--&gt;{{cite Q|Q128434874}}
* &lt;!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). &quot;
Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime&quot;
. Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.--&gt;{{cite Q|Q55932802}}
* &lt;!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) --&gt;{{cite Q|Q104888067}}.
* &lt;!-- Robert W. McChesney; John Nichols (2016). People get ready--&gt;{{cite Q|Q87619174}}
* &lt;!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)--&gt;{{cite Q|Q136118590}}
* &lt;!--Ashley N. Muchow &amp; Taisiia Stanishevska (2026) &quot;From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest&quot;, Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)--&gt;{{cite Q|Q141760694}}
* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* &lt;!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia--&gt;{{cite Q|Q141759196}}
* &lt;!--John Hely Owen (1938)  War at Sea Under Queen Anne 1702–1708--&gt;{{cite Q|Q141757101}}
* &lt;!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation--&gt;{{cite Q|Q141761223}}
* &lt;!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain--&gt;{{cite Q|Q141761849}}
* &lt;!--Nick Roll (2017-07-16) &quot;Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.--&gt;{{cite Q|Q141735231}}
* &lt;!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)--&gt;{{cite Q|Q137669960}}
* &lt;!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)--&gt;{{cite Q|Q137669987}}
* &lt;!--J. L. van Zanden  and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30--&gt;{{cite Q|Q137670058}} 
* &lt;!--Tom K. Wong (2017-01-26) &quot;The Effects of Sanctuary Policies on Crime and the Economy&quot;--&gt;{{cite Q|Q98775875}}

[[Category:Original research]]
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      <text bytes="45916" sha1="cfu8rllcqj5tphl5xxn7dltl18lf6is" xml:space="preserve">{{Research project}} {{Research project}} 
:''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].''
:''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  
::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]''

== Abstract ==

This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. 

== Maddison Historical Statistics == 

[[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).&lt;ref&gt;See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.&lt;/ref&gt;'']]

The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. 

When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.&lt;ref&gt;Bolt and van Zanden (2024).&lt;/ref&gt; This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]], used in the Maddison data.) 

We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of [[w:North Sea oil|North Sea oil]].&lt;ref&gt;Dośpiał-Borysiak (2017).&lt;/ref&gt; With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. 

This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. 

== Nobel economists and others ==

Banerjee and Duflo (2019, p. 207) said, &quot;despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive.&quot; That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. 

While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, &quot;The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services.&quot; In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. 

Mokyr (2017, p. 255) also said that, &quot;intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished.&quot; That resistance, he suggested, drives &quot;the empirical regularity that no society remains at the cutting edge of technological creativity for very long&quot;.&lt;ref&gt;Mokyr (2017, p. 260).&lt;/ref&gt; This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1.  

Mokyr (2017, p. 60) also mentioned &quot;entrepreneurs of hate&quot;, who convince others to dislike some group in a way that may benefit those &quot;entrepreneurs&quot; and major media organizations, who promote such &quot;entrepreneurs&quot; to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.&lt;ref&gt;See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and the Wikiversity article on &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-14.&lt;/ref&gt; When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites.  

For example, major news outlets often feature leading figures describing immigrants as criminal threats, when the threats are nonexistent&lt;ref&gt;Muchow and Stanishevska (2026); Ajzenman(2023).&lt;/ref&gt; or result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.&lt;ref&gt;Marie and Paolo (2024). See also the Wikipedia article on &quot;[[w:Immigration and crime|Immigration and crime]]&quot;, accessed 2026-10-12.&lt;/ref&gt; Mixed results are reported by research on sanctuary jurisdictions: Some studies show no impact.&lt;ref&gt;Martínez et al. (2017).&lt;/ref&gt; Most other research shows sanctuary jurisdictions have less crime with stronger economies, lower unemployment, higher median incomes, less poverty, less reliance on public assistance, etc.&lt;ref&gt;Wong (2017). See also the Wikipedia article on &quot;[[w:Sanctuary city|sanctuary city]]&quot;, accessed 2026-10-12.&lt;/ref&gt; In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities were ''more'' prone to crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded &quot;that sanctuary policies have no effect on crime rates, despite narratives to the contrary.&quot;&lt;ref&gt;Roll (2017); Gonzalez O’Brien, et al. (2017).&lt;/ref&gt; If this is a balances summary of the research in this area, it suggests that leaders like Trump and Sessions, to name only two, can be fairly describes as &quot;entrepreneurs of hate&quot;. 

We next discuss competition in media markets before discussing immigrants further. 

=== Diversity of ownership of the major media === 

Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations, and in hierarchical societies the religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate the designated evil others and give increasing shares of what they produce so the secular elites would &quot;protect&quot; them in wars against the designated evil others.

Acemoglu and Robinson (2012, p. 461) said, &quot;Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power ... in the United States [and] ... in the context of British democratization. Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799] ... .&quot; ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) 

But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.&lt;ref&gt;Hendrix (2015, p. 64), quoted from the Wikipedia article on the &quot;[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand&lt;ref&gt;Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; and was much more popular than Tetzel's.&lt;ref&gt;Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; 

Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the Church of England, denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature,&lt;ref&gt;Raymond (2006), cited from the Wikipedia article on &quot;[[w:Pamphlet war|pamphlet war]]&quot;, accessed 2026-10-15.&lt;/ref&gt; theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.&lt;ref&gt;Hibbert et al. (2010, p. 928), cited from the Wikipedia article on &quot;[[w:Henry VIII|Henry VIII]]&quot;, accessed 2026-10-15.&lt;/ref&gt;

A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.&lt;ref&gt;Foxley (2013, p. 207), cited from the Wikipedia article on &quot;[[w:Levellers|Levellers]], accessed 2026-10-15.&lt;/ref&gt; However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that became the US over a century later. 

That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792&lt;ref&gt;Wikipedia &quot;[[w:Postal Service Act|Postal Service Act]]&quot;, accessed 2023-07-11.&lt;/ref&gt; made a major contribution to making the US what it is today.  Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.&lt;ref&gt;Historian, USPS (2010).&lt;/ref&gt; McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.&lt;ref name=McC-N2010&gt;McChesney and Nichols (2010, pp. 310-311, note 88).&lt;/ref&gt; 

During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;John (1995). See also the interview with him at &quot;[[Media concentration per Columbia History Professor Richard John]]&quot; on Wikiversity, accessed 2026-10-12.&lt;/ref&gt; In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.&lt;ref&gt;The &quot;6 percent per year&quot; growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in &quot;[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; on Wikiversity, accessed 2026-10-13.&lt;/ref&gt; 

One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. 

FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, which the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.&lt;ref&gt;This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on &quot;[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; in Wikiversity, accessed 2026-10-13.&lt;/ref&gt;

But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, &quot;the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred.&quot; They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. 

Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.&lt;ref&gt;On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of &quot;influencers&quot; by for-profit social media as essentially unleashed &quot;a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures.&quot; In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.&lt;/ref&gt; 

And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2021, p. 139) noted, &quot;In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%.  The top rate was then cut in half, with the announced objective of boosting growth.  But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.&quot;

=== Immigrants === 

We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. [[w:English Council of State|Lord Protector Cromwell]], who replaced Charles I, refused to authorize as many monopolies as his predecessors, presumably supported by the growing number of independent publishers of pamphlets, books, and newspapers mentioned above. He also encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. 

But Mokyr is not alone in proclaiming the contributions of immigrants to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how &quot;the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology.&quot;

Aghion et al. (2021, p. 292) also discuss (a) &quot;a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita&quot; and (b) the overrepresentation of immigrants in patent applications.&lt;ref&gt;e.g., Aghion et al. (2026, pp. 266-267).&lt;/ref&gt; However, [[w:Dean Baker|Baker]] (2016, pp. 77-78) claimed that &quot;over the last four decades ... stronger patent protection seems to be associated with slower growth,&quot; seemingly the opposite of the claim just quoted from Aghion et al. 

Anther example of how technology winners protect their status against competition is the [[w:Supreme Court of the United States|US Supreme Court]] decision in ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]''. [[w:Lawrence Lessig|Lessig]], who represented the plaintiff in that case, asked how could extending the copyright on existing works &quot;promote the Progress of Science and useful Arts&quot;, as required by the [[w:Copyright Clause|Copyright Clause]] of the US Constitution? Lessig lost that case. His (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to limit rather than &quot;promote the Progress of Science and useful Arts&quot;. This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000, which would bankrupt his parents and which they could not recover even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.&lt;ref&gt;Lessig (2004, p. 42).&lt;/ref&gt; This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP). The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, becauses much of their income is derived from copyright royalties, or (b) SLAPP laws, because anti-SLAPP laws, which exist in some jurisdictions but not others,&lt;ref&gt;[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the &quot;JAWBONE act&quot;, to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on &quot;[[Foundation for Individual Rights and Expression]]&quot;, accessed 2026-10-16.&lt;/ref&gt; limit the power of major corporations, which provide most of the money for the media. 

Similarly Graves (2023) asked, &quot;Do copyrights and paywalls on refereed academic journals violate the US constitution?&quot; No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.&lt;ref&gt;Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on &quot;[[Wikimedia concerns with European copyright rules including AI and scientific research]]&quot;. That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).&lt;/ref&gt;

=== Industrial Revolution ===

There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. 

Mokyr (2017, p.  3) says, &quot;The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society.&quot; He described &quot;three cultural elements&quot; required for &quot;sustainable economic growth propelled by technological progress&quot;: (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. &quot;[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.&lt;ref&gt;Mokyr (2017, pp. 19-20).&lt;/ref&gt; Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, &quot;The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution.&quot; 

Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, &quot;European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?&quot; Aghion et al. (2021, p. 20) describe the &quot;first Industrial Revolution&quot; as having been triggered by &quot;the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866.&quot;&lt;ref&gt;The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.&lt;/ref&gt;

The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not &quot;phases of growth and decline&quot; with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. 

Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, &quot;the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward.&quot; ... However, &quot;the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant to thousand or seven thousand years previously.&quot; (chapter 5) They also claim that, &quot;English national production per capita doubled from 1500 to 1700&quot;, (chapter 5), and &quot;Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root.&quot; (p. 45, chapter 2)

Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. 

Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the &quot;Old Pretender&quot;, a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. 

When Queen Anne died in 1702, she was succeeded by George I. His parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, &quot;and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts&quot;, according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs moved to confiscate &quot;[[w:Commons|commons]]&quot;, land whose use had been traditionally shared by commoners, and give to nobles. The Levellers had been excluded from the government of Lord Protector Cromwell, but the spirit of levelling still stalked the land. Some commoners joined &quot;Blacks&quot;, so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.&lt;ref&gt;Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on &quot;[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.&lt;/ref&gt; 

But not all accused were summarily executed. In 1724 &quot;John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized&quot; with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.&lt;ref&gt;Acemoglu and Robinson (2012, pp. 304-305).&lt;/ref&gt; 

These kinds of actions by the parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded &quot;universal [adult male] suffrage&quot; and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, &quot;The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The Manchester Observer called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... .&quot; And the British government placed enough other limits on its power that enough other commoners were allowed to became successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. 

== In sum ==

The above suggests that the rate of economic growth changes with either change in administration -- a new head of state -- or some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. 

However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).&lt;ref&gt;Graves (2025) includes an analysis of the data in Neff and Pickard (2024).&lt;/ref&gt; 

== Caveat ==

The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  

== Notes ==
{{reflist}}

== Bibliography ==

* &lt;!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)--&gt;{{cite Q|Q85764011}}
* &lt;!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)--&gt;{{cite Q|Q141241291}}
* &lt;!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)--&gt;{{cite Q|Q125292212}}
* &lt;!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)--&gt;{{cite Q|Q7997840}} 
* &lt;!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)--&gt;{{cite Q|Q137641358}}
* &lt;!--Ajzenman, Nicolas (29 January 2023). &quot;Migrants don't cause crime rates to increase — but false perceptions endure anyway&quot;. The Conversation.--&gt;{{cite Q|Q141758664}}
* &lt;!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) &quot;European Immigrants and the United States’ Rise to the Technological Frontier&quot;--&gt;{{cite Q|Q141678287}}
* &lt;!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer--&gt;{{cite Q|Q100216001}}

* &lt;!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) &quot;Maddison style estimates of the evolution of the world economy: A new 2023 update&quot;, Journal of Economic Surveys, 1-41--&gt;{{cite Q|Q126723821}}
* &lt;!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__&gt;{{cite Q|Q57945943}}


* &lt;!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition--&gt;{{cite Q|Q141156783}}
* &lt;!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies--&gt;{{cite Q|Q141158362}}
* &lt;!--Katarzyna Dośpiał-Borysiak (2017) &quot;Model of state management of petroleum sector -- Case of Norway--&gt;{{cite Q|Q141774179}}
* &lt;!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)--&gt;{{cite Q|Q136227988}}
* &lt;!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) &quot;The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration--&gt;{{cite Q|Q55932800}}
* &lt;!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)--&gt;{{cite Q|Q132855526}}
* &lt;!--Graves (2023-03-21)  Do copyrights and paywalls on academic journals violate the US Constitution?--&gt;{{cite Q|Q126116187}}
* &lt;!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.--&gt;{{cite Q|Q137188993}}
* &lt;!-- Historian, USPS (2010) Postage Rates for Periodicals --&gt;{{cite Q|Q112167199}}
* &lt;!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse--&gt;{{cite Q|Q54641943}}
* &lt;!--Volker Leppin and Timothy J. Wengert (2015) &quot;Sources for and against the Posting of the Ninety-Five Theses&quot;--&gt;{{cite Q|Q141737347}}
* &lt;!--Lawrence Lessig (2004) Free Culture--&gt;{{cite Q|Q830526}}
* &lt;!--Olivier Marie and Paolo Pinotti (2024-02-01) &quot;Immigration and Crime: An International Perspective&quot;, Journal of Economic Perspectives. 38 (1): 181–200--&gt;{{cite Q|Q128434874}}
* &lt;!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). &quot;
Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime&quot;
. Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.--&gt;{{cite Q|Q55932802}}
* &lt;!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) --&gt;{{cite Q|Q104888067}}.
* &lt;!-- Robert W. McChesney; John Nichols (2016). People get ready--&gt;{{cite Q|Q87619174}}
* &lt;!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)--&gt;{{cite Q|Q136118590}}
* &lt;!--Ashley N. Muchow &amp; Taisiia Stanishevska (2026) &quot;From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest&quot;, Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)--&gt;{{cite Q|Q141760694}}
* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* &lt;!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia--&gt;{{cite Q|Q141759196}}
* &lt;!--John Hely Owen (1938)  War at Sea Under Queen Anne 1702–1708--&gt;{{cite Q|Q141757101}}
* &lt;!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation--&gt;{{cite Q|Q141761223}}
* &lt;!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain--&gt;{{cite Q|Q141761849}}
* &lt;!--Nick Roll (2017-07-16) &quot;Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.--&gt;{{cite Q|Q141735231}}
* &lt;!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)--&gt;{{cite Q|Q137669960}}
* &lt;!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)--&gt;{{cite Q|Q137669987}}
* &lt;!--J. L. van Zanden  and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30--&gt;{{cite Q|Q137670058}} 
* &lt;!--Tom K. Wong (2017-01-26) &quot;The Effects of Sanctuary Policies on Crime and the Economy&quot;--&gt;{{cite Q|Q98775875}}

[[Category:Original research]]
[[Category:Research]]
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[[Category:Gross domestic product]]
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[[Category:Modern Monetary Theory]]
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      <text bytes="45981" sha1="3qjj4yzm5ogx4c3lm12mvk9ozr1dwo0" xml:space="preserve">{{Research project}} 
:''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].''
:''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  
::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]''

== Abstract ==

This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. 

== Maddison Historical Statistics == 

[[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).&lt;ref&gt;See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.&lt;/ref&gt;'']]

The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. 

When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.&lt;ref&gt;Bolt and van Zanden (2024).&lt;/ref&gt; This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]], used in the Maddison data.) 

We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of [[w:North Sea oil|North Sea oil]].&lt;ref&gt;Dośpiał-Borysiak (2017).&lt;/ref&gt; With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. 

This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. 

== Nobel economists and others ==

Banerjee and Duflo (2019, p. 207) said, &quot;despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive.&quot; That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. 

While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, &quot;The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services.&quot; In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. 

Mokyr (2017, p. 255) also said that, &quot;intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished.&quot; That resistance, he suggested, drives &quot;the empirical regularity that no society remains at the cutting edge of technological creativity for very long&quot;.&lt;ref&gt;Mokyr (2017, p. 260).&lt;/ref&gt; This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1.  

Mokyr (2017, p. 60) also mentioned &quot;entrepreneurs of hate&quot;, who convince others to dislike some group in a way that may benefit those &quot;entrepreneurs&quot; and major media organizations, who promote such &quot;entrepreneurs&quot; to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.&lt;ref&gt;See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and the Wikiversity article on &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-14.&lt;/ref&gt; When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites.  

For example, most research on immigrants suggest that on average immigrants are more entrepreneurial and no more likely to commit crime than native born,&lt;ref&gt;e.g., Martínez et al. (2017); Muchow and Stanishevska (2026); Ajzenman(2023).&lt;/ref&gt; and some studies report that sanctuary jurisdictions have on average higher median incomes and less crime.&lt;ref&gt;Martínez et al. (2017); Wong (2017). See also the Wikipedia article on &quot;[[w:Sanctuary city|sanctuary city]]&quot;, accessed 2026-10-12.&lt;/ref&gt; Where immigrant crime is higher, it typically result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.&lt;ref&gt;Marie and Paolo (2024). See also the Wikipedia article on &quot;[[w:Immigration and crime|Immigration and crime]]&quot;, accessed 2026-10-12.&lt;/ref&gt; 

But major media outlets make money from featuring charismatic figures, who attract an audience without offending people who control much of the money for the media. In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities had more crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded &quot;that sanctuary policies have no effect on crime rates, despite narratives to the contrary.&quot;&lt;ref&gt;Roll (2017); Gonzalez O’Brien, et al. (2017).&lt;/ref&gt; To the extent that these comments provide a balanced summary of the research in this area, it suggests that leaders like Trump and Sessions, to name only two, can be fairly describes as &quot;entrepreneurs of hate&quot;. 

We next discuss competition in media markets before discussing immigrants further. 

=== Diversity of ownership of the major media === 

Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations, and in hierarchical societies the religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate the designated evil others and give increasing shares of what they produce so the secular elites would &quot;protect&quot; them in wars against the designated evil others.

Acemoglu and Robinson (2012, p. 461) said, &quot;Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power ... in the United States [and] ... in the context of British democratization. Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799] ... .&quot; ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) 

But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.&lt;ref&gt;Hendrix (2015, p. 64), quoted from the Wikipedia article on the &quot;[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand&lt;ref&gt;Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; and was much more popular than Tetzel's.&lt;ref&gt;Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; 

Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the Church of England, denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature,&lt;ref&gt;Raymond (2006), cited from the Wikipedia article on &quot;[[w:Pamphlet war|pamphlet war]]&quot;, accessed 2026-10-15.&lt;/ref&gt; theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.&lt;ref&gt;Hibbert et al. (2010, p. 928), cited from the Wikipedia article on &quot;[[w:Henry VIII|Henry VIII]]&quot;, accessed 2026-10-15.&lt;/ref&gt;

A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.&lt;ref&gt;Foxley (2013, p. 207), cited from the Wikipedia article on &quot;[[w:Levellers|Levellers]], accessed 2026-10-15.&lt;/ref&gt; However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that became the US over a century later. 

That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792&lt;ref&gt;Wikipedia &quot;[[w:Postal Service Act|Postal Service Act]]&quot;, accessed 2023-07-11.&lt;/ref&gt; made a major contribution to making the US what it is today.  Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.&lt;ref&gt;Historian, USPS (2010).&lt;/ref&gt; McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.&lt;ref name=McC-N2010&gt;McChesney and Nichols (2010, pp. 310-311, note 88).&lt;/ref&gt; 

During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;John (1995). See also the interview with him at &quot;[[Media concentration per Columbia History Professor Richard John]]&quot; on Wikiversity, accessed 2026-10-12.&lt;/ref&gt; In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.&lt;ref&gt;The &quot;6 percent per year&quot; growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in &quot;[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; on Wikiversity, accessed 2026-10-13.&lt;/ref&gt; 

One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. 

FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, which the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.&lt;ref&gt;This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on &quot;[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; in Wikiversity, accessed 2026-10-13.&lt;/ref&gt;

But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, &quot;the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred.&quot; They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. 

Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.&lt;ref&gt;On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of &quot;influencers&quot; by for-profit social media as essentially unleashed &quot;a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures.&quot; In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.&lt;/ref&gt; 

And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2021, p. 139) noted, &quot;In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%.  The top rate was then cut in half, with the announced objective of boosting growth.  But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.&quot;

=== Immigrants === 

We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. [[w:English Council of State|Lord Protector Cromwell]], who replaced Charles I, refused to authorize as many monopolies as his predecessors, presumably supported by the growing number of independent publishers of pamphlets, books, and newspapers mentioned above. He also encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. 

But Mokyr is not alone in proclaiming the contributions of immigrants to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how &quot;the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology.&quot;

Aghion et al. (2021, p. 292) also discuss (a) &quot;a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita&quot; and (b) the overrepresentation of immigrants in patent applications.&lt;ref&gt;e.g., Aghion et al. (2026, pp. 266-267).&lt;/ref&gt; However, [[w:Dean Baker|Baker]] (2016, pp. 77-78) claimed that &quot;over the last four decades ... stronger patent protection seems to be associated with slower growth,&quot; seemingly the opposite of the claim just quoted from Aghion et al. 

Anther example of how technology winners protect their status against competition is the [[w:Supreme Court of the United States|US Supreme Court]] decision in ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]''. [[w:Lawrence Lessig|Lessig]], who represented the plaintiff in that case, asked how could extending the copyright on existing works &quot;promote the Progress of Science and useful Arts&quot;, as required by the [[w:Copyright Clause|Copyright Clause]] of the US Constitution? Lessig lost that case. His (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to limit rather than &quot;promote the Progress of Science and useful Arts&quot;. This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000, which would bankrupt his parents and which they could not recover even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.&lt;ref&gt;Lessig (2004, p. 42).&lt;/ref&gt; This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP). The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, becauses much of their income is derived from copyright royalties, or (b) SLAPP laws, because anti-SLAPP laws, which exist in some jurisdictions but not others,&lt;ref&gt;[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the &quot;JAWBONE act&quot;, to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on &quot;[[Foundation for Individual Rights and Expression]]&quot;, accessed 2026-10-16.&lt;/ref&gt; limit the power of major corporations, which provide most of the money for the media. 

Similarly Graves (2023) asked, &quot;Do copyrights and paywalls on refereed academic journals violate the US constitution?&quot; No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.&lt;ref&gt;Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on &quot;[[Wikimedia concerns with European copyright rules including AI and scientific research]]&quot;. That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).&lt;/ref&gt;

=== Industrial Revolution ===

There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. 

Mokyr (2017, p.  3) says, &quot;The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society.&quot; He described &quot;three cultural elements&quot; required for &quot;sustainable economic growth propelled by technological progress&quot;: (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. &quot;[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.&lt;ref&gt;Mokyr (2017, pp. 19-20).&lt;/ref&gt; Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, &quot;The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution.&quot; 

Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, &quot;European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?&quot; Aghion et al. (2021, p. 20) describe the &quot;first Industrial Revolution&quot; as having been triggered by &quot;the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866.&quot;&lt;ref&gt;The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.&lt;/ref&gt;

The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not &quot;phases of growth and decline&quot; with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. 

Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, &quot;the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward.&quot; ... However, &quot;the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant to thousand or seven thousand years previously.&quot; (chapter 5) They also claim that, &quot;English national production per capita doubled from 1500 to 1700&quot;, (chapter 5), and &quot;Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root.&quot; (p. 45, chapter 2)

Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. 

Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the &quot;Old Pretender&quot;, a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. 

When Queen Anne died in 1702, she was succeeded by George I. His parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, &quot;and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts&quot;, according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs moved to confiscate &quot;[[w:Commons|commons]]&quot;, land whose use had been traditionally shared by commoners, and give to nobles. The Levellers had been excluded from the government of Lord Protector Cromwell, but the spirit of levelling still stalked the land. Some commoners joined &quot;Blacks&quot;, so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.&lt;ref&gt;Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on &quot;[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.&lt;/ref&gt; 

But not all accused were summarily executed. In 1724 &quot;John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized&quot; with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.&lt;ref&gt;Acemoglu and Robinson (2012, pp. 304-305).&lt;/ref&gt; 

These kinds of actions by the parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded &quot;universal [adult male] suffrage&quot; and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, &quot;The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The Manchester Observer called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... .&quot; And the British government placed enough other limits on its power that enough other commoners were allowed to became successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. 

== In sum ==

The above suggests that the rate of economic growth changes with either change in administration -- a new head of state -- or some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. 

However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).&lt;ref&gt;Graves (2025) includes an analysis of the data in Neff and Pickard (2024).&lt;/ref&gt; 

== Caveat ==

The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  

== Notes ==
{{reflist}}

== Bibliography ==

* &lt;!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)--&gt;{{cite Q|Q85764011}}
* &lt;!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)--&gt;{{cite Q|Q141241291}}
* &lt;!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)--&gt;{{cite Q|Q125292212}}
* &lt;!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)--&gt;{{cite Q|Q7997840}} 
* &lt;!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)--&gt;{{cite Q|Q137641358}}
* &lt;!--Ajzenman, Nicolas (29 January 2023). &quot;Migrants don't cause crime rates to increase — but false perceptions endure anyway&quot;. The Conversation.--&gt;{{cite Q|Q141758664}}
* &lt;!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) &quot;European Immigrants and the United States’ Rise to the Technological Frontier&quot;--&gt;{{cite Q|Q141678287}}
* &lt;!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer--&gt;{{cite Q|Q100216001}}

* &lt;!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) &quot;Maddison style estimates of the evolution of the world economy: A new 2023 update&quot;, Journal of Economic Surveys, 1-41--&gt;{{cite Q|Q126723821}}
* &lt;!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__&gt;{{cite Q|Q57945943}}


* &lt;!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition--&gt;{{cite Q|Q141156783}}
* &lt;!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies--&gt;{{cite Q|Q141158362}}
* &lt;!--Katarzyna Dośpiał-Borysiak (2017) &quot;Model of state management of petroleum sector -- Case of Norway--&gt;{{cite Q|Q141774179}}
* &lt;!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)--&gt;{{cite Q|Q136227988}}
* &lt;!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) &quot;The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration--&gt;{{cite Q|Q55932800}}
* &lt;!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)--&gt;{{cite Q|Q132855526}}
* &lt;!--Graves (2023-03-21)  Do copyrights and paywalls on academic journals violate the US Constitution?--&gt;{{cite Q|Q126116187}}
* &lt;!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.--&gt;{{cite Q|Q137188993}}
* &lt;!-- Historian, USPS (2010) Postage Rates for Periodicals --&gt;{{cite Q|Q112167199}}
* &lt;!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse--&gt;{{cite Q|Q54641943}}
* &lt;!--Volker Leppin and Timothy J. Wengert (2015) &quot;Sources for and against the Posting of the Ninety-Five Theses&quot;--&gt;{{cite Q|Q141737347}}
* &lt;!--Lawrence Lessig (2004) Free Culture--&gt;{{cite Q|Q830526}}
* &lt;!--Olivier Marie and Paolo Pinotti (2024-02-01) &quot;Immigration and Crime: An International Perspective&quot;, Journal of Economic Perspectives. 38 (1): 181–200--&gt;{{cite Q|Q128434874}}
* &lt;!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). &quot;
Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime&quot;
. Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.--&gt;{{cite Q|Q55932802}}
* &lt;!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) --&gt;{{cite Q|Q104888067}}.
* &lt;!-- Robert W. McChesney; John Nichols (2016). People get ready--&gt;{{cite Q|Q87619174}}
* &lt;!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)--&gt;{{cite Q|Q136118590}}
* &lt;!--Ashley N. Muchow &amp; Taisiia Stanishevska (2026) &quot;From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest&quot;, Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)--&gt;{{cite Q|Q141760694}}
* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* &lt;!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia--&gt;{{cite Q|Q141759196}}
* &lt;!--John Hely Owen (1938)  War at Sea Under Queen Anne 1702–1708--&gt;{{cite Q|Q141757101}}
* &lt;!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation--&gt;{{cite Q|Q141761223}}
* &lt;!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain--&gt;{{cite Q|Q141761849}}
* &lt;!--Nick Roll (2017-07-16) &quot;Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.--&gt;{{cite Q|Q141735231}}
* &lt;!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)--&gt;{{cite Q|Q137669960}}
* &lt;!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)--&gt;{{cite Q|Q137669987}}
* &lt;!--J. L. van Zanden  and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30--&gt;{{cite Q|Q137670058}} 
* &lt;!--Tom K. Wong (2017-01-26) &quot;The Effects of Sanctuary Policies on Crime and the Economy&quot;--&gt;{{cite Q|Q98775875}}

[[Category:Original research]]
[[Category:Research]]
[[Category:Economics]]
[[Category:Macroeconomics]]
[[Category:Gross domestic product]]
[[Category:Economic growth]]
[[Category:Modern Monetary Theory]]
[[Category:Political science]]
[[Category:Freedom and abundance]]
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:''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].''
:''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  
::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]''

== Abstract ==

This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. 

== Maddison Historical Statistics == 

[[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).&lt;ref&gt;See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.&lt;/ref&gt;'']]

The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. 

When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.&lt;ref&gt;Bolt and van Zanden (2024).&lt;/ref&gt; This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]], used in the Maddison data.) 

We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of [[w:North Sea oil|North Sea oil]].&lt;ref&gt;Dośpiał-Borysiak (2017).&lt;/ref&gt; With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. 

This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. 

== Nobel economists and others ==

Banerjee and Duflo (2019, p. 207) said, &quot;despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive.&quot; That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. 

While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, &quot;The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services.&quot; In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. 

Mokyr (2017, p. 255) also said that, &quot;intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished.&quot; That resistance, he suggested, drives &quot;the empirical regularity that no society remains at the cutting edge of technological creativity for very long&quot;.&lt;ref&gt;Mokyr (2017, p. 260).&lt;/ref&gt; This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1.  

Mokyr (2017, p. 60) also mentioned &quot;entrepreneurs of hate&quot;, who convince others to dislike some group in a way that may benefit those &quot;entrepreneurs&quot; and major media organizations, who promote such &quot;entrepreneurs&quot; to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.&lt;ref&gt;See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and the Wikiversity article on &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-14.&lt;/ref&gt; When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites.  

For example, most research on immigrants suggest that on average immigrants are more entrepreneurial and no more likely to commit crime than native born,&lt;ref&gt;e.g., Martínez et al. (2017); Muchow and Stanishevska (2026); Ajzenman(2023).&lt;/ref&gt; and some studies report that sanctuary jurisdictions have on average higher median incomes and less crime.&lt;ref&gt;Martínez et al. (2017); Wong (2017). See also the Wikipedia article on &quot;[[w:Sanctuary city|sanctuary city]]&quot;, accessed 2026-10-12.&lt;/ref&gt; Where immigrant crime is higher, it typically result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.&lt;ref&gt;Marie and Paolo (2024). See also the Wikipedia article on &quot;[[w:Immigration and crime|Immigration and crime]]&quot;, accessed 2026-10-12.&lt;/ref&gt; 

But major media outlets make money from featuring charismatic figures, who attract an audience without offending people who control much of the money for the media. In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities had more crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded &quot;that sanctuary policies have no effect on crime rates, despite narratives to the contrary.&quot;&lt;ref&gt;Roll (2017); Gonzalez O’Brien, et al. (2017).&lt;/ref&gt; To the extent that these comments provide a balanced summary of the research in this area, it suggests that leaders like Trump and Sessions, to name only two, can be fairly describes as &quot;entrepreneurs of hate&quot;. 

We next discuss competition in media markets before discussing immigrants further. 

=== Diversity of ownership of the major media === 

Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations. In such hierarchical societies some religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate designated evil others and give increasing shares of what they produce so the secular elites would &quot;protect&quot; them in wars against the designated evil others.

Acemoglu and Robinson (2012, p. 461) said, &quot;Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power ... in the United States [and] ... in the context of British democratization. Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799] ... .&quot; ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].) 

But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.&lt;ref&gt;Hendrix (2015, p. 64), quoted from the Wikipedia article on the &quot;[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand&lt;ref&gt;Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; and was much more popular than Tetzel's.&lt;ref&gt;Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; 

Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the Church of England, denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature,&lt;ref&gt;Raymond (2006), cited from the Wikipedia article on &quot;[[w:Pamphlet war|pamphlet war]]&quot;, accessed 2026-10-15.&lt;/ref&gt; theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.&lt;ref&gt;Hibbert et al. (2010, p. 928), cited from the Wikipedia article on &quot;[[w:Henry VIII|Henry VIII]]&quot;, accessed 2026-10-15.&lt;/ref&gt;

A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.&lt;ref&gt;Foxley (2013, p. 207), cited from the Wikipedia article on &quot;[[w:Levellers|Levellers]], accessed 2026-10-15.&lt;/ref&gt; However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that became the US over a century later. 

That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792&lt;ref&gt;Wikipedia &quot;[[w:Postal Service Act|Postal Service Act]]&quot;, accessed 2023-07-11.&lt;/ref&gt; made a major contribution to making the US what it is today.  Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.&lt;ref&gt;Historian, USPS (2010).&lt;/ref&gt; McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.&lt;ref name=McC-N2010&gt;McChesney and Nichols (2010, pp. 310-311, note 88).&lt;/ref&gt; 

During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;John (1995). See also the interview with him at &quot;[[Media concentration per Columbia History Professor Richard John]]&quot; on Wikiversity, accessed 2026-10-12.&lt;/ref&gt; In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.&lt;ref&gt;The &quot;6 percent per year&quot; growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in &quot;[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; on Wikiversity, accessed 2026-10-13.&lt;/ref&gt; 

One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. 

FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, which the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.&lt;ref&gt;This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on &quot;[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; in Wikiversity, accessed 2026-10-13.&lt;/ref&gt;

But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, &quot;the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred.&quot; They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. 

Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.&lt;ref&gt;On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of &quot;influencers&quot; by for-profit social media as essentially unleashed &quot;a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures.&quot; In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.&lt;/ref&gt; 

And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2021, p. 139) noted, &quot;In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%.  The top rate was then cut in half, with the announced objective of boosting growth.  But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.&quot;

=== Immigrants === 

We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. [[w:English Council of State|Lord Protector Cromwell]], who replaced Charles I, refused to authorize as many monopolies as his predecessors, presumably supported by the growing number of independent publishers of pamphlets, books, and newspapers mentioned above. He also encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. 

But Mokyr is not alone in proclaiming the contributions of immigrants to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how &quot;the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology.&quot;

Aghion et al. (2021, p. 292) also discuss (a) &quot;a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita&quot; and (b) the overrepresentation of immigrants in patent applications.&lt;ref&gt;e.g., Aghion et al. (2026, pp. 266-267).&lt;/ref&gt; However, [[w:Dean Baker|Baker]] (2016, pp. 77-78) claimed that &quot;over the last four decades ... stronger patent protection seems to be associated with slower growth,&quot; seemingly the opposite of the claim just quoted from Aghion et al. 

Anther example of how technology winners protect their status against competition is the [[w:Supreme Court of the United States|US Supreme Court]] decision in ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]''. [[w:Lawrence Lessig|Lessig]], who represented the plaintiff in that case, asked how could extending the copyright on existing works &quot;promote the Progress of Science and useful Arts&quot;, as required by the [[w:Copyright Clause|Copyright Clause]] of the US Constitution? Lessig lost that case. His (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to limit rather than &quot;promote the Progress of Science and useful Arts&quot;. This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000, which would bankrupt his parents and which they could not recover even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.&lt;ref&gt;Lessig (2004, p. 42).&lt;/ref&gt; This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP). The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, becauses much of their income is derived from copyright royalties, or (b) SLAPP laws, because anti-SLAPP laws, which exist in some jurisdictions but not others,&lt;ref&gt;[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the &quot;JAWBONE act&quot;, to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on &quot;[[Foundation for Individual Rights and Expression]]&quot;, accessed 2026-10-16.&lt;/ref&gt; limit the power of major corporations, which provide most of the money for the media. 

Similarly Graves (2023) asked, &quot;Do copyrights and paywalls on refereed academic journals violate the US constitution?&quot; No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.&lt;ref&gt;Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on &quot;[[Wikimedia concerns with European copyright rules including AI and scientific research]]&quot;. That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).&lt;/ref&gt;

=== Industrial Revolution ===

There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. 

Mokyr (2017, p.  3) says, &quot;The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society.&quot; He described &quot;three cultural elements&quot; required for &quot;sustainable economic growth propelled by technological progress&quot;: (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. &quot;[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.&lt;ref&gt;Mokyr (2017, pp. 19-20).&lt;/ref&gt; Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, &quot;The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution.&quot; 

Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, &quot;European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?&quot; Aghion et al. (2021, p. 20) describe the &quot;first Industrial Revolution&quot; as having been triggered by &quot;the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866.&quot;&lt;ref&gt;The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.&lt;/ref&gt;

The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not &quot;phases of growth and decline&quot; with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. 

Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, &quot;the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward.&quot; ... However, &quot;the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant to thousand or seven thousand years previously.&quot; (chapter 5) They also claim that, &quot;English national production per capita doubled from 1500 to 1700&quot;, (chapter 5), and &quot;Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root.&quot; (p. 45, chapter 2)

Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. 

Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the &quot;Old Pretender&quot;, a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. 

When Queen Anne died in 1702, she was succeeded by George I. His parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, &quot;and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts&quot;, according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs moved to confiscate &quot;[[w:Commons|commons]]&quot;, land whose use had been traditionally shared by commoners, and give to nobles. The Levellers had been excluded from the government of Lord Protector Cromwell, but the spirit of levelling still stalked the land. Some commoners joined &quot;Blacks&quot;, so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.&lt;ref&gt;Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on &quot;[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.&lt;/ref&gt; 

But not all accused were summarily executed. In 1724 &quot;John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized&quot; with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.&lt;ref&gt;Acemoglu and Robinson (2012, pp. 304-305).&lt;/ref&gt; 

These kinds of actions by the parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded &quot;universal [adult male] suffrage&quot; and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, &quot;The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The Manchester Observer called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... .&quot; And the British government placed enough other limits on its power that enough other commoners were allowed to became successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. 

== In sum ==

The above suggests that the rate of economic growth changes with either change in administration -- a new head of state -- or some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. 

However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).&lt;ref&gt;Graves (2025) includes an analysis of the data in Neff and Pickard (2024).&lt;/ref&gt; 

== Caveat ==

The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  

== Notes ==
{{reflist}}

== Bibliography ==

* &lt;!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)--&gt;{{cite Q|Q85764011}}
* &lt;!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)--&gt;{{cite Q|Q141241291}}
* &lt;!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)--&gt;{{cite Q|Q125292212}}
* &lt;!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)--&gt;{{cite Q|Q7997840}} 
* &lt;!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)--&gt;{{cite Q|Q137641358}}
* &lt;!--Ajzenman, Nicolas (29 January 2023). &quot;Migrants don't cause crime rates to increase — but false perceptions endure anyway&quot;. The Conversation.--&gt;{{cite Q|Q141758664}}
* &lt;!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) &quot;European Immigrants and the United States’ Rise to the Technological Frontier&quot;--&gt;{{cite Q|Q141678287}}
* &lt;!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer--&gt;{{cite Q|Q100216001}}

* &lt;!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) &quot;Maddison style estimates of the evolution of the world economy: A new 2023 update&quot;, Journal of Economic Surveys, 1-41--&gt;{{cite Q|Q126723821}}
* &lt;!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__&gt;{{cite Q|Q57945943}}


* &lt;!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition--&gt;{{cite Q|Q141156783}}
* &lt;!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies--&gt;{{cite Q|Q141158362}}
* &lt;!--Katarzyna Dośpiał-Borysiak (2017) &quot;Model of state management of petroleum sector -- Case of Norway--&gt;{{cite Q|Q141774179}}
* &lt;!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)--&gt;{{cite Q|Q136227988}}
* &lt;!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) &quot;The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration--&gt;{{cite Q|Q55932800}}
* &lt;!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)--&gt;{{cite Q|Q132855526}}
* &lt;!--Graves (2023-03-21)  Do copyrights and paywalls on academic journals violate the US Constitution?--&gt;{{cite Q|Q126116187}}
* &lt;!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.--&gt;{{cite Q|Q137188993}}
* &lt;!-- Historian, USPS (2010) Postage Rates for Periodicals --&gt;{{cite Q|Q112167199}}
* &lt;!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse--&gt;{{cite Q|Q54641943}}
* &lt;!--Volker Leppin and Timothy J. Wengert (2015) &quot;Sources for and against the Posting of the Ninety-Five Theses&quot;--&gt;{{cite Q|Q141737347}}
* &lt;!--Lawrence Lessig (2004) Free Culture--&gt;{{cite Q|Q830526}}
* &lt;!--Olivier Marie and Paolo Pinotti (2024-02-01) &quot;Immigration and Crime: An International Perspective&quot;, Journal of Economic Perspectives. 38 (1): 181–200--&gt;{{cite Q|Q128434874}}
* &lt;!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). &quot;
Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime&quot;
. Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.--&gt;{{cite Q|Q55932802}}
* &lt;!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) --&gt;{{cite Q|Q104888067}}.
* &lt;!-- Robert W. McChesney; John Nichols (2016). People get ready--&gt;{{cite Q|Q87619174}}
* &lt;!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)--&gt;{{cite Q|Q136118590}}
* &lt;!--Ashley N. Muchow &amp; Taisiia Stanishevska (2026) &quot;From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest&quot;, Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)--&gt;{{cite Q|Q141760694}}
* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* &lt;!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia--&gt;{{cite Q|Q141759196}}
* &lt;!--John Hely Owen (1938)  War at Sea Under Queen Anne 1702–1708--&gt;{{cite Q|Q141757101}}
* &lt;!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation--&gt;{{cite Q|Q141761223}}
* &lt;!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain--&gt;{{cite Q|Q141761849}}
* &lt;!--Nick Roll (2017-07-16) &quot;Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.--&gt;{{cite Q|Q141735231}}
* &lt;!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)--&gt;{{cite Q|Q137669960}}
* &lt;!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)--&gt;{{cite Q|Q137669987}}
* &lt;!--J. L. van Zanden  and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30--&gt;{{cite Q|Q137670058}} 
* &lt;!--Tom K. Wong (2017-01-26) &quot;The Effects of Sanctuary Policies on Crime and the Economy&quot;--&gt;{{cite Q|Q98775875}}

[[Category:Original research]]
[[Category:Research]]
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[[Category:Gross domestic product]]
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      <text bytes="45914" sha1="qeo45oap5k4j05cf6xr1njsijvp7by4" xml:space="preserve">{{Research project}} 
:''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].''
:''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  
::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]''

== Abstract ==

This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. 

== Maddison Historical Statistics == 

[[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).&lt;ref&gt;See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.&lt;/ref&gt;'']]

The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. 

When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.&lt;ref&gt;Bolt and van Zanden (2024).&lt;/ref&gt; This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]], used in the Maddison data.) 

We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of [[w:North Sea oil|North Sea oil]].&lt;ref&gt;Dośpiał-Borysiak (2017).&lt;/ref&gt; With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. 

This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. 

== Nobel economists and others ==

Banerjee and Duflo (2019, p. 207) said, &quot;despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive.&quot; That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. 

While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, &quot;The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services.&quot; In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. 

Mokyr (2017, p. 255) also said that, &quot;intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished.&quot; That resistance, he suggested, drives &quot;the empirical regularity that no society remains at the cutting edge of technological creativity for very long&quot;.&lt;ref&gt;Mokyr (2017, p. 260).&lt;/ref&gt; This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1.  

Mokyr (2017, p. 60) also mentioned &quot;entrepreneurs of hate&quot;, who convince others to dislike some group in a way that may benefit those &quot;entrepreneurs&quot; and major media organizations, who promote such &quot;entrepreneurs&quot; to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.&lt;ref&gt;See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and the Wikiversity article on &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-14.&lt;/ref&gt; When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites.  

For example, most research on immigrants suggest that on average immigrants are more entrepreneurial and no more likely to commit crime than native born,&lt;ref&gt;e.g., Martínez et al. (2017); Muchow and Stanishevska (2026); Ajzenman(2023).&lt;/ref&gt; and some studies report that sanctuary jurisdictions have on average higher median incomes and less crime.&lt;ref&gt;Martínez et al. (2017); Wong (2017). See also the Wikipedia article on &quot;[[w:Sanctuary city|sanctuary city]]&quot;, accessed 2026-10-12.&lt;/ref&gt; Where immigrant crime is higher, it typically result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.&lt;ref&gt;Marie and Paolo (2024). See also the Wikipedia article on &quot;[[w:Immigration and crime|Immigration and crime]]&quot;, accessed 2026-10-12.&lt;/ref&gt; 

But major media outlets make money from featuring charismatic figures, who attract an audience without offending people who control much of the money for the media. In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities had more crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded &quot;that sanctuary policies have no effect on crime rates, despite narratives to the contrary.&quot;&lt;ref&gt;Roll (2017); Gonzalez O’Brien, et al. (2017).&lt;/ref&gt; To the extent that these comments provide a balanced summary of the research in this area, it suggests that leaders like Trump and Sessions, to name only two, can be fairly describes as &quot;entrepreneurs of hate&quot;. 

We next discuss competition in media markets before discussing immigrants further. 

=== Diversity of ownership of the major media === 

Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations. In such hierarchical societies some religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate designated evil others and give increasing shares of what they produce so the secular elites would &quot;protect&quot; them in wars against the designated evil others.

Acemoglu and Robinson (2012, p. 461) said, &quot;Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power. ... Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799]&quot; and in the US. ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].)

But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.&lt;ref&gt;Hendrix (2015, p. 64), quoted from the Wikipedia article on the &quot;[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand&lt;ref&gt;Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; and was much more popular than Tetzel's.&lt;ref&gt;Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; 

Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the Church of England, denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature,&lt;ref&gt;Raymond (2006), cited from the Wikipedia article on &quot;[[w:Pamphlet war|pamphlet war]]&quot;, accessed 2026-10-15.&lt;/ref&gt; theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.&lt;ref&gt;Hibbert et al. (2010, p. 928), cited from the Wikipedia article on &quot;[[w:Henry VIII|Henry VIII]]&quot;, accessed 2026-10-15.&lt;/ref&gt;

A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.&lt;ref&gt;Foxley (2013, p. 207), cited from the Wikipedia article on &quot;[[w:Levellers|Levellers]], accessed 2026-10-15.&lt;/ref&gt; However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that became the US over a century later. 

That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792&lt;ref&gt;Wikipedia &quot;[[w:Postal Service Act|Postal Service Act]]&quot;, accessed 2023-07-11.&lt;/ref&gt; made a major contribution to making the US what it is today.  Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.&lt;ref&gt;Historian, USPS (2010).&lt;/ref&gt; McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.&lt;ref name=McC-N2010&gt;McChesney and Nichols (2010, pp. 310-311, note 88).&lt;/ref&gt; 

During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;John (1995). See also the interview with him at &quot;[[Media concentration per Columbia History Professor Richard John]]&quot; on Wikiversity, accessed 2026-10-12.&lt;/ref&gt; In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.&lt;ref&gt;The &quot;6 percent per year&quot; growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in &quot;[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; on Wikiversity, accessed 2026-10-13.&lt;/ref&gt; 

One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. 

FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, which the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.&lt;ref&gt;This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on &quot;[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; in Wikiversity, accessed 2026-10-13.&lt;/ref&gt;

But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, &quot;the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred.&quot; They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. 

Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.&lt;ref&gt;On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of &quot;influencers&quot; by for-profit social media as essentially unleashed &quot;a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures.&quot; In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.&lt;/ref&gt; 

And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2021, p. 139) noted, &quot;In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%.  The top rate was then cut in half, with the announced objective of boosting growth.  But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.&quot;

=== Immigrants === 

We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. [[w:English Council of State|Lord Protector Cromwell]], who replaced Charles I, refused to authorize as many monopolies as his predecessors, presumably supported by the growing number of independent publishers of pamphlets, books, and newspapers mentioned above. He also encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. 

But Mokyr is not alone in proclaiming the contributions of immigrants to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how &quot;the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology.&quot;

Aghion et al. (2021, p. 292) also discuss (a) &quot;a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita&quot; and (b) the overrepresentation of immigrants in patent applications.&lt;ref&gt;e.g., Aghion et al. (2026, pp. 266-267).&lt;/ref&gt; However, [[w:Dean Baker|Baker]] (2016, pp. 77-78) claimed that &quot;over the last four decades ... stronger patent protection seems to be associated with slower growth,&quot; seemingly the opposite of the claim just quoted from Aghion et al. 

Anther example of how technology winners protect their status against competition is the [[w:Supreme Court of the United States|US Supreme Court]] decision in ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]''. [[w:Lawrence Lessig|Lessig]], who represented the plaintiff in that case, asked how could extending the copyright on existing works &quot;promote the Progress of Science and useful Arts&quot;, as required by the [[w:Copyright Clause|Copyright Clause]] of the US Constitution? Lessig lost that case. His (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to limit rather than &quot;promote the Progress of Science and useful Arts&quot;. This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000, which would bankrupt his parents and which they could not recover even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.&lt;ref&gt;Lessig (2004, p. 42).&lt;/ref&gt; This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP). The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, becauses much of their income is derived from copyright royalties, or (b) SLAPP laws, because anti-SLAPP laws, which exist in some jurisdictions but not others,&lt;ref&gt;[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the &quot;JAWBONE act&quot;, to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on &quot;[[Foundation for Individual Rights and Expression]]&quot;, accessed 2026-10-16.&lt;/ref&gt; limit the power of major corporations, which provide most of the money for the media. 

Similarly Graves (2023) asked, &quot;Do copyrights and paywalls on refereed academic journals violate the US constitution?&quot; No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.&lt;ref&gt;Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on &quot;[[Wikimedia concerns with European copyright rules including AI and scientific research]]&quot;. That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).&lt;/ref&gt;

=== Industrial Revolution ===

There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. 

Mokyr (2017, p.  3) says, &quot;The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society.&quot; He described &quot;three cultural elements&quot; required for &quot;sustainable economic growth propelled by technological progress&quot;: (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. &quot;[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.&lt;ref&gt;Mokyr (2017, pp. 19-20).&lt;/ref&gt; Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, &quot;The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution.&quot; 

Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, &quot;European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?&quot; Aghion et al. (2021, p. 20) describe the &quot;first Industrial Revolution&quot; as having been triggered by &quot;the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866.&quot;&lt;ref&gt;The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.&lt;/ref&gt;

The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not &quot;phases of growth and decline&quot; with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. 

Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, &quot;the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward.&quot; ... However, &quot;the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant to thousand or seven thousand years previously.&quot; (chapter 5) They also claim that, &quot;English national production per capita doubled from 1500 to 1700&quot;, (chapter 5), and &quot;Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root.&quot; (p. 45, chapter 2)

Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. 

Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the &quot;Old Pretender&quot;, a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. 

When Queen Anne died in 1702, she was succeeded by George I. His parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, &quot;and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts&quot;, according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs moved to confiscate &quot;[[w:Commons|commons]]&quot;, land whose use had been traditionally shared by commoners, and give to nobles. The Levellers had been excluded from the government of Lord Protector Cromwell, but the spirit of levelling still stalked the land. Some commoners joined &quot;Blacks&quot;, so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.&lt;ref&gt;Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on &quot;[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.&lt;/ref&gt; 

But not all accused were summarily executed. In 1724 &quot;John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized&quot; with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.&lt;ref&gt;Acemoglu and Robinson (2012, pp. 304-305).&lt;/ref&gt; 

These kinds of actions by the parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded &quot;universal [adult male] suffrage&quot; and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, &quot;The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The Manchester Observer called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... .&quot; And the British government placed enough other limits on its power that enough other commoners were allowed to became successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. 

== In sum ==

The above suggests that the rate of economic growth changes with either change in administration -- a new head of state -- or some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. 

However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).&lt;ref&gt;Graves (2025) includes an analysis of the data in Neff and Pickard (2024).&lt;/ref&gt; 

== Caveat ==

The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  

== Notes ==
{{reflist}}

== Bibliography ==

* &lt;!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)--&gt;{{cite Q|Q85764011}}
* &lt;!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)--&gt;{{cite Q|Q141241291}}
* &lt;!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)--&gt;{{cite Q|Q125292212}}
* &lt;!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)--&gt;{{cite Q|Q7997840}} 
* &lt;!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)--&gt;{{cite Q|Q137641358}}
* &lt;!--Ajzenman, Nicolas (29 January 2023). &quot;Migrants don't cause crime rates to increase — but false perceptions endure anyway&quot;. The Conversation.--&gt;{{cite Q|Q141758664}}
* &lt;!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) &quot;European Immigrants and the United States’ Rise to the Technological Frontier&quot;--&gt;{{cite Q|Q141678287}}
* &lt;!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer--&gt;{{cite Q|Q100216001}}

* &lt;!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) &quot;Maddison style estimates of the evolution of the world economy: A new 2023 update&quot;, Journal of Economic Surveys, 1-41--&gt;{{cite Q|Q126723821}}
* &lt;!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__&gt;{{cite Q|Q57945943}}


* &lt;!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition--&gt;{{cite Q|Q141156783}}
* &lt;!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies--&gt;{{cite Q|Q141158362}}
* &lt;!--Katarzyna Dośpiał-Borysiak (2017) &quot;Model of state management of petroleum sector -- Case of Norway--&gt;{{cite Q|Q141774179}}
* &lt;!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)--&gt;{{cite Q|Q136227988}}
* &lt;!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) &quot;The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration--&gt;{{cite Q|Q55932800}}
* &lt;!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)--&gt;{{cite Q|Q132855526}}
* &lt;!--Graves (2023-03-21)  Do copyrights and paywalls on academic journals violate the US Constitution?--&gt;{{cite Q|Q126116187}}
* &lt;!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.--&gt;{{cite Q|Q137188993}}
* &lt;!-- Historian, USPS (2010) Postage Rates for Periodicals --&gt;{{cite Q|Q112167199}}
* &lt;!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse--&gt;{{cite Q|Q54641943}}
* &lt;!--Volker Leppin and Timothy J. Wengert (2015) &quot;Sources for and against the Posting of the Ninety-Five Theses&quot;--&gt;{{cite Q|Q141737347}}
* &lt;!--Lawrence Lessig (2004) Free Culture--&gt;{{cite Q|Q830526}}
* &lt;!--Olivier Marie and Paolo Pinotti (2024-02-01) &quot;Immigration and Crime: An International Perspective&quot;, Journal of Economic Perspectives. 38 (1): 181–200--&gt;{{cite Q|Q128434874}}
* &lt;!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). &quot;
Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime&quot;
. Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.--&gt;{{cite Q|Q55932802}}
* &lt;!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) --&gt;{{cite Q|Q104888067}}.
* &lt;!-- Robert W. McChesney; John Nichols (2016). People get ready--&gt;{{cite Q|Q87619174}}
* &lt;!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)--&gt;{{cite Q|Q136118590}}
* &lt;!--Ashley N. Muchow &amp; Taisiia Stanishevska (2026) &quot;From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest&quot;, Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)--&gt;{{cite Q|Q141760694}}
* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* &lt;!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia--&gt;{{cite Q|Q141759196}}
* &lt;!--John Hely Owen (1938)  War at Sea Under Queen Anne 1702–1708--&gt;{{cite Q|Q141757101}}
* &lt;!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation--&gt;{{cite Q|Q141761223}}
* &lt;!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain--&gt;{{cite Q|Q141761849}}
* &lt;!--Nick Roll (2017-07-16) &quot;Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.--&gt;{{cite Q|Q141735231}}
* &lt;!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)--&gt;{{cite Q|Q137669960}}
* &lt;!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)--&gt;{{cite Q|Q137669987}}
* &lt;!--J. L. van Zanden  and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30--&gt;{{cite Q|Q137670058}} 
* &lt;!--Tom K. Wong (2017-01-26) &quot;The Effects of Sanctuary Policies on Crime and the Economy&quot;--&gt;{{cite Q|Q98775875}}

[[Category:Original research]]
[[Category:Research]]
[[Category:Economics]]
[[Category:Macroeconomics]]
[[Category:Gross domestic product]]
[[Category:Economic growth]]
[[Category:Modern Monetary Theory]]
[[Category:Political science]]
[[Category:Freedom and abundance]]
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      <text bytes="45914" sha1="jdow8zdmyn7h4hfyzg97kwxndqu377y" xml:space="preserve">{{Research project}} 
:''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].''
:''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  
::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]''

== Abstract ==

This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. 

== Maddison Historical Statistics == 

[[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).&lt;ref&gt;See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.&lt;/ref&gt;'']]

The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. 

When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.&lt;ref&gt;Bolt and van Zanden (2024).&lt;/ref&gt; This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]], used in the Maddison data.) 

We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of [[w:North Sea oil|North Sea oil]].&lt;ref&gt;Dośpiał-Borysiak (2017).&lt;/ref&gt; With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. 

This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. 

== Nobel economists and others ==

Banerjee and Duflo (2019, p. 207) said, &quot;despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive.&quot; That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. 

While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, &quot;The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services.&quot; In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. 

Mokyr (2017, p. 255) also said that, &quot;intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished.&quot; That resistance, he suggested, drives &quot;the empirical regularity that no society remains at the cutting edge of technological creativity for very long&quot;.&lt;ref&gt;Mokyr (2017, p. 260).&lt;/ref&gt; This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1.  

Mokyr (2017, p. 60) also mentioned &quot;entrepreneurs of hate&quot;, who convince others to dislike some group in a way that may benefit those &quot;entrepreneurs&quot; and major media organizations, who promote such &quot;entrepreneurs&quot; to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.&lt;ref&gt;See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and the Wikiversity article on &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-14.&lt;/ref&gt; When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites.  

For example, most research on immigrants suggest that on average immigrants are more entrepreneurial and no more likely to commit crime than native born,&lt;ref&gt;e.g., Martínez et al. (2017); Muchow and Stanishevska (2026); Ajzenman(2023).&lt;/ref&gt; and some studies report that sanctuary jurisdictions have on average higher median incomes and less crime.&lt;ref&gt;Martínez et al. (2017); Wong (2017). See also the Wikipedia article on &quot;[[w:Sanctuary city|sanctuary city]]&quot;, accessed 2026-10-12.&lt;/ref&gt; Where immigrant crime is higher, it typically result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.&lt;ref&gt;Marie and Paolo (2024). See also the Wikipedia article on &quot;[[w:Immigration and crime|Immigration and crime]]&quot;, accessed 2026-10-12.&lt;/ref&gt; 

But major media outlets make money from featuring charismatic figures, who attract an audience without offending people who control much of the money for the media. In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities had more crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded &quot;that sanctuary policies have no effect on crime rates, despite narratives to the contrary.&quot;&lt;ref&gt;Roll (2017); Gonzalez O’Brien, et al. (2017).&lt;/ref&gt; To the extent that these comments provide a balanced summary of the research in this area, it suggests that leaders like Trump and Sessions, to name only two, can be fairly describes as &quot;entrepreneurs of hate&quot;. 

We next discuss competition in media markets before discussing immigrants further. 

=== Diversity of ownership of the major media === 

Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations. In such hierarchical societies some religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate designated evil others and give increasing shares of what they produce so the secular elites would &quot;protect&quot; them in wars against the designated evil others.

Acemoglu and Robinson (2012, p. 461) said, &quot;Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power. ... Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799]&quot; and in the US. ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].)

But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.&lt;ref&gt;Hendrix (2015, p. 64), quoted from the Wikipedia article on the &quot;[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand&lt;ref&gt;Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; and was much more popular than Tetzel's.&lt;ref&gt;Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; 

Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the Church of England, denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature.&lt;ref&gt;Raymond (2006), cited from the Wikipedia article on &quot;[[w:Pamphlet war|pamphlet war]]&quot;, accessed 2026-10-15.&lt;/ref&gt; Theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.&lt;ref&gt;Hibbert et al. (2010, p. 928), cited from the Wikipedia article on &quot;[[w:Henry VIII|Henry VIII]]&quot;, accessed 2026-10-15.&lt;/ref&gt;

A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.&lt;ref&gt;Foxley (2013, p. 207), cited from the Wikipedia article on &quot;[[w:Levellers|Levellers]], accessed 2026-10-15.&lt;/ref&gt; However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that became the US over a century later. 

That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792&lt;ref&gt;Wikipedia &quot;[[w:Postal Service Act|Postal Service Act]]&quot;, accessed 2023-07-11.&lt;/ref&gt; made a major contribution to making the US what it is today.  Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.&lt;ref&gt;Historian, USPS (2010).&lt;/ref&gt; McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.&lt;ref name=McC-N2010&gt;McChesney and Nichols (2010, pp. 310-311, note 88).&lt;/ref&gt; 

During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;John (1995). See also the interview with him at &quot;[[Media concentration per Columbia History Professor Richard John]]&quot; on Wikiversity, accessed 2026-10-12.&lt;/ref&gt; In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.&lt;ref&gt;The &quot;6 percent per year&quot; growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in &quot;[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; on Wikiversity, accessed 2026-10-13.&lt;/ref&gt; 

One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. 

FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, which the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.&lt;ref&gt;This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on &quot;[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; in Wikiversity, accessed 2026-10-13.&lt;/ref&gt;

But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, &quot;the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred.&quot; They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. 

Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.&lt;ref&gt;On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of &quot;influencers&quot; by for-profit social media as essentially unleashed &quot;a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures.&quot; In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.&lt;/ref&gt; 

And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2021, p. 139) noted, &quot;In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%.  The top rate was then cut in half, with the announced objective of boosting growth.  But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.&quot;

=== Immigrants === 

We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. [[w:English Council of State|Lord Protector Cromwell]], who replaced Charles I, refused to authorize as many monopolies as his predecessors, presumably supported by the growing number of independent publishers of pamphlets, books, and newspapers mentioned above. He also encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. 

But Mokyr is not alone in proclaiming the contributions of immigrants to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how &quot;the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology.&quot;

Aghion et al. (2021, p. 292) also discuss (a) &quot;a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita&quot; and (b) the overrepresentation of immigrants in patent applications.&lt;ref&gt;e.g., Aghion et al. (2026, pp. 266-267).&lt;/ref&gt; However, [[w:Dean Baker|Baker]] (2016, pp. 77-78) claimed that &quot;over the last four decades ... stronger patent protection seems to be associated with slower growth,&quot; seemingly the opposite of the claim just quoted from Aghion et al. 

Anther example of how technology winners protect their status against competition is the [[w:Supreme Court of the United States|US Supreme Court]] decision in ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]''. [[w:Lawrence Lessig|Lessig]], who represented the plaintiff in that case, asked how could extending the copyright on existing works &quot;promote the Progress of Science and useful Arts&quot;, as required by the [[w:Copyright Clause|Copyright Clause]] of the US Constitution? Lessig lost that case. His (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to limit rather than &quot;promote the Progress of Science and useful Arts&quot;. This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000, which would bankrupt his parents and which they could not recover even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.&lt;ref&gt;Lessig (2004, p. 42).&lt;/ref&gt; This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP). The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, becauses much of their income is derived from copyright royalties, or (b) SLAPP laws, because anti-SLAPP laws, which exist in some jurisdictions but not others,&lt;ref&gt;[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the &quot;JAWBONE act&quot;, to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on &quot;[[Foundation for Individual Rights and Expression]]&quot;, accessed 2026-10-16.&lt;/ref&gt; limit the power of major corporations, which provide most of the money for the media. 

Similarly Graves (2023) asked, &quot;Do copyrights and paywalls on refereed academic journals violate the US constitution?&quot; No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.&lt;ref&gt;Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on &quot;[[Wikimedia concerns with European copyright rules including AI and scientific research]]&quot;. That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).&lt;/ref&gt;

=== Industrial Revolution ===

There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. 

Mokyr (2017, p.  3) says, &quot;The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society.&quot; He described &quot;three cultural elements&quot; required for &quot;sustainable economic growth propelled by technological progress&quot;: (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. &quot;[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.&lt;ref&gt;Mokyr (2017, pp. 19-20).&lt;/ref&gt; Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, &quot;The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution.&quot; 

Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, &quot;European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?&quot; Aghion et al. (2021, p. 20) describe the &quot;first Industrial Revolution&quot; as having been triggered by &quot;the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866.&quot;&lt;ref&gt;The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.&lt;/ref&gt;

The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not &quot;phases of growth and decline&quot; with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. 

Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, &quot;the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward.&quot; ... However, &quot;the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant to thousand or seven thousand years previously.&quot; (chapter 5) They also claim that, &quot;English national production per capita doubled from 1500 to 1700&quot;, (chapter 5), and &quot;Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root.&quot; (p. 45, chapter 2)

Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. 

Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the &quot;Old Pretender&quot;, a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. 

When Queen Anne died in 1702, she was succeeded by George I. His parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, &quot;and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts&quot;, according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs moved to confiscate &quot;[[w:Commons|commons]]&quot;, land whose use had been traditionally shared by commoners, and give to nobles. The Levellers had been excluded from the government of Lord Protector Cromwell, but the spirit of levelling still stalked the land. Some commoners joined &quot;Blacks&quot;, so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.&lt;ref&gt;Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on &quot;[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.&lt;/ref&gt; 

But not all accused were summarily executed. In 1724 &quot;John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized&quot; with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.&lt;ref&gt;Acemoglu and Robinson (2012, pp. 304-305).&lt;/ref&gt; 

These kinds of actions by the parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded &quot;universal [adult male] suffrage&quot; and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, &quot;The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The Manchester Observer called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... .&quot; And the British government placed enough other limits on its power that enough other commoners were allowed to became successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. 

== In sum ==

The above suggests that the rate of economic growth changes with either change in administration -- a new head of state -- or some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. 

However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).&lt;ref&gt;Graves (2025) includes an analysis of the data in Neff and Pickard (2024).&lt;/ref&gt; 

== Caveat ==

The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  

== Notes ==
{{reflist}}

== Bibliography ==

* &lt;!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)--&gt;{{cite Q|Q85764011}}
* &lt;!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)--&gt;{{cite Q|Q141241291}}
* &lt;!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)--&gt;{{cite Q|Q125292212}}
* &lt;!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)--&gt;{{cite Q|Q7997840}} 
* &lt;!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)--&gt;{{cite Q|Q137641358}}
* &lt;!--Ajzenman, Nicolas (29 January 2023). &quot;Migrants don't cause crime rates to increase — but false perceptions endure anyway&quot;. The Conversation.--&gt;{{cite Q|Q141758664}}
* &lt;!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) &quot;European Immigrants and the United States’ Rise to the Technological Frontier&quot;--&gt;{{cite Q|Q141678287}}
* &lt;!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer--&gt;{{cite Q|Q100216001}}

* &lt;!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) &quot;Maddison style estimates of the evolution of the world economy: A new 2023 update&quot;, Journal of Economic Surveys, 1-41--&gt;{{cite Q|Q126723821}}
* &lt;!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__&gt;{{cite Q|Q57945943}}


* &lt;!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition--&gt;{{cite Q|Q141156783}}
* &lt;!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies--&gt;{{cite Q|Q141158362}}
* &lt;!--Katarzyna Dośpiał-Borysiak (2017) &quot;Model of state management of petroleum sector -- Case of Norway--&gt;{{cite Q|Q141774179}}
* &lt;!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)--&gt;{{cite Q|Q136227988}}
* &lt;!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) &quot;The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration--&gt;{{cite Q|Q55932800}}
* &lt;!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)--&gt;{{cite Q|Q132855526}}
* &lt;!--Graves (2023-03-21)  Do copyrights and paywalls on academic journals violate the US Constitution?--&gt;{{cite Q|Q126116187}}
* &lt;!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.--&gt;{{cite Q|Q137188993}}
* &lt;!-- Historian, USPS (2010) Postage Rates for Periodicals --&gt;{{cite Q|Q112167199}}
* &lt;!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse--&gt;{{cite Q|Q54641943}}
* &lt;!--Volker Leppin and Timothy J. Wengert (2015) &quot;Sources for and against the Posting of the Ninety-Five Theses&quot;--&gt;{{cite Q|Q141737347}}
* &lt;!--Lawrence Lessig (2004) Free Culture--&gt;{{cite Q|Q830526}}
* &lt;!--Olivier Marie and Paolo Pinotti (2024-02-01) &quot;Immigration and Crime: An International Perspective&quot;, Journal of Economic Perspectives. 38 (1): 181–200--&gt;{{cite Q|Q128434874}}
* &lt;!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). &quot;
Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime&quot;
. Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.--&gt;{{cite Q|Q55932802}}
* &lt;!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) --&gt;{{cite Q|Q104888067}}.
* &lt;!-- Robert W. McChesney; John Nichols (2016). People get ready--&gt;{{cite Q|Q87619174}}
* &lt;!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)--&gt;{{cite Q|Q136118590}}
* &lt;!--Ashley N. Muchow &amp; Taisiia Stanishevska (2026) &quot;From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest&quot;, Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)--&gt;{{cite Q|Q141760694}}
* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* &lt;!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia--&gt;{{cite Q|Q141759196}}
* &lt;!--John Hely Owen (1938)  War at Sea Under Queen Anne 1702–1708--&gt;{{cite Q|Q141757101}}
* &lt;!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation--&gt;{{cite Q|Q141761223}}
* &lt;!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain--&gt;{{cite Q|Q141761849}}
* &lt;!--Nick Roll (2017-07-16) &quot;Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.--&gt;{{cite Q|Q141735231}}
* &lt;!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)--&gt;{{cite Q|Q137669960}}
* &lt;!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)--&gt;{{cite Q|Q137669987}}
* &lt;!--J. L. van Zanden  and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30--&gt;{{cite Q|Q137670058}} 
* &lt;!--Tom K. Wong (2017-01-26) &quot;The Effects of Sanctuary Policies on Crime and the Economy&quot;--&gt;{{cite Q|Q98775875}}

[[Category:Original research]]
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:''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].''
:''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  
::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]''

== Abstract ==

This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. 

== Maddison Historical Statistics == 

[[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).&lt;ref&gt;See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.&lt;/ref&gt;'']]

The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. 

When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.&lt;ref&gt;Bolt and van Zanden (2024).&lt;/ref&gt; This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]], used in the Maddison data.) 

We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of [[w:North Sea oil|North Sea oil]].&lt;ref&gt;Dośpiał-Borysiak (2017).&lt;/ref&gt; With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. 

This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. 

== Nobel economists and others ==

Banerjee and Duflo (2019, p. 207) said, &quot;despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive.&quot; That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. 

While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, &quot;The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services.&quot; In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. 

Mokyr (2017, p. 255) also said that, &quot;intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished.&quot; That resistance, he suggested, drives &quot;the empirical regularity that no society remains at the cutting edge of technological creativity for very long&quot;.&lt;ref&gt;Mokyr (2017, p. 260).&lt;/ref&gt; This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1.  

Mokyr (2017, p. 60) also mentioned &quot;entrepreneurs of hate&quot;, who convince others to dislike some group in a way that may benefit those &quot;entrepreneurs&quot; and major media organizations, who promote such &quot;entrepreneurs&quot; to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.&lt;ref&gt;See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and the Wikiversity article on &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-14.&lt;/ref&gt; When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites.  

For example, most research on immigrants suggest that on average immigrants are more entrepreneurial and no more likely to commit crime than native born,&lt;ref&gt;e.g., Martínez et al. (2017); Muchow and Stanishevska (2026); Ajzenman(2023).&lt;/ref&gt; and some studies report that sanctuary jurisdictions have on average higher median incomes and less crime.&lt;ref&gt;Martínez et al. (2017); Wong (2017). See also the Wikipedia article on &quot;[[w:Sanctuary city|sanctuary city]]&quot;, accessed 2026-10-12.&lt;/ref&gt; Where immigrant crime is higher, it typically result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.&lt;ref&gt;Marie and Paolo (2024). See also the Wikipedia article on &quot;[[w:Immigration and crime|Immigration and crime]]&quot;, accessed 2026-10-12.&lt;/ref&gt; 

But major media outlets make money from featuring charismatic figures, who attract an audience without offending people who control much of the money for the media. In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities had more crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded &quot;that sanctuary policies have no effect on crime rates, despite narratives to the contrary.&quot;&lt;ref&gt;Roll (2017); Gonzalez O’Brien, et al. (2017).&lt;/ref&gt; To the extent that these comments provide a balanced summary of the research in this area, it suggests that leaders like Trump and Sessions, to name only two, can be fairly describes as &quot;entrepreneurs of hate&quot;. 

We next discuss competition in media markets before discussing immigrants further. 

=== Diversity of ownership of the major media === 

Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations. In such hierarchical societies some religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate designated evil others and give increasing shares of what they produce so the secular elites would &quot;protect&quot; them in wars against the designated evil others.

Acemoglu and Robinson (2012, p. 461) said, &quot;Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power. ... Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799]&quot; and in the US. ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].)

But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.&lt;ref&gt;Hendrix (2015, p. 64), quoted from the Wikipedia article on the &quot;[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand&lt;ref&gt;Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; and was much more popular than Tetzel's.&lt;ref&gt;Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; 

Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the [[w:Church of England|Church of England]], denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature.&lt;ref&gt;Raymond (2006), cited from the Wikipedia article on &quot;[[w:Pamphlet war|pamphlet war]]&quot;, accessed 2026-10-15.&lt;/ref&gt; Theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.&lt;ref&gt;Hibbert et al. (2010, p. 928), cited from the Wikipedia article on &quot;[[w:Henry VIII|Henry VIII]]&quot;, accessed 2026-10-15.&lt;/ref&gt;

A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.&lt;ref&gt;Foxley (2013, p. 207), cited from the Wikipedia article on &quot;[[w:Levellers|Levellers]], accessed 2026-10-15.&lt;/ref&gt; However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that became the US over a century later. 

That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792&lt;ref&gt;Wikipedia &quot;[[w:Postal Service Act|Postal Service Act]]&quot;, accessed 2023-07-11.&lt;/ref&gt; made a major contribution to making the US what it is today.  Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.&lt;ref&gt;Historian, USPS (2010).&lt;/ref&gt; McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.&lt;ref name=McC-N2010&gt;McChesney and Nichols (2010, pp. 310-311, note 88).&lt;/ref&gt; 

During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;John (1995). See also the interview with him at &quot;[[Media concentration per Columbia History Professor Richard John]]&quot; on Wikiversity, accessed 2026-10-12.&lt;/ref&gt; In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.&lt;ref&gt;The &quot;6 percent per year&quot; growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in &quot;[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; on Wikiversity, accessed 2026-10-13.&lt;/ref&gt; 

One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. 

FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, which the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.&lt;ref&gt;This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on &quot;[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; in Wikiversity, accessed 2026-10-13.&lt;/ref&gt;

But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, &quot;the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred.&quot; They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. 

Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.&lt;ref&gt;On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of &quot;influencers&quot; by for-profit social media as essentially unleashed &quot;a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures.&quot; In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.&lt;/ref&gt; 

And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2021, p. 139) noted, &quot;In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%.  The top rate was then cut in half, with the announced objective of boosting growth.  But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.&quot;

=== Immigrants === 

We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. [[w:English Council of State|Lord Protector Cromwell]], who replaced Charles I, refused to authorize as many monopolies as his predecessors, presumably supported by the growing number of independent publishers of pamphlets, books, and newspapers mentioned above. He also encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. 

But Mokyr is not alone in proclaiming the contributions of immigrants to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how &quot;the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology.&quot;

Aghion et al. (2021, p. 292) also discuss (a) &quot;a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita&quot; and (b) the overrepresentation of immigrants in patent applications.&lt;ref&gt;e.g., Aghion et al. (2026, pp. 266-267).&lt;/ref&gt; However, [[w:Dean Baker|Baker]] (2016, pp. 77-78) claimed that &quot;over the last four decades ... stronger patent protection seems to be associated with slower growth,&quot; seemingly the opposite of the claim just quoted from Aghion et al. 

Anther example of how technology winners protect their status against competition is the [[w:Supreme Court of the United States|US Supreme Court]] decision in ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]''. [[w:Lawrence Lessig|Lessig]], who represented the plaintiff in that case, asked how could extending the copyright on existing works &quot;promote the Progress of Science and useful Arts&quot;, as required by the [[w:Copyright Clause|Copyright Clause]] of the US Constitution? Lessig lost that case. His (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to limit rather than &quot;promote the Progress of Science and useful Arts&quot;. This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000, which would bankrupt his parents and which they could not recover even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.&lt;ref&gt;Lessig (2004, p. 42).&lt;/ref&gt; This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP). The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, becauses much of their income is derived from copyright royalties, or (b) SLAPP laws, because anti-SLAPP laws, which exist in some jurisdictions but not others,&lt;ref&gt;[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the &quot;JAWBONE act&quot;, to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on &quot;[[Foundation for Individual Rights and Expression]]&quot;, accessed 2026-10-16.&lt;/ref&gt; limit the power of major corporations, which provide most of the money for the media. 

Similarly Graves (2023) asked, &quot;Do copyrights and paywalls on refereed academic journals violate the US constitution?&quot; No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.&lt;ref&gt;Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on &quot;[[Wikimedia concerns with European copyright rules including AI and scientific research]]&quot;. That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).&lt;/ref&gt;

=== Industrial Revolution ===

There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. 

Mokyr (2017, p.  3) says, &quot;The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society.&quot; He described &quot;three cultural elements&quot; required for &quot;sustainable economic growth propelled by technological progress&quot;: (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. &quot;[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.&lt;ref&gt;Mokyr (2017, pp. 19-20).&lt;/ref&gt; Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, &quot;The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution.&quot; 

Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, &quot;European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?&quot; Aghion et al. (2021, p. 20) describe the &quot;first Industrial Revolution&quot; as having been triggered by &quot;the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866.&quot;&lt;ref&gt;The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.&lt;/ref&gt;

The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not &quot;phases of growth and decline&quot; with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. 

Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, &quot;the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward.&quot; ... However, &quot;the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant to thousand or seven thousand years previously.&quot; (chapter 5) They also claim that, &quot;English national production per capita doubled from 1500 to 1700&quot;, (chapter 5), and &quot;Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root.&quot; (p. 45, chapter 2)

Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. 

Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the &quot;Old Pretender&quot;, a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. 

When Queen Anne died in 1702, she was succeeded by George I. His parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, &quot;and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts&quot;, according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs moved to confiscate &quot;[[w:Commons|commons]]&quot;, land whose use had been traditionally shared by commoners, and give to nobles. The Levellers had been excluded from the government of Lord Protector Cromwell, but the spirit of levelling still stalked the land. Some commoners joined &quot;Blacks&quot;, so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.&lt;ref&gt;Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on &quot;[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.&lt;/ref&gt; 

But not all accused were summarily executed. In 1724 &quot;John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized&quot; with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.&lt;ref&gt;Acemoglu and Robinson (2012, pp. 304-305).&lt;/ref&gt; 

These kinds of actions by the parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded &quot;universal [adult male] suffrage&quot; and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, &quot;The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The Manchester Observer called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... .&quot; And the British government placed enough other limits on its power that enough other commoners were allowed to became successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. 

== In sum ==

The above suggests that the rate of economic growth changes with either change in administration -- a new head of state -- or some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. 

However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).&lt;ref&gt;Graves (2025) includes an analysis of the data in Neff and Pickard (2024).&lt;/ref&gt; 

== Caveat ==

The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  

== Notes ==
{{reflist}}

== Bibliography ==

* &lt;!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)--&gt;{{cite Q|Q85764011}}
* &lt;!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)--&gt;{{cite Q|Q141241291}}
* &lt;!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)--&gt;{{cite Q|Q125292212}}
* &lt;!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)--&gt;{{cite Q|Q7997840}} 
* &lt;!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)--&gt;{{cite Q|Q137641358}}
* &lt;!--Ajzenman, Nicolas (29 January 2023). &quot;Migrants don't cause crime rates to increase — but false perceptions endure anyway&quot;. The Conversation.--&gt;{{cite Q|Q141758664}}
* &lt;!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) &quot;European Immigrants and the United States’ Rise to the Technological Frontier&quot;--&gt;{{cite Q|Q141678287}}
* &lt;!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer--&gt;{{cite Q|Q100216001}}

* &lt;!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) &quot;Maddison style estimates of the evolution of the world economy: A new 2023 update&quot;, Journal of Economic Surveys, 1-41--&gt;{{cite Q|Q126723821}}
* &lt;!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__&gt;{{cite Q|Q57945943}}


* &lt;!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition--&gt;{{cite Q|Q141156783}}
* &lt;!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies--&gt;{{cite Q|Q141158362}}
* &lt;!--Katarzyna Dośpiał-Borysiak (2017) &quot;Model of state management of petroleum sector -- Case of Norway--&gt;{{cite Q|Q141774179}}
* &lt;!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)--&gt;{{cite Q|Q136227988}}
* &lt;!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) &quot;The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration--&gt;{{cite Q|Q55932800}}
* &lt;!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)--&gt;{{cite Q|Q132855526}}
* &lt;!--Graves (2023-03-21)  Do copyrights and paywalls on academic journals violate the US Constitution?--&gt;{{cite Q|Q126116187}}
* &lt;!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.--&gt;{{cite Q|Q137188993}}
* &lt;!-- Historian, USPS (2010) Postage Rates for Periodicals --&gt;{{cite Q|Q112167199}}
* &lt;!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse--&gt;{{cite Q|Q54641943}}
* &lt;!--Volker Leppin and Timothy J. Wengert (2015) &quot;Sources for and against the Posting of the Ninety-Five Theses&quot;--&gt;{{cite Q|Q141737347}}
* &lt;!--Lawrence Lessig (2004) Free Culture--&gt;{{cite Q|Q830526}}
* &lt;!--Olivier Marie and Paolo Pinotti (2024-02-01) &quot;Immigration and Crime: An International Perspective&quot;, Journal of Economic Perspectives. 38 (1): 181–200--&gt;{{cite Q|Q128434874}}
* &lt;!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). &quot;
Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime&quot;
. Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.--&gt;{{cite Q|Q55932802}}
* &lt;!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) --&gt;{{cite Q|Q104888067}}.
* &lt;!-- Robert W. McChesney; John Nichols (2016). People get ready--&gt;{{cite Q|Q87619174}}
* &lt;!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)--&gt;{{cite Q|Q136118590}}
* &lt;!--Ashley N. Muchow &amp; Taisiia Stanishevska (2026) &quot;From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest&quot;, Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)--&gt;{{cite Q|Q141760694}}
* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* &lt;!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia--&gt;{{cite Q|Q141759196}}
* &lt;!--John Hely Owen (1938)  War at Sea Under Queen Anne 1702–1708--&gt;{{cite Q|Q141757101}}
* &lt;!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation--&gt;{{cite Q|Q141761223}}
* &lt;!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain--&gt;{{cite Q|Q141761849}}
* &lt;!--Nick Roll (2017-07-16) &quot;Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.--&gt;{{cite Q|Q141735231}}
* &lt;!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)--&gt;{{cite Q|Q137669960}}
* &lt;!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)--&gt;{{cite Q|Q137669987}}
* &lt;!--J. L. van Zanden  and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30--&gt;{{cite Q|Q137670058}} 
* &lt;!--Tom K. Wong (2017-01-26) &quot;The Effects of Sanctuary Policies on Crime and the Economy&quot;--&gt;{{cite Q|Q98775875}}

[[Category:Original research]]
[[Category:Research]]
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[[Category:Gross domestic product]]
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      <text bytes="45940" sha1="p60jt13on9uu45mbkbd29gh691hgv6i" xml:space="preserve">{{Research project}} 
:''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].''
:''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  
::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]''

== Abstract ==

This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. 

== Maddison Historical Statistics == 

[[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).&lt;ref&gt;See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.&lt;/ref&gt;'']]

The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. 

When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.&lt;ref&gt;Bolt and van Zanden (2024).&lt;/ref&gt; This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]], used in the Maddison data.) 

We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of [[w:North Sea oil|North Sea oil]].&lt;ref&gt;Dośpiał-Borysiak (2017).&lt;/ref&gt; With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. 

This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. 

== Nobel economists and others ==

Banerjee and Duflo (2019, p. 207) said, &quot;despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive.&quot; That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. 

While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, &quot;The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services.&quot; In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. 

Mokyr (2017, p. 255) also said that, &quot;intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished.&quot; That resistance, he suggested, drives &quot;the empirical regularity that no society remains at the cutting edge of technological creativity for very long&quot;.&lt;ref&gt;Mokyr (2017, p. 260).&lt;/ref&gt; This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1.  

Mokyr (2017, p. 60) also mentioned &quot;entrepreneurs of hate&quot;, who convince others to dislike some group in a way that may benefit those &quot;entrepreneurs&quot; and major media organizations, who promote such &quot;entrepreneurs&quot; to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.&lt;ref&gt;See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and the Wikiversity article on &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-14.&lt;/ref&gt; When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites.  

For example, most research on immigrants suggest that on average immigrants are more entrepreneurial and no more likely to commit crime than native born,&lt;ref&gt;e.g., Martínez et al. (2017); Muchow and Stanishevska (2026); Ajzenman(2023).&lt;/ref&gt; and some studies report that sanctuary jurisdictions have on average higher median incomes and less crime.&lt;ref&gt;Martínez et al. (2017); Wong (2017). See also the Wikipedia article on &quot;[[w:Sanctuary city|sanctuary city]]&quot;, accessed 2026-10-12.&lt;/ref&gt; Where immigrant crime is higher, it typically result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.&lt;ref&gt;Marie and Paolo (2024). See also the Wikipedia article on &quot;[[w:Immigration and crime|Immigration and crime]]&quot;, accessed 2026-10-12.&lt;/ref&gt; 

But major media outlets make money from featuring charismatic figures, who attract an audience without offending people who control much of the money for the media. In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities had more crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded &quot;that sanctuary policies have no effect on crime rates, despite narratives to the contrary.&quot;&lt;ref&gt;Roll (2017); Gonzalez O’Brien, et al. (2017).&lt;/ref&gt; To the extent that these comments provide a balanced summary of the research in this area, it suggests that leaders like Trump and Sessions, to name only two, can be fairly describes as &quot;entrepreneurs of hate&quot;. 

We next discuss competition in media markets before discussing immigrants further. 

=== Diversity of ownership of the major media === 

Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations. In such hierarchical societies some religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate designated evil others and give increasing shares of what they produce so the secular elites would &quot;protect&quot; them in wars against the designated evil others.

Acemoglu and Robinson (2012, p. 461) said, &quot;Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power. ... Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799]&quot; and in the US. ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].)

But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.&lt;ref&gt;Hendrix (2015, p. 64), quoted from the Wikipedia article on the &quot;[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand&lt;ref&gt;Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; and was much more popular than Tetzel's.&lt;ref&gt;Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; 

Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the [[w:Church of England|Church of England]], denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature.&lt;ref&gt;Raymond (2006), cited from the Wikipedia article on &quot;[[w:Pamphlet war|pamphlet war]]&quot;, accessed 2026-10-15.&lt;/ref&gt; Theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.&lt;ref&gt;Hibbert et al. (2010, p. 928), cited from the Wikipedia article on &quot;[[w:Henry VIII|Henry VIII]]&quot;, accessed 2026-10-15.&lt;/ref&gt;

A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.&lt;ref&gt;Foxley (2013, p. 207), cited from the Wikipedia article on &quot;[[w:Levellers|Levellers]], accessed 2026-10-15.&lt;/ref&gt; However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that (over a century later) became the US. 

That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792&lt;ref&gt;Wikipedia &quot;[[w:Postal Service Act|Postal Service Act]]&quot;, accessed 2023-07-11.&lt;/ref&gt; made a major contribution to making the US what it is today.  Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.&lt;ref&gt;Historian, USPS (2010).&lt;/ref&gt; McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.&lt;ref name=McC-N2010&gt;McChesney and Nichols (2010, pp. 310-311, note 88).&lt;/ref&gt; 

During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;John (1995). See also the interview with him at &quot;[[Media concentration per Columbia History Professor Richard John]]&quot; on Wikiversity, accessed 2026-10-12.&lt;/ref&gt; In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.&lt;ref&gt;The &quot;6 percent per year&quot; growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in &quot;[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; on Wikiversity, accessed 2026-10-13.&lt;/ref&gt; 

One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. 

FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, which the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.&lt;ref&gt;This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on &quot;[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; in Wikiversity, accessed 2026-10-13.&lt;/ref&gt;

But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, &quot;the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred.&quot; They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. 

Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.&lt;ref&gt;On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of &quot;influencers&quot; by for-profit social media as essentially unleashed &quot;a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures.&quot; In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.&lt;/ref&gt; 

And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2021, p. 139) noted, &quot;In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%.  The top rate was then cut in half, with the announced objective of boosting growth.  But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.&quot;

=== Immigrants === 

We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. [[w:English Council of State|Lord Protector Cromwell]], who replaced Charles I, refused to authorize as many monopolies as his predecessors, presumably supported by the growing number of independent publishers of pamphlets, books, and newspapers mentioned above. He also encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. 

But Mokyr is not alone in proclaiming the contributions of immigrants to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how &quot;the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology.&quot;

Aghion et al. (2021, p. 292) also discuss (a) &quot;a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita&quot; and (b) the overrepresentation of immigrants in patent applications.&lt;ref&gt;e.g., Aghion et al. (2026, pp. 266-267).&lt;/ref&gt; However, [[w:Dean Baker|Baker]] (2016, pp. 77-78) claimed that &quot;over the last four decades ... stronger patent protection seems to be associated with slower growth,&quot; seemingly the opposite of the claim just quoted from Aghion et al. 

Anther example of how technology winners protect their status against competition is the [[w:Supreme Court of the United States|US Supreme Court]] decision in ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]''. [[w:Lawrence Lessig|Lessig]], who represented the plaintiff in that case, asked how could extending the copyright on existing works &quot;promote the Progress of Science and useful Arts&quot;, as required by the [[w:Copyright Clause|Copyright Clause]] of the US Constitution? Lessig lost that case. His (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to limit rather than &quot;promote the Progress of Science and useful Arts&quot;. This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000, which would bankrupt his parents and which they could not recover even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.&lt;ref&gt;Lessig (2004, p. 42).&lt;/ref&gt; This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP). The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, becauses much of their income is derived from copyright royalties, or (b) SLAPP laws, because anti-SLAPP laws, which exist in some jurisdictions but not others,&lt;ref&gt;[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the &quot;JAWBONE act&quot;, to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on &quot;[[Foundation for Individual Rights and Expression]]&quot;, accessed 2026-10-16.&lt;/ref&gt; limit the power of major corporations, which provide most of the money for the media. 

Similarly Graves (2023) asked, &quot;Do copyrights and paywalls on refereed academic journals violate the US constitution?&quot; No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.&lt;ref&gt;Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on &quot;[[Wikimedia concerns with European copyright rules including AI and scientific research]]&quot;. That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).&lt;/ref&gt;

=== Industrial Revolution ===

There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. 

Mokyr (2017, p.  3) says, &quot;The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society.&quot; He described &quot;three cultural elements&quot; required for &quot;sustainable economic growth propelled by technological progress&quot;: (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. &quot;[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.&lt;ref&gt;Mokyr (2017, pp. 19-20).&lt;/ref&gt; Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, &quot;The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution.&quot; 

Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, &quot;European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?&quot; Aghion et al. (2021, p. 20) describe the &quot;first Industrial Revolution&quot; as having been triggered by &quot;the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866.&quot;&lt;ref&gt;The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.&lt;/ref&gt;

The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not &quot;phases of growth and decline&quot; with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. 

Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, &quot;the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward.&quot; ... However, &quot;the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant to thousand or seven thousand years previously.&quot; (chapter 5) They also claim that, &quot;English national production per capita doubled from 1500 to 1700&quot;, (chapter 5), and &quot;Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root.&quot; (p. 45, chapter 2)

Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. 

Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the &quot;Old Pretender&quot;, a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. 

When Queen Anne died in 1702, she was succeeded by George I. His parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, &quot;and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts&quot;, according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs moved to confiscate &quot;[[w:Commons|commons]]&quot;, land whose use had been traditionally shared by commoners, and give to nobles. The Levellers had been excluded from the government of Lord Protector Cromwell, but the spirit of levelling still stalked the land. Some commoners joined &quot;Blacks&quot;, so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.&lt;ref&gt;Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on &quot;[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.&lt;/ref&gt; 

But not all accused were summarily executed. In 1724 &quot;John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized&quot; with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.&lt;ref&gt;Acemoglu and Robinson (2012, pp. 304-305).&lt;/ref&gt; 

These kinds of actions by the parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded &quot;universal [adult male] suffrage&quot; and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, &quot;The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The Manchester Observer called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... .&quot; And the British government placed enough other limits on its power that enough other commoners were allowed to became successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. 

== In sum ==

The above suggests that the rate of economic growth changes with either change in administration -- a new head of state -- or some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. 

However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).&lt;ref&gt;Graves (2025) includes an analysis of the data in Neff and Pickard (2024).&lt;/ref&gt; 

== Caveat ==

The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  

== Notes ==
{{reflist}}

== Bibliography ==

* &lt;!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)--&gt;{{cite Q|Q85764011}}
* &lt;!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)--&gt;{{cite Q|Q141241291}}
* &lt;!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)--&gt;{{cite Q|Q125292212}}
* &lt;!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)--&gt;{{cite Q|Q7997840}} 
* &lt;!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)--&gt;{{cite Q|Q137641358}}
* &lt;!--Ajzenman, Nicolas (29 January 2023). &quot;Migrants don't cause crime rates to increase — but false perceptions endure anyway&quot;. The Conversation.--&gt;{{cite Q|Q141758664}}
* &lt;!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) &quot;European Immigrants and the United States’ Rise to the Technological Frontier&quot;--&gt;{{cite Q|Q141678287}}
* &lt;!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer--&gt;{{cite Q|Q100216001}}

* &lt;!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) &quot;Maddison style estimates of the evolution of the world economy: A new 2023 update&quot;, Journal of Economic Surveys, 1-41--&gt;{{cite Q|Q126723821}}
* &lt;!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__&gt;{{cite Q|Q57945943}}


* &lt;!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition--&gt;{{cite Q|Q141156783}}
* &lt;!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies--&gt;{{cite Q|Q141158362}}
* &lt;!--Katarzyna Dośpiał-Borysiak (2017) &quot;Model of state management of petroleum sector -- Case of Norway--&gt;{{cite Q|Q141774179}}
* &lt;!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)--&gt;{{cite Q|Q136227988}}
* &lt;!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) &quot;The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration--&gt;{{cite Q|Q55932800}}
* &lt;!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)--&gt;{{cite Q|Q132855526}}
* &lt;!--Graves (2023-03-21)  Do copyrights and paywalls on academic journals violate the US Constitution?--&gt;{{cite Q|Q126116187}}
* &lt;!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.--&gt;{{cite Q|Q137188993}}
* &lt;!-- Historian, USPS (2010) Postage Rates for Periodicals --&gt;{{cite Q|Q112167199}}
* &lt;!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse--&gt;{{cite Q|Q54641943}}
* &lt;!--Volker Leppin and Timothy J. Wengert (2015) &quot;Sources for and against the Posting of the Ninety-Five Theses&quot;--&gt;{{cite Q|Q141737347}}
* &lt;!--Lawrence Lessig (2004) Free Culture--&gt;{{cite Q|Q830526}}
* &lt;!--Olivier Marie and Paolo Pinotti (2024-02-01) &quot;Immigration and Crime: An International Perspective&quot;, Journal of Economic Perspectives. 38 (1): 181–200--&gt;{{cite Q|Q128434874}}
* &lt;!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). &quot;
Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime&quot;
. Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.--&gt;{{cite Q|Q55932802}}
* &lt;!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) --&gt;{{cite Q|Q104888067}}.
* &lt;!-- Robert W. McChesney; John Nichols (2016). People get ready--&gt;{{cite Q|Q87619174}}
* &lt;!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)--&gt;{{cite Q|Q136118590}}
* &lt;!--Ashley N. Muchow &amp; Taisiia Stanishevska (2026) &quot;From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest&quot;, Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)--&gt;{{cite Q|Q141760694}}
* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* &lt;!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia--&gt;{{cite Q|Q141759196}}
* &lt;!--John Hely Owen (1938)  War at Sea Under Queen Anne 1702–1708--&gt;{{cite Q|Q141757101}}
* &lt;!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation--&gt;{{cite Q|Q141761223}}
* &lt;!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain--&gt;{{cite Q|Q141761849}}
* &lt;!--Nick Roll (2017-07-16) &quot;Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.--&gt;{{cite Q|Q141735231}}
* &lt;!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)--&gt;{{cite Q|Q137669960}}
* &lt;!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)--&gt;{{cite Q|Q137669987}}
* &lt;!--J. L. van Zanden  and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30--&gt;{{cite Q|Q137670058}} 
* &lt;!--Tom K. Wong (2017-01-26) &quot;The Effects of Sanctuary Policies on Crime and the Economy&quot;--&gt;{{cite Q|Q98775875}}

[[Category:Original research]]
[[Category:Research]]
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[[Category:Gross domestic product]]
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:''This article invites all to contribute references and interpretations to the growth in average annual income, Gross Domestic Product (GDP) per capita at purchasing power parity, as applied to leading countries in the [[w:Maddison Project|Maddison Historical Statistics Project]].''
:''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  
::''This article uses [[w:ISO 8601|ISO 8601]] dates except for References, which are controlled by standard Wikidata formatting, and direct quotes. In the initial author's experience, [[ISO 8601 and computing differences between dates|ISO 8601 dates seem to make it easier to remember dates and to compute differences between them.]]''

== Abstract ==

This article first identifies and plots GDP per capita for leading countries in the Maddison data then discusses comments by Nobel prize winning economists and others to interpret what appears in said plot. While no one really knows how to make economies grow, immigrants and free, competitive media markets have been suggested as playing major roles in the creative destruction that is required for economic growth at the technology frontier. 

== Maddison Historical Statistics == 

[[File:MaddisonDataLeaders1349-2022.svg|thumb|''Figure 1. World leaders in GDP per capita 1349-2022 (NLD = initially Holland to 1809 and the Netherlands after; GBR = initially England to 1700, Great Britain to 1870, then the UK; USA starting with the 13 colonies that became the US; SGP = Singapore).&lt;ref&gt;See Bolt and van Zanden (2024) for the Maddison Data generally, Broadberry et al. (2015) for the data on England 1252–1700 and on Great Britain until 1870, Sugimoto (2011) for Singapore to 2007, van Zanden and van Leeuwen (2012) for the data on Holland 1349–1807, and Smits et al. (2000) for the data on the Netherlands 1808-1913. The dramatic drop in the orange line could be due to the change in reference, as [[w:Holland|Holland]] at that time was more prosperous than the rest of the Netherlands.&lt;/ref&gt;'']]

The [[w:Maddison Project|Maddison Historical Statistics Project]] (aka Maddison Project) is widely recognized as the premier data source on historical macroeconomic data. It is named after [[w:Angus Maddison|Angus Maddison]] (1926-2010), who was a pioneer in [[w:National accounts|national accounts]], especially estimating [[w:Gros Domestic Product|gross domestic product]] (GDP) per capita (GDPpc) and population (pop) at various times dating back to the year 1 of the [[w:Common Era|Common Era]] (CE / AD). After Maddison's death, the Maddison Project has continued to update the database to include the best sources available on any country for any historical period since year 1. 

When accessed 2026-10-10 the version of the data available had been released 2024-09-18 containing data to 2022.&lt;ref&gt;Bolt and van Zanden (2024).&lt;/ref&gt; This dataset includes 23,280 observations on at least one of GDPpc and pop for an average of 137 years for 169 countries. Only 18 countries had the highest GDPpc for at least one year. Annual data starts in 1252, and that's only for one country, GBR = England / Great Britain / the United Kingdom. NLD (Holland / the Netherlands) had the highest GDPpc for 97 percent of the years between 1349 and 1807, and the Dutch leadership in Figure 1 may have ended then, not because of the devastation from the [[w:Napoleonic Wars|Napoleonic Wars]] (which negatively impacted them) but because the available data prior to 1807 are for [[w:Holland|Holland]], while more recent data are for the Netherlands, of which Holland is only a part, though probably the most prosperous part at that time. This analysis focuses on data since 1349, in part because data were available for at most 4 countries for most years prior to that date. (The 3-letter country codes used here are [[w:ISO 3166-1 alpha-3|ISO 3166-1 alpha-3]], used in the Maddison data.) 

We are interested in technology leaders, so we eliminate the [[w:petrostates|petrostates]] of Qatar (QAT), Kuwait (KWT), and United Arab Emirates (ARE), plus Norway (NOR), which owes a substantial portion of their wealth to democratic management of [[w:North Sea oil|North Sea oil]].&lt;ref&gt;Dośpiał-Borysiak (2017).&lt;/ref&gt; With these restrictions 12 countries had the highest GDPpc for at least one year. However, FRA (France), ITA (Italy), SWE (Sweden), BEL (Belgium), NZL (New Zealand) and CHE (Switzerland) led for at most 7 of the 675 years between 1349 and 2022; we eliminate those, because including them would seem to add more clutter than clarity. We also eliminate AUS (Australia), which led for 17 of the 39 years between 1853 and 1891, when it was competing for the leadership with GBR and USA, for the same reason. And we eliminate LUX (Luxembourg), which has a population under a million. 

This leaves NLD, GBR, USA, and SGP (Singapore), plotted in Figure 1. This plot has some interesting features, which we discuss in the remainder of this research report. 

== Nobel economists and others ==

Banerjee and Duflo (2019, p. 207) said, &quot;despite the best efforts of generations of economists, the deep mechanisms of persistent economic growth remain elusive.&quot; That appeared shortly before they shared the 2019 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]] with [[w:Michael Kremer|Michael Kremer]] for documenting how [[w:Randomized controlled trial|randomized controlled trial]]s could be used to alleviating poverty in [[w:Development economics|development economics]]. 

While Banerjee and Duflo insist that no one knows how to make an economy grow, other leading economists recommend partial solutions. For example, [[w:Joel Mokyr|Mokyr]] (2017, p. 53) said, &quot;The willingness of the Netherlands and later Britain and the United States to tolerate Jews and dissenting Christians contributed a great deal to their economies, especially in high-skilled manufacturing and financial services.&quot; In other words, immigrants made an outsized contribution to the growth of NLD, GBR, and US, visible in Figure 1. Mokyr's comment appeared over a year before Banerjee and Duflo (2019) and roughy eight years before Mokyr shared the 2025 Nobel Memorial Prize in Economics with [[w:Philippe Aghion|Aghion]] and [[w:Peter Howitt (economist)|Howitt]]. 

Mokyr (2017, p. 255) also said that, &quot;intellectual innovation will eventually end up being increasingly resisted by an incumbent technology; if that resistance is not overcome, technological progress may be extinguished.&quot; That resistance, he suggested, drives &quot;the empirical regularity that no society remains at the cutting edge of technological creativity for very long&quot;.&lt;ref&gt;Mokyr (2017, p. 260).&lt;/ref&gt; This provides one explanation for the end of growth of the economy of Holland shortly before 1600 and for the slowing of economic growth in recent decades in the US, the UK, and the Netherlands, visible in Figure 1.  

Mokyr (2017, p. 60) also mentioned &quot;entrepreneurs of hate&quot;, who convince others to dislike some group in a way that may benefit those &quot;entrepreneurs&quot; and major media organizations, who promote such &quot;entrepreneurs&quot; to please those who control much of the money for the media. For-profit social media have been particularly effective in herding their audiences into echo chambers, reinforcing their preconceptions in ways that increase political polarization and violence and threaten democracy.&lt;ref&gt;See, e.g., DiResta (2026), DiResta and Keinfeld (2025), and the Wikiversity article on &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-14.&lt;/ref&gt; When successful this protects current elites from competition that would otherwise drive [[w:creative destruction|creative destruction]], benefitting the public at large while threatening existing elites.  

For example, most research on immigrants suggest that on average immigrants are more entrepreneurial and no more likely to commit crime than native born,&lt;ref&gt;e.g., Martínez et al. (2017); Muchow and Stanishevska (2026); Ajzenman(2023).&lt;/ref&gt; and some studies report that sanctuary jurisdictions have on average higher median incomes and less crime.&lt;ref&gt;Martínez et al. (2017); Wong (2017). See also the Wikipedia article on &quot;[[w:Sanctuary city|sanctuary city]]&quot;, accessed 2026-10-12.&lt;/ref&gt; Where immigrant crime is higher, it typically result from anti-immigrant labor market restrictions or from young less-educated males with irregular status.&lt;ref&gt;Marie and Paolo (2024). See also the Wikipedia article on &quot;[[w:Immigration and crime|Immigration and crime]]&quot;, accessed 2026-10-12.&lt;/ref&gt; 

But major media outlets make money from featuring charismatic figures, who attract an audience without offending people who control much of the money for the media. In 2017 President Trump's Attorney General [[w:Jeff Sessions|Jeff Sessions]] quoted a research study that supposedly showed that sanctuary cities had more crime than cities without sanctuary policies. The authors of that study insisted that Sessions had ''misrepresented'' their work, which concluded &quot;that sanctuary policies have no effect on crime rates, despite narratives to the contrary.&quot;&lt;ref&gt;Roll (2017); Gonzalez O’Brien, et al. (2017).&lt;/ref&gt; To the extent that these comments provide a balanced summary of the research in this area, it suggests that leaders like Trump and Sessions, to name only two, can be fairly describes as &quot;entrepreneurs of hate&quot;. 

We next discuss competition in media markets before discussing immigrants further. 

=== Diversity of ownership of the major media === 

Acemoglu and Johnson (2023, esp. ch. 4) describe how religious leaders in hierarchical societies prior to [[w:James VI and I|King James]] of the [[w:King James Version|King James Bible]] convinced commoners to live in poverty while giving increasing shares of what they produced, so religious and secular elites could live in opulence. Prior to King James the major media were religious organizations. In such hierarchical societies some religious leaders were entrepreneurs of hate, exhorting the faithful to fear and hate designated evil others and give increasing shares of what they produce so the secular elites would &quot;protect&quot; them in wars against the designated evil others.

Acemoglu and Robinson (2012, p. 461) said, &quot;Empowerment of society at large is difficult to coordinate and maintain without widespread information about whether there are economic and political abuses by those in power. ... Pamphlets and books informing and galvanizing people played an important role during the [[w:Glorious Revolution|Glorious Revolution]] [1688] in England, the French Revolution [1789-1799]&quot; and in the US. ([[w:Daron Acemoglu|Acemoglu]], [[w:Simon Johnson (economist)|Johnson]] and [[w:James A. Robinson|Robinson]] shared the 2024 [[w:List of Nobel Memorial Prize laureates in Economic Sciences|Nobel Memorial Prize in Economics]].)

But pamplets started challenging established power structures much earlier. The publication of [[w:Martin Luther|Martin Luther]]'s ''[[w:Ninety-five Theses|Ninety-five Theses]]'' in Latin 1517-10-31 was quickly condemned by [[w:Pope Leo X|Pope Leo X]] and his hierarchy. [[w:Johann Tetzel|Johann Tetzel]], who had been selling [[w:Indulgence|indulgence]]s, published a pamphlet calling for Luther to be burnt for [[w:heresy|heresy]]. Eight hundred copies were reportedly sent to [[w:Wittenberg|Wittenberg]] to be sold, but students seized and burned them.&lt;ref&gt;Hendrix (2015, p. 64), quoted from the Wikipedia article on the &quot;[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; This led to a pamphlet war. Luther's brief German-language reply was short and easy for commoners to understand&lt;ref&gt;Leppin and Wengert (2015, p. 389), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; and was much more popular than Tetzel's.&lt;ref&gt;Pettegree (2015, p. 145), cited from the Wikipedia article on the ''[[w:Ninety-five Theses|Ninety-five Theses]]'', accessed 2026-10-14.&lt;/ref&gt; 

Less than twenty years later, King [[w:Henry VIII|Henry VIII]] declared himself head of the [[w:Church of England|Church of England]], denying the authority of the Pope. To secure the support of his subjects, he drove a propaganda war that included print literature.&lt;ref&gt;Raymond (2006), cited from the Wikipedia article on &quot;[[w:Pamphlet war|pamphlet war]]&quot;, accessed 2026-10-15.&lt;/ref&gt; Theatre and minstrel troupes funded by the king traveling around the land to promote the new religious practices. Henry was portrayed as the glorious king of England, bravely and heroically defending the true faith against foreign devils, especially the Pope and Catholic priests, monks, etc.&lt;ref&gt;Hibbert et al. (2010, p. 928), cited from the Wikipedia article on &quot;[[w:Henry VIII|Henry VIII]]&quot;, accessed 2026-10-15.&lt;/ref&gt;

A century later during the [[w:English Civil War|English Civil War]] (1642-1651), pamphlets and newspapers helped build the [[w:Levellers|Levellers]], who supported radical ideas like [[w:popular sovereignty|popular sovereignty]], extended suffrage, equality before the law and religious tolerance. Many were part of the [[w:New Model Army|New Model Army]], which won the war. The Levellers were excluded from the government that followed the [[w:Execution of Charles I of England|beheading of King Charles I]], son of King James, in 1649.&lt;ref&gt;Foxley (2013, p. 207), cited from the Wikipedia article on &quot;[[w:Levellers|Levellers]], accessed 2026-10-15.&lt;/ref&gt; However, that new government stopped granting as many monopolies and allowed so many commoners to become entrepreneurs that the GDP per capita began to grow at rates that are key features of Figure 1 for England and the 13 English colonies that (over a century later) became the US. 

That growth was presumably supported by the diversity of independent publishers of pamphlets, books and newspapers. [[w:Robert W. McChesney|McChesney]] and [[w:John Nichols (journalist)|Nichols]] (2010, 2016) suggested that the US [[w:Postal Service Act|Postal Service Act]] of 1792&lt;ref&gt;Wikipedia &quot;[[w:Postal Service Act|Postal Service Act]]&quot;, accessed 2023-07-11.&lt;/ref&gt; made a major contribution to making the US what it is today.  Under that act, newspapers were delivered up to 100 miles for a penny, when postage for letters was between 6 and 25 cents depending on distance.&lt;ref&gt;Historian, USPS (2010).&lt;/ref&gt; McChesney and Nichols estimated that between 1840 and 1844, the US postal subsidy was a little over 0.2% of GDP.&lt;ref name=McC-N2010&gt;McChesney and Nichols (2010, pp. 310-311, note 88).&lt;/ref&gt; 

During the first half of the nineteenth century the US had more independent newspaper publishers per million population than at any other time or place in human history.&lt;ref&gt;John (1995). See also the interview with him at &quot;[[Media concentration per Columbia History Professor Richard John]]&quot; on Wikiversity, accessed 2026-10-12.&lt;/ref&gt; In 1932 with official unemployment over 20 percent, the conservative argument that blames the poor for their poverty did not sell newspapers, and the US still had sufficient competition in media markets that presidential candidate Franklin Roosevelt (FDR) got a mandate to spend the money to put humans back to work while taxing the ultra-wealthy like they had never been taxed before or since and during World War II to institute wage and price controls under the [[w:Office of Price Administration|Office of Price Administration]]. The latter prevented price gouging by government contractors that had generated inflation and stifled economic growth in previous major wars (World War I, the Civil War, and the War of 1812). Instead, the US averaged 7 percent per year growth for FDR's 12 years.&lt;ref&gt;The &quot;6 percent per year&quot; growth during FDR's 12 years was computed as the average of log(GDPpc) in the Maddison Data. To be precise, that computation produced 0.0597; converting that from a log scale to percent increase gives 0.0615. Using data from [[w:MeasuringWorth|MeasuringWorth]] instead of Maddison, we get 0.783 and 0.815, respectively. More documentation of this is available in &quot;[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; on Wikiversity, accessed 2026-10-13.&lt;/ref&gt; 

One of the most interesting features of Figure 1 is the behavior of the US economy in the administrations of [[w:Herbert Hoover|Herbert Hoover]] and FDR: Under Hoover, the economy declined at 9 percent per year for 4 years, a financial disaster that created the public demand for change that gave FDR the mandate to do what he did. Economic growth under two other presidents are numerically comparable to FDR's numbers but for much shorter periods: (1) [[w: Warren G. Harding|Warren G. Harding]] averaged 7 percent annual growth for two years before he died in 1923 during the [[w:Roaring Twenties|Roaring Twenties]]. (2) [[w:Rutherford B Hayes|Rutherford B Hayes]], who took office in 1877 at the end of the [[w:Panic of 1873|Panic of 1873]], oversaw 5.5 percent growth per year for his 4 years as president. Those impressive sounding average growth figures are so short that they are not noticeably different from other minor features visible in Figure 1. 

FDR also dramatically reduced inequality. For over a century between about 1820 and 1932 the top 1 percent of the US population owned roughly 45 percent of net personal wealth in the US, while the bottom 90 percent owned roughly 22 percent. Shortly after FDR died, the wealth of the top 1 percent and bottom 90 percent were both roughly 30 percent. FDR also oversaw dramatic growth in the power of organized labor, whose successes continued to reduce inequality to roughly 22 percent for the top 1 percent vs. 37 percent for the bottom 90 percent when Ronald Reagan became president. Since then, [[w:Reaganomics|Reaganomics]] have been rebuilding the [[w:Robber baron (industrialist)|Robber Baron]]s.&lt;ref&gt;This history of inequality is documented in [[:File:Share of US wealth 90p99.svg|Figure 7. Shares of US wealth - bottom 90 and top 1 percent, 1820-2023]] in the Wikiversity article on &quot;[[w:Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future]]&quot; in Wikiversity, accessed 2026-10-13.&lt;/ref&gt;

But FDR made enemies among the wealthiest and most powerful. In a [[q:Franklin D. Roosevelt#Address at Madison Square Garden (1936)|speech in Maddison Square Garden in 1936]], FDR mentioned, &quot;the old enemies of peace: business and financial monopoly, speculation, reckless banking, class antagonism, sectionalism, war profiteering. ... They are unanimous in their hate for me -- and I welcome their hatred.&quot; They doubtless could see that they could no longer afford as many personal servants -- maids, butlers, cooks, chauffeurs, etc. -- as they had before FDR. 

Broadcasting was relatively new when FDR took office. The economics of broadcasting naturally favored a very few networks, whose power concerned FDR. In 1941 his [[w:Federal Communications Commission| Federal Communications Commission]] (FCC) adopted the [[w:Mayflower doctrine|Mayflower doctrine]], which prohibited broadcasters from advocacy. When FDR died, people with power were able to get the Mayflower doctrine replaced by the more lenient [[w:Fairness Doctrine|Fairness Doctrine]], which opened the floodgates for entrepreneurs of hate, who drove the [[w:McCarthyism|McCarthy Red Scare]] in the US and many other problems since. Over time this became worse facilitated by increasing concentration of ownership of the media. That contributed to the end of the Fairness Doctrine starting in 1985. That revocation and especially the more recent rise of for-profit social media have amplified the ability of entrepreneurs of hate to make money both for commercial social media and for themselves by disseminating lies about others, e.g., immigrants.&lt;ref&gt;On how for-profit social media companies promote entrepreneurs of hate, see, e.g., DiResta (2026) and the Wikiversity article on, &quot;[[Managing the good and the evils of social media]]&quot;, accessed 2026-10-12. DiResta (2026, p. 1) described the promotion of &quot;influencers&quot; by for-profit social media as essentially unleashed &quot;a war for power, influence, and reality itself—a conflict in which the ends justify any means, and one that has ripped America apart, threatened our very democracy, and consumed my own life for the past decade, leading to death threats, congressional subpoenas, lawsuits, and legal bills running into seven figures.&quot; In the interview on Wikiversity, DiResta said her legal bills to that point had exceeded $7 million.&lt;/ref&gt; 

And the rate of economic growth in the US (and the Netherlands and the UK) have been slowing in recent decades, as is visible in Figure 1. Inequality expert [[w:Thomas Piketty|Piketty]] (2021, p. 139) noted, &quot;In the United States, the national income per inhabitant rose at a rate ... of 2.2% between 1950 to 1990 when the top tax rate reached on average 72%.  The top rate was then cut in half, with the announced objective of boosting growth.  But in fact, growth fell by half, to 1.1% per annum between 1990 and 2020 ... . Beyond a certain level of inequality, repeatedly increasing differences in income and wealth has clearly had no positive effect on economic dynamism. In sum, all the data at our disposal today suggest that virtually confiscatory tax rates have been an immense historical success. They have made it possible to greatly reduce the divergences of fortunes and incomes, while at the same time improving the situation of the middle and lower classes, developing the welfare state, and stimulating better economic and social performance overall. Historically, it is the battle for equality and education that has made economic development and human progress possible, and not the veneration of property, stability, and inequality.&quot;

=== Immigrants === 

We now return to discussing the initiation of economic growth following the beheading of Charles I in 1649 visible in Figure 1. [[w:English Council of State|Lord Protector Cromwell]], who replaced Charles I, refused to authorize as many monopolies as his predecessors, presumably supported by the growing number of independent publishers of pamphlets, books, and newspapers mentioned above. He also encouraged Jews and dissenting Christians to settle in England, as mentioned by Mokyr (2017, p. 53), cited above. 

But Mokyr is not alone in proclaiming the contributions of immigrants to economic growth. Aghion et al. (2021, p. 266) cite Arkolakis et al. (2020) for explaining how &quot;the period 1880–1920 is noteworthy for two parallel evolutions. First, the United States caught up with England and France to become the most technologically advanced country in the world as well as the wealthiest in terms of GDP per capita. Second, the United States welcomed large numbers of immigrants, most notably from Europe. The purpose of the cited study was to demonstrate a causal connection between these two phenomena: in other words, to show that European immigration was responsible for the United States’ taking the lead in technology.&quot;

Aghion et al. (2021, p. 292) also discuss (a) &quot;a positive relationship between anticorruption measures in a country and rate of innovation in that country as measured by patents per capita&quot; and (b) the overrepresentation of immigrants in patent applications.&lt;ref&gt;e.g., Aghion et al. (2026, pp. 266-267).&lt;/ref&gt; However, [[w:Dean Baker|Baker]] (2016, pp. 77-78) claimed that &quot;over the last four decades ... stronger patent protection seems to be associated with slower growth,&quot; seemingly the opposite of the claim just quoted from Aghion et al. 

Anther example of how technology winners protect their status against competition is the [[w:Supreme Court of the United States|US Supreme Court]] decision in ''[[w:Eldred v. Ashcroft|Eldred v. Ashcroft]]''. [[w:Lawrence Lessig|Lessig]], who represented the plaintiff in that case, asked how could extending the copyright on existing works &quot;promote the Progress of Science and useful Arts&quot;, as required by the [[w:Copyright Clause|Copyright Clause]] of the US Constitution? Lessig lost that case. His (2004) ''[[w:Free Culture (book)|Free Culture]]'' describes other examples, where US copyright law seems to limit rather than &quot;promote the Progress of Science and useful Arts&quot;. This includes a case where a 2002 freshman, Jesse Jordan, modified a search engine to make it easier for other student to find pictures, research, notes, movie clips, etc., on an [[w:intranet|intranet]] at [[w:Rensselaer Polytechnic Institute|Rensselaer Polytechnic Institute]] (RPI). The [[w:Recording Industry Association of America|Recording Industry Association of America]] (RIAA) sued Jordan and three other students for close to $100 billion for copyright violations -- six times the total profit of the film industry in 2001. Jordan had an uncle, who was an attorney, who explained that the legal bills for fighting that case would be at least $250,000, which would bankrupt his parents and which they could not recover even if they won. Jordan had saved $12,000 to cover part of his college expenses. RIAA accepted that and settled the case.&lt;ref&gt;Lessig (2004, p. 42).&lt;/ref&gt; This is an example of a [[w:Strategic lawsuit against public participation|strategic lawsuit against public participation]] (SLAPP). The major media have conflicts of interest in honestly reporting on anything involving (a) copyright laws, becauses much of their income is derived from copyright royalties, or (b) SLAPP laws, because anti-SLAPP laws, which exist in some jurisdictions but not others,&lt;ref&gt;[[w:Robert Corn-Revere|Robert Corn-Revere]], Chief Counsel for the [[w:Foundation for Individual Rights and Expression|Foundation for Individual Rights and Expression]], supports anti-SLAPP laws and the &quot;JAWBONE act&quot;, to limit the power of the government to threaten questionable actions, like the administrations threats against the ABC network because they didn't like a Jimmy Kimmel monolog. See the Wikiversity article on &quot;[[Foundation for Individual Rights and Expression]]&quot;, accessed 2026-10-16.&lt;/ref&gt; limit the power of major corporations, which provide most of the money for the media. 

Similarly Graves (2023) asked, &quot;Do copyrights and paywalls on refereed academic journals violate the US constitution?&quot; No one expects to make money from copyright royalties for drafts submitted to refereed academic journals. They do it out of a felt need (a) to contribute to the future of humanity or (b) to build their reputation or (c) because promotions at many universities are based partly on publication records. Graves is not alone in his concern about this: Many European countries do not allow reports of research they fund to be published behind paywalls.&lt;ref&gt;Dimi Zagorski is concerned that copyright exceptions for scientific research are different in different European countries, and that's a problem for the Wikimedia Foundation. See the discussion of this in the Wikiversity article on &quot;[[Wikimedia concerns with European copyright rules including AI and scientific research]]&quot;. That's the opposite of US law, which grants patents to universities, research institutions, private companies, and individuals for innovations developed under government contracts, per the Bayh-Dole Act of 1980, described by Baker (2016, p. 80).&lt;/ref&gt;

=== Industrial Revolution ===

There seems to be a broad consensus that the [[w:Industrial Revolution|Industrial Revolution]] began in England. However, there is less agreement on when it began. 

Mokyr (2017, p.  3) says, &quot;The British Industrial Revolution of the late eighteenth century unleashed a phenomenon never before even remotely experienced by any society.&quot; He described &quot;three cultural elements&quot; required for &quot;sustainable economic growth propelled by technological progress&quot;: (1, 2) The belief that it was both ''possible'' and ''desirable''. (3) Supportive policy measures had to be implemented. &quot;[B]efore 1750 they did not produce anything like an Industrial Revolution or sustainable economic growth propelled by technological progress.&lt;ref&gt;Mokyr (2017, pp. 19-20).&lt;/ref&gt; Acemoglu (2026, p. 53) similarly mentioned the eighteenth century in saying, &quot;The breakthroughs in production technology that started in the middle of the eighteenth century in Britain unleashed the Industrial Revolution.&quot; 

Aghion et al. (2021, esp. pp. 29-30) offer a ''later'' date for the start of the Industrial Revolution: They report that, &quot;European economies prior to 1820 experienced a series of phases of growth and decline. This raises a question: How did the pre-1820 period differ from the takeoff that started with the first Industrial Revolution?&quot; Aghion et al. (2021, p. 20) describe the &quot;first Industrial Revolution&quot; as having been triggered by &quot;the invention of the steam engine by James Watt in the 1770s ... . The invention of electricity set off the second Industrial Revolution, whose golden age was in the first half of the twentieth century. This second revolution originated with the invention of the [[w:Incandescent light bulb|light bulb]] by [[w:Thomas Edison|Thomas Edison]] in 1879 and of the [[w:dynamo|dynamo]] by [[w:Werner von Siemens|Werner von Siemens]] in 1866.&quot;&lt;ref&gt;The dynamo was independently invented by [[w:Henry Wilde (engineer)|Henry Wilde]], [[w:Charles Wheatstone|Charles Wheatstone]], [[w:Samuel Alfred Varley|Samuel Alfred Varley]] and Siemens, all about the same time, according to the Wikipedia article on [[w:Dynamo#Practical designs|dynamo]], accessed 2026-10-18.&lt;/ref&gt;

The image in Figure 1 raises questions about these claims by Mokyr, Acemogu, and Aghion et al.: It shows growth followed by stagnation in Holland but not &quot;phases of growth and decline&quot; with the exception of wars and [[w:Herbert Hoover|Herbert Hoover]]. It also does ''not'' show the slope (i.e., rate of growth) increasing starting around 1750 or the 1770s or 1879 or 1886. Instead it shows sustained growth in GDP per capita for England / Great Britain / the UK starting abruptly after 1649 with economic disruptions during the reign of [[w:Anne, Queen of Great Britain|Queen Anne]] (1702-1714) and the [[w:War of the Spanish Succession|War of the Spanish Succession]] (1701-1714) followed by relatively steady but slower growth as England was ruled by Kings [[w:House of Hanover#Monarchs of Great Britain, Ireland, and Hanover|George I, II, and III]] (1714-1820), then another dramatic increase in the slope starting abruptly about 1819. 

Acemoglu and Johnson (2023, chapter 1) are more consistent with Figure 1. They said that, &quot;the Industrial Revolution ... [was] rooted in institutional changes that started empowering the middling sort of English people from the sixteenth and seventeenth centuries onward.&quot; ... However, &quot;the quality of life of a European peasant circa 1700 was not much different from that of an Egyptian peasant to thousand or seven thousand years previously.&quot; (chapter 5) They also claim that, &quot;English national production per capita doubled from 1500 to 1700&quot;, (chapter 5), and &quot;Growth emerged slowly in the second half of the eighteenth century as the Industrial Revolution, based on major technological breakthroughs and their application in industry, took root.&quot; (p. 45, chapter 2)

Indeed, Figure 1 shows English GDP per capita doubling between 1500 and 1700, but it appears to have been fairly constant from 1500 to 1649, then roughly doubled in the next half century. However, the data on England up to 1700 in Figure 1 came from Broadberry et al. (2015), which was not available when Acemoglu and Robinson were writing ''Why Nations Fail'', which appeared in 2012. 

Acemoglu and Robinson (2012, ch. 11) describe the financial instability and slow growth during the reigns of Queen Anne and George I, II, and III. After the Glorious Revolution, France, Spain, the pope, and others refused to recognize [[w:William III of England|William and Mary]] (1689-1702) and then Queen Anne as heads of state of England. Instead they continued to support the claims of James II and then his son, [[w:James Francis Edward Stuart|James Francis Edward Stuart]] (the &quot;Old Pretender&quot;, a brother of Queen Anne), after James II died in 1701. During the War of the Spanish Succession, each side tried to exploit the internal divisions of the other. Owen (1938, ch. 8) said France almost succeeded in an attempt in 1708 to [[w:Planned French invasion of Britain (1708)|land between 5 and 6 thousand soldiers in northeast Scotland]]. [[w:Louis XIV|Louis XIV]] had hoped to get the Old Protector named as King James VIII of Scotland. There were still [[w:Jacobitism|Jacobites]] in Scotland, who supported the Old Pretender and likely would have supported the invaders if they had landed. If they had succeeded, it would have created major problems for Queen Anne and her supporters. However, the Royal Navy prevented the invaders from disembarking, and they returned to France. 

When Queen Anne died in 1702, she was succeeded by George I. His parliament was dominated by the Whig party, which represented the new mercantile and economic interests and had been the main organization behind the Glorious Revolution. Once in power, they were tempted to use their newly found position to prey on the rights of others but were constrained both by competing groups in Parliament, &quot;and by the very institutions that they had fought to introduce to strengthen Parliament and to prevent the emergence of a new absolutism and the return of the Stuarts&quot;, according to Acemoglu and Robinson (2012, pp. 302-303). The Whigs moved to confiscate &quot;[[w:Commons|commons]]&quot;, land whose use had been traditionally shared by commoners, and give to nobles. The Levellers had been excluded from the government of Lord Protector Cromwell, but the spirit of levelling still stalked the land. Some commoners joined &quot;Blacks&quot;, so called, because they blackened their faces when hunting on former commons or destroying the property of the nobility or extorting money from nobles or their employees. Parliament retaliated by passing the [[w:Black Act 1723|Black Act 1723]], under which someone accused of [[w:Poaching|poaching]] a [[w:Hare|hare]], for example, could under certain circumstances receive a summary judgment of guilty and then be executed without delay if apprehended later.&lt;ref&gt;Newman and Brown, eds. (1997, p. 58). See also the Wikipedia article on &quot;[[w:Black Act 1723|Black Act 1723]], accessed 2026-10-17.&lt;/ref&gt; 

But not all accused were summarily executed. In 1724 &quot;John Huntridge was accused of aiding deer stealers and abetting known Blacks, both crimes punishable by hanging. The prosecution of Huntridge came right from the top, initiated by the Regency Council of Lords Justices ... . After a trial of eight or nine hours, the jury found Huntridge innocent, partly on procedural grounds, since there were irregularities with the way the evidence had been collected. ... The jury was made up not of Huntridge’s peers, but of major landowners and gentry, who ought to have sympathized&quot; with the noble, whose property had been attacked by Blacks allegedly aided by Huntridge.&lt;ref&gt;Acemoglu and Robinson (2012, pp. 304-305).&lt;/ref&gt; 

These kinds of actions by the parliaments of George I, II, and III might explain the slower growth during that period compared to that of the last half of the seventeenth century. That period came to an abrupt end at the time of the [[w:Peterloo massacre|Peterloo Massacre]], 1819-08-16. The growth of factories implied growth of cities, where workers lived closer together and could more easily organize. A campaign arose with multiple demands: They opposed the [[w:Corn Laws|Corn Laws]], which kept prices of cereal grains and products made by them, high. They also demanded &quot;universal [adult male] suffrage&quot; and secret ballots in elections. A series of public meetings discussing these grievances led to one 1819-08-16, which attracted roughly 60,000. Acemoglu and Robinson (2012, p. 207) reported that, &quot;The authorities were very nervous about the meeting, and a force of six hundred cavalry of the Fifteenth Hussars had been assembled. As the speeches began, a local magistrate decided to issue a warrant for the arrest of the speakers. As police tried to enforce the warrant, they met with the opposition of the crowd, and fighting broke out. At this point the Hussars charged the crowd. Within a few chaotic minutes, eleven people were dead and probably six hundred wounded. The Manchester Observer called it the Peterloo Massacre. But given the changes that had already taken place in economic and political institutions, long-run repression was not a solution in England. The Peterloo Massacre would remain an isolated incident. Following the riot, the political institutions in England gave way to the pressure, and the destabilizing threat of much wider social unrest, particularly after the 1830 revolution in France against [[w:Charles X of France|Charles X]], who had tried to restore the absolutism destroyed by the French Revolution of 1789. In 1832 the government passed the [[w:Reform Act 1832|First Reform Act]]. It enfranchised [[w:Birmingham|Birmingham]], [[w:Leeds|Leeds]], [[w:Manchester|Manchester]], and [[w:Sheffield|Sheffield]], and broadened the base of voting so that manufacturers could be represented in Parliament. ... [I]n 1846 they managed to get the hated Corn Laws repealed ... .&quot; And the British government placed enough other limits on its power that enough other commoners were allowed to became successful entrepreneurs that the rate of economic growth in the UK increased immediately, as indicated by the increase in the slope of the UK line in Figure 1 until World Wars I and II. 

== In sum ==

The above suggests that the rate of economic growth changes with either change in administration -- a new head of state -- or some other major event like war, the Peterloo Massacre, or the [[w:Wall Street crash of 1929|Wall Street crash of 1929]]. Policy changes that can increase growth include (1) diverse ownership and control of the major media and (2) immigrants. 

However, correlation does not imply causation. [[w:Randomized controlled trial|Randomized controlled trial]]s could make important contributions to human understanding of economic growth, as suggested by Banerjee, Duflo, and Kramer, cited above and recommended in the Wikiversity article on &quot;[[Information is a public good: Designing experiments to improve government]]&quot;. Failing that, more analyses of data from different political jurisdictions with different media policies could be useful, as described by Neff and Pickard (2024).&lt;ref&gt;Graves (2025) includes an analysis of the data in Neff and Pickard (2024).&lt;/ref&gt; 

== Caveat ==

The above attempts to accurately reflect the perspectives of all sources cited. Readers are invited to revise this article, subject to the standard Wikimedia rules of writing from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- while raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]] -- and treating others with respect.''  

== Notes ==
{{reflist}}

== Bibliography ==

* &lt;!--Abhijit V. Banerjee and Esther Duflo (2019) Good Economics for Hard Times (PublicAffairs)--&gt;{{cite Q|Q85764011}}
* &lt;!-- Daron Acemoglu (2026-08-11) What Happened to Liberal Democracy?: Remaking a Politics of Shared Prosperity (Function)--&gt;{{cite Q|Q141241291}}
* &lt;!--Daron Acemoglu and Simon Johnson (2023) Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity (PublicAffairs)--&gt;{{cite Q|Q125292212}}
* &lt;!--Daron Acemoglu and James A. Robinson (2012) Why Nations Fail (Crown)--&gt;{{cite Q|Q7997840}} 
* &lt;!--Philippe Aghion, Céline Antonin, and Simon Bunel (2021) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations (Harvard University Press)--&gt;{{cite Q|Q137641358}}
* &lt;!--Ajzenman, Nicolas (29 January 2023). &quot;Migrants don't cause crime rates to increase — but false perceptions endure anyway&quot;. The Conversation.--&gt;{{cite Q|Q141758664}}
* &lt;!--Costas Arkolakis, Michael Peters, and Sun Kyoung Lee, (2020) &quot;European Immigrants and the United States’ Rise to the Technological Frontier&quot;--&gt;{{cite Q|Q141678287}}
* &lt;!--Dean Baker (2016) Rigged: How globalization and the rules to the modern economy were structured to make the rich richer--&gt;{{cite Q|Q100216001}}

* &lt;!--Jutta Bolt and Jan Luiten van Zanden (2024-09-18) &quot;Maddison style estimates of the evolution of the world economy: A new 2023 update&quot;, Journal of Economic Surveys, 1-41--&gt;{{cite Q|Q126723821}}
* &lt;!--S. N. Broadberry, B. Campbell, A. Klein, M. Overton and B. van Leeuwen (2015) ''British Economic Growth 1270-1870'' (Cambridge University Press)__&gt;{{cite Q|Q57945943}}


* &lt;!--Renée DiResta (2026) Invisible Rulers: The People Who Turn Lies into Reality, updated edition--&gt;{{cite Q|Q141156783}}
* &lt;!--Renée DiResta and Rachel Kleinfeld (2025-09-10) For Expertise to Matter, Nonpartisan Institutions Need New Communications Strategies--&gt;{{cite Q|Q141158362}}
* &lt;!--Katarzyna Dośpiał-Borysiak (2017) &quot;Model of state management of petroleum sector -- Case of Norway--&gt;{{cite Q|Q141774179}}
* &lt;!--Rachel Foxley (2013) The Levellers: Radical Political Thought in the English Revolution (Oxford University Press)--&gt;{{cite Q|Q136227988}}
* &lt;!--Benjamin Gonzalez O’Brien, Loren Collingwood, Stephen Omar El-Khatib (2017-05-07) &quot;The Politics of Refuge: Sanctuary Cities, Crime, and Undocumented Immigration--&gt;{{cite Q|Q55932800}}
* &lt;!--Graves (2025-01-08) Defend Free Speech For All (Town Hall)--&gt;{{cite Q|Q132855526}}
* &lt;!--Graves (2023-03-21)  Do copyrights and paywalls on academic journals violate the US Constitution?--&gt;{{cite Q|Q126116187}}
* &lt;!--Christopher Hibbert, Ben Weinreb, John Keay, Julia Keay, and Matthew Weinreb (2011-09-09) The London Encyclopaedia, 3rd ed.--&gt;{{cite Q|Q137188993}}
* &lt;!-- Historian, USPS (2010) Postage Rates for Periodicals --&gt;{{cite Q|Q112167199}}
* &lt;!--Richard R. John (1995) Spreading the News: The American Postal System from Franklin to Morse--&gt;{{cite Q|Q54641943}}
* &lt;!--Volker Leppin and Timothy J. Wengert (2015) &quot;Sources for and against the Posting of the Ninety-Five Theses&quot;--&gt;{{cite Q|Q141737347}}
* &lt;!--Lawrence Lessig (2004) Free Culture--&gt;{{cite Q|Q830526}}
* &lt;!--Olivier Marie and Paolo Pinotti (2024-02-01) &quot;Immigration and Crime: An International Perspective&quot;, Journal of Economic Perspectives. 38 (1): 181–200--&gt;{{cite Q|Q128434874}}
* &lt;!--Martínez, Daniel E.; Martínez-Schuldt, Ricardo D.; Cantor, Guillermo (2017). &quot;
Providing Sanctuary or Fostering Crime? A Review of the Research on 'Sanctuary Cities' and Crime&quot;
. Sociology Compass. 12 e12547. doi:10.1111/soc4.12547. ISSN 1751-9020.--&gt;{{cite Q|Q55932802}}
* &lt;!-- Robert W. McChesney; John Nichols (2010). The Death and Life of American Journalism (Bold Type Books) --&gt;{{cite Q|Q104888067}}.
* &lt;!-- Robert W. McChesney; John Nichols (2016). People get ready--&gt;{{cite Q|Q87619174}}
* &lt;!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Princeton University Press)--&gt;{{cite Q|Q136118590}}
* &lt;!--Ashley N. Muchow &amp; Taisiia Stanishevska (2026) &quot;From Headlines to Handcuffs: Local News Coverage of Immigrant Crime and Hispanic Arrest&quot;, Justice Quarterly, vol. 43(3) (https://doi.org/10.1080/07418825.2025.2550307)--&gt;{{cite Q|Q141760694}}
* &lt;!--Neff and Pickard (2024) &quot;Funding Democracy: Public Media and Democratic Health in 33 Countries&quot;--&gt;{{cite Q|Q131468289}}
* &lt;!--Gerald G. Newman and Leslie Ellen Brown, eds. (1997) Britain in the Hanoverian Age, 1714–1837: An Encyclopedia--&gt;{{cite Q|Q141759196}}
* &lt;!--John Hely Owen (1938)  War at Sea Under Queen Anne 1702–1708--&gt;{{cite Q|Q141757101}}
* &lt;!--Andrew Pettegree (2015-10-27) Brand Luther: How an Unheralded Monk Turned His Small Town into a Center of Publishing, Made Himself the Most Famous Man in Europe--and Started the Protestant Reformation--&gt;{{cite Q|Q141761223}}
* &lt;!--Joad Raymond (2006-11-02) Pamphlets and Pamphleteering in Early Modern Britain--&gt;{{cite Q|Q141761849}}
* &lt;!--Nick Roll (2017-07-16) &quot;Correcting Jeff Sessions: Attorney general railed against crime in sanctuary cities, citing two professors’ work. But his claims are contrary to their conclusions.--&gt;{{cite Q|Q141735231}}
* &lt;!--J.P. Smits, E. Horlings and J.L. van Zanden (2000) Dutch GDP and its Components 1800-1913 (Groningen Growth and Development Centre)--&gt;{{cite Q|Q137669960}}
* &lt;!--I. Sugimoto (2011) ''Economic growth of Singapore in the twentieth century: historical GDP estimates and empirical investigations'' ( World Scientific Publishing)--&gt;{{cite Q|Q137669987}}
* &lt;!--J. L. van Zanden  and B. van Leeuwen (2012), ‘Persistent but not consistent: the growth of national income in Holland 1347–1807’, Explorations in Economic History, 49, pp. 119–30--&gt;{{cite Q|Q137670058}} 
* &lt;!--Tom K. Wong (2017-01-26) &quot;The Effects of Sanctuary Policies on Crime and the Economy&quot;--&gt;{{cite Q|Q98775875}}

[[Category:Original research]]
[[Category:Research]]
[[Category:Economics]]
[[Category:Macroeconomics]]
[[Category:Gross domestic product]]
[[Category:Economic growth]]
[[Category:Modern Monetary Theory]]
[[Category:Political science]]
[[Category:Freedom and abundance]]
&lt;!--
https://en.wikiversity.org/wiki/Category_Review
--&gt;</text>
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      <comment>Open Research Book - Assessing Wikimedia Research Reproducibility (https://meta.wikimedia.org/wiki/Research:Assessing_Wikimedia_Research_Reproducibility:_A_Study_on_Collaborative_Practices)</comment>
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== Open Research Book - Assessing Wikimedia Research Reproducibility: A Study on Collaborative Practices ==

=== Abstract ===
Reproducibility underpins scientific credibility. The Wikimedia movement advocates open knowledge, yet the reproducibility of its research outputs has not been evaluated. This project applies a two-phase mixed-methods design. Phase I surveys peer-reviewed publications and documentation (including preprints and white papers) related to Wikimedia, published between 2010 and 2025. A structured reproducibility checklist is applied to a corpus derived from bibliographic databases, generating standardized z-scores for each publication. Phase II uses these scores to draw a stratified random sample, from which corresponding authors are selected for semi-structured interviews on research practices and the influence of their work on the Wikimedia community. Outcomes include a reproducibility package with protocols, data, and code; one peer-reviewed article; and a white paper with recommendations and dissemination strategies. The project engages the Wikimedia research community and connects with funded initiatives such as the bibliometric mapping by Buttliere et al. (2025). It aims to reinforce the epistemological basis of research about the Wikimedia movement.

'''Project period:''' July 1, 2026 to June 30, 2027.

'''Funding:''' Wikimedia Research Fund 2026.

'''Team:''' Lilian Cássia Bórnia Jacob (Universidade de São Paulo, Brazil), Hector Gabriel Corrale de Matos (Universidade de São Paulo, Brazil), Alexandre Hannud Abdo (Centre National de la Recherche Scientifique, France).

=== What is an Open Research Book? ===
An Open Research Book is a living, publicly editable document in which a research team records the whole course of a project while it happens, rather than only reporting final results. It works as an open lab notebook and project logbook at the same time: decisions, protocols, versions of instruments, problems found along the way, and deviations from the original plan are written down openly, with dates, so that anyone can follow how the findings were produced.

By keeping the research process visible and citable, an Open Research Book supports transparency, reproducibility, and collaboration. Because it lives on a wiki, it keeps a full page history, allows community comments on the talk pages, and can be reused and improved by others. In this project, the book is the public notebook of the team and complements the formal outputs (the article, the dataset, the code, and the white paper).

=== Notes ===
==== Project setup and sourcing ====
* Project log
* Corpus and search strategy
* Screening decisions
* Full-text retrieval
==== Methods and reproducibility ====
* Reproducibility checklist
* Annotation pipeline
* Statistical analysis
==== Qualitative and interview work ====
* Interview protocol
* Qualitative analysis
==== Ethics, protocol, and outputs ====
* Ethics and data management
* Deviations from the protocol
* Outputs and dissemination
* Reading notes and references
==== External links ====
* Preregistration
* Data management plan
* Datasets
* Code repository
* Meta-Wiki project page</text>
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      <text bytes="654" sha1="p01nvitigt5wanzf9dxut1utge27b7e" xml:space="preserve">Unillustrated lot project: a permanent record of coins which were offered in old auction sales or sold in private treaty, but without illustrations, to preserve documentary evidence which may otherwise be lost in trade or by institutions. 
{| class=&quot;wikitable&quot;
|+
!Item ID
!Territory
!Reference
!Coin photograph
!Document photograph
!Notes
|-
|1
|Kingdom of Macedon
|Price 316
|[[File:Alexander_III_AE_as_Price_316.png|thumb|Obv./Rev. (6.39 g)]]
|[[File:Ticket_re._Price_316.png|thumb|Macedonien, Alexander IV. od. III. 323-311 bronze Herakles kopf r. Rs. Kende n. Koecher 15,-]]
|Ticket: Germany circa. 1960s or earlier.
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  <page>
    <title>Pageoryu</title>
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      <comment>Created page with &quot;'''破距流 — Pageoryu'''  ''The Lost Art of Breaking Distance''  '''Classification:''' Traditional East Asian Combat System · Privately Transmitted Martial Art  '''Origins:''' Late 19th-century Philippines  '''Formal Development:''' Late Qing Dynasty, Guangdong Province, China  '''Original Purpose:''' Protection of High-Ranking Individuals, Threat Neutralization, and Covert Operations  '''Known Regions of Transmission:''' Mainland China, Hong Kong, Taiwan, the Phili...&quot;</comment>
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      <text bytes="58777" sha1="srzui3ae31njoluzdza84han4fyc9ha" xml:space="preserve">'''破距流 — Pageoryu'''

''The Lost Art of Breaking Distance''

'''Classification:''' Traditional East Asian Combat System · Privately Transmitted Martial Art

'''Origins:''' Late 19th-century Philippines

'''Formal Development:''' Late Qing Dynasty, Guangdong Province, China

'''Original Purpose:''' Protection of High-Ranking Individuals, Threat Neutralization, and Covert Operations

'''Known Regions of Transmission:''' Mainland China, Hong Kong, Taiwan, the Philippines, Japan, South Korea, and select overseas communities

'''Estimated Number of Fully Qualified Masters:''' 17 worldwide

'''Core Principles:''' Distance Disruption, Body Mechanics, Anticipatory Perception, Balance Control, Unconventional Striking, and Close-Quarters Combat

'''Principal Investigators:''' Shen Zhiyuan (沈知远) and John Anderson

'''Research Period:''' 2015–2026

'''I. Overview — A Martial Art Lost to History'''

Pageoryu (破距流) is an obscure traditional combat system believed to have originated in the Philippines during the late 19th century before developing into a distinct martial art in southern China during the final years of the Qing Dynasty.

Unlike most martial arts practiced today, Pageoryu was not originally developed for competition, public instruction, or demonstrations.

According to surviving lineage accounts, its early development was associated with the protection of prominent individuals, the rapid neutralization of physical threats, and, in certain circumstances, covert operations involving the elimination of designated targets.

Its primary objective was not simply to deliver more powerful attacks. The system focused on disrupting the distance, balance, and timing an opponent needed to fight effectively.

This principle is reflected in the characters 破距, which can be interpreted as ''breaking distance''.

Rather than treating distance as a fixed measurement between two fighters, Pageoryu approaches it as a constantly changing relationship between position, balance, movement, and the ability to act.

Its distinctive methods are traditionally attributed to Chen Weishan (陳威山, 1862–1931), a Chinese-Filipino martial artist who reportedly spent much of his life examining the mechanics of human movement.

Chen is said to have been particularly interested in movements that occur before an attack becomes fully visible: shifts in weight, adjustments in posture, changes in muscular tension, and the preparatory actions involved in maintaining balance.

Later practitioners developed these observations into a broader system of close-range striking, positional control, and movement anticipation.

Pageoryu's reputation for exceptional effectiveness appears to have developed primarily through private encounters and accounts passed between instructors and students.

Certain lineages maintain that highly accomplished practitioners could consistently disrupt attacks from experienced fighters trained in other martial arts.

The extent of these claims remains difficult to evaluate because no standardized competitive records or independently documented demonstrations of the complete system have been identified.

As of 2026, researchers estimate that approximately 17 individuals worldwide may possess the full curriculum and the ability to transmit it independently.

The estimate is based on reconstructed transmission histories, private documents, and interviews rather than membership records from a formal organization.

'''II. Origins in the Philippines (1872–1891)'''

The earliest accounts associated with Pageoryu place its beginnings in the commercial districts and port communities of Manila during the 1870s.

At the time, the Philippines was under Spanish colonial administration. Manila served as an important trading center connecting Chinese merchants, Filipino laborers, and foreign shipping interests.

Chinese commercial communities had maintained connections with the Philippines for centuries.

By the 19th century, merchants and migrants formed extensive networks linking ports in southern China with trading centers throughout Southeast Asia.

Protecting goods, transportation routes, and merchants created a demand for private guards and escorts.

These individuals employed regional fighting methods, including early forms of Filipino empty-hand combat associated with what would later be known as Panantukan.

Their methods developed primarily in practical environments rather than within organized sporting traditions.

Crowded markets, ships, warehouses, and narrow streets presented conditions in which conventional fighting distance could change abruptly.

Guards also had to remain close to the people or property they were protecting.

Some later accounts suggest that certain security personnel participated in activities beyond ordinary protection, including confidential assignments and violent disputes involving commercial organizations.

Documentation of these activities is limited, and researchers have been unable to establish which accounts describe actual events rather than stories added by later generations.

'''Chen Weishan and the Earliest Training Tradition'''

Chen Weishan (陳威山), traditionally identified as the founder of Pageoryu, is believed to have been born in 1862 to a Chinese family living in the Philippines.

Biographical details concerning his early life come primarily from family genealogies and references preserved in later correspondence.

He reportedly became involved in transportation and security work associated with Chinese merchant communities while still young.

Through this work, Chen encountered practitioners of several regional fighting traditions.

He eventually became interested in a problem that appeared across different methods of combat.

A fighter could possess considerable strength and technical ability yet struggle when forced outside the distance at which those skills had been developed.

Chen began to regard control of distance as a fundamental requirement for effective fighting.

He also reportedly examined the physical responses that accompanied sudden changes in posture and balance.

These observations later became central to the system associated with his name.

In 1891, Chen traveled to Guangdong Province in southern China.

At that point, the methods he had learned and developed were not yet recognized as a separate martial art.

'''The Earliest Surviving Reference'''

One of the earliest documents associated with Chen is a letter dated September 1898, believed to have been written while he was living in Guangdong.

The document was identified during a later investigation of privately held correspondence associated with Chinese merchant families.

Only a handwritten copy is known to researchers.

The original has not been located.

One passage, transcribed by investigators, reads:

'''「勿逐其拳，先察其步。」'''

''Do not chase the fist. Watch the step that carries it.''

The passage does not identify a martial art by name.

However, Shen Zhiyuan and John Anderson later considered its emphasis on movement and positioning consistent with principles preserved in Pageoryu's oral tradition.

The letter is cataloged in their research notes as document '''CW-1898-01'''.

Its precise date and authorship remain dependent on the privately held copy and associated family records.

'''III. The Formation of Pageoryu in China (1891–1905)'''

During his time in Guangdong, Chen reportedly studied several Chinese martial arts, including Xingyiquan (形意拳), Baji Quan (八極拳), and Shuai Jiao (摔跤).

He observed that different traditions had developed distinct strengths.

Certain Filipino fighting methods emphasized unconventional angles and interference with an opponent's movement.

Xingyiquan demonstrated efficient linear force generation.

Baji Quan placed considerable emphasis on explosive movement at close range.

Shuai Jiao offered an extensive approach to balance disruption and throwing.

Chen did not intend simply to combine techniques from these systems.

According to later accounts, he wanted to identify the physical principles shared by effective methods and organize them into a single approach to combat.

'''The Development of the Poju Principle'''

The principle that emerged was known as Poju (破距).

It was based on the observation that a technique becomes effective only when the conditions required for its execution are present.

These conditions include distance, body alignment, timing, balance, and the ability to generate force.

Pageoryu therefore sought to interfere with these conditions rather than relying exclusively on blocking or countering individual attacks.

For example, an opponent might be capable of delivering a powerful strike from a particular range.

If that range changes before the strike is completed, the technique may lose much of its intended effect.

The same principle applies to grappling movements that depend on a stable position or a particular relationship between the bodies of two opponents.

Over time, these observations became part of Pageoryu's broader theory of distance disruption.

'''The Study of Human Movement'''

An important part of Pageoryu's traditional history concerns Chen's interest in human anatomy and movement.

He reportedly examined how posture, muscular tension, weight distribution, and joint movement influenced a person's ability to attack or maintain balance.

There is no evidence that this work involved modern laboratory experiments or formal anatomical research.

The surviving descriptions suggest a practical study based on repeated observation, physical training, and comparison between martial arts.

Chen appears to have been particularly interested in the fact that different attacks often share similar preparatory movements.

Changes in foot pressure, shoulder orientation, and balance can provide information about an intended action even before its main movement becomes apparent.

Later practitioners reportedly refined these observations through controlled exercises and private sparring.

Within the tradition, this approach eventually became associated with anticipatory perception.

'''The 1903 Correspondence'''

A second document attributed to Chen is a letter dated March 1903.

The surviving copy is believed to have originated from correspondence with a business associate in southern China.

Unlike the earlier letter, the document contains the characters 破距.

A passage attributed to Chen states:

'''「拳有其法，距有其限。先破其距，則法難成。」'''

''Every strike has its method, and every method has its required distance. Disrupt that distance first, and the technique becomes difficult to complete.''

Investigators regard this passage as significant because it connects the term Poju with the principle of disrupting an opponent's effective range.

The document is cataloged as '''CW-1903-02'''.

Its surviving form is a later transcription, and the original document's chain of custody is incomplete.

Nevertheless, its terminology resembles language found in several manuscripts collected from different regions during the 2010s.

By approximately 1904, Chen is believed to have organized his methods into a distinct martial system.

Early references use the name Poju Shu (破距術).

The name Pageoryu (破距流) became established as the methods were transmitted through separate branches of students.

The system subsequently incorporated selected elements associated with Savate, Silat, Lethwei, and other fighting traditions.

These additions were interpreted according to Pageoryu's emphasis on distance control, balance, and efficient movement.

'''IV. The Qing Court and the Private Guards of the Imperial Household (1905–1912)'''

One of the most prominent traditions surrounding Pageoryu concerns its alleged association with the Qing imperial household.

The Qing Dynasty maintained formal military and security institutions responsible for protecting the emperor and members of the imperial family.

Individual nobles and influential households also employed private guards.

According to reconstructed transmission histories, a student of Chen Weishan traveled to Beijing around 1905.

Elements of Pageoryu may subsequently have entered the private security arrangements of certain aristocratic households.

No known record establishes Pageoryu as an official martial art of the Qing imperial guard.

The accounts concern privately employed escorts, household retainers, and security personnel.

'''The 1907 Household Ledger'''

During their investigation, Shen Zhiyuan and John Anderson examined a transcription of an expense ledger attributed to a princely household in Beijing.

The ledger contained payments associated with security personnel from Guangdong.

One entry, dated to 1907, referred to a Guangdong-born guard and accompanying attendants whose names partially matched those found in separate family records.

The ledger did not identify Pageoryu.

Its significance lay in the possible connection between individuals associated with southern Chinese merchant-security networks and private security work in Beijing.

Researchers classified the record as supporting evidence for a possible transmission route rather than direct confirmation that Pageoryu was practiced at the court.

The transcription is identified in their notes as '''BJ-1907-04'''.

'''A System Developed for Protection'''

The requirements of close personal protection were particularly compatible with the principles attributed to Pageoryu.

A guard accompanying a senior official through a crowded street could not necessarily retreat or create space when confronted by an attacker.

The guard also could not remain engaged with a single opponent for an extended period.

The objective was to regain control of the situation while minimizing the time during which the protected individual remained exposed.

A saying attributed to this period expresses the principle:

'''“A guard is judged not by the number of men he defeats, but by how little time his charge remains in danger.”'''

The statement appears in later lineage writings, although researchers have not identified a contemporaneous Qing document containing the exact wording.

'''Protection and Covert Elimination'''

Some Pageoryu traditions distinguish between methods intended for protection and those associated with covert elimination.

The protective methods emphasized positioning, obstruction, restraint, and rapid control of immediate threats.

The second category reportedly consisted of restricted techniques taught only to selected practitioners.

Descriptions of these techniques occur primarily in later oral testimony.

No surviving record conclusively establishes a standardized assassination curriculum during the Qing period.

Nevertheless, the repeated appearance of such accounts across separate lineages suggests that this interpretation became an important part of Pageoryu's historical identity.

'''The Reputation of the Private Guards'''

According to several accounts, practitioners associated with aristocratic households rarely disclosed their martial arts background.

Official records typically identified them as attendants, escorts, or employees.

Some were described as appearing physically unremarkable and avoiding conspicuous fighting postures.

Witnesses reportedly remembered their ability to react decisively during sudden confrontations.

These descriptions later contributed to the belief that Pageoryu masters possessed an unusual ability to recognize threatening movements at an early stage.

The tradition explains this ability through observation, experience, and control of positioning rather than supernatural perception.

'''V. The Fall of the Qing Dynasty and the Fragmentation of the Lineages (1912–1949)'''

The collapse of the Qing Dynasty in 1912 disrupted the employment and social networks that had supported many private guards.

Some practitioners continued working for families associated with the former aristocracy.

Others relocated throughout China or returned to commercial communities in the south.

Pageoryu gradually divided into several regional traditions.

Practitioners in Guangdong reportedly attempted to preserve the principles associated with Chen Weishan's original teachings.

Branches that traveled through Fujian and into Southeast Asia retained stronger connections to Filipino fighting methods.

Other lineages developed through contact with established Chinese martial arts in Beijing and inland provinces.

'''The Loss of Complete Systems'''

Political instability and armed conflict during the 1930s and 1940s are believed to have interrupted the transmission of several Pageoryu lineages.

Some instructors died before teaching their complete systems.

Others passed on a limited number of techniques without the broader principles that connected them.

Later accounts distinguish between students who inherited recognizable movements and those who understood the complete method.

This distinction became important in determining who could be considered a fully qualified master.

Certain restricted techniques associated with early security and covert operations appear to have disappeared from most surviving branches.

After 1949, some practitioners reportedly relocated to Hong Kong, Taiwan, and Southeast Asia.

As a result, several lineages outside mainland China may have preserved material that was lost in their original regions.

'''VI. Pageoryu in Japan — The Alleged Yamaguchi-gumi Connection'''

The exact date on which Pageoryu reached Japan is unknown.

Some lineage accounts describe Chinese martial artists traveling between China and Japan during the 1930s.

However, documentation establishing a direct transmission route from that period has not been located.

Accounts became more prominent after World War II, particularly in connection with Kobe.

Kobe was a major international port with established Chinese communities, extensive commercial activity, and a large population involved in shipping and transportation.

These circumstances provided opportunities for the private transmission of Chinese martial arts.

The Yamaguchi-gumi (山口組), which was founded in Kobe in 1915 and later became Japan's largest yakuza organization, also developed within this port environment.

'''The 1978 Kobe Incident'''

The most frequently cited story connecting Pageoryu to Japan concerns an alleged private gathering in Kobe in 1978.

According to the account, a senior figure associated with a Yamaguchi-gumi-affiliated organization demonstrated unusual movements during a brief physical confrontation.

A witness with previous martial arts experience reportedly considered the movements distinct from familiar forms of karate, judo, and boxing.

The senior figure was described as making a small positional adjustment while an opponent was initiating an attack.

The opponent subsequently lost balance.

The incident was brief and apparently involved no elaborate techniques.

At the time, no connection to Pageoryu was identified.

'''The Witness's Notebook'''

Decades later, investigators reportedly obtained a reproduction of a personal notebook attributed to someone present at the gathering.

The notebook contained a short description of an asymmetrical posture.

One hand was held relatively low, while the other remained closer to the face.

The description resembled elements of Yishou Shi (一手勢), the fundamental stance of Pageoryu.

The notebook also mentioned a subtle change in the individual's posture during the confrontation.

Shen and Anderson compared the account with descriptions preserved in Chinese and Hong Kong manuscripts.

The similarities were considered noteworthy but not conclusive.

Further interviews reportedly produced references to a Chinese private martial arts instructor who had known the individual.

No complete record of that instructor's teachings has been recovered.

The 1978 incident remains a secondary piece of evidence in the reconstructed Japanese transmission history.

There is no established evidence connecting Japan's two presumed fully qualified Pageoryu masters to the Yamaguchi-gumi.

'''VII. Modern Rediscovery — The Investigations of Shen Zhiyuan and John Anderson'''

The modern reconstruction of Pageoryu is primarily associated with two independent researchers, '''Shen Zhiyuan (沈知远)''' and '''John Anderson'''.

Their work reportedly began in 2015 and continued through 2026.

Shen concentrated on Chinese-language documents, family genealogies, handwritten manuscripts, and oral traditions preserved in East Asian communities.

Anderson focused on comparing transmission histories, organizing interview material, examining documentary relationships, and evaluating inconsistencies between accounts.

Neither researcher initially set out to reconstruct a complete martial art.

Their investigation began with a small collection of documents containing unfamiliar terminology.

'''The Initial Discovery'''

During the mid-2010s, Shen reportedly examined privately held documents from southern China.

Among them was an incomplete manuscript containing sketches of physical postures and several short written passages.

The manuscript had no surviving title page.

However, the characters 破距 appeared repeatedly.

At first, Shen considered whether the term referred to a general concept of military strategy or physical training.

Further comparisons revealed similar terminology in unrelated collections.

Several documents also contained descriptions of asymmetrical postures and methods of shifting body weight.

These similarities led Shen to investigate whether the documents belonged to a common fighting tradition.

'''The Chen Weishan Letters'''

One of the investigation's most important developments was the identification of correspondence attributed to Chen Weishan.

The letters were preserved through different private family collections.

The two most frequently cited documents are:
{| class=&quot;wikitable&quot;
| valign=&quot;top&quot; |'''Document'''
| valign=&quot;top&quot; |'''Reported Date'''
| valign=&quot;top&quot; |'''Principal Content'''
| valign=&quot;top&quot; |'''Surviving Form'''
|-
| valign=&quot;top&quot; |CW-1898-01
| valign=&quot;top&quot; |September 1898
| valign=&quot;top&quot; |Early observations on positioning and preparatory movement
| valign=&quot;top&quot; |Handwritten copy
|-
| valign=&quot;top&quot; |CW-1903-02
| valign=&quot;top&quot; |March 1903
| valign=&quot;top&quot; |Use of the term 破距 and discussion of effective fighting distance
| valign=&quot;top&quot; |Later transcription
|}
The documents contain terminology consistent with principles later associated with Pageoryu.

Their historical importance depends heavily on the reliability of the copies.

Neither original has been made available for unrestricted archival examination.

'''A Third Correspondence Reference'''

A family inventory compiled during the early 1930s reportedly listed additional correspondence belonging to Chen.

One item was described as a letter discussing the difference between protecting a person and defeating an opponent in a formal contest.

The complete letter has not been recovered.

Only a brief summary survives in the inventory.

This reference has been included in the investigators' working notes as '''CW-1932-I3'''.

Because the original letter is missing, it has not been treated as direct evidence of Chen's precise teachings.

'''The 1907 Beijing Record'''

The investigators also examined the previously mentioned Beijing household ledger.

The entry was compared with merchant-community documents and family records from Guangdong.

Several names and dates were considered compatible with a possible movement of security personnel from southern China to Beijing.

However, the connection to Pageoryu remains indirect because the ledger does not identify the martial art practiced by those individuals.

'''The Three Regional Manuscripts'''

Between 2017 and 2020, the investigators reportedly compared three privately held martial arts manuscripts associated with Hong Kong, Taiwan, and the Philippines.

The manuscripts differed in terminology and the arrangement of techniques.

However, certain descriptions of posture, balance, and movement were remarkably similar.

One passage concerned an asymmetrical stance.

Another described the relationship between changes in body height and the generation of force.

A third referred to disrupting an opponent's position before attempting a decisive technique.

Investigators compared handwriting, ownership histories, paper characteristics, family relationships, and repeated terminology.

They concluded that at least portions of the manuscripts might share a common transmission history.

'''The Limits of the Documentary Evidence'''

Not every item identified during the investigation could be independently authenticated.

Some materials were available only as reproductions.

Others were preserved through families unwilling to release their original documents.

Several historical dates were reconstructed from contextual evidence rather than confirmed by contemporary institutional records.

Shen and Anderson therefore separated the materials into three broad categories:

# Documents with identifiable provenance and supporting contextual records.
# Materials consistent with an established transmission route but lacking complete authentication.
# Oral accounts or secondary copies that could not be independently corroborated.

This distinction became especially important when the researchers attempted to estimate the number of surviving masters.

'''Tracing the Japanese Lineage'''

The alleged 1978 Kobe incident was reexamined during the investigation.

Researchers compared descriptions from the witness's notebook with the technical terminology and postures found in other manuscripts.

They also collected testimony concerning a Chinese martial arts instructor who reportedly had connections to individuals involved in the incident.

The resulting evidence supported a possible historical relationship but did not conclusively identify the martial art involved.

'''Identifying the Korean Lineage'''

The Korean connection was first investigated around 2019.

A Korean martial artist who had reportedly received private instruction in Taiwan during the late 1980s was identified through references preserved in unrelated documents.

Terminology associated with his training was compared with manuscripts from Hong Kong and Taiwan.

Several descriptions appeared consistent.

The individual reportedly had never operated a public school devoted to Pageoryu.

Investigators concluded that he might represent one of the few surviving practitioners capable of teaching the complete system.

As of 2026, he remains the only fully qualified master identified within the Korean lineage.

'''The 2026 Research Summary'''

By 2026, the investigators had assembled a reconstructed history extending from late 19th-century Filipino commercial communities to contemporary private martial arts lineages.

Their work identified approximately 17 individuals believed to possess the complete system.

Eleven lineages were classified as having comparatively stronger supporting evidence.

Six remained provisional.

The researchers did not claim to have recovered every branch or established a complete list of practitioners.

Their findings were presented as a reconstruction based on fragmentary documentation rather than a definitive history.

'''VIII. Worldwide Distribution — The 2026 Lineage Survey'''

The 2026 investigation estimated that approximately 17 individuals worldwide retained the complete Pageoryu curriculum.

A fully qualified master was defined as a practitioner who understood the system's underlying principles, had achieved advanced technical proficiency, and could independently transmit the complete curriculum.

Individuals who had learned only selected techniques were excluded.
{| class=&quot;wikitable&quot;
| valign=&quot;top&quot; |'''Country or Region'''
| valign=&quot;top&quot; |'''Estimated Masters'''
| valign=&quot;top&quot; |'''Principal Lineage'''
|-
| valign=&quot;top&quot; |Mainland China
| valign=&quot;top&quot; |5
| valign=&quot;top&quot; |Guangdong, Fujian, Beijing, and inland traditions
|-
| valign=&quot;top&quot; |Hong Kong
| valign=&quot;top&quot; |2
| valign=&quot;top&quot; |Late Qing private-security and Guangdong traditions
|-
| valign=&quot;top&quot; |Taiwan
| valign=&quot;top&quot; |2
| valign=&quot;top&quot; |Chinese lineages relocated after 1949
|-
| valign=&quot;top&quot; |Philippines
| valign=&quot;top&quot; |2
| valign=&quot;top&quot; |Traditions linked to early Filipino fighting methods
|-
| valign=&quot;top&quot; |Japan
| valign=&quot;top&quot; |2
| valign=&quot;top&quot; |Transmission through postwar Chinese martial artists
|-
| valign=&quot;top&quot; |South Korea
| valign=&quot;top&quot; |'''1'''
| valign=&quot;top&quot; |Lineage inherited from Taiwan
|-
| valign=&quot;top&quot; |Malaysia
| valign=&quot;top&quot; |1
| valign=&quot;top&quot; |Overseas Chinese merchant communities
|-
| valign=&quot;top&quot; |Thailand
| valign=&quot;top&quot; |1
| valign=&quot;top&quot; |Southeast Asian migrant lineage
|-
| valign=&quot;top&quot; |United States
| valign=&quot;top&quot; |1
| valign=&quot;top&quot; |Late 20th-century overseas migration
|-
| valign=&quot;top&quot; |'''Total'''
| valign=&quot;top&quot; |'''17'''
| valign=&quot;top&quot; |
|}
The estimate was developed through comparisons of family documents, reported teacher-student relationships, historical correspondence, and independent testimony.

Some individuals were identified through multiple sources.

Others were included because separate accounts appeared to describe the same practitioner or transmission route.

Many of the presumed masters are elderly.

Several are believed to have stopped teaching actively.

The number currently accepting new students is probably smaller than the total number of identified masters.

'''IX. Why Pageoryu Has Almost No Internet Presence'''

The absence of Pageoryu from most modern martial arts records is one of the most frequently discussed aspects of its history.

Investigators have proposed several explanations.

'''1. No Public Governing Organization'''

Pageoryu has no known international federation, national association, or standardized ranking system.

Unlike established competitive martial arts, it has not maintained a public network of schools or regular competitions.

Instruction traditionally occurred through private relationships between individual masters and small numbers of students.

'''2. Most Documents Were Never Digitized'''

Much of the material associated with Pageoryu reportedly survives as handwritten correspondence, personal training notes, photographs, and family records.

These materials are largely absent from searchable archives.

Different lineages also preserved different names for related techniques.

Some historical records used Poju Shu (破距術), Poju Men (破距門), or other regional terminology.

'''3. Historical Records Identified Occupations Rather Than Fighting Systems'''

Many early practitioners reportedly worked as security personnel, merchants, escorts, or household attendants.

Historical records might therefore identify their employment without naming the martial art they practiced.

'''4. Masters Avoided Public Disclosure'''

Certain lineages discouraged students from revealing their instructors or training methods.

Some masters reportedly refused to recognize students who had not completed the full curriculum.

Public demonstrations and competitive appearances were uncommon.

'''5. Similar Techniques Exist in Other Martial Arts'''

Pageoryu incorporates principles also found in Xingyiquan, Baji Quan, Filipino martial arts, and other fighting traditions.

Consequently, a resemblance between movements cannot establish a direct historical relationship.

Investigators emphasized combinations of terminology, documentary evidence, and plausible teacher-student relationships.

These circumstances help explain why Pageoryu has remained difficult to trace.

'''X. Technical System and Its Relationship to Modern Combat Sports'''

Pageoryu is organized around a relatively small number of fundamental techniques, supported by several variations of its principal fighting posture.

Its technical philosophy emphasizes timing, positioning, balance, and efficient use of body movement.

Individual techniques are considered less important than the ability to apply them under appropriate conditions.

'''1. Fundamental Stances'''

'''Yishou Shi (一手勢) — The One-Hand Stance'''

Yishou Shi is regarded as the fundamental stance of Pageoryu.

It uses an asymmetrical hand position rather than a conventional symmetrical guard.

The stance is intended to support transitions between defensive movements, striking, and close-range control.

Its effectiveness depends on the practitioner's ability to maintain balance and adapt the posture to changing distance.

'''Yinjian Shi (隱肩勢) — The Concealed Shoulder Stance'''

Yinjian Shi emphasizes reducing the exposed profile of the torso and limiting openings during striking exchanges.

It incorporates changes in shoulder position and body orientation.

'''Xuanchui Shi (懸捶勢) — The Suspended Hammer Stance'''

Xuanchui Shi is an offensive variation characterized by a distinctive upper-body posture.

Its purpose is to create several possible striking actions from an unconventional position.

'''Panshi Shi (盤石勢) — The Rock Stance'''

Panshi Shi emphasizes structural stability and close-range control.

It is associated with resisting positional disruption and maintaining balance during physical contact.

These stances are understood as different expressions of a single fighting system rather than independent disciplines.

'''2. Principal Striking Techniques'''

'''Banbu Bengquan (半步崩拳) — Half-Step Crushing Fist'''

Banbu Bengquan is one of Pageoryu's fundamental linear strikes.

It emphasizes coordinated movement of the body rather than relying exclusively on the arm.

According to lineage descriptions, a properly executed Bengquan can produce substantial impact with relatively little visible preparation.

The technique shares principles with traditional Chinese linear striking methods, although Pageoryu places particular emphasis on its integration with changes in distance.

'''Dingzhou (頂肘) — Rising Elbow'''

Dingzhou is an elbow-based technique developed for close-range encounters.

It requires less space than many conventional striking movements.

Accounts describe it as especially effective when an opponent has moved too close for longer-range attacks to be used comfortably.

'''Tieshankao (鐵山靠) — Iron Mountain Lean'''

Tieshankao is a body-impact technique associated with Baji Quan and related traditions.

Within Pageoryu, it emphasizes coordinated body movement and the disruption of an opponent's balance.

It is typically described as a method of gaining positional control through close physical contact.

'''3. Signature Techniques'''

'''Chenchui (沈捶) — Sinking Strike'''

Chenchui is among the techniques most strongly associated with Pageoryu.

It uses coordinated changes in body position and weight distribution to support a short-range strike.

Its movements may appear less pronounced than those of conventional punches.

According to several lineage accounts, experienced practitioners could execute Chenchui without the large shoulder or arm movements commonly associated with powerful strikes.

Witnesses reportedly described its impact as unexpectedly heavy relative to the visible movement involved.

'''Yinzhui (引墜) — Drawing Descent'''

Yinzhui is a family of techniques centered on disrupting an opponent's balance through coordinated movement.

Rather than depending entirely on physical strength, it attempts to exploit changes in posture and weight distribution.

Its effectiveness is traditionally associated with timing and the ability to recognize when an opponent's balance is already compromised.

'''4. Luobu Bengquan (落步崩拳) — Falling-Step Crushing Fist'''

Luobu Bengquan is regarded as one of Pageoryu's most powerful linear striking techniques.

It combines principles associated with Bengquan and Chenchui.

The technique emphasizes coordinated forward movement and body-weight transfer.

Traditional descriptions portray it as capable of delivering substantial impact without the extensive preparation required by some larger strikes.

No reliable measurements of its actual force have been recovered.

Its reputation rests primarily on training accounts and the testimony of practitioners.

'''5. Finishing Techniques'''

'''Xuanguan (旋貫)''' is classified as an advanced rotational striking technique.

Its effectiveness is associated with balance, timing, and the precise coordination of body movement.

'''Luotoujiao (落頭絞)''' refers to a family of close-range restraint techniques.

It appears in accounts associated with early security and protective duties.

Within the tradition, both techniques are considered advanced methods requiring judgment and substantial prior training.

Pageoryu instructors reportedly place greater emphasis on the decision to use a technique than on its theoretical maximum power.

'''X-1. Why Pageoryu Is Considered Superior Within Its Traditional Lineages'''

Comparisons between Pageoryu and modern mixed martial arts have appeared repeatedly in recent accounts of the system.

MMA integrates striking, wrestling, and submission grappling through extensive practical training and competitive testing.

Elite mixed martial artists demonstrate high levels of technical proficiency across multiple fighting distances.

Pageoryu lineages acknowledge these strengths while arguing that their system places greater emphasis on disrupting the circumstances that make an opponent's techniques effective.

'''Distance Control'''

Most fighting systems develop techniques appropriate to particular ranges.

Boxing emphasizes punches and defensive movement.

Wrestling involves methods for establishing physical control.

Submission grappling concentrates on positional dominance and joint or choke-based submissions.

Pageoryu emphasizes the transitions between such positions.

Its practitioners seek to recognize when an opponent is attempting to establish a preferred range and interfere with that process.

The tradition holds that this approach can reduce the effectiveness of even technically accomplished fighters when their expected distance and timing are repeatedly disrupted.

'''Anticipatory Perception'''

Pageoryu places considerable importance on recognizing preparatory movements.

Weight shifts, changes in posture, and adjustments in body orientation may indicate an approaching attack.

Experienced fighters in many disciplines develop similar observational abilities.

Pageoryu differs primarily in the degree of emphasis its tradition places on studying and exploiting these signals.

At advanced levels, practitioners are said to recognize patterns in an opponent's movement early enough to improve their own positioning.

'''Body Mechanics'''

Pageoryu emphasizes coordinated movement of the entire body.

Its traditional instruction focuses on balance, force transfer, posture, and efficient changes of direction.

Practitioners maintain that understanding these principles allows relatively simple techniques to remain effective against opponents with different fighting backgrounds.

'''Unconventional Technical Transitions'''

Certain Pageoryu techniques appear similar to methods found in other martial arts.

However, the system reportedly uses distinctive transitions between striking, balance disruption, and close-range control.

These transitions may be unfamiliar to fighters whose training has emphasized different technical sequences.

'''Historical Accounts of Encounters With Other Martial Artists'''

A small number of private accounts describe Pageoryu practitioners performing successfully against experienced fighters from other disciplines.

Some accounts refer to encounters in Guangdong during the 20th century.

Others concern private training sessions in Hong Kong and Taiwan.

Descriptions commonly emphasize positional control rather than overwhelming physical force.

Several witnesses reportedly observed that Pageoryu practitioners were able to interrupt attacks or move into advantageous positions with relatively economical movements.

The surviving accounts are insufficient to establish a universal competitive advantage.

There are no independently verified records showing that Pageoryu practitioners consistently defeated elite modern MMA competitors under standardized conditions.

Its reputation for superiority therefore rests primarily on lineage testimony, private encounters, and its distinctive technical philosophy.

Within the tradition, however, Pageoryu continues to be regarded as a highly effective system for close-range confrontation, particularly in situations involving rapid changes in distance and positioning.

'''X-2. Restricted Techniques — Jueshengjiao (絕聲絞)'''

Certain Pageoryu traditions refer to a small category of restricted techniques that were not included in ordinary instruction.

Among them is '''Jueshengjiao (絕聲絞)''', sometimes translated as ''The Silence Choke''.

The technique is described in later lineage accounts as having been associated with covert operations and the rapid elimination of designated targets.

No complete technical manuscript has been recovered.

Some surviving descriptions refer to a crossed-arm configuration resembling the letter X.

The precise historical form of the technique remains uncertain.

Certain oral accounts claim that Jueshengjiao could prevent an opponent from calling out during a confrontation.

This reputation contributed to its classification as a forbidden technique, or ''jinshou'' (禁手), within some lineages.

However, researchers have been unable to establish whether the descriptions refer to a single standardized technique or several related methods grouped under the same name.

The term appears most frequently in later oral testimony rather than in securely dated early manuscripts.

It is unknown whether any of the 17 presumed fully qualified masters retain the original method.

'''XI. How Pageoryu Masters Selected Their Successors'''

One explanation for Pageoryu's near disappearance is the unusually selective approach its masters reportedly took toward succession.

Traditional instructors did not necessarily accept everyone who requested training.

Even students who practiced for many years might receive only part of the curriculum.

A master selected successors based on several characteristics.

These included physical ability, observational skill, judgment, emotional control, and the capacity to understand and correct movement.

Particular importance was placed on knowing when a technique should be used.

A student who could execute powerful techniques but lacked sound judgment was not necessarily considered suitable for succession.

Some masters reportedly recognized only one successor during their lifetime.

Others designated no successor at all.

This approach may have helped preserve the system's distinctive principles, but it also increased the risk that entire lineages would disappear.

'''XI-1. The Next Generation — Successors of the Last Masters'''

The 2026 investigation identified several individuals who reportedly received instruction from masters associated with Pageoryu.

However, the total number of students remains unknown.

Most lineages have no public enrollment records.

Some instructors taught only through personal introductions.

Furthermore, receiving instruction does not necessarily indicate an intention to inherit the complete system.

Students may have pursued training out of personal interest, for practical self-defense, or to supplement other martial arts.

'''1. Known Students by Country and Region'''
{| class=&quot;wikitable&quot;
| valign=&quot;top&quot; |'''Country or Region'''
| valign=&quot;top&quot; |'''Individuals Mentioned'''
| valign=&quot;top&quot; |'''Status'''
|-
| valign=&quot;top&quot; |Mainland China
| valign=&quot;top&quot; |Chen ○○, Lin ○○
| valign=&quot;top&quot; |Historical instruction partly documented
|-
| valign=&quot;top&quot; |Hong Kong
| valign=&quot;top&quot; |Liang ○○, W. C****
| valign=&quot;top&quot; |Limited teacher-student records
|-
| valign=&quot;top&quot; |Taiwan
| valign=&quot;top&quot; |Huang ○○, Wu ○○, C. L***
| valign=&quot;top&quot; |Some private transmission records
|-
| valign=&quot;top&quot; |Philippines
| valign=&quot;top&quot; |R. D****
| valign=&quot;top&quot; |Historical training references only
|-
| valign=&quot;top&quot; |Japan
| valign=&quot;top&quot; |Yamamoto ○○, K. N****
| valign=&quot;top&quot; |Identities and relationships partly inferred
|-
| valign=&quot;top&quot; |South Korea
| valign=&quot;top&quot; |Kim**, Min**, Park**
| valign=&quot;top&quot; |Three mentioned; two partially traceable
|-
| valign=&quot;top&quot; |Malaysia
| valign=&quot;top&quot; |Unknown
| valign=&quot;top&quot; |Existence of students unconfirmed
|-
| valign=&quot;top&quot; |Thailand
| valign=&quot;top&quot; |Unknown
| valign=&quot;top&quot; |Later transmission untraceable
|-
| valign=&quot;top&quot; |United States
| valign=&quot;top&quot; |J. H****
| valign=&quot;top&quot; |Indirect evidence of private instruction
|}
This list does not represent the total number of students.

It includes only those individuals whose names or partial identities appear in materials examined during the investigation.

'''2. Mainland China'''

'''Chen ○○ (陳○○)'''

Chen is believed to have received private instruction from a master in Guangdong.

He reportedly had previous experience in Chinese martial arts and became interested in Pageoryu through a personal introduction.

His understanding of balance and coordinated body movement was described favorably in later accounts.

His current training status remains unknown.

'''Lin ○○ (林○○)'''

Lin is associated with another southern Chinese lineage.

He is believed to have been a relatively young adult when he began studying.

He reportedly sought instruction to supplement skills acquired through other martial arts.

His sense of distance and positional awareness were noted as strengths.

No reliable record establishes that he completed the curriculum.

'''3. Hong Kong'''

'''Liang ○○ (梁○○)'''

Liang reportedly received instruction through a lineage derived from the Guangdong tradition.

He appears to have begun studying as an adult, initially motivated by an interest in practical self-defense.

His movements were described as economical, with particular attention to controlling distance.

'''W. C****'''

Another private student associated with Hong Kong.

His precise identity and age remain unknown.

He reportedly studied Pageoryu to better understand its differences from other fighting methods.

Whether he continues to train is uncertain.

Neither individual has been confirmed as a formally designated successor.

'''4. Taiwan'''

'''Huang ○○ (黃○○)'''

Huang is believed to have been an adult practitioner with experience in Chinese martial arts.

He reportedly showed an interest in balance control and changes in body angle.

His technical proficiency was described favorably in some accounts.

His succession status is unknown.

'''Wu ○○ (吳○○)'''

Wu is believed to have started training later than Huang.

He may have been a young adult when he first received instruction.

He reportedly had an interest in comparing different fighting systems and was noted for his ability to adapt movements to changing circumstances.

Fragmentary testimony suggests that he remained in contact with individuals associated with the lineage during the 2020s.

'''C. L***'''

This individual appears only through initials in Taiwanese lineage records.

His age, nationality, and training history are unknown.

He may have received instruction in selected techniques through a private introduction.

'''5. The Philippines'''

'''R. D****'''

This individual is believed to have been associated with a Chinese-Filipino martial arts community.

Historical accounts suggest that he began receiving instruction at a relatively young age.

He was reportedly familiar with methods involving changes in attacking angle and disruptions to an opponent's defensive posture.

It remains unclear whether he knew the system by the name Pageoryu.

His current whereabouts are unknown.

'''6. Japan'''

'''Yamamoto ○○ (山本○○)'''

Yamamoto is believed to have encountered Pageoryu through a Chinese martial arts lineage in postwar Japan.

He reportedly began receiving instruction while already practicing other martial arts.

Some accounts describe his movements as involving relatively small positional adjustments.

He may have studied the system alongside other disciplines rather than pursuing complete mastery.

'''K. N****'''

Another Japanese practitioner whose exact identity remains undisclosed.

He was reportedly relatively young when he began training.

Some accounts describe strong observational ability and sound decision-making during practice.

His current activities are unknown.

No evidence establishes a direct connection between either individual and the alleged 1978 Kobe incident.

'''7. South Korea'''

The Korean lineage contains references to three students who reportedly received instruction from the country's only known fully qualified master.

Their names appear as '''Kim**, Min**, and Park**'''.

Of these, only Kim and Min could be partially traced.

'''Kim**'''

As of 2026, Kim is believed to be either a high school student or a young adult.

The circumstances of his introduction to Pageoryu remain uncertain.

He may have begun training through personal interest or a connection with the instructor.

He was reportedly relatively comfortable with fundamental postures and balance control.

Some accounts describe steady improvement through regular practice.

Kim may still train occasionally, although there is no evidence that he works professionally as a martial artist.

'''Min**'''

Min is believed to have begun receiving instruction relatively recently.

As of 2026, he is estimated to be a middle school or high school student.

Fragmentary descriptions suggest that he appears noticeably young.

Compared with other identified students, Min is believed to have relatively limited training experience.

Nevertheless, certain accounts describe his ability to interpret movement and assess developing situations as promising.

He reportedly showed an interest in observing an opponent's movements and anticipating possible responses.

Some observers associated these characteristics with developing combat judgment.

His actual fighting ability and technical proficiency remain unknown.

Min may have begun training primarily out of personal curiosity or an interest in martial arts rather than an intention to inherit the lineage.

He is believed to continue receiving some instruction while attending school and maintaining an otherwise ordinary daily life.

'''Park**'''

Park is mentioned as the third student associated with the Korean lineage.

Almost no information survives beyond the reference to private instruction.

His age, training history, and current activities remain unknown.

None of the three has been confirmed as a fully qualified independent master.

'''8. Malaysia'''

The Malaysian lineage is believed to have developed through Chinese merchant communities in Southeast Asia.

However, investigators could not establish whether the country's presumed fully qualified master has accepted a successor.

Some historical accounts mention exchanges of martial arts instruction within local Chinese communities.

The available evidence does not establish whether these involved Pageoryu.

No reliable records identifying next-generation students have been recovered.

'''9. Thailand'''

The Thai lineage is associated with Chinese migration and martial arts transmission through Southeast Asian communities.

Some oral accounts suggest that private instruction took place in earlier decades.

Investigators have been unable to determine whether those students received the complete system or only selected techniques.

Their identities and subsequent activities remain unknown.

Unlike Malaysia, where the existence of students has not been established, Thailand has fragmentary indications of past instruction but no traceable continuation.

'''10. The United States'''

'''J. H****'''

This individual appears in accounts associated with a Chinese martial artist who reportedly immigrated to the United States during the latter half of the 20th century.

He may have been a young adult when he began studying.

According to the available accounts, he became interested in Pageoryu because of its distinctive approach to distance control.

He was reportedly noted for observing changes in posture and balance before attacks.

His long-term training history remains unknown.

'''11. The Uncertain Future of the Next Generation'''

The identified students appear to have pursued Pageoryu for different reasons.

Some may have trained for years.

Others may have received only limited instruction.

Being identified as a student does not necessarily establish an intention to become a successor.

No currently identified member of the next generation has been confirmed as a fully qualified independent master.

It also remains unknown how many of the 17 presumed surviving masters are actively transmitting their complete systems.

The future of Pageoryu may depend largely on private teacher-student relationships that have never been documented publicly.

'''XII. The Highest Level — Perception Before Movement'''

One of the most distinctive elements of Pageoryu is the tradition surrounding its most accomplished practitioners.

In most martial arts, increased proficiency is associated with improvements in speed, timing, accuracy, and efficiency.

Pageoryu describes a similar progression, but places particular emphasis on eliminating unnecessary movement.

At advanced levels, practitioners are said to move with greater economy.

Their movements may appear less dramatic than those of less experienced fighters.

Yet they are reportedly able to maintain favorable positioning and respond effectively to changes in an opponent's movement.

Within the tradition, this ability is sometimes described as '''Xianxing Renshi (先行認識), or Anticipatory Perception'''.

The concept refers to recognizing the physical signs that precede a more obvious action.

Changes in body weight, shoulder orientation, hip position, and muscular tension can provide information about an opponent's intended movement.

Experienced practitioners of many martial arts develop similar observational skills through repeated training.

Pageoryu places these skills at the center of its advanced curriculum.

Certain private accounts describe practitioners who appeared capable of recognizing an opponent's intentions unusually early.

This did not mean that they could predict movements without information or react before any physical indication existed.

Rather, their experience allowed them to identify patterns and respond to subtle preparatory cues that less experienced fighters might overlook.

Some individuals who reportedly sparred with Pageoryu masters described the experience as unusual because their opponents seemed consistently well positioned.

Their attacks were often interrupted or redirected before they could be completed effectively.

Within the tradition, these experiences came to represent the highest expression of Pageoryu's central principle: controlling a confrontation by understanding movement before committing to force.

Whether any of the 17 presumed surviving masters has reached the highest level described in the historical accounts remains unknown.

'''XIII. The Silence of the Last Masters'''

Pageoryu remains one of the least publicly documented martial arts traditions associated with East Asia.

It has no known international governing organization, no standardized worldwide ranking system, and no established competitive circuit.

Instruction is believed to take place almost entirely through private relationships between masters and students.

Some lineages reportedly no longer use the name Pageoryu.

Others may preserve only portions of the original technical curriculum.

The surviving masters are not known to have pursued widespread public recognition.

According to the tradition, preserving the principles of the system has generally been considered more important than expanding the number of students.

Some instructors reportedly spent their entire lives teaching only a handful of individuals.

Others may have died without identifying a qualified successor.

This has raised concerns that several of the remaining lineages could disappear within the next few decades.

Nevertheless, the traditional requirements for succession have reportedly remained strict.

Certain practitioners are said to believe that transmitting an incomplete system under the original name would undermine the very principles they were attempting to preserve.

An old saying attributed to the later generations of Pageoryu expresses this philosophy:

'''「下者見拳，上者見勢，至者見未動。」'''

''Those of lesser skill see the fist. Those of greater skill see the developing situation. Those who have reached the highest level see what has yet to move.''

Another saying traditionally associated with the system reads:

'''“The ordinary fighter fears an opponent's strength. The skilled fighter respects an opponent's technique. But to one who has mastered Poju, neither arrives first.”'''

A further passage describes the same principle:

'''“It is not his strength that causes the opponent to fall. By the time the opponent chooses to act, he is already standing at the end of that decision.”'''

The final teaching of Pageoryu is represented by four Chinese characters:

'''未動先破'''

'''Weidong Xianpo — Broken Before Movement.'''

The phrase does not refer to supernatural foresight or impossible physical speed.

It describes the ideal of recognizing a confrontation's developing conditions early enough to control how it unfolds.

At the highest level, Pageoryu traditions describe offense and defense not as isolated actions, but as interconnected parts of a continuous exchange.

Movement, balance, positioning, and timing become aspects of a single process.

The practitioner who understands that process most clearly is believed to have the greatest ability to influence its outcome.

'''The ultimate objective of Pageoryu is not simply to develop the strength to overwhelm an opponent. It is to develop sufficient control over distance, balance, and timing that an opponent's opportunities to attack are substantially reduced before the confrontation reaches its decisive moment.'''</text>
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